NAS NUMERICAL 

AERODYNAMIC 

SIMULATION 

PROGRAM 

Summaries 

MARCH 1989 - FEBRUARY 1990 
The use of color graphics is a powerful and 

flexible visualization tool for the science of 

-- computational fluid dynamics. Without color 

graphics, the millions of numbers which form 

the supercompdter solutions to the studies 

contained in th5 ieport and on the cover 

would be vi6ually incomprehensible. 
NAS NUMERICAL 

AERODYNAMIC 

SIMULATION 

PROGRAM 

Technical 

Summaries 

MARCH 1989 - FEBRUARY 1990 

(NASA-TM-107960) NAS (NUMERICAL 

AERODYNAMIC SIMULATION PROGRAM) 

TECHNICAL SUMMARIES, MARCH 1989 - 

FEBRUARY 1990 (NASA) 221 p 

National Aeronautics and 

Space Administration 

Ames Research Center 

Moffett Field, California 94035-1 000 

N92-31852 

Uncl qs 

G3/99 0114?98 
Preface 

NASA created the Numerical Aerodynamic Simulation (NAS) 

Program to focus resources on solving critical problems in 

aeroscience and related disciplines by utilizing the power of 

the most advanced supercomputers available. The NAS 

Program not only provides scientists with the computing 

power they need to solve today's most demanding computational fluid dynamics problems, it also benefits other 

supercomputer centers, both in Government and industry, 

by serving as a pathfinder in integrating leading-edge 

Supercomputing technologies. 

This report contains selected scientific results from the NAS 

Program's third year of operation, designated as the 1989- 

90 Operational Year. The year began March 1, 1989, and 

ended March 4, 1990. During this year, the scientific 

community was given access to a Cray-2 and a Cray Y-MP 

supercomputer. The Cray-2, the NAS Program's firstgeneration supercomputer, has four processors, 256 

megawords of central memory, and a total sustained speed 

of 250 million floating-point operations per second (250 

MFLOPS). 

NAS Users 

87-88 Year 

The second-generation supercomputer, the Cray Y-MP, has 

eight processors producing a total sustained processing 

speed of 1 billion floating-point operations per second (1 

GFLOPS). The Cray Y-MP had 32 megawords of central 

memory for most of the year and was upgraded to 128 

megawords in February 1990. The Cray Y-MP also has 256 

megawords of SSD memory. The Mass Storage Subsystem, 

which provides the primary file storage for the user community, improved significantly during this operational year. In 

addition to 260 gigabytes of online disk, two Storage 

Technology tape robots were installed to provide 2.4 

terabytes of archival data storage. 

The size of the scientific user community continued to 

increase. The total number of users for the first year was 

740, and the total for the second year increased to 1246. 

By the end of this year, the number of users reached 1733. 

The users were from 140 sites throughout the United States 

and represented NASA, the Department of Defense, and 

other Government agencies; private industry; and 

universities. 

Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb 

iii 

PRECEDING PAGE BLANK NO1 FILMED 

.mmmnmv ska 
A total of 459 individual research projects were accepted to Year. Of these projects, 89% were aeronautics oriented, as 

use the NAS resources during the 1988-89 Operational shown in the following chart. 

Astrophysics 

Ott 

v 

Structural Mechanics Turbulence 

At the end of each operational year, a NAS Technical additional copies of the report for this operational year or to 

Summaries Report is published to provide an overview of order reports from previous years, please address your 

the significant scientific results for that year. To order either request to: 

NAS Documentation Center 

NASA Ames Research Center 

Mail Stop 258-6 

Moffett Field, CA 94035-1000 

(41 5) 604-4632 
Table of Contents 

Principal 

Investigator NAS Summary Page 

David Adamec Large-Scale Ocean Modeling. .............................................................................................................. 1 

Co-investigators: Michele M. Rienecker and Antonio J..Busalacchi 

NASA Goddard Space Flight Center 

Ramesh K. Agarwal Helicopter Fuselage and Rotor Flow-Field Calculations in Hover and Forward Flight .......................... 2 

Co-investigator: Jerry E. Deese 

McDonnell Douglas Research LaboratoriesINASA Ames Research Center 

Ramesh K. Agarwal Numerical Solution of the Reynolds-Averaged Navier-Stokes Equations for Flow About 

an Almost Compete Aircraft.. ................................................................................................................ .3 

Co-investigator: Jerry E. Deese 

McDonnell Douglas Research LaboratoriesINASA Ames Research Center 

Shreekant Agrawal Separated and Vortical Flow-Field Analysis on Fighter Wing Configurations.. .................................... ..4 

Co-investigators: Tom A. Kinard and Brian A. Robinson 

McDonnell Aircraft Company 

Donald Baganoff 

R. Balasubramanian 

John T. Batina 

William W. Bower 

Stephen H. Brecht 

Edwin B. Brewer 

Adam C. Bricker 

Jeffrey C. Buell 

Pieter G. Buning 

Discrete Particle Simulation of Compressible Flow ....................... ................................................... 5 

Co-investigators: William J. Feiereisen, Jeffrey McDonald, Brian Haas, Michael Woronowicz, 

Michael Fallavollita, and Leo Dagum 

Stanford UniversityINASA Ames Research Center 

Direct Simulation of Large-Eddy Breakup Devices .............................................................................. 6 

Spectrex Inc. 

Validation of a Three-Dimensional Flux-Split Euler Algorithm for Unstructured Grids .......................... 7 

Co-investigators: Elizabeth M. Lee, Russ D. Rausch, and William L. Kleb 

NASA Langley Research Center 

Calculations of Unsteady, Supersonic-Jet Flow Fields and Acoustics .................................................. 8 

Co-investigators: Robert E. Childs and Gerald E. Chmielewski 

McDonnell Douglas Research LaboratoriesINielsen Engineering & Research, Inc. 

Hybrid Simulations of the Global Venus/Solar Wind Interaction .................... .................................... 9 

Berkeley Research Associates 

Direct Simulation of Aerothermal Loads for the Aeroassist Flight Experiment ................................... 10 

NASA Marshall Space Flight Center 

Hypersonic Air-Breathing Missile Aero/Propulsion Integration.. ........................... ........................ I 1 

Co-investigators: Brad K. Bergman, Kurt Abrahamson, and Nancy Wilkins 

General Dynamics, Convair Division 

Three-Dimensional Shear Layers and Wall-Bounded Compressible Turbulence ............................. 12 

NASA Ames Research Center 

Space Shuttle Flow Field. ................................................................................................................. .13 

Co-investigators: J. L. Steger, R. L. Meakin, F. W. Martin, I.-T. Chiu, Y. M. Rizk, 

M. Yarrow, and S. Obayashi 

NASA Ames Research Center 

Geoffrey Butler Two-Body Hypersonic Separation Analysis.. ................................................................................... 14 

Co-investigators: Brian Nguyen, Eric Sharnhorst, and David King 

General Dynamics, Convair Division 

Alan B. Cain Receptivity, Eigenfunction Modeling, and Simulation of a Wall-Bounded Flow .................................. 15 

Co-investigators: William W. Bower and Nagi N. Mansour 

McDonnell Douglas Research LaboratoriesINASA Ames Research Center . . 
Principal 

Investigator 

Steven C. Caruso 

Sukumar R. Chakravarthy 

R. Rexford Chamberlain 

Dean R. Chapman 

Denny S. Chaussee 

Lee T. Chen 

W. J. Chyu 

William J. Coirier 

William B. Compton Ill 

Raymond R. Cosner 

Russell B. Dahlburg 

Roger L. Davis 

Bill Davy 

Pramote Dechaumphai 

Nabeel A. 0. Demerdash 

Robert DeParvine 

NAS Summary Page 

An Unstructured Triangular-Mesh/Navier-Stokes Method for Computing 

the Aerodynamics of Aircraft with Ice Accretion ................................................................................. 16 

Nielsen Engineering & Research, Inc. 

FueVAir Turbulent Combustion in a Three-Dimensional Combustor Geometry 

in Supersonic Flow .............................................................................................................................. 17 

Co-investigators: Uriel C. Goldberg and Sampath Palaniswamy 

Rockwell International Science Center 

Three-Dimensional Calculations of Multiple Control-Jet Interactions for Defense Interceptors.. ........ 18 

Lockheed Missiles and Space Company, Inc. 

Continuum Computational Fluid Dynamicsfor Hypersonic High-Altitude Flight ................................ 19 

Co-investigator: Robert W. MacCormack 

Stanford University 

Hypersonic Flow Past Generic Lifting Bodies ..................................................................................... 20 

Co-investigators: Scott L. Lawrence, Thomas A. Edwards, and Bradford Bennett 

NASA Arnes Research Center 

Calculation of Transonic and Supersonic Flows Using an Interactive Scheme Based 

on Euler and Boundary-Layer Equations ............................................................................................ 21 

Co-investigators: Minh H. Bui and Hsun H. Chen 

Douglas Aircraft Company 

Airframe/lnlet Aerodynamics. .............................................................................................................. 22 

NASA Ames Research Center 

Three-Dimensional Shock/Boundary-Layer Interactions in Hypersonic Inlets .................................... 23 

NASA Lewis Research Center 

Transonic Navier-Stokes Solutions of Three-Dimensional Afterbody Flows ..................................... 24 

Co-investigator: Khaled Sayed Abdol-Hamid 

NASA Langley Research CenterIAnalytical Services and Materials, Inc. 

Hornet 2000 Flow-Field Analysis. ...................................................................................................... 25 

Co-investigators: Shreekant Agrawal and Patrick J. Malloy 

McDonnell Aircraft Company 

Dynamical Modeling of the Solar Atmosphere .................................................................................... 26 

Co-investigators: Jill P. Dahlburg, John T. Mariska, and J. M. Picone 

Naval Research Laboratory 

The Impact of Hot-Streak Migration on Turbine Heat Transfer ........................................................... 27 

Co-investigators: Daniel J. Dorney and Diane M. Rodimon 

United Technologies Research Center 

Three-Dimensional Aeroassist Flight Experiment Flow Simulations.. ............... ............................... 28 

Co-investigators: Grant Palmer, Dinesh Prabhu, and Ellis Whiting 

NASA Ames Research Center 

Integrated Fluid-Thermal-Structural Analyzer Demonstrates HeatTransfer/Deformation Coupling. ....................................................................................................... 29 

NASA Langley Research Center 

Finite-Element Computation of Three-Dimensional Magnetic Fields for Design 

Optimization of Generators for Space Station Solar Dynamic Power ................................................. 30 

Co-investigator: R. Wang 

Clarkson University 

High-Angle-of-Attack Inlet Analysis and Design Using Computational Fluid 

Dynamics Methods .............................................................................................................................. 31 

Co-investigator: Ben Smith 

General Dynamics, Fort Worth Division 
Principal 

Investigator 

Robert DeParvine 

Dan F. Dominik 

J. Philip Drummond 

George S. Dulikravich 

John K. Eaton 

Thomas A. Edwards 

Thomas A. Edwards 

T. Alan Egolf 

S. E. Elghobashi 

S. E. Elghobashi 

N. M. El-Hady 

John J. Erhart 

G. Erlebacher 

Fort F. Felker 

Jolen Flores 

NAS Summary Page 

Validation of a Computational Fluid Dynamics Code for High-Speed-Inlet Design ............................ 32 

Co-investigator: Ben Smith 

General Dynamics, Fort Worth Division 

Advanced Solid Rocket Motor Study ................................................................................................... 33 

Co-investigators: Vedat Akdag, Shmuel Ben-Shmuel, William Riba, Robert Williams, 

Cheng L. Chen, S. Ramakrishnan, K. Ragagopal, and S. Chakravathy 

Rockwell International, Space Transportation Systems Division and Science Center 

Simulation of Supersonic Chemically Reacting Flow Fields ................................................................ 34 

Co-investigators: Mark H. Carpenter, Peyman Givi, Johnny R. Narayan, David W. Riggins, 

Balu Sekar, and Jeffrey A. White 

NASA Langley Research Center 

Acceleration of Iterative Algorithms for Euler and Navier-Stokes Equations.. ....................................35 

Co-investigator: Seungsoo Lee 

The Pennsylvania State University 

The Interaction of Particles with Homogeneous Turbulence ............................................................... 36 

Co-investigator: Kyle D. Squires 

Stanford University 

Hypersonic Chemically Reacting Flow over Blended Wing-Body Vehicles ..................................... 37 

Co-investigators: Jolen Flores, Uwe Jettmar, and Greg Molvik 

NASA Ames Research Center 

Numerical Simulation of Hydrogen-Air Combustion in Hypersonic-Vehicle 

Propulsion Systems ............................................................................................................................. 38 

Co-investigators: Jolen Flores and Uwe Jettmar 

NASA Ames Research Center 

Advanced CFD Codes for Rotary-Wing Airloads and Performance Prediction.. ............... ... ....... 39 

Co-investigator: Brian E. Wake 

United Technologies Research Center 

Direct Simulation of Turbulent Reacting Flows .................................................................................... 40 

Co-investigator: K. K. Nomura 

University of California, lrvine 

Dispersion of Solid and Fluid Particles in Turbulent Homogeneous Flows With and 

Without Turbulence Modulation ......................................................................................................... .41

Co-investigator: G. C. Truesdell 

University of California, lrvine 

Control of the Flow Field about an Airfoil Section by Localized Surface Heating ................................ 42 

Co-investigator: L. Maestrello 

NASA Langley Research CenterIAnalytical Services and Materials, Inc. 

CFD Analysis of the Flow Paths of Spherical Convergent Flap Nozzles .............................................. 43 

Co-investigators: Saadat A. Syed and Eric W. King 

United Technologies, Pratt & Whitney 

Compressible Turbulence ................................................................................................................... 44 

Co-investigators: S. Sarkar, C. Shu, and T. A. Zang 

NASA Langley Research CenterIlCASE 

Three-Dimensional Viscous Drag Prediction for Rotor Blades ............................................................ 45 

Co-investigator: Ching S. Chen 

NASA Ames Research Center 

Compressible Navier-Stokes Code Development ............................................................................... 46 

Co-investigators: Steve Ryan and Tom Edwards 

NASA Ames Research Center 
Principal 

Investigator 

Arthur J. Freeman 

K.-Y. Fung 

Javier A. Garriz 

Gary A. Glatzmaier 

Peter A. Gnoffo 

Robert A. Golub 

Aga M. Goodsell 

Fernando F. Grinstein 

W. L. Grose 

G. P. Guruswamy 

Karl E. Gustafson 

Kadosa Halasi 

Edward J. Hall 

Richard L. Haller 

Julius E. Harris 

Peter M. Hartwich 

Peter M. Hartwich 

H. A. Hassan 

NAS Summary Page 

Electronic-Structure Study of High Superconductors.. ....................................................................... 47 

Co-investigators: A. Continenza, S. Massidda, and J. Yu 

Northwestern University 

Computational Studies of Compressibility Effects on Dynamic Stall .......................... ............ 48 

University of Arizona 

Validation of 3-D Wind Tunnel Wall Interference Assessment/Correction Codes.. .......................... 49 

NASA Langley Research Center 

Numerical Simulations of Deep Global Convection in Jupiter ............................................................ 50 

Los Alamos National Laboratory 

Hypersonic Flows in Chemical and Thermal Nonequilibrium .............................................................. 51 

NASA Langley Research Center 

Flow-Field Simu!ation Around Different Rotor Planforms .................................................................. 52 

Co-investigator: Forooz F. Badavi 

NASA Langley Research CenterILockheed Engineering and Sciences Company 

A Supersonic Computational Fluid Dynamic Analysis of a Generic Fighter ................................... 53 

NASA Ames Research Center 

Simulation of Compressible, Spatially Evolving, Reactive Planar Shear Flows ................................... 54 

Naval Research Laboratory 

Three-Dimensional Atmospheric Simulation Model ........................................................................... 55 

Co-investigators: W. T. Blackshear, R. W. Turner, and R. S. Eckman 

NASA Langley Research Center 

Simulation of Fluid/Structural Interactions .......................................................................................... 56 

Co-investigators: S. Obayashi, N. M. Chaderjian, and P. M. Goorjian 

NASA Ames Research Center 

Vortex Dynamics in Aerodynamic Flows ............................................................................................ 57 

Co-investigator: Robert R. Leben 

University of Colorado, Boulder 

Parameter Study in the Driven Cavity .................................................................................................. 58 

Co-investigator: Karl E. Gustafson 

Kansas State UniversityIUniversity of Colorado, Boulder 

Ducted Propfan Analysis ................................................................................................................... 59 

Allison Gas Turbine Division, General Motors Corporation 

Evaluation of the CAP-TSD Computer Code Using an F- 16 Study Case ...................... ............. 60 

Co-investigators: Kevin Penning and Lam-son Vinh 

General Dynamics, Fort Worth Division 

Supersonic Laminar-Flow-Control Computational Fluid Dynamics.. ............... .............................. 61 

Co-investigators: Venkit lyer and Robert E. Spall 

NASA Langley Research Center 

General, Fast, Accurate Floating Shock Fitting Procedure for Unadapted Meshes ........................ 62 

ViGYAN, Inc./NASA Langley Research Center 

Navier-Stokes Solutions for Vortical Flows over a Forebody ......................................................... 63 

ViGYAN, Inc./NASA Langley Research Center 

Monte Carlo Simulation of Hypersonic Flows ...................................................................................... 64 

Co-investigators: David P. Olynick and Jeff C. Taylor 

North Carolina State University 
Principal 

Investigator 

H. A. Hassan 

H. A. Hassan 

Henry J. Haussling 

James D. Heidmann 

James C. Hill 

Scott D. Holland 

C. C. Horstman 

C.-H. HSU 

Thomas T. Huang 

Gary W. Huband 

Ching-mao Hung 

Harley E. Hurlburt 

Danny Hwang 

Sieven H, lzen 

Laurence R. Keefe 

John L. Klann 

Ajay Kumar 

NAS Summary Page 

Turbulence Modeling of Separated Flows.. ......................................................................................... 65 

Co-investigators: Robert A. Mitcheltree and Richard L. Gaffney, Jr. 

North Carolina State University 

Turbulent Supersonic Mixing Layers.. ................................................................................................. .66 

Co-investigators: Dean R. Eklund, Steven H. Frankel, and Erick J. S. Gantt 

North Carolina State University 

Multiblock Solutions of the Navier-Stokes Equations ........................................................................... 67 

Co-investigators: Joseph J. Gorski and Roderick M. Coleman 

David Taylor Research Center 

An Analysis of the Viscous Flow through a Compact Radial Turbine by the AveragePassage Approach ............................................................................................................................. 68 

NASA Lewis Research Center 

Direct Simulation of Turbulent Reacting Flows .................................................................................... 69 

Co-investigators: Andy D. Leonard and Dana G. Haugli 

Iowa State University 

A Computational and Experimental Parametric Study of Three-Dimensional Side- Wall 

Compression Scramjet Inlets at Mach 10 ........................................................................................ 70 

Co-investigator: John N. Perkins 

North Carolina State University 

Turbulence Modeling for Compressible/Hypersonic Flows.. ............................................................ 71 

Co-investigators: J. R. Viegas, T. J. Coakley, and P. Rodi 

NASA Ames Research Center 

Prediction of Vortical Flows Using lncornpressible Navier-Stokes Equations ..................................... 72 

ViGYAN, Inc./NASA Langley Research Center 

Turbulence Modeling for Submarine Flow Field Computation ............... ... ..................................73 

Co-investigator: Yu-Tai Lee 

David Taylor Research Center 

Numerical Simulation of an F- 16A at Angle of Attack.. ..................................................................... .74 

Co-investigators: J. S. Shang and Michael J. Aftosmis 

Wright Research and Development Center 

Computation of Steady Three-Dimensional Separation.. ................................................................. -75 

NASA Ames Research Center 

Eddy-Resolving Model of the Pacific Ocean ...................................................................................... .76 

Co-investigators: Alan J. Wallcraft and Jimmy L. Mitchell 

Naval Oceanographic and Atmospheric Research LaboratoryIJAYCOR 

Computational Advanced Propulsion Technology Research ........................................................... .77 

Co-investigators: John Wolter, Joe Nenni, Mark Krein, and Dave Georgevich 

NASA Lewis Research Center 

Numerical Inversion of a Limited-Data X-Ray Transform .................................................................... 78

Case Western Reserve University 

Linking Attractor Geometry to Turbulence Physics ........................................... .............................. 79 

NASA Ames Research Center 

Solar Dynamic Space Power-System Design and Performance Analysis ....................................... 80 

Analex CorporationINASA Lewis Research Center 

Three-Dimensional Shock/Shock Interactions on the Inlet Side Wall .................................................. 81 

Co-investigator: Dal J. Singh 

NASA Langley Research Center 
Principal 

Investigator 

Geojoe Kuruvila 

Dochan Kwak 

H. T. Lai 

C. C. Lee 

S. J. Leib 

S. J. Lin 

Rung T. Ling 

C. H. Liu 

James M. Luckring 

Gregory A. Lyzenga 

Edward C. Ma 

M. G. Macaraeg 

Robert W. MacCormack 

Robert D. MacElroy 

Michael D. Madson 

L. Maestrello 

NAS Summary Page 

Numerical Study of Fundamental Fluid Dynamics using Navier-Stokes Equations ............................ 82 

NASA Langley Research Center 

lncompressible Navier-Stokes Calculations for the Space Shuttle Main Engine ................................ 83 

Co-investigators: Stuart Rogers, Seokkwan Yoon, Moshe Rosenfeld, and Cetin Kiris 

NASA Ames Research Center 

Computation of Single-Expansion-Ramp and Scramjet Nozzles ........................................................ E4 

Sverdrup Technology, Inc. 

Numerical Investigation of NASP-Like Vehicles .................................................................................. 85 

Co-investigators: William Bower, Shawn Hagmeier, Scott Van Horn, Pat Vogel, 

and Darrell Weber 

McDonnell Douglas Corporation 

Nonlinear Instability of Shear Layers ................................................................................................... 86 

Sverdrup Technology, Inc./NASA Lewis Research Center 

Computational Fluid Dynamics Analysis of Space Shuttle Main Engine Turbopump 

Rotor/Stator Flows in Two and Three Dimensions ............................................................................. 87 

Co-investigator: R. J. Yang 

Rockwell International, Rocketdyne Division 

Application of Computational Fluid Dynamics Methods to Radar Cross 

Section Computations ...................................................................................................................... 88 

Northrop Aircraft Division 

Computational Prediction and Control of Steady and Unsteady Asymmetric Vortex Flows 

around Cones ...................................................................................................................................... 89 

Co-investigator: Osama A. Kandil 

NASA Langley Research CenterIOld Dominion University 

Transonic Navier-Stokes Solutions about a Complex High-speed Accelerator Configuration .........90 

Co-investigators: Farhad Ghaffari, James L. Thomas, and Brent L. Bates 

NASA Langley Research Center 

Earthquake-Cycle Stress Simulations .................................................................................................. 91 

Co-investigators: Arthur Raefsky and Stephanie G. Mulligan 

Jet Propulsion Laboratorylcalifornia Institute of Technology 

Numerical Investigation of a Space Shuttle Orbiter Contingency Abort. ......................................... 92 

Co-investigator: Thomas C. Wey 

Lockheed Engineering and Sciences Company 

Nonlinear Evolution of Supersonic Disturbances in Mixing Layers .................................................. 93 

NASA Langley Research Center 

Simulation of Highly Ionized Flows ...................................................................................................... 94 

Co-investigator: Philippe Rostand 

Stanford UniversityIAnalatom, Inc. 

Computer Simulation of Ion Transport across Membranes .............................................................. 95 

Co-investigator: Andrew Pohorille 

NASA Ames Research Center 

Transonic Analysis About the F-16A and Other Complex Configurations .......................... ....... 96 

Co-investigators: Alex C. Woo, Ralph L. Carmichael, F. T. Johnson, S. S. Samant, 

D. P. Young, R. G. Melvin, M. B. Bieterman, and J. E. Bussoletti 

NASA Ames Research CenterIBoeing Advanced Systems 

Radiation and Control of the Acoustic Field Caused by a Wave Packet Evolving along 

a Concave-Convex Surface ................................................................................................................ 97 

Co-investigator: N. M. El-Hady 

NASA Langley Research CenterIAnalytical Services and Materials, Inc. 
Principal

Investigator NAS Summary Page

Mujeeb R. Malik Transition in Hypersonic and Three-DimensionalBoundary Layers....................................................98

Co-investigators: C.-L. Chang and R. E.Spall

High Technology Corporation/NASALangley Research Center

John Mangus Navier-StokesAnalysis of theAir Force VortexFlap Model and the F/A-18........................................99

Co-investigators:Shreekant Agrawal, Robert Lowrie, and BrianRobinson

Northrop Aircraft Division/McDonnellAircraftCompany

Nagi N. Mansour Direct Simulation of Compressible Turbulent Flows ..........................................................................100

Co-investigators: J. Chen and G. Blaisdell

NASAAmes Research Center

Fred W. Martin,Jr. Space Shuttle Flow Field ..................................................................................................................... 101

Co-investigators:Joseph Steger, PieterBuning, Steve Labbe, Ray Gomez, PhilStuart,

Jeff Slotnick, Steve Parks, and Stan Johnson

NASAJohnson Space Flight Center/NASAAmes Research Center

Dimitri J. Mavriplis Solution of theSteady State Navier-Stokes Equations on Unstructured and

Adaptive Meshes ...............................................................................................................................102

NASA Langley Research Center/ICASE

Hans G. Mayr Numerical Study ofPlanetary Atmospheres ......................................................................................103

Co-investigator: Kwing L. Chan

NASA Goddard Space Flight Center

Charles R. McClinton National Aero-Space Plane Propulsion Flow-PathAnalysis and Code Certification..........................104

Co-investigators: R. Bittner, G. Bobskill, R. Hawkins, T. Jentink, P. Kamath, M. Mao,

G. Mekkes, and D. Riggins

NASALangley Research Center

W. J. McCroskey Aerodynamic Flows about High-Performance Rotor Blade Tips....................................................... 105

Co-investigators: J. D. Baeder, G. R. Srinivasan, and E.P. N. Duque

U. S.Army Aeroflightdynamics Directorate--AVSCOM/NASA Ames Research Center

W. J. McCroskey Airloads and Acoustics of Rotorcraft ................................................................................................. 106

Co-investigators: J. D. Baeder, E. P. Duque, and G. R. Srinivasan

U. S.Army Aeroflightdynamics Directorate--AVSCOM/NASA Ames Research Center

W. J. McCroskey Tilt-RotorAerodynamic Interactions ...................................................................................................107

Co-investigators: V. Raghavan and S.Stanaway

NASAAmes Research Center

S. Naomi McMillin Incipient Leading-Edge Separation ................................................................................................... 108

NASALangley Research Center

N. Duane Melson Multiblock, Multigrid Method for the Solution of the Three-Dimensional

Euler Equations ..................................................................................................................................109

Co-investigators: Frank E. Cannizzaro, Alaa Elmiligui, and E. von Lavante

NASA Langley Research Center

John E. Melton Computational Fluid Dynamics Analysis of Advanced Turboprop Configurations ............................110

Co-investigators: Ronald G. Langhi and Brian A. Nishida

NASAAmes Research Center

Michael R. Mendenhall Vortex-Induced Nonlinearities on Submarines ..................................................................................111

Co-investigator: Stanley C. Perkins, Jr.

Nielsen Engineering & Research, Inc.

Gene P. Menees Standing Oblique Detonation Waves................................................................................................. 112

Co-investigators: Henry G. Adelman and Jean-Luc Cambier

NASAAmes Research Center
Principal 

Investigator 

Suresh Menon 

Suresh Menon 

Charles L. Merkle 

Christopher J. Miller 

William H. Miller 

Joseph H. Morrison 

Robert D. Moser 

Wolfgang Mueller 

D. A. Naik 

R. M. Nallasamy 

David Nixon 

Charles R. Olling 

Charles R. Olling 

Elaine S. Oran 

Ajay K. Pandey 

NAS Summary Page 

Large-Eddy Simulations of Ramjet Combustion Instability ................................................................ 1 13 

Co-investigator: Wen-Huei Jou 

QUEST Integrated, Inc. 

Mixing Enhancement for Scramjet Flameholders .................. ........................................................ 1 14 

Co-investigator: Emerick Fernando 

QUEST Integrated, Inc. 

Absorption of Microwave Energy in a Flowing Gas .......................................................................... 1 15 

Co-investigator: S. Venkateswaran 

The Pennsylvania State University 

Numerical Simulation of Advanced Propellers ................... .......................................................... 116 

Co-investigator: Saif A. Warsi 

NASA Lewis Research CenterISverdrup Technology, Inc. 

Quantum Mechanical Reactive Scattering.. ................................................................................... 1 17 

Co-investigator: John Z. H. Zhang 

University of California, Berkeley 

Multi-Tasked Numerical Simulation of Complex Configurations in Hypersonic Flow ........................ 1 18 

Co-investigator: David L. Whitaker 

NASA Langley Research Center 

Wall-Bounded Turbulent Flows ....................................................................................................... 1 19 

Co-investigator: John Kim 

NASA Ames Research Center 

Electronic Structure of Superconductors ........................................................................................ 1 20 

Analatom, Inc./NASA Lewis Research Center 

Transonic Potential Flow about Transport Aircraft. ........................................................................... 121

Co-investigators: A. M. Ingraldi, R. G. Jorstad, T. A. Reyhner, and S. F. Yaros 

ViGYAN, Inc./NASA Langley Research CenterlThe Boeing Company 

Unsteady Flow Field on an Advanced Propeller.. .......................................................................... 122 

Sverdrup Technology, Inc./NASA Lewis Research Center 

PegasusTM Aerodynamic Analyses.. ............................ ................................................................ 123 

Co-investigators: Gary D. Kuhn, Steven Caruso, and Michael R. Mendenhall 

Nielsen Engineering & Research, Inc. 

Navier-Stokes Simulation of Separated Turbulent Flow around a Generic 

Fighter Aircraft.. ............................................................................................................................... 124 

Co-investigators: Pradeep Raj and Josef S. Sikora 

Lockheed Aeronautical Systems Company 

Navier-Stokes Simulation of Turbulent Flow over Rectangular Cavities 

Containing Stores. .......................... .. ............................................................................................ 125 

Co-investigators: Pradeep Raj and James E. Brennan 

Lockheed Aeronautical Systems Company 

Unsteady Diffusion Flames.. .............................................................................................................. 126 

Co-investigator: Janet L. Ellzey 

Naval Research LaboratoryIBerkeley Research Associates 

Flux-Based Finite-Element Formulation Reduces CPU Time for Thermal-Structural 

Analysis ......................... ............................................................................................................ 127 

Lockheed Engineering and Sciences CompanyINASA Langley Research Center 

Hydrodynamics of Self-Propelled Bodies.. ........................ .......................................................... 128 

Co-investigator: F. Stern 

lowa Institute of Hydraulic ResearchIUniversity of lowa 
Principal 

Investigator 

James L. Pittman 

James L. Pittman 

Richard H. Pletcher 

Andrew Pohorille 

Ramadas K. Prabhu 

Thomas H. Pulliam 

Man Mohan Rai 

Man Mohan Rai 

Man Mohan Rai 

M. S. Raju 

R. Ramakrishnan 

David A. Randall 

James A. Rhodes 

Ben R. Riley 

Charles L. Rino 

Michael M. Rogers 

R. Clayton Rogers 

NAS Summary Page 

Generic National Aero-Space Plane Afterbody.. .................. ...................................................... 1 29 

Co-investigators: Kenneth E. Tatum and Mohamed E. El-Eshaky 

NASA Langley Research Center 

NASP-TMP Forebody/lnlet ............................................................................................ Integration 130 

Co-investigator: Lawrence D. Huebner 

NASA Langley Research Center 

Development and Evaluation of Computational Methods for Turbomachinery Applications ........... .I31 

Co-investigator: Edward J. Hall 

Iowa State University/Allison Gas Turbine Division, General Motors Corporation 

Vapor-Phase Growth of Crystals in Microgravity, .......... ................................................................ 132 

University of California, Berkeley 

Finite-Element Analysis of Equilibrium and Nonequilibrium Flows ................................................... 133 

NASA Langley Research CenterILockheed Engineering and Sciences Company 

Chaotic, Unsteady, Low-Reynolds Number Navier-Stokes Flow .................... ............................ .I34 

NASA Ames Research Center 

A Finite-Difference Approach to Direct Simulations and Large-Eddy Simulations 

of Turbulent Flow.. ............................................................................................................................. .I35 

NASA Ames Research Center 

Three-Dimensional Multi-Airfoil Navier-Stokes Simulations of Rotor/Stator Interaction ....................................................................................................................................... in Turbines.. ,136 

Co-investigators: Nateri K. Madavan and Akil A. Rangwalla 

NASA Ames Research Center 

Unsteady Flow in a Multistage Compressor ..................... ..... ............................................... 1 37 

Co-investigators: Karen L. Gundy-Burlet and Akil Rangwalla 

NASA Ames Research Center 

Analysis of Rotary Engine Processes and Computer Codes ............................................................. 138 

Sverdrup Technology, Inc. 

An Adaptation Procedure Combining Mesh Refinement with Mesh Movement .................................................................................................................... for Compressible Flows.. 1 39 

NASA Langley Research Center 

Modeling Global Cloudiness.. ......................................................................................................... 140 

Colorado State University 

Computation of ASTOVL Flow Fields ............................................................................................... 141 

McDonnell Aircraft Company 

Kinetic Theory Model for the Flow of a Simple Gas from a Three-Dimensional 

Axisymmetric Nozzle.. .................... .............................................................................................. 142 

University of Evansville 

Scattering from Ocean Surfaces and Near-Surface Objects ......................................................... 143 

Co-investigators: Hoc D. Ngo and Thomas L. Crystal 

Vista Research, Inc. 

Turbulent Reacting Flows ................................................................................................................ ,144 

Co-investigators: Robert Moser and Chris Rutland 

NASA Ames Research Center 

Hydrogen-Air Combustion Simulation in a Pulse Facility ............ .................................................. 145 

Co-investigator: Elizabeth H. Weidner 

NASA Langley Research Center 
Principal

Investigator NAS Summary Page

William C. Rose National Aero-Space Plane Inlet Boundary Layer Control, Phase II................................................. 146

NASA Lewis Research Center/Rose Engineering & Research, Inc.

William C. Rose National Aero-Space Plane Inlet Flow Fields .................................................................................... 147

Co-investigator: Edward W. Perkins

NASAAmes Research Center/RoseEngineering & Research, Inc.

William C. Rose Three-Dimensional Viscous Flow in High-Speed Inlets .................................................................... 148

Co-investigator: Edward W. Perkins

NASAAmes Research Center/Rose Engineering & Research, Inc.

M. B.Salamon Advanced Computational Materials ................................................................................................. 14_

Co-investigators: R.Averback, Y.-C. Chang, J. Kogut, R. Martin, and P. Wolynes

University of Illinois, Urbana-Champaign

Matthew T. Scott Computational Methods for Rotor-Blade Drag Prediction ................................................................ 150

Bell Helicopter Textron, Inc.

Balu Sekar Direct Simulation of High-Speed Mixing Layers Withand Without Chemical Heat Release ............ 151

Co-investigators: H. S. Mukunda and Mark H. Carpenter

NASA Langley Research Center

John V. Shebalin Ionized FlowAround a Reentry Vehicle ............................................................................................ 152

NASA Langley Research Center

PeterK. Shih Afterbody Aerothermodynamic Studies for the Hypersonic Glide Vehicle ....................................... 153

Co-investigator: Che-Shing Kang

General Dynamics, Convair Division

Jian-Shun Shuen Advanced Numerical AIgorithms for Chemically Reacting Flows..................................................... 154

Sverdrup Technology, Inc./NASA Lewis Research Center

William A. Sirignano Ignition and Flame Spread above Liquid FuelPools: GravityEffects ............................................... 155

Co-investigators: Fanghei Tsau and David N. Schiller

University of California, Irvine

Philippe R. Spalart Transition and Turbulence in Three-Dimensional Flows................................................................... 156

NASAAmes Research Center

FrankJ. Spera Magma Chamber Convection ........................................................................................................... 157

University of California, Santa Barbara

B. M. Steinetz National Aero-Space Plane Engine Corner-Flow .............................................................................. 158

Co-investigators: W. J. Coirier and Mike Tong

NASA Lewis Research Center/Sverdrup Technology, Inc.

Roger C. Strawn Computational Fluid Dynamics Prediction ofAdvanced Rotor Performance ................................... 159

Co-investigators: John Bridgeman, K. Ramachandran, and Frank Caradonna

U.S.Army Aeroflightdynamics Directorate--AVSCOM/NASA Ames Research Center

Craig L. Streett Numerical Simulation of Wave Interactions Related to Transition..................................................... 166

Co-investigator: S.Balachandar

NASALangley Research Center

Craig L. Streett TransitionSimulations in Nonhcmogeneous Geometries.................................................................. 16i

NASALangley Research Center

Phil C. Stuart Mars Rover/Sample Return Aerocapture Vehicle.............................................................................. 162

Co-investigator: Chien-Peng Li

NASAJohnson Space Center

xiv
Principal 

Investigator NAS Summary Page 

Sundaresa V. Subramanian Numerical Study of Three-Dimensional Viscous Reacting Flows with Application 

to Scramjet Propulsion .................................................................................................................... 1 63 

Co-investigator: Michael J. Epstein 

General Electric Aircraft Engines 

Dennis Sullivan Microwave Hyperthermia Computer Modeling ............................ ............................................... 164 

Co-investigator: Bryan James 

Stanford University School of Medicine 

Chao-Ho Sung Naval Applications of Computational Fluid Dynamics ...................................................................... 165 

Co-investigator: Michael J. Griffin 

David Taylor Research Center 

R. C. Swanson Development of Algorithms for Solving the Three-Dimensional Navier-Stokes Equations ................ 166 

Co-investigator: M. Sanetrik 

NASA Langley Research Center 

Tsze C. Tai 

Tsze C. Tai 

Ronald K. Takahashi 

Luen T. Tam 

John C. Tannehill 

Rajiv Thareja 

Rajiv Thareja 

Donald G. Truhlar 

Hydrodynamic Prediction Methods for Advanced Submarine Configurations.. ............................... .I67 

Co-investigators: Steven C. Fisher, Cheng-Wen Lin, and Gerald D. Smith 

David Taylor Research Center 

Low-Speed Maneuver Aerodynamics in a Nonuniform Free Stream.. .............................................. 168 

David Taylor Research Center 

Unsteady Euler Analysis of the Redistribution of an Inlet Temperature Distortion ..................................................................................................................................... in a Turbine 169 

Co-investigator: Ron-Ho Ni 

United Technologies, Pratt & Whitney 

Thermochemical and Radiative Nonequilibrium Flow Simulation for the Aeroassist 

Flight Experiment.. ............................................................................................................................. 1 70 

Co-investigator: Chien P. Li 

Lockheed Engineering and Sciences CompanyINASA Johnson Space Center 

Development of a Robust Parabolized Navier-Stokes Code for Computing 

Three-Dimensional, Chemically Reacting Flow Fields ....................................................................... 171 

Co-investigators: Phil E. Buelow and John 0. levalts 

Iowa State University 

Computation of Three-Dimensional Flows Using Unstructured Grids. ........................................... 172 

Co-investigators: Ken Morgan, Jaime Peraire, Obey Hassan, and Joaquin Peiro 

NASA Langley Research Center 

Viscous Hypersonic Flow over a 24-Degree Compression Corner ............................................. 173 

Co-investigators: Ken Morgan and Jaime Peraire 

NASA Langley Research Center 

Scattering Theory and Calculations for Chemical Reactions and Molecular 

Energy Transfer .............................................................................................................................. 174 

Co-investigators: David C. Chatfield, Philippe Halvick, David W. Schwenke, 

Thanh N. Truong, Michael J. Unekis, and Meishan Zhao 

University of Minnesota 

Pratap Vanka Hot Gas Ingestion by STOVL Aircraft ................................................................................................ 175 

Co-investigators: D. K. Tafti and W. Pegeus 

University of Illinois, Urbana-Champaign 

Bram vanLeer Calculation of Hypersonic Flows with Strong Surface Blowing .......................................................... 176 

Co-investigators: T. C. Adamson, A. F. Messiter, N. D. Carter, and M. D. Matarrese 

The University of Michigan 

Veer N. Vatsa High Reynolds Number, Transonic, Viscous Flow over Aircraft Components ............................. 177 

Co-investigator: Bruce W. Wedan 

NASA Langley Research Center 
Principal 

Investigator NAS Summary Page 

Bill J. Walker Tactical Missile Aero-Propulsion Interaction.. ................................................................................ 1 78 

Co-investigators: C. D. Mikkelsen, K. D. Kennedy, K. L. Cornelius, and M. E. Vaughn, Jr. 

U.S. Army Missile Command-Redstone Arsenal 

Robert W. Walters Development of Unstructured and Nonequilibrium Chemistry Upwind Algorithms 

for Hypersonic Flows.. ..................................................................................................................... 179 

Co-investigators: Bernard Grossman, P. Cinnella, Andrew S. Godfrey, 

William D. McGrory, and David C. Slack 

Virginia Polytechnic lnstitute and State University 

Jong H. Wang Navier-Stokes Predictions of Hypersonic Chemically Reacting Flows ......................................... 180 

Co-Investigators: David Yeh and Mike George 

Rockwell International, North American Aircraft Division 

Kurt F. Weber Simulation of Three-Dimensional Flow in a Transonic Fan Rotor ..................................................... 181 

Co-investigator: Dale W. Thoe 

Allison Gas Turbine Division, General Motors Corporation 

Kenneth J. Weilmuenster Winged Entry Vehicle Computations ................................................................................................. 182 

Co-investigator: Francis A. Greene 

NASA Langley Research Center 

Robert A. West Optical Properties of Nonspherical Particles in Planetary Atmospheres ......................................... 183 

Jet Propulsion LaboratorylCalifornia lnstitute of Technology 

Thomas C. Wey Application of Unstructured Grids to Shuttle Computational Fluid Dynamics .................................. 184 

Co-investigator: Chien-Peng Li 

Lockheed Engineering and Sciences CompanylNASA Johnson Space Center 

Richard G. Wilmoth Shock Interactions in Rarefied Hypersonic Flows ............................................................................ 185 

Co-investigator: Bradford Sturtevant 

NASA Langley Research CenterICalifornia lnstitute of Technology 

Chung-Jin Woan Computational Fluid Dynamics Design of a Laminar-Flow Control Glove ........................................ 186 

Co-investigator: Michael W. George 

Rockwell International. North American Aircraft Division 

Cheng-l Yang Numerical Simulation of Submarine Propulsion ................................................................................ 1 87 

David Taylor Research Center 

Ruey-Jen Yang Multistage Rotor/Stator Interaction in the Space Shuttle Main Engine Turbopump Turbine.. ........... 188 

Co-investigator: Shyi-Jang Lin 

Rockwell International, Rocketdyne Division 

Larry Young Tilt-Rotor Download Prediction ......................................................................................................... Co-investigator: C. S. Lee 

NASA Ames Research Center 

Richard E. Young Simulation of the Climatology of the El Chichon Volcanic Aerosol Cloud in the Stratosphere.. ........ 190 

Co-investigators: Owen B. Toon and James B. Pollack 

NASA Ames Research Center 

T. A. Zang 

Development of an Euler-Based Method for Turboprop Integration ........... ................................. 191 

Co-investigators: H. C. Chen, T. J. Kao, and D. A. Naik 

The Boeing CompanyNiGYAN, Inc./NASA Langley Research Center 

lncompressible Transition to Turbulence.. .............. .................................................................... 192 

Co-investigators: S. Dinavahi, B. Singer, and U. Piomelli 

NASA Langley Research Center 

Index by Research Sites ................... ................................................................................................................................... 193 

xvi 
NAS 

Summaries 

Large-Scale Ocean Modeling 

David Adamec, Principal Investigator 

Co-investigators: Michele M. Rienecker and Antonio J. Busalacchi 

NASA Goddard Space Flight Center 

Research Objective 

To develop tools that allow simulations of ocean flows, which 

help in understanding the role of the oceans in the Earth 

climate system. 

Approach 

three-dimensional quasi-geostrophic and primitive-equation 

ocean models were used to examine ocean mesoscale variability in the midlatitudes. Multigrid techniques were developed to help speed model calculations. 

Accomplishment Description 

Three-dimensional, linear stability analyses were used to study 

the stability of various Gulf Stream flow paths. In particular, the 

following aspects of an assumed basic flow were studied, as 

they relate to the sensitivity of growing instabilities: meander 

wavelength, meander steepness, trough width and steepness, 

ridge width and steepness, strength of initial flow, and ratio of 

barotropic to baroclinic energy in the basic flow. The accompanying figure shows the results of a stability analysis for a 

flow path with a narrow trough. The initial flow is indicated by 

the white arrows. Both the three-dimensional surface and the 

color scheme indicate the magnitude of the fastest growing 

instability. The instability with the largest magnitude occurs 

just downstream of the trough crest. Each analysis requires 

45 Cray Y-MP minutes and 10 megawords of memory. Also, a 

new three-dimensional computer model based on the differentiated form of the momentum equations was coded, tested, 

and optimized for Cray Y-MP use. This new code also uses 

our own newly developed multigrid solvers for spherical 

coordinates. 

SignifiC?mce 

The exact role of the ocean in the meridional exchange of heat 

and momentum is not well understood. These types of ocean 

simulations and calculations help in understanding and quantifying the effect of the ocean on the Earth climate system. 

Future Plans 

The three-dimensional stability analyses will be continued 

using Gulf Stream paths determined from satellite data, and 

the new primitive-equation code will be used to study the formation and maintenance mechanisms of ocean fronts. 

PuMications 

"Three-Dimensional Stability of Gulf Stream Flow." Presented 

at the Goddard Space Flight Center Ocean Seminar Series, 

Feb. 1990. 

Stability analysis for a flow path with a narrow trough. 
Helicopter Fuselage and Rotor Flow-Field Calculations in Hover and 

Forward Flight 

Ramesh K. Agarwal, Principal Investigator 

Co-investigator: Jerry E. Deese 

McDonnell Douglas Research LaboratoriesINASA Ames Research Center 

Research Objective 

To develop computational codes capable of predicting the 

transonic viscous flow about helicopter fuselages and multibladed helicopter rotors both in hover and in forward flight. 

Approach 

For calculating turbulent flow about helicopter fuselages, the 

Reynolds-averaged Navier-Stokes equations are solved in an 

inertial frame on a body-conforming curvilinear grid using a 

finite-volume explicit Runge-Kutta time-stepping scheme. For 

calculating turbulent flow about rotor blades, Reynoldsaveraged Navier-Stokes equations are solved in a rotating 

coordinate system. Rotor-wake effects are modeled in the form 

of a correction applied to the geometric angle of attack along 

the blades. This correction is obtained by computing the local 

induced downwash with a prescribed- or free-wake analysis 

program. 

Accomplishment Description 

For helicopter fuselage flow-field calculations, the Reynoldsaveraged Navier-Stokes code MDNS3D was installed on a 

Cray-2. Flow fields about an Apache and an MDX fuselage 

were computed. The accompanying figure shows the pressure 

distribution on the MDX fuselage. A typical calculation on a 

112 x 20 x 20 grid required 6 megawords (64 bits each) of 

Cray-2 memory and approximately 2.5 hours of CPU time. For 

rotor flow-field calculations, the Eulerlthin-layer rotor code 

MDROTH was used. Calculations were performed for the flow 

field about the Gazelle rotor and about a rotor with a British 

Experimental Rotor Program (BERP) -like tip in forward flight 

(Publications 1 and 2). A typical calculation on a 97 x 33 x 21 

grid required 8 megawords (64 bits each) of Cray-2 memory, 

and approximately 40 minutes of CPU time for hover and 

8 hours of CPU time for forward flight. 

Significance 

The development of MDNS3D and MDROTH codes would be 

of great value in the design and development of rotorcraft. A 

computational data base consisting of a number of blade 

shapes at various flight conditions could significantly reduce - the time and cost for configuration selection. 

Future Plans 

The main focus will be on the calculation of rotorlbody interaction flow fields. MDNS3D and MDROTH will be combined for 

this purpose. Fine-grid calculations will be performed on multibladed helicopter rotor configurations with unconventional 

blade tips, including the BERP and Puma tips, and the results 

will be compared with the experimental data whenever possible. Calculations will also be performed for a no-tail-rotor 

(NOTAR) configuration and a trail-rotorconvertible (TRC) 

configuration. 

Publications 

1. Agarwal, R. K., and Deese, J. E. "EulerlNavier-Stokes 

Calculations of the Flowfield of a Helicopter Rotor in Hover and 

Forward Flight." Proceedings of the Second International 

Conference on Rotor Craft Basic Research. Univ. of Maryland, 

Feb. 1988. 

2. Agarwal, R. K., and Deese, J. E. "Navier-Stokes Calculations of the Flowfield of a Helicopter Rotor in Hover." AlAA 

Paper 88-0106, Jan. 1988. 

HELICOPTER FUSELAGE PREDICTIONS 

MinP = 0.4 AOA = -5.0 RE = 60 MILLION 

Pressure distribution on the MDX fuselage; Minf = 0.4, a = -5.0°, Re = 60 x lo6. 
Numerical Solution of the Reynolds-Averaged Navier-Stokes Equations for Flow 

About an Almost Compete Aircraft 

Ramesh K. Agarwal, Principal Investigator 

Co-investigator: Jerry E. Deese 

McDonnell Douglas Research LaboratoriesINASA Ames Research Center 

Research Objective 

To develop a computational code capable of predicting the 

viscous flow field over a complete aircraft. 

Approach 

Reynolds-averaged Navier-Stokes equations are solved on a 

global body-conforming curvilinear grid by using a finitevolume Runge-Kutta time-stepping scheme. The global grid 

about the aircraft is generated by using a three-dimensional 

grid-generation code based on the blended grid-generation 

technique. Turbulence effects are modeled using a simple 

algebraic eddy-viscosity model. Variable time steps and 

implicit smoothing of the residuals are used to enhance 

convergence to steady state. 

Accomplishment Description 

The EulerIReynolds-averaged Navier-Stokes code 

MDAIRPLANE was installed on a Cray-2. Of a number of 

significant accomplishments, especially noteworthy are transonic flow-field calculations about complete F-15 and MD-80 

configurations and T-45. MD-11, and MD-91 winglbody configurations (Publications 1 and 2). Computations compared 

well with experimental data. The accompanying figure shows 

the pressure distribution on an MD-80 aircraft. A typical calculation was performed on a 160 x 34 x 42 mesh and required 

26 megawords (64 bits each) of Cray-2 memory and approximately 10 hours of CPU time. 

Significance 

The development of the MDAIRPLANE code would be of great 

value in the design and development of transport and fighter 

aircraft, because a greater number of candidate vehicle configurations could be considered and their performance over a 

wide range of flight conditions could be evaluated, thereby 

reducing the cost and time required in the design cycle. 

Future Plans 

Three-dimensional grids will be generated for a complete 

MD-11 transport, a C-17 transport, and an F-18 fighter aircraft. 

Calculations will be performed using fine grids and requiring 

approximately 32 megawords (64 bits each) of Cray-2 memory. The results will be compared with experimental data for 

transonic Mach numbers. 

Publications 

1. Agarwal, R. K.; Deese, J. E.; Johnson, J. G.; and 

Steinhoff, J. S. "Euler Calculations for Flow Over a Complete 

Aircraft." AlAA Paper 89-2221, 1989. 

2. Deese, J. E., and Agarwal, R. K. "Turbulent Flow Calculations for Flow Over Wings Near Maximum Lift." AlAA Paper 89- 

2239, 1989. 

TRANSPORT AIRCRAFT PREDICTIONS 

Minf = 0.76 AOA = 2.0 

Pressure distribution on an MD-80 aircraft; Minf = 0.76, a = 2.0". 
Separated and Vortical Flow-Field Analysis on Fighter Wing Configurations 

Shreekant Agrawal, Principal Investigator 

Co-investigators: Tom A. Kinard and Brian A. Robinson 

McDonnell Aircraft Company 

Research Objective 

One objective of this study is to perform an evaluation of 

various Navier-Stokes solvers using different solution algorithms for transonic wing flow-field calculations. The evaluation 

focuses on accuracy, efficiency, speed, and convergence, 

and seeks areas for future research. A second objective (not 

described here) is to analyze differences between Euler and 

Navier-Stokes solutions on a flat-plate delta wing at high 

angles of attack. 

Approach 

Three different Navier-Stokes solvers are used to predict transonic flow fields on the ONERA M6 wing for two flow conditions, attached flow (M = 0.84, angle of attack = 3.06') and 

separated flow (M = 0.837, angle of attack = 6.06'). The three 

flow solvers are CFL3D, TLNS3D, and TNS. 

Accomplishment Description 

A C-0-type grid of dimensions 193 (streamwise), 49 (normal), 

and 33 (spanwise) was used for the CFL3D and TLNS3D 

codes. Because of the four-zone structure of the TNS code, 

the dimensions and viscous stretching parameters had to be 

adjusted to yield a similar number of surface grid points and 

points in the boundary layer as the C-0 grid. The turbulent 

eddy viscosity for all solutions was computed using the 

Baldwin-Lomax model. The TLNS3D solutions were also 

obtained with a Johnson-King turbulence model. Computed 

surface pressure coefficients are compared with experimental 

data in the accompanying figure. For attached flow, similar 

solutions are found with the different codes, except for some 

differences near shock waves and leading-edge regions; the 

scatter in the shock wave locations is approximately 6%. For 

separated flow, however, the scatter band of the solutions 

from the different codes is considerably larger; shock 

strengths and locations are predicted very differently. With 

the Johnson-King turbulence model, a remarkable improvement in the TLNS3D solution is noticeable. The upper-surface 

particle traces due to the three codes are also shown. The 

CPU time for TLNS3D was 1.5 Cray-2 hours for the attachedflow case and 2.0 hours for the separated-flow case. The CPU 

times for TNS and CFL3D were about two times longer than for 

TLNS3D. The amount of central memory used for an average ' 

job run was 20 megawords. 

Significance 

Various three-dimensional Navier-Stokes codes differ from 

each other in several respects, such as numerical algorithms, 

boundary condition treatment, dissipation models, convergence acceleration techniques, and turbulence models. 

Because of these differences, the results obtained from various codes differ from each other, even though they solve the 

same equations of fluid mechanics. Therefore, in order to 

select the most accurate and efficient flow solver for a particular application, an evaluation of the codes is important. 

Future Plans 

The performance of the codes will be further evaluated on 

more complete (e.g., wing-fuselage) aircraft geometries. 

Publications 

Agrawal, Shreekant; Barnett, Matt; and Robinson, Brian A. 

"Investigation of Vortex Breakdown on a Delta Wing Using 

Euler and Navier-Stokes Equations." Presented at the AGARD 

Symposium on Vortex Flow Aerodynamics, Scheveningen, 

Netherlands, Oct. 1990. 

(Top) Particle traces on upper surface of the ONERA M6 wing; M, = 0.8337, a = 6.06', Re = 11.7 x lo6 based on MAC, BaldwinLomax turbulence model. The CFL3D and TLNS3D grids are 193 x 49 x 33. The TNS four-zone grid is Zone 1,101 x 33 x 25; 

Zone 2,101 x 37 x 21; Zone 4,93 x 35 x 25. (Bottom) Surface pressure coefficients. 
Discrete Particle Simulation of Compressible Flow 

Donald Baganoff, Principal Investigator 

Co-investigators: William J. Feiereisen, Jeffrey McDonald, Brian Haas, Michael Woronowicz, Michael Fallavollita, and Leo Dagum 

Stanford UniversityINASA Ames Research Center 

Research Objective 

To develop, test, and extend a new particle simulation method 

for rarefied hypersonic flow, and to assess its ability to treat 

realistic three-dimensional geometries. 

Approach 

Oirect particle simulation methods model a rarefied flow as a 

large collection of discrete particles that interact with each 

other through collisions. The well-known collision-selection 

rule used in the direct simulation Monte Carlo (DSMC) method 

is replaced by a new statistical rule that is highly compatible 

with the requirements for vectorization. Many algorithmic 

improvements that go beyond those that are related only to 

vectorization issues are also used. 

AccomplOshment Description 

The collision-selection rule was shown to give results that were 

identical to those of the DSMC method in predicting shockwave structure and in predicting the correct mean-free-path 

variation with density and temperature, for power-law interactions ranging from hard sphere to Maxwell molecule. A singlespecies version of the vectorized code, which assumes an 

ideal diatomic gas, was used to study flow in a flat-plate 

boundary layer, flow past a wedge, and full three-dimensional 

flow past the Aeroassist Flight Experiment (AFE) aircraft body. 

The accompanying figure depicts the pressure distribution in 

the central plane of the body and in a downstream crosssection of the wake, giving an approximate image of the threedimensional structure of the flow. The simulated conditions 

correspond to a Mach number of 35 at an altitude of 100 km, 

assuming a 4.25-m-diameter body. The simulation used 

9.5 million particles and 0.43 million cells. The run required 

4.5 hours of Cray-2 CPU time and 125 megawords of central 

memory. The performance of the code is presently 1 to 

2 microseconds per particle per time step. 

Significance 

With the increasing interest in hypersonic flight, a need arises 

to develop a computational predictive capability for the aerodynamic and thermal environment found around vehicles such 

as the National Aero-Space Plane or the AFE. Because of the 

difficulties in applying the continuum equations to the very low 

density hypersonic regimes these vehicles will encounter, it 

is appropriate to consider the application of direct particle 

simulation methods. The numerical efficiency of the current 

approach enables direct particle simulations to be carried out 

on a much larger scale than previously possible. 

Future Plans 

A new version of the vectorized code, which includes provisions for multiple species and rotational and vibrational 

nonequilibrium, as well as chemical reactions, is being prepared, and early indications are that its performance will be 

comparable with the present single-species code. 

Publications 

1. Feiereisen, W. J., and McDonald, J. D. "ThreeDimensional Discrete Particle Simulation of an AOTV." AlAA 

Paper 89-1 71 1, 1989. 

2. Woronowicz, M. S., and McDonald, J. D. 'Application of a 

Vectorized Particle Simulation in High-Speed Near-Continuum 

Flow." AlAA Paper 89-1665, 1989. 

3. McDonald, J. D. "A Computationally Efficient Particle 

Simulation Method Suited to Vector Computer Architectures." 

SUDAAR No. 589, Stanford Univ., 1989. 

Normalized 

Pressure I 

Pressure distribution in the central plane of the body, and downstream. 
Direct Simulation of Large-Eddy Breakup Devices 

R. Balasubramanian, Principal Investigator 

Spectrex lnc. 

Research Objective 

The ultimate objective of this work is to obtain a data base of 

numerically generated turbulence data for complex geometries such as large-eddy breakup (LEBU) devices, using a 

nonperiodic, fully spectral, Navier-Stokes complex-geometry 

multidomain algorithm. 

Approach 

A patched spectral element technique forms the basis for 

the direct-simulation solver; it uses spectral algorithms 

(Chebyshev polynomials in two directions and Fourier spectral 

representations in the third direction) with direct enforcement 

(Green's function method) of inter-element continuities at 

patch boundaries. The patched-element approach makes 

possible the application of a flow code to the flow over 

complex geometries, such as LEBU geometries, by proper 

decomposition of the computational domain to appropriate 

spectral patches. 

Future Plans 

The patched-spectral-element code will be further used to 

extend Spalart's turbulence data from Re = 1300 to higher 

Reynolds numbers, using patches in the downstream direction. Complex-flow turbulence data for LEBU devices at intermediate Reynolds numbers will also be developed. Plans are 

also under way to incorporate compressibility effects, so that . studies can be made of the suppression of turbulent noise by 

LEBU devices with their attendant ASW implications. 

~ccomplishment Description 

During this phase of the work, the patched-spectral-element 

algorithm was used to gain understanding of the flow physics 

of vortex interactions in shear flows. This engendered a clearer 

understanding of how the large-scale structures that populate 

turbulent outer layers sustain themselves by interaction with 

the wall-layer structures. The role of a predominantly longitudinal, transverse, or normal vortical structure interacting with 

shear flow was carefully documented by numerical flow visualization. Also, appropriate initial data bases, originating from 

Spalart's direct-simulation data base, have been developed 

and used for direct simulation of turbulence in the complex 

geometry case. These studies are still in their infancy. 

Significance 

Direct simulation of turbulence using nonperiodic boundary 

conditions is a relative newcomer to the field of computational 

fluid mechanics; patching techniques that we have developed 

allow the examination of distances further downstream than 

previously thought possible. Patching also makes possible the 

study of highly complex flow fields bydirect simulation through 

appropriate geometric discretizations of the flow modules. 

Thus, direct comparisons of laboratory flows with computergenerated turbulence data may one day be possible using 

these high-order flow modules. 

Interaction of an elliptical ring vortex in shear flow at various 

times of evolution. Contours of total vorticity are color coded. 

The wall, the H = 6 planes, and the inflow plane are shaded. 
Validation of a Three-Dimensional Flux-Split Euler Algorithm for 

Unstructured Grids 

John T. Batina, Principal Investigator 

Co-investigators: Elizabeth M. Lee, Russ D. Rausch, and William L. Kleb 

NASA Langley Research Center 

Research Objective 

New algorithms are being developed for the solution of the 

three-dimensional unsteady Euler equations, based on the use 

of unstructured grids. These algorithms require validation 

before they can be used with confidence for general applications, so the objective of this research was to determine the 

accuracy of a new flux-split method of solving the Euler equations on an unstructured grid of tetrahedra. 

Approach 

The new algorithm contains recently developed improvements to the spatial and temporal discretizations used by 

unstructured-grid flow solvers. The spatial discretization now 

involves a flux-split approach, which is naturally dissipative 

and captures shock waves sharply with only one grid point 

within the shock structure. The temporal discretization uses 

either explicit or implicit time marching. The explicit time 

marching is a four-stage Runge-Kutta integration and the 

implicit time marching is a two-sweep Gauss-Seidel relaxation 

procedure. The algorithm is validated by performing calculations using the explicit integration for a well-defined wing (an 

AGARD standard configuration) and making comparisons with 

experimental steady-pressure data. 

Accomplishment Description 

To assess the accuracy of the new three-dimensional flux-split 

Euler solver, calculations were performed for the ONERA M6 

wing. The M6 wing has a leading-edge sweep angle of 30°, an 

aspect ratio of 3.8, and a taper ratio of 0.562. The airfoil section of the wing is the ONERA "D" airfoil, which is a convenONERA M6 Wing 

A 30" A 

tional section with a 10% maximum thickness-to-chord ratio. 

The results were obtained using a grid that has 154,134 nodes 

and 869,056 tetrahedra. The surface triangulation for the 

upper surface of the wing is shown in the left half of the 

accompanying figure. Results were obtained for the M6 wing 

at a free-stream Mach number of 0.84 and an angle of attack 

of 3.06". These conditions were chosen for comparison with 

experimental pressure data, as shown in the right half of the 

figure. Because of the large number of tetrahedra used in this 

case, the solution required approximately 150 Cray-2 CPU 

hours and 125 megawords of memory. 

Significance 

The Euler results are in good agreement with the experimental 

pressure data, especially in predicting the strength and location of the shock waves; this tends to verify the new Euler 

algorithm. The shocks are sharply captured with only one grid 

point within the shock structure, and there are no overshoots 

or undershoots. 

Future Plans 

Unsteady applications will be performed to determine the 

accuracy as well as the efficiency of the new flux-split algorithm for such cases. 

Publications 

Batina, John T. "Accuracy of an Unstructured-Grid UpwindEuler Algorithm for the ONERA M6 Wing." Presented at the 

Accuracy of Unstructured Grid Techniques Workshop, NASA 

Langley Research Center, Jan. 1990. 

(Left) Surface triangulation for the upper surface of the ONERA M6 wing. (Right) Comparison of computed pressures with 

experimental pressures; M = 0.84, a = 3.06". 
Calculations of Unsteady, Supersonic-Jet Flow Fields and Acoustics 

William W. Bower, Principal Investigator 

Co-investigators: Robert E. Childs and Gerald E. Chmielewski 

McDonnell Douglas Research Laboratories/Nielsen Engineering & Research, Inc. 

Research Objective 

To predict the dynamic behavior and acoustic fields 

associated with supersonic free and impinging jets. 

Approach 

The generation and radiation of aerodynamic noise is 

governed by the unsteady, compressible Navier-Stokes 

equations. Therefore, numerical solutions of the Navier-Stokes 

equations should yield predictions of the acoustic field in 

addition to the flow field, provided that the dominant physical 

phenomena of the flow that affect noise are resolved in the 

simulation. The present work is an effort to predict the flow 

field and noise generation for supersonic jets by means of 

numerical simulations based on the Navier-Stokes equations. 

Accomplishment Description 

Numerical simulations were performed for two flows: a free jet 

with a nozzle pressure ratio (NPR) of unity and a jet Mach 

number (M) of 1.19; and an impinging jet with NPR = 1.0, 

M = 1.46, and a height above ground of four nozzle diameters. 

The Reynolds number based on nozzle diameter for both 

cases was 70,000, and the jets were cold, having approximately the same stagnation temperature as the ambient fluid. 

The accompanying figure illustrates the pressure and vorticity 

in the free jet at a given time in the simulation. Small, randomly 

spaced vortices form not far downstream of the nozzle exit 

and merge, commonly in pairs, until the vortices are comparable in size to the jet radius. At this stage the axisymmetric 

structure is saturated and can grow no further. In the impinging jet case, the higher Mach number reduces the growth rate 

of the axisymmetric mode. However, the impingement process 

produces a strong acoustic signal that forces the initial shear 

layer at frequencies below its natural instability frequency. The 

simulation shows that a large vortex is formed about one - 

nozzle diameter downstream of the nozzle exit, and there is 

no vortex pairing before the structure encounters the impingement plane. Two noise-generation mechanisms associated 

with the impingement process are observed. When a vortex - 

strikes the surface, its major axis expands; this stretches the 

ring vortices, intensifying the vorticity and significantly reducing the pressure at the vortex core. Also, the impingement 

shock is unsteady. Each simulation required approximately 

1 Cray Y-MP hour and 1 megaword of central memory. 

Significance 

The present simulation provides insight into the sources of 

noise for supersonic jets and therefore can provide guidance 

for the development of techniques to reduce the jet acoustic 

signatures. 

Future Plans 

Continuation of this work will include comparisons of predicted 

overall sound-pressure levels with experimental data for 

supersonic jets, and an extension of the simulations to three 

dimensions. 

Color contours of instantaneous pressure (top) and vorticity (bottom) for the unsteady, axisymmetric free jet in quiescent air; 

M = 1.19, Re = 70,000, NPR = 1.0, time = 140.5910. 

arj~sji~; -.:- 7Af;Z 

COLOR PHOTOGRAPH 
Hybrid Simulations of the Global VenusISolar Wind Interaction 

Stephen H. Brecht, Principal Investigator 

Berkeley Research Associates 

Research Objective 

The objective of this research is to obtain a better understanding of how the solar wind interacts with an unmagnetized 

planet such as Venus. Specifically we want to understand the 

dynamics of the shock and magnetic-barrier location as a 

function of solar wind parameters and ionospheric masskading rate. 

Approach 

We have developed a three-dimensional hybrid-particle code 

\hat simulates the electrons as a fluid and the ions as individual particles. Multiple species of ions are included, as is their 

complete kinetic behavior. 

Accomplishment Description 

The three-dimensional hybrid code called HALFSHEL was 

developed and is running on both Navier and Reynolds. We 

completed a study of the interaction of the solar wind with 

planets of various sizes. The sizes range from 1000 km to 

6000 km in radius. These studies were performed with no 

ionosphere in the simulation. It was found, contrary to current 

thinking, that the shock and the magnetic barrier that forms to 

shield the planet surface are both asymmetric, without the 

presence of heavy ionospheric ions. It was found that the 

asymmetry is a function of the ratio of the planetary radius to 

the solar wind ion gyro-radius. In addition, it was seen that the 

plasma does not remain frozen to the magnetic field. A typical 

simulation of a 6000-km-radius planet required 40 megawords 

of memory and about 16 hours of Cray Y-MP time. 

Significance 

The results of these simulations and the visualization of these 

results are changing the way scientists view the interaction of 

the solar wind with planets such as Venus and Mars. These 

results are beginning to have an impact on how the data 

received from the Pioneer Venus Orbiter are interpreted. 

Specifically, the role of the ionospheric oxygen that is picked 

up during the interaction is being questioned. 

Future Plans 

The code is now being modified to include the ion mass loading produced by the charge exchange, ultraviolet ionization, 

and impact ionization of the oxygen in the Venusian 

atmosphere. 

Publications 

1. "Computer Simulation of the Solar Wind Interaction with 

Planetary Ionospheres." Invited paper, presented at the 6th 

International Association of Geomagnetism and Aeronomy, 

Exeter, England, July 1989. 

2. "Magnetic Asymmetry of Unmagnetized Planets, EOS 

Transactions." Amer. Geophys. Union 70 (1989): 1176. 

3. "Magnetic Asymmetries of Unmagnetized Planets." 

Submitted to Geophys. Res. Lett., Feb. 1990. 

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Hybrid simulations of the global Venuslsolar wind interaction. 

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Direct Simulation of Aerothermal Loads for the Aeroassist Flight Experiment 

Edwin B. Brewer, Principal Investigator 

NASA Marshall Space Flight Center 

Research Objective 

It is NASA's goal to develop computational codes to design 

the Aeroassisted Space Transfer Vehicle (ASTV). The Aeroassist Flight Experiment (AFE) will obtain the experimental 

data required to benchmark these codes for rarefied 

hypersonic flight with nonequilibrium reacting chemistry. The 

objective of the investigation described here is to develop a 

three-dimensional code applicable to the complex geometry of 

the AFE that can numerically determine the vehicle aerodynamics and aerothermodynamics in the transitional flow 

regime. 

Approach 

The computational approach used is the variable hard sphere 

(VHS) direct simulation Monte Carlo (DSMC) technique developed by G. A. Bird; a multispecies chemistry model is 

included. The DSMC approach is probably the only technique that can handle the complex physics involved. 

Accomplishment Description 

A three-dimensional body-fitted grid was generated for the 

AFE, including the carrier vehicle. The grid spacing, which 

varies with altitude, was adjusted to meet the size requirements relative to the local mean free path. The aerodynamics 

and aerotherrnodynamics of the AFE were obtained in the 

transitional flow regime from altitudes of 152 km down to 

100 km, the lowest altitude that seemed practical using conventional DSMC. In addition, the flow field about the AFE, 

including the wake region, was determined. The approximate 

effects of a small reaction-control thruster was determined at 

the 100-km trajectory point. The accompanying figure shows 

the variation of velocity magnitude about the AFE with and 

without the thruster plume. The ammonia almost completely = 

escapes the AFE wake, whereas a significant amount of 

hydrogen is caught up in the wake and base region. The 

100-km computation required about 182 Cray-2 hours and 

38 megawords of memory, with the simulation using about a 

million molecules and 80,000 computational cells. 

Significance 

It is expected that the ASTV will operate in the rarefied upper 

atmosphere in flight regimes that cannot be simulated in 

ground facilities. The AFE will furnish the benchmark data 

required to verify the ability of this code to predict ASTV 

design data in the transitionalflow regime. In the meantime, 

the code is being used to verify the AFE design. 

Future Plans 

The effects of the control thrusters on the vehicle aerodynamics, the flow field, and the science experiments will be 

investigated during the NAS 1990-91 operational year. 

Jet On 

Velocity magnitude about the AFE; altitude = 100 km. 

oK:~?li~: -.:. F;,"?.? 

CCLm PHOTOGRAPH 
Hypersonic Air-Breathing Missile Aero/Propulsion Integration 

Adam C. Bricker, Principal Investigator 

Co-investigators: Brad K. Bergman, Kurt Abrahamson, and Nancy Wilkins 

General Dynamics, Convair Division 

Research Objective 

The objective of this work is to develop computational fluid 

dynamics (CFD)-based analytical methods applicable to the 

design of highly integrated, hypersonic air-breathing vehicles. 

Primary interest lies in the Mach 4 to Mach 6 speed regime. 

Complete configuration calculations including mass flowing 

inlets and nozzles are required. Specific developments 

required to accomplish this task are in turbulent flow modeling, 

blocked gridding concepts, flow-field grid adaptation, and 

b'leed boundary conditions. 

Approach 

Three existing full Navier-Stokes (FNS) algorithms were investigated for accuracy and efficiency. Validations were made on 

various two- and three-dimensional hypersonic internal and 

external geometries. The three codes investigated were 

CFL3D (NASA Langley), PARC2Dl3D (NASA Ames, AEDC), 

and FLOGD (General Dynamics Convair). 

Accomplishment Description 

A CFD-based method was developed for analyzing Mach 4 to 

Mach 6 class air-breathing vehicles. Three existing FNS algorithms were evaluated for a variety of internal- and externalflow cases. The codes vary substantially in their approaches to 

the solution of the Navier-Stokes equations, as indicated 

below. 

CFL3D: upwind flux-split, finite volume, implicit time 

marching, LU-AD1 

PARC2Dl3D: central differenced, finite difference, implicit 

time marching, AD1 

FLOGD: central differenced, finite volume, explicit time 

marching, Runge-Kutta 

Conclusions drawn from this study indicate PARC and FLOGD 

solutions to be adequate for flows in this speed regime. Excellent correlation with existing test data was found for both 

codes. The shock-capturing ability of these central difference 

schemes was enhanced by an elliptic flow-field grid adaptation routine developed in-house. A sample FLOGD FNS solution for a recently tested NASA Lewis Mach 5 inlet is presented in the accompanying figure. The calculation required 

6 Cray-2 hours and 31 megawords of memory. The flux-split 

upwind scheme used in CFL3D was found to be highly 

unstable for the cases run. Extremely low time steps were 

required to attain convergence, resulting in excessive run 

times. Researchers at NASA Langley are investigating reasons 

for this behavior and are presently investigating our test cases. 

Significance 

There has been increased emphasis on Mach 4 to Mach 6 

class air-breathing vehicles. Presently there exists a void of 

aerolpropulsion test data in this speed regime. The CFD tools 

provide an alternative source of data until testing results are 

made available. As in all situations, these tools require an 

initial development and validation phase. 

Future Plans 

Additional benchmarking as well as validation of the FLOGD . 

and PARC codes is still required on more complex cases. 

Other tasks include the development of a two-equation turbulence model and investigation of multiprocessing capabilities. 

MACH NUMBER 

nncH 5 NASA ~3n INLET 

FLOGD 30 NRUIER-STOKES SOLUTION 

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3.05000 

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A FLOGD, three-dimensional, full Navier-Stokes solution for a Mach 5 NASA A3M inlet. ORiGINAL PAGE 

COLOR PIiOTOGRAPH 11 
Three-Dimensional Shear Layers and Wall-Bounded Compressible Turbulence 

Jeffrey C. Buell, Principal Investigator 

NASA Ames Research Center 

Research Objective 

To develop three-dimensional direct numerical simulation data 

bases and basic physical understanding of two flows: spatially 

developing, incompressible shear flows and turbulent wallbounded compressible flows. 

Approach 

Direct numerical simulations of the full three-dimensional 

Navier-Stokes equations are used with resolution adequate to 

resolve all length scales. A mixed Fourierlfinite-difference 

method is used in the incompressible shear flow code. Plane 

Couette flow was chosen as a special case of wall-bounded 

compressible turbulent flow and is studied using a new 

spectral code based on Fourier and Legendre polynomial 

expansions. 

Accomplishment Description 

Three-dimensional spatially developing mixing-layer calculations were carried out at a higher Reynolds number (Re = 400) 

than during the previous year (Re = 200). The new results 

show a more inviscid-like behavior during roll-up and pairing. 

The mixture fraction calculated from a "conserved" passive 

scalar and fast-chemistry assumptions is approximately 

midway between that of a temporal mixing layer (i.e., 0.5) and 

a two-dimensional spatial mixing layer. This implies that the 

longitudinal vortices tend to mix equal parts of the fast and 

slow streams and that the asymmetric entrainment of the 

spatial mixing layer is a two-dimensional effect. For the 

CplIl#R I FUFI S 45 no -0.3lUuo 

-u.wuu rl; Fii 

compressible wall-bounded turbulence project, a new spectral 

code was developed, and the first production runs were made 

by the end of the year. Fourier series are used in the horizontal 

directions and Legendre polynomials in the vertical direction. 

A partially implicit time-integration scheme is used that avoids 

time step restrictions that result from acoustic or diffusive 

effects. Shown in the figure are instantaneous strearnwise . velocity (top) and temperature (bottom) perturbations in a 

cross-stream plane at M = 1. In addition to the low- and highspeed streaks imbedded in the boundary layers, large eddies 

that scale on the channel width also form. On a typical 

256 x 144 x 36 grid, the incompressible free-shear code 

requires about 25 megawords of memory and 16 hours of 

Cray-2 CPU time per physical flow-through time. The compressible code requires about 50 hours of Cray Y-MP CPU time to 

obtain good statistics using 110 x 64 x 60 modes. 

Significance 

The prediction of threedimensional shear flows is part of many 

problems of engineering importance, especially ones related 

to combustion. Simulation data from the compressible Couette 

flow will be useful for supersonic boundary-layer turbulence 

modeling. 

Future Plans 

Different inflow boundary conditions will be studied using the 

incompressible shear flow code. Higher Mach numbers will be 

simulated with the compressible Couette code. 

Instantaneous streamwise velocity (top) and temperature (bottom) perturbations in a cross-stream plane; M = 1. cE;c ji F/j\!;E 

CCI;(+% :=HOTOGRAPH 
Space Shuttle Flow Field 

Pieter G. Buning, Principal Investigator 

Co-investigators: J. L. Steger, R. L. Meakin, F. W. Martin, I.-T. Chiu, Y. M. Rizk, M. Yarrow, and S. Obayashi 

NASA Ames Research Center 

Research Objective 

To develop the capability for accurate computational fluid 

dynamic (CFD) prediction of pressure loads on the Space 

Shuttle launch vehicle, and to explore flow-field simulation 

during such unsteady maneuvers as solid rocket booster 

(SRB) separation. 

Approach 

The three-dimensional thin-layer Navier-Stokes composite-grid 

qhimera/F3D code is used for the simulation of the flow about 

the Space Shuttle launch vehicle. For steady-state calculations, nine overlapped grids are used to represent the orbiter, 

external tank, solid rocket boosters with plume, and various 

pieces of attach hardware between the components. For 

unsteady SRB separation, three relatively coarse grids and 

350,000 grid points are used. Approximately 12 hours of 

Cray Y-MP time are required for simulation of the first 

0.68 seconds of SRB separation. 

Accomplishment Description 

During this year, wing-load increments resulting from the 

addition of SRB plumes were evaluated and shown to be 

comparable to wind tunnel-derived increments. Additional 

protuberances and pieces of attach hardware were modeled, 

also showing significant effects on orbiter loads. A pioneering 

unsteady simulation of SRB separation at Mach 4.5 was made, 

showing the effect of SRB bow-shock impingement on the 

orbiter and external-tank surface pressures. Finally, the effect 

of acceleration on shock location and on the unsteady flow 

behind the external tank was studied. 

Significance 

Continuing uncertainties in orbiter structural loads limit 

payloads and affect gust-related launch constraints. Calculations resulting from this study are being used as a "third 

opinion" to add to wind tunnel and flight measurements, in an 

effort to resolve these uncertainties. In addition, the collection 

of flow calculations from Mach 0.6 through Mach 4.5 has 

served as a flow-field data base in analyzing the origin of 

excessive debris damage on STS-27. 

Future Plans 

The addition of real-gas effects for more accurate plume 

modeling is being undertaken, as is the development of 

techniques for handling pieces of geometry that intersect. New 

demonstration calculations will include Space Shuttle main 

engine plumes, flight Reynolds number, and return-to-launchsite abort flow fields. 

CR;G!i'.j/'\L PAGE 

COLOR PIiSI3GRAPH 

Unsteady aerodynamic simulation of multiple bodies in relative motion; Space Shuttle SRB separation sequence. 
Two-Body Hypersonic Separation Analysis 

Geoffrey Butler, Principal Investigator 

Co-investigators: Brian Nguyen, Eric Sharnhorst, and David King 

General Dynamics, Convair Division 

Research Objective 

This research studies the practical problems of store separation from hypersonic vehicles. The ultimate goal is to develop 

analysis procedures for the prediction of multiple bodies separating at high speed. The intermediate steps involve the solution of hypersonic flow fields through the use of computational 

fluid dynamics (CFD) techniques. 

Approach 

An approximate method using quasi-steady assumptions, and 

a completely unsteady method, are considered. In the approximate method, a single CFD solution of the hypersonic flow 

field about a carrier vehicle is obtained (see figure), and a 

multiple-body, six-degree-of-freedom (6DOF) simulation program is used to model the trajectory of a submissile flying 

through the flow field. The unsteady simulation method solves 

the flow equations and the 6DOF rigid-body equations simultaneously. The unsteady flow equations are solved on an 

unstructured grid that evolves with the problem's changing 

geometry. 

Accomplishment Description 

The implicit finite-difference code PARC was used to generate 

axisymmetric solutions for the body and wake of a generic 

hypersonic vehicle. Since wake solutions using PARC have not 

been thoroughly validated, these solutions were converted to 

interferogram fringes and compared to laser interferograms of 

similar vehicles in free flight at the AFATUFXA Aeroballistic 

Range Facility. Good general agreement was obtained 

between the CFD solutions and the test data. The CFD solutions were then used to predict the trajectories of submissiles 

ejected into the wake of the generic carrier. Two- and threedimensional unstructured-grid generators were developed 

and used on arbitrary, multiple-body configurations. A twodimensional unstructured-grid flow solver was developed and 

run, giving preliminary results. The cases so far run needed 

about 10 minutes and less than 1 megaword on the 

Cray Y-MP. 

Significance 

Vehicle separation during high-speed flight is seen in 

weaponlexternal-tank separation systems for supersonic and . hypersonic platforms, in crew escape modules from the 

National Aero-Space Plane (NASP) or other high-speed 

vehicles, and in the stage separation of launch vehicles. Such 

separations can be extremely hazardous, but existing groundbased facilities are unable to simulate multiple bodies at 

release flight conditions. This research is dedicated to the 

development of a complete simulation for case studies of store 

separation as well as a less costly simulation that can be used 

to perform preliminary studies. 

Future Plans 

The flow solver will be expanded to three dimensions and to 

include viscous terms and real gas effects. The grid generator 

and flow solver will be combined to adapt the grid to gradients 

in the solution. Moving boundaries and moving grid points will 

be incorporated. Finally the codes will be used to give timeaccurate solutions of multiple moving bodies. 

Publications 

Butler, G.; King, D.; Nguyen, B.; and Abate, G. "Ballistic 

Range Flowfield Measurements of the Hypervelocity Near 

Wake of Generic Shapes and Correlation with CFD Simulations." AlAA Paper 90-0621, Jan. 1990. 

. The hype~sonic flow field about a carrier vehicle. ... *. ., 5 ,., I *. I 
Receptivity, Eigenfunction Modeling, and Simulation of a Wall-Bounded Flow 

Alan B. Cain, Principal Investigator 

Co-investigators: William W. Bower and Nagi N. Mansour 

McDonnell Douglas Research LaboratoriesINASA Ames Research Center 

Research Objective 

To better and more usefully characterize transition and 

turbulence. 

Approach 

Qne recent effort of this study focused on the use of a fractional step code developed by Nagi N. Mansour and Jeffery C. 

Buell of NASA Ames, to investigate the flow over a backwardfacing step. A separate effort utilized a McDonnell Douglas 

Qesearch Laboratories (MDRL) spectral code to simulate an 

excited free shear flow. 

Accomplishment Description 

The Mansour-Buell code was used to investigate the flow over 

the backward-facing step. Recent results of subharmonic and 

fundamental forcing show a close correspondence to MDRL 

experimental results and confirm some speculation on the 

nature of the unsteady reattachment process. The MDRL 

spectral code simulations have identified key mechanisms that 

also explain experimental observations for free shear flows. 

The accompanying figure illustrates the vorticity contours for 

the backward-facing step at t = 164 sec in the unsteady 

simulation for a Reynolds number of 2000, based on step 

height. A grid containing 201 points in the streamwise 

direction and 65 in the normal was used in the simulation, 

which required slightly more than an hour of CPU time. 

Significance 

The results of this basic study are important to the beneficial 

use of techniques for actively controlling shear flows. These 

results also provide the insight and motivation to try new 

approaches to the modeling of large-scale turbulence in these 

flows. 

Future Plans 

We are branching into new directions from our initial work. 

The extended effort is focusing on linear, nonlinear, incompressible, and compressible formulations to examine the 

behavior of receptivity and transition. The fully simulated 

calculations will be compared with simplified models of the 

flow fields. 

Publications 

1. Cain, A. B.; Roos, F. W.; and Kegelman, J. T. "Computational and Experimental Observations on Modal Characteristics of an Excited Free-Shear Layer." Presented at the Twelfth 

Symposium on Turbulence, Univ. of Missouri-Rolla, Oct. 1990. 

2. Cain, A. B.; Mansour, N. N.; Buell, J. C.; and Bower, W. W. 

"Simulations of Flow over a Backward-Facing Step with 

Flow over 

(Vorticity 

a Backward 

Contours) 

Forcing." 

Facing 

To be submitted. 

Step 1 

f 

Fundamental and Subharmonic Excitation of Shear Layer r 

Applied at Upper Surface of the Step Corner 

L 

Grid: 201 x 65 Re (based on step height) = 2000 

NOTE: Separation occurs on upper wall downstream 

of the shear-layer reattachment position 

Vorticity contours for a backward-facing%tep. CR;Gl?<AL PAGE 

COL=R .PliG;'DGRAPtl 
An Unstructured Triangular-Mesh/Navier-Stokes Method for Computing 

the Aerodynamics of Aircraft with Ice Accretion 

Steven C. Caruso, Principal Investigator 

Nielsen Engineering & Research, Inc. 

Research Objective 

The long-range objective of this work is to develop a flow-field 

prediction method that can be used for the analysis of 

complex, time-dependent, ice accretion shapes on threedimensional aircraft components and full configurations. 

Approach 

An unstructured, triangular-mesh/Navier-Stokes prediction 

method will be developed to compute flow fields about airfoils 

with quasi-time-dependent leading-edge ice accretions. 

Accomplishment Description 

A new method was developed to permit efficient mesh 

generation about airfoils with time-dependent leading-edge 

ice accretions. Unstructured meshes are generated about 

quasi-steady, iced airfoil surfaces using an approach in which 

only a small portion of the mesh in the vicinity of the new ice 

surface must be regenerated at each time step. Steady, 

unstructured-mesh Euler flow-field computations were made 

for clean and iced airfoils. Similar calculations were also made 

with a structured-mesh code. The results show that numerical 

accuracies are comparable; however, the unstructured-mesh 

CPU times are lower because of the efficient use of grid 

points. More importantly, the new unstructured-mesh 

approach requires significantly fewer man-hours to generate 

a mesh about a complicated leading-edge ice shape (see 

figure). A single flow-field calculation requires about 

10 minutes and 2 megawords on the Cray-2. A total of 

16 Cray-2 CPU hours were used in the course of this study. ' 

Significance 

The results of the study demonstrate that the unstructuredmesh approach is a feasible flow-field prediction method for - 

use in icing analyses. Further development is required before 

it can be used as a practical engineering tool. 

Future Plans 

The flow solver will be extended to the Navier-Stokes equations, with a suitable turbulence model. The grid generation 

method will be further automated to permit time-dependent 

icing analyses. Subsequent development will include extension of the method to three dimensions. 

Publications 

Caruso, S. "Development of an Unstructured MeshINavierStokes Method for Aerodynamics of Aircraft with Ice Accretions." AlAA Paper 90-0758, 1990. 

Flow-field computation for airfoil with simulated leading-edge ice accretion. (Left) Mesh near leading edge. (Right) Normalized 

pressures near leading edge. 
FuelIAir Turbulent Combustion in a Three-Dimensional Combustor Geometry in 

Supersonic Flow 

Sukumar R. Chakravarthy, Principal Investigator 

Co-investigators: Uriel C. Goldberg and Sampath Palaniswamy 

Rockwell International Science Center 

Research Objective 

To understand the details of supersonic mixing and its 

influence on the stability of the combustion process. 

Approach 

The unified solution algorithms (USA) series codes are highly 

suited for simulating turbulent supersonic reacting flows. They 

qse a second-order-accurate (in space) finite-volume, multizone, total-variation-diminishing upwind scheme to solve 

compressible, chemically reacting flows. This scheme avoids 

spurious numerical oscillations without adding an artificial 

dissipation term to the discretized equations. It has an 

algebraic model (a modified Baldwin-Lomax model with 

Goldberg's shear-layer treatment away from wall boundary 

layers), a one-equation model (a partial differential equation 

for the turbulent kinetic energy), and a two-equation model 

(partial differential equations for turbulent kinetic energy and 

turbulence dissipation) to solve the Reynolds-averaged 

Navier-Stokes equations. All models incorporate Goldberg's 

backflow model to treat recirculatory flow regions. 

Accomplishment Description 

Experimental work done at the University of Virginia with tangential injection of fuel in a supersonic airstream was chosen 

as one of the case studies since it was designed to enhance 

mixing using vortical main flow. Using NAS resources we have 

obtained a three-dimensional solution to the mixing problem 

(nonreacting flow). The algebraic turbulence model available 

in the USA code was used and the flow was computed using 

a four-zone grid with 67,000 grid points. Comparison with 

preliminary experimental data shows that we can predict the 

splitting of the fuel jet caused by the swirling throughflow, as 

well as the tracer concentration (see figure). Fifty Cray Y-MP 

hours and 8 megawords of CPU memory were required for this 

computation. 

Significance 

An essential part of a hypersonic flight vehicle is an engine in 

which fuel can be burned efficiently in a supersonic airstream. 

Constraints on the weight and the size of the combustion 

chamber require that the fuel-air interactions be optimized to 

enhance mixing and that the geometry be selected to stabilize 

the flame within the chamber. Since the airflow inside the 

scramjet engine is supersonic, the goal is to achieve mixing 

with minimal losses and complete combustion of the fuel. 

Mixing in the shear layer can be increased if vortical flows can 

be established in the fuel and/or airstreams. Computational 

tools that can accurately predict the mixing rate are critical to 

scramjet engine development. The numerical algorithm should 

have high-order accuracy to avoid smearing and numerical 

mixing. This requires the numerical scheme to have minimal 

dissipation even while resolving flows with strong shock waves 

and shock-wave boundary-layer interactions. The turbulence 

models used in the Reynolds-averaged Navier-Stokes equations should faithfully reproduce the effect of turbulent mass, 

momentum, and energy transport on the mean flow. 

Future Plans 

We plan to direct our efforts on two fronts. On the first front we 

plan to (a) test and validate our turbulence models for threedimensional supersonic flows with multispecies mixing and 

chemical reactions, (b) improve existing and develop new turbulence models for these flows, and (c) quantify and predict 

mixing rates. These tasks will be performed using the geometry proposed by researchers at the University of Virginia. On 

the other front, parallel with the first one, we propose to study 

various geometries and predict optimal configurations for 

secondary flow-induced mixing enhancements for scramjet 

applications. We have begun looking at swept ramps (delta 

wing forms) as one possibility. 

CFD RESULTS SHOW GOOD AGREEMENT WITH 

UNIVERSITY OF VIRGINIA TEST DATA (U) 

3-D, FNS, FC, TR CALCULATIONS - 67,045 GRID POINTS 

CFD TRACER CONCENTRATION PREDICTIONS UNIVERSITY OF VIRGINIA PLlF DATA 5C51964 

YID = 0 YID = 0 

SUBSCALE SINGLE INJECTOR (1 O0 RAMP) TESTED AT M = 2 AT 

UNIVERSITY OF VIRGINIA 

IODINE BASED PLlF MEASUREMENTS SHOW BIFURCATION OF JET 

SEEN IN COLD FLOW CFD SIMULATIONS 

RESULTS SHOW DESIRED VORTEX INDUCED MlXlNGS 

CHARACTERISTICS Cs;G!:;AL PAGE 

COLCR I'IiO T3GRAPH 

Fuellair turbulent combustion in a three-dimensional combustor geometry in supersonic flow. 
Three-Dimensional Calculations of Multiple Control-Jet Interactions for 

Defense Interceptors 

R. Rexford Chamberlain, Principal Investigator 

Lockheed Missiles and Space Company, Inc. 

Research Objective 

The present objective is to develop the ability to predict the 

influence of multiple control-jet-interaction phenomena on the 

forces and moments experienced by hypersonic defense 

interceptors. As a first step, numerical simulations of a single 

supersonic jet exhausting into hypersonic crossflow at various 

jet exit pressures, angles of attack, and Mach numbers are 

considered. 

Approach 

A three-dimensional upwind Navier-Stokes code is used to 

compute the jet interaction flow field about a generic interceptor configuration. Predicted surface pressures are compared 

with wind tunnel data, and forces and moments are 

calculated. 

Accomplishment Description 

An implicit, upwind, finite-volume Navier-Stokes code was 

developed and validated for both two- and three-dimensional 

applications. The inviscid fluxes were treated using either fluxvector (van Leer) or flux-difference-splitting (Roe) techniques 

so that the complicated shock systems that result from the jet 

interaction could be crisply resolved. The full viscous terms 

were included using central differencing throughout. Calculations at various jet exit pressures and angles of attack were 

used to examine the nature of the jet interactions over a 

generic configuration. The accompanying graphic shows the 

pressure contours over the vehicle at Mach 8 and 0" angle of 

attack. The jet plume extends beyond the body bow shock 

and leaves a trace of high pressure along the rearward portion 

of the surface (flare). The interaction accounts for about a 10% 

increase in the thrust of the jet, and the distribution of the force 

is such that the pitching moment is also amplified. This calculation required about 15 Cray-2 hours and 10 megawords of 

memory. 

Significance 

For future- and current-generation defense interceptors, 

designers are examining the head-end steering concept, in 

which a single reaction-control system located near the nose 

of the vehicle is responsible for maneuvering during the boost 

phase as well as the end game. The evaluation of this concept 

will depend on a detailed understanding of the fluid dynamics 

associated with control-jet interactions as well as on predictions of the control effectiveness. Numerical simulations will 

contribute significantly to the performance evaluation of proposed interceptor configurations under the desired operating 

conditions. In addition, the creation of a simulation data base 

will enhance the intuitive understanding that is required to 

make critical design decisions. 

Future Plans 

The existing code will be used to continue the study of the 

complex flow structures associated with the interaction of 

single and multiple control jets. A natural extension of the 

present method is to incorporate a turbulence model that is 

fully consistent with the upwind treatment of the convective 

transport terms in the finite volume setting. 

Publications 

Chamberlain. R. R. "Calculation of Three-Dimensional Jet 

Interaction Flowfields." AlAA Paper 90-2099. July 1990. 

HEST Pressan Contours 

Ran 87 

HEST pressure contours, run 87; M, = 8.01, a = O.OO, Re = 6.984 x lo6, T, = 99.7R. 
Continuum Computational Fluid Dynamics for Hypersonic High-Altitude Flight 

Dean R. Chapman, Principal Investigator 

Co-investigator: Robert W. MacCormack 

Stanford University 

Research Objective 

To develop advanced continuum equations of gas motion that 

are more physically realistic than the conventional NavierStokes equations for hypersonic flows at high altitude, and to 

develop numerical solution methods for the advanced set of 

Gquations. 

Approach 

Modifications of the Burnett equations are explored for adequately representing the strongly nonequilibrium flow conditions that exist in hypersonic shock-wave structures at high 

altitudes. Both experimental data and direct simulation Monte 

Carlo (DSMC) computations are used for test purposes. 

Accomplishment Description 

The Burnett equations were recently found to be much more 

accurate than the Navier-Stokes equations for computing onedimensional hypersonic shock structure in monatomic gases 

and nitrogen (see accompanying graph). In the latter case, a 

rotational energy relaxation model must be added to the 

Burnett equations. Solutions of the Burnett equations for planar 

two-dimensional flow fields were recently undertaken. A fundamental problem of Burnett instability in regard to flow perturbations of very small wavelengths was encountered and 

overcome in one-dimensional flow by the formulation of 

"augmented" Burnett equations. The Burnett equations for 

axially symmetric flow were derived for the first time, although 

no numerical solutions have yet been attempted. Preliminary 

coarse-mesh computations of planar two-dimensional flow 

indicates that the CPU time required for Burnett solutions is 

about 40% greater than that required for corresponding 

Navier-Stokes solutions. An average job run would need 

about 1.5 hours and 5 megawords of memory. 

Significance 

Vehicles such as the Aeroassisted Space Transfer Vehicle 

and the Aeroassist Flight Experiment, which use atmosphere 

braking for orbital changes, operate at altitudes well above the 

range where the conventional Navier-Stokes equations are 

accurate. Ground-based experimental facilities are incapable 

of reproducing the combined flow parameters necessary for 

simulating these nonequilibrium hypersonic flow conditions. 

Therefore, advanced continuum equation sets, such as the 

Burnett equations, are needed for the efficient and accurate 

design of these particular hypersonic vehicles. Other relevant 

applications involve the flow over small-radius cowl lips and 

leading edges on the National Aero-Space Plane. 

Future Plans 

Solutions will be attempted to the full Burnett equations for 

axially-symmetric flow as well as two-dimensional planar flow. 

Once successful, three-dimensional solutions will be 

attempted. 

1 .o I I I 

Navier-Stokes, eq. rot. 

Reciprocal shock-wave thickness in nitrogen. 
Hypersonic Flow Past Generic Lifting Bodies 

Denny S. Chaussee, Principal Investigator 

Co-investigators: Scott L. Lawrence, Thomas A. Edwards, and Bradford Bennett 

NASA Ames Research Center 

Research Objective 

The ultimate goal of this effort is the development of the 

capability to compute the entire aerothermal environment of a 

vehicle such as the National Aero-Space Plane (NASP) in 

hypersonic flight. The computations include the external flow 

as well as the flow into the inlet, through the combustor, and 

out the nozzle-the so-called tip-to-tail capability. 

Approach 

The CNS and UPS codes solve the Navier-Stokes and parabolized Navier-Stokes equations, respectively, using algorithms 

appropriate for high Mach number flows. Because of its speed 

and relative efficiency, the UPS code is used for streamlined 

regions of a configuration. The zonal method used by the CNS 

code makes the CNS code well suited for complex portions of 

the vehicle, such as inlets, wings, and fins. Both codes include 

turbulence, transition, and equilibrium and finite-rate air 

chemistry models. 

Accomplishment Description 

Validation has begun for the nonequilibrium air chemistry 

models implemented in the CNS and UPS codes. A version of 

CNS was created for the calculation of hypersonic internal 

flows, and this version is in the process of validation using a 

side-wall compression inlet case for which experimental pressure and pitot pressure data exist. The UPS code was used in 

the investigation of the kind of shock-shock interaction that 

might occur where a bow shock impinges on a wing or tail * 

(see accompanying figure). A highly refined grid was necessary to resolve the details of the interaction. In order to provide 

the same type of resolution with fewer grid points, a solutionadaptive gridding procedure is being implemented within the' 

UPS code. 

Significance 

Because ground-based facilities are unable to simulate the 

environment that the NASP will encounter, it has been determined that the NASP program needs the full support of cornputational fluid dynamics research to design a flight vehicle. 

The current effort has been undertaken to develop technology 

for use by the contractors in the design process as well as by 

the government in the assessment of proposed designs. 

"sfis 

RAMP SHOCK/FIN SHOCK INTERACTlON 

M., = 7.96 

Density Contours 

"71 

Turbulent ramp-shocklfin-shock interaction; M, = 7.96, ReD = 2.46 x lo5, To = 778 K. . .. 
Calculation of Transonic and Supersonic Flows Using an Interactive Scheme 

Based on Euler and Boundary-Layer Equations 

Lee T. Chen, Principal Investigator 

Co-investigators: Minh H. Bui and Hsun H. Chen 

Douglas Aircraft Company 

Research Objective 

To develop and validate an interactive scheme based on Euler 

and boundary-layer equations, and to apply the scheme to 

calculate solutions about generic National Aero-Space Plane 

(NASP) vehicles and subsoniclsupersonic transport aircraft. 

Approach 

The Euler method is based on Jameson's cell-centered and 

mll-vertex schemes, and the boundary-layer method is based 

on Cebeci's inverse-boundary-layer method. The Euler method 

was modified for various grid topologies so that it could be 

applied to vehicles with different body-nose and wing-tip 

geometries. The boundary-layer calculation was performed 

along prescribed approximate streamlines. 

Accomplishment Description 

The present scheme was applied to calculate transonic and 

supersonic flow solutions about generic NASP configurations 

and a Douglas AST wind tunnel model. A series of surface 

solutions obtained using H-0 and C-C-C grid topologies were 

compared. The comparison indicated the importance of the 

mesh size and the choice of grid topologies. Typical runs 

based on grid systems with 120,000 to 350,000 grid points 

required about 5 to 20 megawords of memory and used about 

5 minutes to 1 hour of Cray-2 CPU time. 

Significance 

The Eulerlinverse-boundary-layer method was successfully 

applied to calculate transonic solutions for various configurations including the NASP vehicle. The integrated force and 

moment components agree with test data. 

Future Plans 

The present method will be further used to validate solutions 

for generic NASP, AST, and subsonic transport configurations. 

More accurate streamlines will be prescribed for the 

boundary-layer calculation. 

Publications 

Chen, Lee T., and Bui, Minh N. "An Interactive Scheme for 

Transonic WingIBody Flows Based on Euler and Inverse 

Boundary-Layer Equations." AlAA Paper 90-1586, June 1990. 

DOUGLAS AST at M=0.9, and alpha=5. 

Flow about a Douglas AST wind tunnel model; M = 0.9, a = 5. 
Airframellnlet Aerodynamics 

W. J. Chyu, Principal Investigator 

NASA Ames Research Center 

Research Objective 

To develop efficient numerical techniques for the analysis of 

inlets on highly maneuverable aircraft. 

Approach 

A compressible Navier-Stokes solver capable of handling a 

multiblock grid system is used to compute integrated external 

and internal flow fields. 

Accomplishment Description 

Computational capabilities for handling highly threedimensional inlet geometries are being developed by using a 

multiblock, modified version of the implicit, partially flux-split, 

Navier-Stokes code F-3D. Flow fields are computed over an 

offset super-elliptic subsonic diffuser inlet (cross sections 

varying from rectangular to circular) with aspect ratio 4.0 and 

an offset of one exit diameter. The computed result compares 

well with the measured static pressures on the inlet wall and 

the total pressures on the engine face. It also reveals flow 

Mach Contours 

features of a complex inlet flow field involving separated 

boundary layers and streamwise vortices. The solution takes 

about 32 Cray-2 hours and uses less than 15 megawords of 

central memory for the flow field containing 874,000 computational grid points. 

Significance 

The increased maneuvering requirements of advanced aircraff 

dictate much more complicated inlet geometries than are currently being used. The current level of computational techniques permits analysis of these more complex inlets, making 

possible the investigation of design variables associated with ' 

integration of the forebodylinlet system. 

Future Plans 

Future efforts will focus on the code validation cases for these 

unconventional inlet geometries, including the integration of 

internal and forebody solutions. 

Airframelinlet aerodynamics; Mach contours. 
Three-Dimensional Shock/Boundary-Layer Interactions in Hypersonic Inlets 

William J. Coirier, Principal Investigator 

NASA Lewis Research Center 

Research Objective 

The goal of this research is to investigate and characterize 

three-dimensional shockiboundary-layer interaction phenomena in rectangular supersonic and hypersonic inlets. The 

glancing shockiboundary-layer interactions in these inlets can 

sause highly distorted profiles at the inlet face, which in turn 

can drastically impair the inlet performance. A detailed 

understanding of the genesis of these distortions may help in 

the elimination or reduction of their effect on the performance 

ef the entire vehicle. 

Approach 

An existing three-dimensional Reynolds-averaged NavierStokes code is modified to improve its modeling of highenthalpy, high-Mach number flows, by including a high-order 

monotone upwinding scheme and by implementing an efficient approach to account for real gas effects. The original 

implicit algorithm in the code is replaced by a more robust and 

efficient implicit scheme for solving the three-dimensional 

Navier-Stokes equations. 

Accomplishment Description 

The original second-order central-differencing scheme of the 

code was replaced by a high-order monotone upwinding 

scheme that was based on flux vector splitting. Monotonicity 

was achieved by using either a MUSCL primitives extrapolation approach or a flux extrapolation approach. Real gas 

effects were included using a generalized equation of state, 

which was shown to be very efficient by allowing complete 

vectorization without restructuring of the code, and was shown 

to be flexible by allowing different equations of state to be 

easily supplied to the code. The original diagonalized BeamWarming implicit scheme was replaced by the lower-upper 

symmetric Gauss-Seidel scheme, which was shown to be 

efficient and robust for solving the three-dimensional NavierStokes equations with real gas effects. The improved code 

was then validated against experimental data for the hypersonic flow through a corner geometry, and was used to investigate the aerodynamic and heat transfer loads on a simulated 

scramjet inlet gap-seal system. Typical calculations used 

approximately 10 Cray-2 single processor hours and approximately 8 megawords of memory. 

Significance 

Good performance of hypersonic inlets is crucial to the viability of the hypersonic air-breathing vehicles being considered 

for future deployment. The ability to understand and characterize the inlet-face distortion phenomena of these configurations 

is limited in ground-based test facilities, which cannot yield 

sufficiently high resolution of the flow field and are pressed to 

produce flows with total enthalpies that are high enough to 

simulate actual flight conditions. A numerical simulation of 

these flow fields results in a high resolution of the underlying 

fluid dynamic phenomena and can account for thermodynamic effects that more closely simulate actual flight 

conditions. 

Future Plans 

Current and future state-of-the-art schemes for simulating the 

flows of interest with high resolution and accuracy will be 

developed and investigated. 

Publications 

1. Coirier, W. J. "High Speed Corner and Gap-Seal Computations Using an LU Scheme." AlAA Paper 89-2669, July 1989. 

2. Coirier, W. J. "Efficient Real Gas Navier-Stokes Computations of High Speed Flows Using an LU Scheme." AlAA 

Paper 90-0391, Jan. 1990. 

Normalized pressure on a GASL inlet; M = 3.54, cowl mods with inj. ports. 
Transonic NaviermStokes Solutions of Three=Dimensional Afterbody Flows 

William B. Compton Ill, Principal Investigator 

Co-investigator: Khaled Sayed Abdol-Hamid 

NASA Langley Research CenterIAnalytical Services and Materials, Inc. 

Research Objective 

The goal of this project is to develop a numerical method for 

investigating the propulsion-integration effects of a fighter 

airplane at subsonic, transonic, and supersonic speeds. Intermediate steps include (1) obtaining accurate solutions for 

afterbodies with attached and massively separated flows, 

(2) including the jet exhaust in the calculations, and (3) including tails and multiple jets in the calculations. 

Approach 

The three-dimensional thin-layer Navier-Stokes codes CFL3D 

and PAB3D are used to solve for the transonic flow about a 

nonaxisymmetric afterbody typical of those advocated for 

advanced fighter airplanes. Different turbulence models are 

evaluated for predicting the flow in attached and massively 

separated regions. Comprehensive wind tunnel experiments 

are planned for validating the computations. 

Accomplishment Description 

Three algebraic turbulence models were evaluated for their 

ability to solve the thin-layer Navier-Stokes equations over the 

nonaxisymmetric nozzle at a free-stream Mach number of 1.2. 

The angle of attack was 0°, and the Reynolds number based 

on the model length was 21 x lo6. The turbulence models 

evaluated were the Baldwin-Lomax model, the Johnson-King 

model, and the Goldberg modification coupled with the 

Baldwin-Lomax model. All three models gave good agreement 

with data up to the point of shock-induced separation. The 

Johnson-King and Goldberg models gave the best predictions 

of the separation location and the best agreement in the separated region aft of the shock. The three models predicted 

considerably different flow fields. 

Significance 

Up to one-half of the drag of a modern fighter airplane is 

associated with its afterbody. In the afterbody region, flows 

over the fuselage and empennage merge and further interact 

with the propulsive exhaust to create a flow field that is 

complex, rotational, and highly interactive. A Navier-Stokes 

solution technique for this problem would be very useful to 

designers for analyzing the afterbody flow and deriving configurations with the highest possible performance. 

Future Plans 

Two main efforts are proposed for the coming year. The first is 

to include the jet exhaust in the calculations and study its 

effects on the afterbody flow field. The second is to include a 

more advanced turbulence model and study its effect. Ultimately, the procedure will be used to study design concepts. 

Publications 

1. Abdol-Hamid, Khaled S., and Compton, William B. 111. 

"Supersonic Navier-Stokes Simulations of Turbulent Afterbody 

Flows." AlAA Paper 89-2194, July 1989. 

2. Abdol-Hamid, Khaled S., and Compton, William 8. 111. 

"Comparison of Eddy-Viscosity Turbulence Models for Supersonic Afterbody Flows." Submitted to the AlAA J., Dec. 1989. 

Computed oil flows for the Goldberg turbulence model; M, = 1.2, a = 0°, Re = 21 x lo6. 

.-t-, T!r. - . I.,. .- I -AGE 

CCLd< PA0 Ti!GRAPH 
Hornet 2000 Flow-Field Analysis 

Raymond R. Cosner, Principal Investigator 

Co-investigators: Shreekant Agrawal and Patrick J. Malloy 

McDonnell Aircraft Company 

Research Objective 

To demonstrate the usefulness of computational fluid dynamics (CFD) in engineering studies of a current fighter aircraft, by 

validating computed solutions against existing wind tunnel and 

flight test data. 

Approach 

The approach is first to apply state-of-the-art CFD methods to 

a fighterlike aircraft, starting with a wing-alone geometry, and 

then to assess the impacts of grid density, interference, 

viscosity, and flexibility on such wing component loads as 

shear, bending moment, torsion, and hinge moments. Both 

Euler and Navier-Stokes solutions are obtained, using FL067 

and TLNS3D codes, respectively. These codes are based on 

explicit finite-volume central-difference formulations. The 

flexible-wing solutions are obtained by coupling the flow 

solvers with a simple NASTRAN model. Results are compared 

with flight data. 

Accomplishment Description 

All computations are performed at a free-stream Mach number 

of 0.90 and an angle of attack of lo0, which corresponds to a 

flight condition with a very high wing loading. Solutions using 

TLNS3D codes are obtained with a nonequilibrium halfequation Johnson-King turbulence model. Navier-Stokes 

results improve the predictions considerably over the inviscid 

results. For example, the inboard bending moment is within 

8.7% of the flight data, and the torque is within 3.3%. Predicted values for shear, bending moment, and torque at the 

outboard station are within 1.6%, 5.2%, and 7.6%, respectively, of the flight data. The control-surface hinge moments 

also show dramatic improvement over all of the inviscid 

results. We also find that viscosity is more important than 

elasticity or complete geometry in this application. Upper surface pressure contours from FL067 and TLNS3D are shown in 

the accompanying figure, for both rigid and flexible wings. The 

CPU time for TLNS3D was 2.0 Cray-2 hours. The amount of 

central memory for an average job run was 

20 megawords. 

Significance 

Computational fluid dynamics analysis methods of impressive 

power have shown high accuracy and dependability for 

selected classes of problems. However, the method has not 

been well developed for effective application of CFD to practical problems in flight-vehicle design-particularly the analysis 

of modern fighter-aircraft component loads at transonic and 

low supersonic maneuvering conditions. 

Future Plans 

The codes will be used to compute flow fields on more 

complete vehicle geometries. 

Publications 

Agrawal, Shreekant; Malloy, Patrick J.; and Fuglsang, 

Dennis F. "Design Predictions on a Fighter-Like Aircraft Wing 

Using Euler and Navier-Stokes Equations." Presented at the 

Winter Meetino of ASME. Dallas. Nov. 1990. 

Pressure contours on a fighter wing; M,= 0.90, a = lo0, Re = 68 x lo6, load factor = 7.3 g. 

OE~GI?:I'I. ?AGE , COLOR f HO'TOGRAPM 
Dynamical Modeling of the Solar Atmosphere 

Russell B. Dahlburg, Principal Investigator 

Co-investigators: Jill P. Dahlburg, John T. Mariska, and J. M. Picone 

Naval Research Laboratory 

Research Objective 

To investigate turbulent magnetohydrodynamic (MHD) 

processes in the solar atmosphere. 

Approach 

Our approach was the direct numerical simulation, using 

spectral methods, of the dissipative compressible and incompressible MHD equations in two- and three-dimensional 

geometries. 

Accomplishment Description 

We have used our spectral method codes to investigate 

(1) supersonic two-dimensional MHD turbulence (typical run 

required 10 megawords of memory and 10 CPU hours), 

(2) subsonic three-dimensional compressible MHD turbulence 

(typical run required 23 megawords of memory and 30 CPU 

hours), (3) driven two-dimensional compressible turbulence 

(typical run required 3 megawords of memory and 20 CPU 

hours), and (4) three-dimensional magnetic reconnection via 

twisting of magnetic field lines in the solar corona (typical run 

required 8 megawords of memory and 20 CPU hours). The b) 

accompanying figure shows the magnetic field (a) before and 

(b) after twisting. 

Significance 

These kinds of MHD activity are thought to occur in the solar 

corona and the solar wind, where observations are incomplete. The numerical simulation of magnetofluids increases our 

understanding, especially for systems like these for which 

analytic work is difficult. 

Future Plans 

We plan to extend previous incompressible-coronal-heating 

calculations to the fully compressible case and to extend previous supersonic two-dimensional solar wind calculations to 

the fully three-dimensional case. 

The magnetic field lines of the solar corona (a) before and 

(b) after twisting. 
The Impact of Hot-Streak Migration on Turbine Heat Transfer 

Roger L. Davis, Principal Investigator 

Co-investigators: Daniel J. Dorney and Diane M. Rodimon 

United Technologies Research Center 

Research Objective 

The objective of this multi-year effort is to simulate the 

migration of a three-dimensional combustor hot streak in the 

flow of an axial turbine stage and to predict the effects of the 

Qot streak on turbine-blade surface heat transfer. A second 

objective is to predict blade loading distributions and the secondary flow structure in a centrifugal compressor impeller. 

Approach 

An extended version of the unsteady, three-dimensional 

Navier-Stokes code, ROTORB, developed by Rai et al. at 

NASA Ames Research Center, is used to simulate threedimensional viscous flows in axial and centrifugal turbomachinery. This approach is a third-order-accurate, upwind, 

approximately factored, implicit finite-difference procedure. 

Accomplishment Description 

A three-dimensional one-statorlone-rotorlone-hot-streak 

simulation with a hot-streak stagnation temperature 20% 

greater than the free stream was completed, and the predicted results compared with experimental data. The experimentally observed accumulation of hot fluid on the rotor pressure surface and the radial migration of the hot streak from the 

rotor hub to the tip were accurately captured by the numerical 

analysis. Two unsteady one-statorlone-rotorlone-hot-streak 

interaction calculations, one using specified heat-flux boundary conditions and one using inviscid boundary conditions. 

were initiated to help identify the roles of heat transfer and 

viscous effects in hot-streak migration. The calculation of 

three-dimensional, steady, adiabatic flow through a low-speed 

centrifugal compressor, with and without the effects of tip 

clearance, was completed and the results compared with 

experimental data. The predicted blade loadings and secondary flow structures were generally in good agreement with 

the experimental data. 

Significance 

The development of a numerical procedure that can accurately predict the migration of combustor hot streaks and their 

effects on turbine surface heat transfer will aid turbine blade 

designers in determining optimum blade internal-cooling distributions and will add to the experimental data base currently 

available. The ability to use the same numerical analysis for 

centrifugal geometries has helped support the proposition of 

"numerical wind tunnels." 

Future Plans 

Upon completion of the current heat transfer and inviscid 

one-statorlone-rotorlone-hot-streak interaction calculations 

and subsequent detailed inspection of the resulting flow field, 

further hot-streak interaction computations will be performed to 

study the effects of film cooling on the turbine-blade surface 

heat transfer. In addition, an improved turbulence model for 

centrifugal geometries will be implemented, and further centrifugal compressor simulations (both steady and unsteady) 

will be performed. Scientific visualization will be extensively 

used to improve understanding of the computed flow fields in 

axial and centrifugal turbomachinery. 

Publications 

1. Dorney, Daniel J., and Davis, Roger L. "Centrifugal Compressor Impeller Aerodynamics (A Numerical Investigation)." 

The impact of hot-streak migration on turbine heat transfer. 

OKIGIF:j'.l. ?AGE 

CCLCR PHOTCSRAPH 27 
Three-Dimensional Aeroassist Flight Experiment Flow Simulations 

Bill Davy, Principal Investigator 

Co-investigators: Grant Palmer, Dinesh Prabhu, and Ellis Whiting 

NASA Ames Research Center 

Research Objective 

To numerically compute the flow around the Aeroassist Flight 

Experiment (AFE) vehicle at one of its flight trajectory points. 

The results will be useful for designing the AFE base flow 

radiometer experiment. 

Approach 

The three-dimensional thermochemical nonequilibrium NavierStokes equations with finite-rate chemical reactions are solved 

using upwind-differencing fully-coupled flow codes around the 

AFE vehicle geometry. 

Accomplishment Description 

Two different codes are being used to compute flows over the 

AFE vehicle. The first, an explicit code, has been producing 

AFE flow-field solutions for over a year. The code uses a twotemperature physical model and includes 11 species and 

30 chemical reactions. Comparisons with experimental and 

computational data have been used to validate this code. A 

full flow-field calculation, including the most detailed computation of the base flow to date, has been completed at the 78-km 

trajectory point. The explicit code's efficiency is comparable 

with that of implicit codes being used elsewhere. A solution 

over an 85 x 23 x 85 grid consumes about 60 hours of Cray-2 

CPU time. The second code, still in development, is a timeaccurate implicit method that includes a turbulence model. 

When completed it will be used to study the unsteady aspects 

of the base region. This code also uses 11 species and uses 

the same two-temperature physical model as the explicit code. 

The accompanying figure shows vibrational temperature con-" 

tours computed with the explicit code over the AFE vehicle. 

Significance 

The AFE project will test the validity of using aerobraking as % 

fuel-saving technique for atmospheric entry and will gather 

data for real-gas code validation. The altitudes and velocities 

of the planned AFE trajectory dictate that the vehicle design 

and the designs of the experiments carried aboard will 

depend significantly on numerical simulations. 

Future Plans 

The codes will continue to be enhanced and used to study 

aspects of the AFE flow field, particularly in the base region. 

Publications 

Palmer, Grant. "The Development of an Explicit Thermochemical Nonequilibrium Algorithm and its Application to Compute 

Three-Dimensional AFE Flowfields." AlAA Paper 89-1701, June 

1 989. 

FiFE Vehicle at 78 Kn 

Uibrat ional Tenperature Contours (Keluinl 

CONTOUR LEVELS 

I .,IIUIUU & 

nn, awn 

111011 

ono. onn ~.snn. non C*OOO. 000 

6WLl.008 

Vibrational temperature contours (Kelvin) for the AFE vehicle at 78 km. 

28 

ORfGIN '.!. PAGE 

COLOR pH9 TOGRAPH 
lntegrated Fluid-Thermal-Structural Analyzer Demonstrates 

Heat-TransferIDeformation Coupling 

Pramote Dechaumphai, Principal Investigator 

NASA Langley Research Center 

Research Objective 

The design of leading edges for hypersonic vehicles that 

experience intense stagnation-point pressures and heating 

rates depends on accurate prediction of the aerodynamic 

flc~w, the structural temperature response, and the structural 

deformations and stresses. Significant coupling occurs 

between the aerodynamic flow field, structural heat transfer, 

and structural response, creating an interdisciplinary interactbn. Understanding the fluid-thermal-structural interaction is 

important for designing leading edges to survive such severe 

aerothermal environment. 

Approach 

An integrated fluid-thermal-structural analyzer has been 

developed and used to investigate the interdisciplinary interaction of an aerodynamically heated leading edge in a simulated test environment. The analyzer uses a finite-element 

method to solve (1) the Navier-Stokes equations for the flow 

solution, (2) the energy equation of the structure for the temperature response, and (3) the equilibrium equations of 

the structure for the structural deformation and stresses. A 

schematic of a proposed experimental setup of a 0.25-in.- 

diameter, 3-in.-long, 0.1-in.-thick leading edge is shown in the 

upper left figure. The leading edge is initially exposed to the 

undisturbed Mach 5.25 flow (position A) behind the oblique 

shock generated by the free-stream Mach 8 flow. After one 

minute, the leading edge is raised instantaneously to the 

predetermined position B to produce the type IV shock-shock 

interference pattern that results in a supersonic jet impingement normal to the leading-edge surface, causing intense 

stagnation-point pressure and heating rate. The fluid analysis 

is first performed to predict the flow behavior and aerothermal 

loads on the leading edge when it is at position A. An adaptive 

mesh-refinement technique is used in the fluid analysis to 

minimize the number of unknowns. The finite-element flow 

model and flow Mach numbers are shown in the lower left 

figure. The predicted aerodynamic heating rate is in excellent 

agreement with the Fay and Riddell solution, as shown in the 

upper right figure. This heating rate causes the.leading-edge 

temperature to increase nonuniformly, resulting in the leading 

edge bending upward, as shown in the centered right figure. 

As mentioned, the deformed leading edge is raised to the 

predetermined position B at one minute to produce the type IV 

shock-shock interference pattern. Because of the leadingedge deformation, the type IV interference pattern does not 

occur. The deformed shape results in the type Ill interference 

pattern, as shown in the figure. The heating-rate distribution 

shown in the lower right figure reflects this type Ill interference 

pattern and the high leading-edge surface temperature. The 

peak heating rate is caused by the shear-layerlboundary-layer 

interaction, and the minimum heating rate is at the nose of the 

leading edge, where the temperature is maximum. 

Accomplishment Description 

The demonstration has shown the ability of the integrated fluidthermal-structural analysis approach to provide solutions to 

complex aerothermostructural behavior and the interdisciplinary interaction. The analysis computation needed about 

10 Cray-2 hours and 15 megawords of memory. 

Significance 

The integrated fluid-thermal-structural result underlines the 

importance of the interdisciplinary interaction that must be 

considered in the design and testing of the aerodynamically 

heated leading edges subjected to shock-shock interference 

loading. 

Future Plans 

The integrated code will be modified to improve the structural 

analysis module, which includes the adaptive mesh refinement 

capability and implementation of unified viscoplastic theory. 

Also, the current computational fluid dynamics module will be 

applied to other structural configurations, such as sharp leading edges and compression corners. 

Exmrirnental mnfimration Surface heatina tatq (Position A) 

Flow f) 

M = 8 Oblique shock 

Ada~tive flow mesh and 

wch number contou[ 

"1 0 Fay & Rlddell i - F.. 

- 

40 0.4 

01234567 S, in. 

Tanaential stress on deformed leadina edae 

gt wsition B with tvDe Ill interference Dattem 

formed 5 ka 

SurfaceQ (Position 8) 

2r 

,,,. I 

0 12 3.4 5 6 7 

s, in. 

Integrated fluid-thermal-structural analyzer demonstrates heat-transferldeformation coupling. 

1 :. 29 
Finite-Element Computation of Three-Dimensional Magnetic Fields for Design 

Optimization of Generators for Space Station Solar Dynamic Power 

Nabeel A. 0. Demerdash, Principal Investigator 

Co-investigator: R. Wang 

Clarkson University 

Research Objective 

The ultimate objective of this work is the development of a 

three-dimensional finite-element magnetic-field-computation 

code for the parameter identification and design optimization 

of extra high speed modified Lundell alternators (MLA). These 

alternators are intended for use as electric energy generators 

in the solar dynamic power system of NASA's Space Station 

Freedom. 

Approach 

A three-dimensional finite-element (3D-FE) computer code is 

being developed for the computation of the magnetic fields 

throughout the magnetic circuit and windings of extra high 

speed MIAs. This 3D-FE code is based on a novel approach 

that mixes magnetic vector potential and magnetic scalar 

potential formulations. This is in addition to the development 

of post processors for MLA performance computations. 

Accomplishment Description 

The modeling effort required the development of very complex 

3D-FE grids, which discretize the entire solution region of the 

MLA. (See samples of armature-core, armature-winding, and 

rotor 3D-FE grids in the accompanying figures.) A 14.3-kVA 

MLA is presently being analyzed using the computer code 

being developed in this project. Winding inductances, 

induced EMF waveforms, flux distributions, and open-circuit, 

short-circuit, and load characteristics of this machine are - 

being obtained and analyzed using this computer code, with 

successful agreement between computer simulation and 

experimental results. The Cray-2 and Cray Y-MP were used, 

with 30 to 40 megawords of memory and approximately - 

2 hours of CPU time for a case of alternator analysis. 

Significance 

This computer code will be extremely useful for the design 

optimization and parameter identification of MIAs for space 

station solar dynamic power generation. This will lead to optimum generator performance and characteristics, including the 

volume and weight reductions that are always important in 

hardware that is intended for deployment in outer space. 

Future Plans 

Continued development and verification of this computer code 

is planned. This is in addition to anticipated use in actual 

design optimization demonstrations for space station solar 

dynamic MLA-type extra high speed electric generators. 

L.. I... _ 1, 

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Three-dimensional finite-element grids for an armature core, 

an armature winding, and a rotor. 
High-Angle-of-Attack lnlet Analysis and Design Using Computational Fluid 

Dynamics Methods 

Robert DeParvine, Principal Investigator 

Co-investigator: Ben Smith 

General Dynamics, Fort Worth Division 

Research Objective 

To develop the capability to apply computational fluid 

dynamics (CFD) to the analysis of inlet flow fields at a highangle-of-attack flight condition. 

hpproach 

A Navier-Stokes code is applied to a complex threedimensional geometry at a flight condition that represents a 

severe condition for inlet performance. The codes are validated with detailed experimental data. 

Accomplishment Description 

A CFD solution of the F-16 inlet was obtained for a Mach 0.3, 

40" angle-of-attack flight condition. Solutions were obtained 

for several inlet airflows at this flight condition. This condition 

causes flow separation in the inlet duct and excessively high 

distortion at the engine face, which are of concern for 

enginelinlet compatibility. Preliminary results indicate good 

agreement with static pressure data along the duct and with 

total pressure rakes located at the geometric throat. 

Significance 

The results of this study demonstrate a capability to predict 

complex, three-dimensional flow fields that have large regions 

of separated flow. This capability can be applied early in an 

inlet development program to predict inlet performance, allowing time for design refinements. Obtaining an understanding of 

the flow field will help to minimize risk and cost. 

Publications 

Howlett, Doug; McCallum, Brent; and Smith, Brian. "A CFD 

Study of the F-16 lnlet at High Angle-of-Attack." Presented at 

the AlAA Propulsion Conference, Orlando, FL, July 1990. 

Mach 

k~srsls 

0.ODOW 

0.10000 

CFD Mach contours for the MCID-771 inlet. 

ORlGlNAL PAGE 

COLOR PHOTOGRAPH 
Validation of a Computational Fluid Dynamics Code for High-Speed-Inlet Design 

Robert DeParvine, Principal Investigator 

Co-investigator: Ben Smith 

General Dynamics, Fort Worth Division 

Research Objective 

The objective of this work is to develop the capability to apply 

computational fluid dynamics (CFD) to the analysis of highMach number inlets. The effects of an improved turbulence 

model are also researched. 

Approach 

A Navier-Stokes code is applied to inlet flows that include 

three-dimensional shocklboundary-layer interactions. The 

code is validated with detailed experimental data. 

Accomplishment Description 

A CFD solution of the glancing shock problem was obtained 

for a Mach 2.94 free-stream condition. The solution shows very 

good agreement with wall static-pressure data and yaw-angle 

data. Pitot pressure data show good agreement with the CFD 

results. The solution shows proper flow-field features throughout the glancing shock interaction region. Strong pressure 

gradients within the shocklboundary-layer interaction region 

lead to a streamwise vortex that also is evident in the experimental results. 

Significance 

The results of this study demonstrate a capability to predict 

complex, three-dimensional, turbulent flow fields. This capability will assist in understanding complex inlet flow fields so 

that analysis costs and risks can be minimized. 

Publications 

"Air Intakes for High Speed Vehicles." To be presented at the 

meeting of the AGARD - FDP Working Group 13. 

0.6 

0 1 2 3 

Y, in. 

Surface static pressure; x = 5.1 in. 
Advanced Solid Rocket Motor Study 

Dan F. Dominik, Principal Investigator 

Co-investigators: Vedat Akdag, Shmuel Ben-Shmuel, William Riba, Robert Williams, Cheng L. Chen, S. Ramakrishnan. 

K. Ragagopal, and S. Chakravathy 

Rockwell International, Space Transportation Systems Division and Science Center 

Research Objective 

The objective of this work is to predict the flow field around the 

Space Shuttle for a modified vehicle configuration-with the 

~dvanced solid rocket motor (ASRM). The vehicle aerodynamic loads will be derived from the flow-field solution 

and will be used for ASRM design evaluation. 

Approach 

A three-dimensional Navier-Stokes code is being used to 

predict the rnultizone flow field around the Space Shuttle in 

ascent configurations. Both current solid rocket motor and 

ASRM flow fields will be calculated. Plumes will be simulated. 

Accomplishment Description 

An existing three-dimensional, total-variation-diminishing, full 

Navier-Stokes code (USA 3D) was used in the flow-field 

calculations of several Space Shuttle ascent configurations. 

Medium-resolution grids were constructed for several solid 

rocket booster (SRB) designs, both with and without an aft 

attach ring. Cases were run mainly at Mach 1.25 and -2.2" 

angle of attack. The results show significant effects of the 

attach ring on the lower-wing surface pressures. Each flow 

field contained approximately 300,000 grid points, and took 

about 35 combined Cray Y-MP and Cray-2 hours and 

12 megawords of memory. 

Significance 

The proposed ASRM vehicle will significantly upgrade the 

Space Shuttle performance and increase flight safety margins. 

The numerical simulations will be used to evaluate design 

configurations and help in the final selection of design candidates for wind tunnel testing. 

Future Plans 

The Space Shuttle model is being expanded to include all 

geometric components affecting the flow field. Also, the grids 

are being refined in order to increase geometric and computational accuracies. The number of grid points are expected to 

increase to over 1 million for zero-sideslip-angle cases and will 

be double that number for nonzero-sideslip-angle solutions. 

Solutions will be obtained for several Mach numbers, angles of 

attack and sideslip, and with and without plume simulation. 

Publications 

1. Ragagopal, K. et al. "Versatile Multi Zonal Gridding 

Technique for Complex Geometries." AIM Paper 90-001 1, 

Jan. 1990. 

2. Chen, C. L. et al. "Multi ~onal'~avier-stokes Solutions 

for the Multi Body Space Shuttle Configuration." AIM 

Paper 90-0434,Jan. 1990. 

RI - FNS Solution at Mach 1.25, a=-2.2 " 

I I PRESSURE COEFFICIENT COLOR CONTOURS 

SRB RING EFFECTS ON ORBITER WING - LOWER SIDE 

NIO RING I 

1. 

1. 

s I 

tyfm AL PA?E 

COLOR p14OTOGRAPH 

Pressure coefficient color contours showing SRB ring effects on the lower surface of the orbiter wing; RI-FNS blution at M = 1.25, 

a = 2.2". 
Simulation of Supersonic Chemically Reacting Flow Fields 

J. Philip Drummond, Principal Investigator 

Co-investigators: Mark H. Carpenter, Peyman Givi, Johnny R. Narayan, David W. Riggins, Balu Sekar, and Jeffrey A. White 

NASA Langley Research Center 

Research Objective 

To study phenomena that control high-speed fuel-air mixing 

and combustion, and to use information gained from these 

studies to improve mixing and combustion efficiency in highspeed propulsion devices. 

Approach 

The combustion processes occurring in a scramjet combustor 

are described by using an accurate numerical algorithm to 

solve the equations governing the mixing and chemical reactions of a multicomponent mixture in combination with a physically realistic chemical kinetics model. 

Accomplishment Description 

A computer program was developed during the previous 

period that solved the equations governing a multicomponent 

mixing and reacting flow. The code was validated against 

experiments involving both nonreacting and reacting flow 

fields, and then applied in studies of combusting high-speed 

engine flows. Recent research has been directed toward 

improving the efficiency of fuel-air mixing and reaction in a 

scramjet. Mixing is significantly reduced in this engine as the 

combustor Mach number increases with flight Mach number, 

and mixing enhancement is required to achieve a sufficient 

degree of combustion efficiency. Because of this difficulty, 

alternate combustor fuel-injector configurations were designed 

and studied, to evaluate their potential for producing an 

improved degree of mixing and reaction. One such configuration is shown in the figure. It consists of two swept-ramp fuel 

injectors that introduce gaseous hydrogen fuel from orifices in 

their bases. The swept-ramp sidewalls induce streamwise vorticity into the inlet air passing the ramps, and this vorticity 

enhances fuel-air mixing downstream of the injectors. The 

resulting hydrogen-fuel mass fraction distribution, keyed to the 

color bar, is also shown in the figure. Without enhancement, 

the fuel jet would spread only slightly over the distance 

studied. With enhancement, however, the fuel jets are captured by the vortices and spread well across the channel 

downstream of the ramps. This dramatic improvement in fuelair mixing results in a significant improvement in combustion , efficiency. A typical run for this problem on the Cray Y-MP 

required approximately 8 hours, and 40 megawords of 

memory. 

Significance 

Numerical simulations provide improved insight into the 

mechanisms controlling high-speed mixing and combustion in 

supersonic reacting flows. Using knowledge gained from 

these basic simulations, techniques can be developed for 

enhancing mixing and reaction in supersonic combustors, 

thus improving the overall level of combustion efficiency in 

these devices. 

Future Plans 

Work is now under way to optimize the degree of enhancement that can be achieved from the fuel-injector configuration 

considered in this study. Other injector configurations that 

utilize shock excitation and vortex bursting for enhancement 

will also be examined. 

Publications 

1. Drummond, J. P.; Carpenter, M. H.; Riggins, D. W.; and 

Adams, M. S. "Mixing Enhancement in a Supersonic 

Combustor." AlAA Paper 89-2794, July 1989. 

2. Carpenter, M. H. "Three-Dimensional Computations of 

Cross-Flow Injection and Combustion in a Supersonic Flow." 

AlAA Paper 89-1 870, June 1989. 

3. Riggins, D. W.; Mekkes, G. L.; McClinton, C. R.; and 

Drummond, J. P. "A Numerical Study of Mixing Enhancement 

in a Supersonic Combustor." AIM Paper 90-0203, Jan. 1990. 

H2 mass 

fraction 

An alternate combustor fuel-injector configuration. 
Acceleration of lterative Algorithms for Euler and Navier-Stokes Equations 

George S. Dulikravich, Principal Investigator 

Co-investigator: Seungsoo Lee 

The Pennsylvania State University 

Research Objective 

To develop a reliable algorithm that gives a faster convergence rate than conventional iterative algorithms, and to 

investigate its dependence on grid and flow conditions. 

Approach 

The distributed minimal residual (DMR) method has been 

developed and successfully applied to the system of Euler 

equations and the system of incompressible Navier-Stokes 

equations. The DMR method belongs to a general class of 

Krylov subspace methods. However, it has two aspects that 

are different than the Krylov subspace methods. First, a different sequence of acceleration factors is used for each equation 

of the system; and second, only two to five steps are needed 

to achieve good convergence rates. 

Accomplishment Description 

The convergence of the conventional explicit and implicit 

algorithms (Runge-Kutta time-stepping method and Euler 

implicit method) have been accelerated. It has been shown 

that the CPU time to achieve steady state for two-dimensional 

problems has been reduced to 20-70% of the time needed by 

the nonaccelerated schemes. The DMR method has been 

extensively tested on the sensitivity to grid and flow conditions, 

including grid clustering, grid nonorthogonality, number of grid 

points, Mach number, and Reynolds number. The sensitivity of 

the DMR method to CFL number has been tested and the 

comparison with the implicit residual smoothing method has 

been performed as well. The DMR method has been proven to 

be less sensitive to grid and flow conditions than the existing 

methods. 

-16 1 I I I I I 

1000 2000 3000 4000 5000 

Number of iterations 

Significance 

As a tool of computational fluid dynamics, the importance of 

computational algorithms cannot be emphasized too much. 

The reliability of a computational algorithm depends on its 

convergence rate and robustness. The performance test of a 

newly developed scheme is of paramount importance. 

Future Plans 

A three-dimensional explicit code has been developed and 

verified against experimental data and published computational results. The DMR method is being incorporated into this 

three-dimensional code. The DMR method will be evaluated 

for its ability to enhance the convergence of three-dimensional 

problems, through a number of tests. Especially, the DMR 

method will be examined for its ability to accelerate the convergence of turbulent flow computations. A three-dimensional 

implicit code will be written and used to evaluate the DMR 

method. 

Publications 

1. Lee, Seungsoo, and Dulikravich, George S. "A Fast 

lterative Algorithm for Incompressible Navier-Stokes Equations." Proceedings of the 10th Brazilian Congress of Mechanical Engineering. Rio de Janeiro, Brazil, Dec. 1989. 

2. Lee, Seungsoo, and Dulikravich, George S. "Distributed 

Minimal Residual (DMR) Method for Accelerations of lterative 

Algorithms." Proceedings of the Computational Fluid Dynamics Symposium on Aeropropulsion. NASA CP-10045, 1990. 

3. Lee, Seungsoo, and Dulikravich, George S. "Performance 

Analysis of the DMR method for Accelerations of lterative 

Algorithms." Presented at the 27th Aerospace Sciences 

Meeting, Reno, NV, Jan. 1991. 

Cpu time (sec) 

Convergence histories of the Runge-Kutta method for Hiemenz flow; Re = 400. 
The Interaction of Particles with Homogeneous Turbulence 

John K. Eaton, Principal Investigator 

Co-investigator: Kyle D. Squires 

Stanford University 

Research Objective 

The objective of this work is to gain an increased physical 

understanding of the interaction of small, solid particles with 

gas-phase turbulence. This understanding will lead to 

improved turbulence models for engineering computations 

of particle-laden turbulent flows. 

Approach 

The interaction of particles with stationary isotropic turbulence 

is studied using direct numerical simulation of the threedimensional, time-dependent, incompressible Navier-Stokes 

equations. A vectorized interpolation algorithm has been 

developed to facilitate the simultaneous tracking of as many 

as'one million particles through the simulated flow fields. 

Accomplishment Description 

Results from the simulations showed significant effects of 

turbulent motions on particle concentration fields. Particles 

were shown to collect in regions of low vorticity and high strain 

rate. This bias in particle motion was quantified using various 

correlations of the particle number density with turbulence 

quantities. Instantaneous values of the particle number density 

were shown to be as much as 30 to 40 times the mean value 

because of particle accumulation in these regions. The effect 

of particle loading on turbulent flow fields was also investigated in the simulations. It was found that the decrease in 

turbulence kinetic energy was relatively insensitive to particle 

inertia, being dependent only on the value of the mass loading. A computation of turbulence modification using 643 points 

for the hydrodynamic calculation and lo6 particles required 

approximately 20 Cray-2 hours and approximately 35 megawords of memory. 

Significance 

The ability to use direct numerical simulation of turbulence to 

compute turbulence modification by particles has been demonstrated. The data base generated from these computations 

may be used as a basis for further developments in turbulence 

modeling for particle-laden turbulent flows. 

Future Plans 

Future plans include the examination of current turbulence 

models of particle transport in turbulent flow fields as well as 

the examination of turbulence modification by particles. 

Publications 

Squires, Kyle D., and Eaton, John K. "Particle Response and 

Turbulence Modification in Isotropic Turbulence." To be published in Physics of Fluids. 

Contours of the particle number-density field from one plane of a direct numerical simulation of the three-dimensional, incompressible Navier-Stokes equations. The contour levels are from the mean value to four times the mean number density for a 

dimensionless particle time constant of 0.15. 
Hypersonic Chemically Reacting Flow over Blended Wing-Body Vehicles 

Thomas A. Edwards, Principal Investigator 

Co-investigators: Jolen Flores, Uwe Jettmar, and Greg Molvik 

NASA Ames Research Center 

Research Objective 

The goal of this research is to establish a computational fluid 

dynamics (CFD) capability to solve external hypersonic flows 

about candidate vehicle configurations, such as the National 

Aero-Space Plane (NASP). This requires adding physical 

fiodels for transition and for the chemical reactions that take 

place in air when it is heated by the strong shock waves 

associated with hypersonic flight. Once these models are 

i~plemented, the code must be validated by comparing the 

calculations with experimental data. 

Approach 

The compressible Navier-Stokes (CNS) code is being 

developed in support of the NASP program. This code was 

enhanced by incorporating a simple transition model, a model 

for air in chemical equilibrium, and a set of equations for air in 

chemical nonequilibrium. These modifications were validated 

by comparing calculated results with experimental data. 

Accomplishment Description 

The CNS code now includes the elements needed to simulate 

the external hypersonic flight environment about a vehicle 

such as the NASP. All features and options of the code have 

been exercised and validated with experimental data. This is 

especially important for hypersonic vehicle design because 

the acquisition of data via experimental techniques is limited 

and costly. A typical CFD calculation of hypersonic, chemically reacting flow past a blunt body requires about 10 hours 

of Cray-2 CPU time and 4 megawords of main memory. 

Significance 

The CNS code is among the first CFD codes with the ability to 

address chemically reacting, hypersonic flows past geometrically complex shapes. This capability will contribute to the 

design of the NASP. 

Future Plans 

The CNS code will continue to be validated as experimental 

data becomes available. A higher order turbulence model will 

be incorporated, and a solution-adaptive grid method will be 

applied. Vectorization and convergence-acceleration techniques will be explored. 

Publications 

1. Flores, J.; Edwards, T. A.; Ryan, J. S.; and Kaul, U. "CNS 

Code Enhancements (U)." Paper 15,6th NASP Symposium, 

Apr. 1989. 

2. Edwards, T. A., and Flores, J. "Toward a CFD Nose-to-Tail 

Capability: Hypersonic Unsteady Navier-Stokes Code Validation." J. Spacecraft Rockets 27, no. 2 (Mar.-Apr. 1990): 123- 

130. (Also: AlAA Invited 1-hour paper 89-1672. June 1989.) 

3. Edwards, T. A. "Numerical Simulation of Hypersonic 

Reentry Flow Fields." Presented at the Workshop on Hypersonic Flows for Reentry Problems, Antibes, France, Jan. 1990. 

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Hypersonic chemically reacting flow past a blunt body. 
Numerical Simulation of Hydrogen-Air Combustion in Hypersonic-Vehicle 

Propulsion Systems 

Thomas A. Edwards, Principal Investigator 

Co-investigators: Jolen Flores and Uwe Jettmar 

NASA Ames Research Center 

Research Objective 

To develop and validate a computational fluid dynamics (CFD) 

capability to solve the flow through the integrated propulsion 

system of air-breathing hypersonic-flight vehicles, and to 

incorporate the boundary conditions and physical models 

necessary to obtain accurate solutions to flows involving 

hydrogen-air combustion, including the recombinationdominated external flow on the afterbody. 

Approach 

First, the compressible Navier-Stokes (CNS) code is extended 

to address forebodylinlet flow fields. Because the vehicle 

propulsion system is highly integrated, the external and 

internal flow fields cannot be analyzed separately. Next, a 

hydrogen-air combustion code is obtained and coupled to 

address the internal portion of the flow. Finally, the CNS code 

is extended to model the recombination-dominated flow on 

the afterbody. 

Accomplishment Description 

The CNS code demonstrated its ability to solve mixed 

externallinternal flow fields on two configurations, one of 

which was a generic forebodylinlet shape characteristic of 

the National Aero-Space Plane (NASP). Correlation with the 

experimental data was very good. The afterbody chemistry 

modeling has been completed and is in the process of being 

incorporated into the CNS code. The internal combustion 

codes available for inclusion are being evaluated. Power-off 

calculations about representative configurations require about 

50 hours of Cray-2 CPU time, 4 megawords of main memory, 

and 20 megawords of secondary memory. It is expected that a 

fully modeled power-on simulation will require about four times 

this amount of CPU time and twice the memory. 

Significance 1 

The CNS code is among the first CFD codes to demonstrate 

the ability to solve the entire flow about candidate NASP configurations, including the forebody, inlet, nozzle, and afterbody 

in a fully-coupled solution. This is the kind of analysis neces- * 

sary to predict performance of proposed NASP designs. This 

kind of information cannot be obtained in such detail by any 

other means. 

Future Plans 

A demonstration calculation will be performed for a generic 

NASP configuration in powered, hypersonic flight. Validation 

cases will be identified and qalculations performed for them, 

and the CNS code will be applied to support the NASP 

program. 

Publications 

1. Bennett , B. C., and Edwards, T. A. "Calculation of Hypersonic Forebodyllnlet Flow Fields (U)." Paper 48, 7th National 

Aero-Space Plane Symposium. Oct. 1989. 

2. Bennett, B. C., and Edwards, T. A. "Numerical Solution of 

TTD Forebodyllnlet Flow Fields (U)." Paper 47, 8th National 

Aero-Space Plane Symposium, Mar. 1990. 

FIVE ZONE VELOCITY VECTORS(U) 

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COLOR PHQiOGRAPH 
Advanced CFD Codes for Rotary-Wing Airloads and Performance Prediction 

T. Alan Egolf, Principal Investigator 

Co-investigator: Brian E. Wake 

United Technologies Research Center 

Research Objective 

To refine and enhance advanced helicopter and high-speedpropeller computational fluid dynamics (CFD) codes and 

wake-modeling codes in order to include more rigorous 

representations of the rotor wake and provide viscous drag 

prediction capability for improved airload and performance 

prediction. 

Approach 

Fotor-wake influence is being incorporated into rotary-wing 

CFD codes using velocity-embedding techniques and transpiration boundary conditions based on prescribed wake geometries from either analytical, empirical, or numerical predictions. 

Improved wake-geometry prediction capability is being developed based on free-wake vortex-lattice methods. 

Accomplishment Description 

Activity during this period of the multi-year effort focused on 

the application of the United Technologies Research Center's 

viscous code NSR3D to complex geometries. The applications 

were directed toward initial investigation of the ability of the 

code to predict the flow-field behavior associated with vortex 

structures generated by such geometries as a helicopter 

blade with a BERP-like tip planform, a high-speed propeller, 

and a fixed-wing configuration. Tip and leading-edge vortex 

structures were predicted. Approximately 15 to 25 hours of 

Cray-2 processor time and about 30 megawords of memory 

were required per case. In addition, the computational performance of the NSR3D and wake prediction codes used in this 

effort is being compared with their performance on other 

advanced computer architectures. 

Significance 

Application of the viscous code NSR3D as part of the 

development and verification effort has demonstrated the 

prediction of fluid flow phenomena associated with real-world 

geometries. 

Future Plans 

Refinements to the solver are planned along with the incorporation of the hover-wake influence into the viscous code 

NSR3D using a refined hover free-wake model. Application 

of the NSR3D code to an advanced blade tip for acoustic 

reduction purposes is also planned under a NASA contract. 

Publications 

1. Egolf, T. A. "Helicopter Free-Wake Analysis on a Massively Parallel Computer." Proceedings of the International 

Symposium on Boundary Element Methods 89, Oct. 1989. 

2. Egolf, T. A. "Connection Machine Utilization and Experience at the United Technologies Research Center." Proceedings of the Fourth SlAM Conference on Parallel Processing for 

Scientific Computing. Chicago, Dec. 1989. 

3. Wake, B. E., and Egolf, T. A. "Implementation of a RotaryWing Three-Dimensional Navier-Stokes Solver on a Massively 

Parallel Computer." AlAA Paper 89-1939, June 1989. 

4. Wake, B. E., and Egolf, T. A. "Application of a Rotary-Wing 

Three-Dimensional Navier-Stokes Solver on a Massively Parallel Computer." AlAA Paper 90-0334, Jan. 1990. 

(Left) A leading-edge vortex structure for a high-speed propeller, predicted by NSR3D and demonstrated by particle traces. 

(Right) The velocity field in a plane downstream of the trailing edge. 
Direct Simulation of Turbulent Reacting Flows 

S. E. Elghobashi, Principal Investigator 

Co-investigator: K. K. Nomura 

University of California, lrvine 

Research Objective 

To study the physical processes of turbulent mixing in a nonpremixed flame with and without the effects of heat release. 

Approach 

Direct numerical simulation of the full, three-dimensional, timedependent Navier-Stokes, continuity, and scalar conservation 

equations are performed. The general equations are valid for 

both incompressible and compressible low-Mach-number 

flows. Initially, nonpremixed reactants in both isotropic and 

homogeneous shear flows are considered. 

Accomplishment Description 

Simulations were performed for an isothermal (negligible heat 

release) nonpremixed reaction in both isotropic and homogeneous shear flows. These simulations provided detailed 

statistics on vorticity, strain rate, and scalar dissipation rate 

fields; the results described their roles and interactions in 

scalar mixing. Simulations using a resolution of 963 grid points 

require approximately 2 to 3 hours on the Cray-2 and 

15 megawords of memory. 

Significance 

The interaction of heat release and turbulence is one of the 

least understood phenomena in chemically reacting flows. 

Results obtained from direct numerical simulations that 

accommodate the effects of variable density due to heat 

release will provide a more accurate description of the flame 

structure and turbulent statistics and will contribute to our 

understanding of these flows. 

Future Plans 

Work is under way to extend the simulations to reactions with - 

heat release. 

Publications 

1. Nomura, K. K., and Elghobashi, S, E. "Direct Simulation of 

an Isothermal Nonpremixed Flame in Homogeneous Turbulent 

Shear Flow." AlAA Paper 90-0148, 1990. 

2. Elghobashi, S. E., and Nomura, K. K. "Direct Simulation of 

a Passive Diffusion Flame in Sheared and Unsheared Homogeneous Turbulence." In Turbulent Shear Flows 7, ed. W. C. 

Reynolds. Berlin: Springer-Verlag, 1990. 

Local instantaneous scalar dissipation rate in a vertical (x-z) plane for (left) homogeneous shear, and (right) isotropic flow. 
Dispersion of Solid and Fluid Particles in Turbulent Homogeneous Flows With 

and Without Turbulence Modulation 

S. E. Elghobashi, Principal Investigator 

Co-investigator: G. C. Truesdell 

University of California, lrvine 

Research Objective 

To study particle dispersion in turbulent isotropic and homogeneous shear flows and to examine the modulation of 

.turbulence in heavily laden flows. 

Approach 

Direct numerical simulation is used to integrate the timedependent three-dimensional Navier-Stokes equations to pro- 

-duce the velocity fields. A second-order Runge-Kutta scheme 

and fourth-order Hermitian polynomial interpolation are used to 

integrate the Lagrangian equation of particle motion. To study 

the two-way coupling between the particles and turbulence 

the two sets of equations are solved simultaneously. 

Accomplishment Description 

A simulation of Snyder and Lumley's experiment (1971) for 

particle dispersion in a decaying grid-generated turbulence 

was performed. Particle dispersion, diffusivity, and Eulerian 

and Lagrangian velocity autocorrelation coefficients for the 

fluid, particles, particles surrounding the fluid, and fluid points 

were just a few of the statistics computed. Good agreement 

with the experimental data was obtained. The figures show the 

dispersion curves and Lagrangian velocity autocorrelation 

coefficients for the simulation and for Snyder and Lumley's 

experiment. The dispersion computation needed about 

82 megawords of memory and 7 Cray-2 hours for one run. 

Significance 

In a large number of mixing applications the mass and 

momentum of the particles are large enough to significantly 

alter the flow structure. Laboratory experiments designed to 

measure the modulation of turbulence in heavily laden flows 

are difficult to perform. The direct numerical simulation of 

particlelflow interaction is a numerical experiment that allows 

almost unlimited measurements of all details of the interaction, 

with relative ease. 

Future Plans 

Particlelflow interactions for heavily laden isotropic turbulence 

and homogeneous turbulent shear flows will be studied with 

various mass loadings and particle response times to determine their effects on the energy and structure of the flow and 

on particle dispersion statistics. 

Publications 

1. Elghobashi, S. E., and Truesdell, G. C. "Direct Simulation 

of Particle Dispersion in a Decaying Grid Turbulence." Presented at the Seventh Symposium on Turbulent Shear Flows, 

Stanford Univ., Palo Alto, CA, 1989. 

2. Elghobashi, S. E., and Truesdell, G. C. "Direct Simulation 

of Particle Dispersion in Grid Turbulence and Homogeneous 

Shear Flow." Bull. Am. Phys. Soc. 34 (1989): 231 1. 

0 .1 .2 .3 .4 .5 .6 .7 0 .1 .2 .3 .4 .5 .6 .7 

Time from To (sec.) Time from To (sec.) 

(ieft) Normalized mean-square displacement. (Right) Lagrangian autocorrelation coefficients. 
Control of the Flow Field about an Airfoil Section by Localized Surface Heating 

N. M. El-Hady, Principal Investigator 

Co-investigator: L. Maestrello 

NASA Langley Research CenterIAnalytical Services and Materials, Inc. 

Research Objective 

This research uses localized surface heating to enhance the 

performance of an airfoil at high angles of attack. The objective is to investigate the flow field and assess its lift, flow 

separation, and stall characteristics with and without control. 

Approach 

The analysis is based on the numerical solution of the twodimensional Reynolds-averaged compressible Navier-Stokes 

equations; an implicit, upwind-biased, finite-volume scheme 

with approximate factorization and flux difference splitting is 

used. Active control by heating is simulated by modifying the 

temperature boundary condition over a narrow strip located 

near the leading edge of the airfoil in the large-pressuregradient region. A temperature control function with specified 

amplitude and frequency is designed to restructure the lift 

characteristics of the airfoil. 

0 

- 

2 4 6 8 101214 

Time 

Accomplishment Description 

At a = 13", the temperature function is tuned to the natural 

shedding frequencies of the shear layer to enhance the coupling between the surface heating and the separated flow. 

This leads to an increase in the rms value of the velocity perturbation, and a decrease in the size of the separated region. - 

The power spectrum of the lift coefficient with control shows an 

amplitude that exceeds that of the uncontrolled lift. The lift and 

drag coefficients at this angle of attack oscillate around average values with an increase in the liftldrag ratio of 7%. - 

Significance 

Separation control by localized surface heating can be used 

to improve the lift and stall characteristics of a maneuvering 

fixed-wing aircraft or of retreating blades on a helicopter rotor. 

Future Plans 

A parametric study is under way to evaluate the power 

required for and the practicality of the method, especially 

when it is applied to three-dimensional geometries. 

ow- 

- 5- 

'0 2 4 6 8 101214 

Time 

Frequency 

(A) Temperature function. (B) Time history of velocity perturbation at xlc = 0.42 and different y locations. (C) Mean velocity profile 

near the surface at x/c = 0.42. (D) Lift coefficient frequency spectrum. (E) Lift time history. 
CFD Analysis of the Flow Paths of Spherical Convergent Flap Nozzles 

John J. Erhart, Principal Investigator 

Co-investigators: Saadat A. Syed and Eric W. King 

United Technologies, Pratt & Whitney 

Research Objective 

To provide analytical support in the development of advanced 

spherical convergent flap (SCF) nozzles. 

Approach 

4 three-dimensional Navier-Stokes code with arbitrary curvilinear coordinates, k-E turbulence model, and transonic flow 

capabilities was used to predict the flow field inside an SCF 

nozzle. An elliptic grid generator was used to create a mesh of 

the nozzle. 

Accomplishment Description 

The internal flow features of various configurations of the SCF 

nozzles were computed. These configurations showed the 

internal flow features inherent in the SCF nozzle, including turbulence, transonic flow, compression and expansion waves, 

boundary-layer skewness recirculation, and significant cross 

flow. Numerous calculations were made for two different SCF 

nozzles in straight, pitched, and pitched and yawed modes. 

These cases were run inviscid and viscid with various grid 

densities. The results were compared with pressure, thrustcoefficient, and vector-angle data. 

Significance 

Exhaust nozzles for the next generation of fighter aircraft will 

be designed to have multiplane thrust-vectoring capability. 

Several studies have shown that the operational effectiveness 

of these aircraft can be enhanced by using advanced nozzles 

with thrust-vectoring/-reversing capabilities. Since the flow 

field generated inside these nozzles is highly threedimensional and viscous, traditional design methods based on 

two-dimensional analyses are not adequate for their successful design. A need therefore exists to develop designs and 

design evaluation systems based on three-dimensional computational fluid dynamics methods that are accurate, economical, and have reasonably short turnaround time when applied. 

Future Plans 

The knowledge obtained from this work will be used to study 

the effect that cooling has on nozzle thrust. 

Publications 

Syed, S. A.; Erhart, J. J.; and King, E. W. "Application of CFD 

to Pitchflaw Thrust Vectoring Spherical Convergent Flap 

Nozzles." Presented at the AIAA/ASME/SAE/ASEE Joint 

Propulsion Conference, Orlando, FL, July 1990. 

LEGEND 

1 0.1200E+02 

2 0.1800E+02 

3 0.2400E+02 

4 0.3000E+02 

5 0.3800E+02 

6 0.4200E+02 

7 0.4800E+02 

8 0.5400E+02 

9 0.6000E+02 

10 0.6900E+02 

11 0.7200E+02 

'I 2 0.7800E+02 

13 0.8400E+02 

LEGEND 

1 0.1200E+02 

2 0.1800E+02 

Pressure contours on nozzles used for aerocontrol; vectoring causes large flap-to-flap pressure gradients. 
Compressible Turbulence 

G. Erlebacher, Principal Investigator 

Co-investigators: S. Sarkar, C. Shu, and T. A. Zang 

NASA Langley Research CenterIlCASE 

Research Objective 

To study the physics of compressible homogeneous turbulence, and to generate accurate data bases against which 

turbulence models can be evaluated. 

Approach 

The approach was to solve the time-dependent Navier-Stokes 

equations with constant viscosity and conductivity in a periodic three-dimensional box. Theory and numerical diagnostics 

were used to distinguish the compressible from the incompressible flow characteristics. 

Accomplishment Description 

A theoretical framework was developed to predict the possible 

states of isotropic, decaying, compressible turbulence as a 

function of initial conditions. Formulas that predict the equilibrium levels of compressibility, dissipation rates, and dilatational variances were established and checked against the 

results of two- and three-dimensional direct numerical simulations (DNS). The key result was that in the absence of shocks, 

the turbulence evolves toward a state of equipartition of the 

compressible components of potential and kinetic energy. 

From theoretical considerations, turbulent models were developed to treat both the pressure dilatation and the compressible dissipation terms in the energy equation. These models, 

when incorporated into a second-order closure model, predicted the correct convective Mach number (M,) dependence 

of the mixing rate in a compressible mixing layer. This can be 

seen in the figure (taken from Publication I), which shows the 

spreading rate of a compressible shear layer as a function of 

M,. Three-dimensional DNSs were conducted on 643 grids to 

calibrate the model constant. Each required about 5 CPU 

hours. An essentially nonoscillatory third-order scheme for 

two- and three-dimensional flows was also developed and 

applied to the simulation of compressible turbulence. The data 

generated were compared with DNS data and were found to 

predict accurately shock locations and speeds. A total of 

approximately 400 CPU hours and 200 deferred hours were 

used during the March 1989 to March 1990 operational 

period. 

Significance 

Two- and three-dimensional direct simulations, properly 

coupled with experiments and theory, improve our understanding of turbulence and provide a good foundation on 

which to build turbulence models. 

Future Plans 

Two- and three-dimensional simulations of turbulent shear 

flows will be performed to assess whether the presence of 

weak curved shocks enhances mixing when the convective 

Mach number is supersonic. 

Publications 

1. Sarkar, S., and Balakrishnan, L. CASE Report No. 90-18. 

2. Erlebacher, G.; Hussaini, M. Y.; Kreiss, H. 0.; and 

Sarkar, S. CASE Report No. 90-15. 

3. Sarkar, S.; Erlebacher, G.; Hussaini, M. Y.; and Kreiss, 

H. 0. CASE Report No. 89-79. 

- -- 

- With Compressible Dissipation Model 

- Without Compressible Dissipation Model 

A Papamoschou and Roshko 

- -0- "Langley Experimental Curve" * Elliott and Samimy 

Petrie, Samimy and Addy 

- 

- A A A A 

The spreading rate of a compressible shear layer. 
Three-Dimensional Viscous Drag Prediction for Rotor Blades 

Fort F. Felker, Principal Investigator 

Co-investigator: Ching S. Chen 

NASA Ames Research Center 

Research Objective 

To provide an accurate and efficient design tool to the rotorcraft industry to predict the rotor-blade drag force for rotorcraft 

in hover and forward flight. 

Approach 

A viscous-inviscid interaction approach is used. Very near the 

blade surface, the flow is assumed viscous and is governed 

by the three-dimensional boundary-layer equations. Outside 

the boundary layer, the flow is assumed inviscid and is governed by the full-potential equations. These two sets of equations are solved separately on a rotating reference frame but 

are coupled together through pressure and displacement 

thickness. 

Accomplishment Description 

The development of the boundary-layer code in the rotating 

reference frame and the coupling of this code with an existing 

transonic full-potential code were completed. The accuracy of 

the numerical scheme was validated by comparing computed 

results with theoretical results and test data for laminar and 

turbulent flow over a flat plate and for nonlifting twodimensional airfoil flows over a range of Mach numbers. The 

method was recently applied to three sets of nonlifting rotor 

flows, two in hover and one in forward flight. The results 

demonstrate that the current analysis is able to predict the 

nonlifting rotor drag for general rotor configurations. The 

comparison of computed torques with test data for the two 

TEST DATA - RECTANGULAR TIP "1 -,=R3wrLmm 

TIP MACH NUMBER 

hovering rotors are shown in the accompanying figure. Each 

rotor flow computation required approximately 1 hour of 

Cray-2 time and 8 mega-words of memory. 

Significance 

The ability to accurately predict drag force for rotating blades 

is extremely important in the design of rotorcraft. The state of 

the art in rotor-blade drag prediction involves the use of twodimensional airfoil tables to extrapolate the drag force on the 

blade. This method does not take the Reynolds number or the 

rotational effects of the blade into account, raising doubts 

about the accuracy of the results. This project addresses this 

problem with the development of an analytical method that 

includes the effects of Reynolds number as well as the rotational motion of the blade. If successful, it is anticipated that 

this analysis will be used extensively in the design of future 

rotorcraft. 

Future Plans 

The codes will be enhanced to allow simulation of lifting rotor 

flows as well as nonlifting flows. In addition, the coupling of the 

current analysis with a rotor wake and blade dynamics model 

will be completed. 

Publications 

Chen, C. S., and Bridgeman, J. 0. "Three-Dimensional Viscous Rotor Flow Calculations Using Boundary-Layer Equations." Presented at the Fifteenth European Rotorcraft Forum, 

Amsterdam, The Netherlands, Sept. 1989. 

20 1 TEST DATA - SWEPT TIP 

TIP MACH NUMBER 

Comparison of computed torques with test data for a nonlifting hovering rotor with ([eft) rectangular-tip blades, and (right) swepttip blades. 
Compressible Navier-Stokes Code Development 

Jolen Flores, Principal Investigator 

Co-investigators: Steve Ryan and Tom Edwards 

NASA Ames Research Center 

Research Objective 

To develop the ability to predict the hypersonic, viscous flow 

over a complicated geometry; perfect, equilibrium, and 

nonequilibrium flows are included. 

Approach 

A three-dimensional Navier-Stokes code is implemented in a 

zonal approach, with options for perfect-gas, equilibrium, and 

nonequilibrium flow. The compressible Navier-Stokes (CNS) 

code is a zonal flow solver for use in hypersonic vehicle 

design. It contains a version of the F3D, partially flux-split, thinlayer Navier-Stokes flow solver. That solver is applied using a 

zonal approach derived from the transonic Navier-Stokes 

(TNS) code. 

Accomplishment Description 

The Cray-2/Cray Y-MP time allotted to the CNS project has 

been used to develop the finite-rate air-chemistry option now 

available in the CNS version 1.4. Development of the code has 

benefited from use of the NAS facilities. Some of the accomplishments of the project are described below. First, a perfectgas solution over the McDonnell-Douglas generic-option 

blended wing-body was computed. The purposes of this 

exercise were to check out the zonal grid interfacing capabilities, to compare the CNS results with those of a spacemarching method, and to create a data base for future code 

enhancements. The figure on the left shows the grid for the 

generic option, which consists of eight zones totaling over 

350,000 points. The flow conditions for this test case were 

M, = 11.35, a = 0°, and Re = 31 x lo6 rn-'. Results were compared with experimental data and a parabolized Navier-Stokes 

calculation. Comparisons for the windward centerline surface 

pressure are shown in the figure on the right. This computation 

required about 30 hours of CPU time and about 10 mega- '- 

words of memory. Second, the finite-rate air option was exercised over a sphere for a variety of Mach numbers. These 

same cases were run for a two-zone sphere case. * 

Significance 

The CNS code is now ready for detailed validation, for application to complicated vehicles, and for integration with an 

interflow code to allow complete nose-to-tail hypersonic 

analyses. 

Future Plans 

The finite-rate version of the CNS code will now be applied, in 

conjunction with the UPS code, to more complicated geometries. Sensitivity studies will be conducted to analyze the 

effects of nonequilibrium flow bn pressure and heat-transfer 

values. 

Publications 

Lawrence, S., and Flores, J. "Air Chemistry Sensitivity Analysis 

Using the CNS/UPS Codes." Presented at the Eighth National 

Aerospace Plane Technology Symposium, Monterey, CA, Mar. 

1990. 

10 20 30 40 

Body Station 

(Left) Geometry and grid for the generic-option aerothermal (Right) Pressure comparisons on windward symmetry plane of 

model. generic-option model at M, = 11.35 and a = 0". 
Electronic-Structure Study of High Superconductors 

Arthur J. Freeman, Principal Investigator 

Co-investigators: A. Continenza, S. Massidda, and J. Yu 

Northwestern University 

Research Objective 

To carry out electronic-structure calculations on the new hightemperature superconductors in order to gain an understanding of their electronic structure and properties, as well as to 

provide insight into the mechanism of superconductivity of 

hese high T, materials. 

Approach 

The highly precise, full-potential, linearized, augmented planewave method is used to solve the time-independent quantum 

mechanical equations in the local density approximation. 

Accomplishment Description 

Recently, the discovery of the so-called electron-doped 

superconductors (e.g., Nd2-,CeXCuO4) added a new 

dimension to the theoretical model for the mechanism of high 

T, superconductivity. The results of our highly precise, localdensity electronic-structure calculations on Nd2Cu04 showed 

its close similarity to the "hole-doped" superconductors. 

(The similarities are the important role of the strongly twodimensional Cu-0 antibonding dpo band, a somewhat lower 

density of states at the Fermi energy, and a highly twodimensional Fermi surface.) This symmetry in electron-hole 

doping appears to be additional evidence for the validity of a 

Fermi liquid description of the normal metallic state of the high 

T, superconductors. An average single run of the calculations, 

which solve secular determinants of the order 1200 x 1200 

many times in the (iterative) self-consistency procedure, uses 

about 100 minutes of Cray-2 time and requires about 

16 megawords of memory. 

Significance 

For years there has been controversy and confusion among 

theorists as well as experimentalists about whether the 

"normal" state of the Cu-oxide superconductors is a Fermi 

liquid or some other exotic ground state. Recent experimental 

observations have confirmed the predictions of our localdensity functional calculations based on the Fermi liquid 

picture; hence the Fermi liquid (metallic) nature of the "normal" 

state of the high T, superconductors has been established. 

Future Plans 

A primary goal will be to develop a microscopic picture for 

the electron-electron interactions in high T, Cu-oxide superconductors, based on our energy band results. In particular, 

we are interested in the dielectric response, which provides 

crucial information for many dynamical properties, including 

structural and magnetic transitions and electron-phonon 

interactions as well as superconductivity in high T, 

superconductors. 

Calculated energy band structure of Nd2Cu04 along the main 

symmetry directions in the Brillouin zone. The single band 

crossing Fermi level EF is the strongly two-dimensional Cu-0 

antibonding dpo band, which is common with the other high 

T, Cu-0 superconductors. 
Computational Studies of Compressibility Effects on Dynamic Stall 

K.-Y. Fung, Principal Investigator 

University of Arizona 

Research Objective 

To identify the onset mechanisms in dynamic stall. 

Approach 

A series of computations was carried out using a Reynoldsaveraged Navier-Stokes code. Two airfoils, the NACA 0012 

and the VR7, were chosen for this study. For each airfoil and 

Mach number, the flows that correspond to different angles 

of attack were obtained. Results of the computations were 

analyzed and compared with available experimental data. 

Accomplishment Description 

It was found that the onset of stall can be delayed by increasi,ng the frequency of oscillation, as long as the flow remains 

subsonic. Once the flow is locally supercritical, the onset of 

stall becomes much less sensitive to increased frequency but 

has a strong dependence on the free-stream Mach number. 

The onset's dependence on the Mach number is not affected 

by the airfoil geometry as much as is its dependence on the 

reduced frequency. Before the onset of stall, the instantaneous pressure distributions over the airfoil can be considered 

quasi-steady and can be predicted using inviscid theory. A 

boundary-layer analysis, using computed inviscid flows and 

classical theory for static stall, suggests that once the flow 

becomes locally supersonic, the onset of stall is a result of the 

interaction between the forming shock and the steepening 

laminar boundary layer. It also explains the differences 

between the onset characteristics of the NACA 0012 and VR7 

airfoils. The sensitivity of stall onset on transition was studied 

by computing the flow over an airfoil at conditions near stall 

and varying the switch-on location of the turbulence model for 

the Reynolds-averaged Navier-Stokes code used in this study. 

It was found that the flow is not sensitive to the switch-on 

location when the angle of attack is below the static stall value. 

For an angle of attack close to the static stall value, e.g., at - 

13.25", a mere change of transition locations from 1.25% to 

1.35% which differ by one grid point and are before and after 

the computed shock location respectively, causes the flow , from reattachment to massive separation (see figure). For a 

lower free-stream Mach number, 0.185, separation is less 

sensitive to the transition location as the angle of attack is 

increased. 

Significance 

Some insight into the onset of dynamic stall has been gained 

from our work. Before the onset, the validity of quasi-steady 

inviscid theory is confirmed. The dependence of the onset of 

stall on the Mach number and leading-edge profile can be 

explained by classical boundary-layer theory. The importance 

of separation bubble bursting and transition effects on 

reattachment deserve a renewed assessment. 

Future Plans 

Numerical experiments will be designed to study the stability 

of reattaching separated flows at dynamic stall conditions. 

Mach contours and velocity vectors. 
Validation of 3-D Wind Tunnel Wall Interference Assessment/Correction Codes 

Javier A. Garriz, Principal Investigator 

NASA Langley Research Center 

Research Objective 

To develop the capability to assess the extent to which wind 

tunnel data can be corrected (by adjustments to the freestream Mach number and configuration angles of attack) to 

account for the effects of the tunnel walls, sting mounts, and 

other tunnel environment parameters. 

~pproach 

To obtain corrections for both Mach number and angle of 

attack, a three-dimensional small-disturbance code (with 

nonisentropic corrections), CAP-TSD, is used to solve two 

boundary-value problems. First, an "in-tunnel" boundary-value 

problem is solved using measured tunnel-wall data as outer 

boundary conditions, subject to matching measured lift and 

pitching moments. Then, a "free-air" boundary-value problem 

is solved in which the free-air Mach number and angle(s) of 

attack are varied so as to minimize the rms error between the 

in-tunnel and free-air model surface Mach numbers, subject to 

matching the total lift. 

Accomplishment Description 

The three-dimensional small-disturbance code CAP-TSD has 

been adapted for use as a wall interference assessment/ 

correction code. The code has been used to assess the 

interference present in several three-dimensional data sets 

involving full-span and semispan tunnel models. The resulting 

corrections have been verified (at least for semispan models) 

by an independent, free-air thin-layer Navier-Stokes solver. 

The correction code required an average of 24 megawords 

and 2 Cray-2 hours, and the independent free-air solver 

required 40 megawords and 4 Cray-2 hours. 

Significance 

The wall interference for models tested in transonic wind 

tunnels must be assessed and perhaps corrected in order to 

meet current data accuracy demands. The need to determine 

the free-air conditions that should be associated with the 

measured tunnel data is shared by anyone interested in using 

such data, including those who use it for comparison with or 

validation of other computational fluid dynamics codes. 

Future Plans 

The code will be used on additional three-dimensional data 

sets to continue the validation process, including data sets 

from the National Transonic Facility, the tunnel for which the 

code was originally developed. 

Publications 

Garriz, Javier A,; Newman, Perry A.; Vatsa, ~eer'~.; Haigler, 

Kara J.; and Burdges, Kenneth P. "Evaluation of Transonic 

Wall lnterference Assessment and Corrections for Semi-span 

Wing Data." Presented at the AlAA 16th Aerodynamic Ground 

Testing Conference, Seattle, WA, June 1990. 

Comparison of results for Lockheed wing C data from CFWT at Re,,, = 10.36 x lo6 and 4% porosity. 

- 

0 CFWF Data, Re-reduced at M 

TLNS3D, Free-air at M, a 

CORRECTED CONDITIONS 

UNCORRECTED Original Present 

CFWF Lockheed WlACX 

Test Conditions Study Study 

M = 0.851 3 M = 0.8463 M = 0.8400 .. 

a = 4.90" a = 4.00" a = 4.32" 

-1.2 

P 

0 0- 

1.2 

- 

- 

- 

- 

- 

- 

-- 

0 1 .o 

- 

0 1 .o 0 

- 

1 .o 

WC WC WC 

semi span = 0.500 
Numerical Simulations of Deep Global Convection in Jupiter 

Gary A. Glatzmaier, Principal Investigator 

Los Alamos National Laboratory 

Research Objective 

The overall objective is to provide a detailed, self-consistent 

physical explanation for the maintenance of the banded zonal 

wind pattern observed on Jupiter by the Voyager spacecraft. 

A successful numerical simulation would also provide predictive descriptions of the three-dimensional velocity, magnetic 

field, and thermodynamic structures and time dependencies 

throughout the entire interior of Jupiter. 

Approach 

A computer code solves an equation of state, a mass conservation equation, a momentum equation, a heat equation, a 

magnetic-flux conservation equation, and a magnetic induction equation to simulate time-dependent, three-dimensional, 

compressible convection and magnetic field generation in a 

stratified, rotating, spherical fluid shell. The anelastic approximation is used to filter out sound waves. The horizontal structures of the velocity, thermodynamic, and magrietic fields are 

represented by spherical harmonic expansions, and the radial 

structures by Chebyshev polynomial expansions. A spectral 

transform method computes, at every time step, all spatial 

derivatives analytically in spectral space and all nonlinear 

terms in grid space. Over one million grid points are used in 

the three-dimensional spherical shell. The time integration 

treats the linear terms implicitly and the nonlinear terms 

explicitly. 

Accomplishment Description 

The original model generated a banded zonal velocity field 

that, except in the equatorial region, was in fair agreement 

with the Voyager observations (see figure in "NAS Technical 

Summaries" Mar. 1988-Feb. 1989). The failure of the model to 

generate the observed equatorial jet was apparently due to 

the large eddy viscosity required by the model. A new version 

of the model that uses a different numerical method is now 

being tested. The accompanying figure shows a snapshot of 

temperatures and velocities in the equatorial plane for a case 

that tests some of the new algorithms. (This case does not use 

the rotation rate of Jupiter.) Reds represent warm fluid rising; 

blues represent cold fluid sinking. The arrows represent the 

direction and relative magnitude of the fluid velocity in this 

plane through the sphere. Each test requires many 4-hour, 

10-megaword runs on the Cray-2. 

Significance 

Although Jupiter's banded zonal wind pattern has been 

accurately measured, there are presently no self-consistent 

physical explanations for why it exists or how deep below the 

surface it persists. A detaileg analysis of the forces responsible for maintaining such a pattern in a successful numerical 

simulation would provide these explanations. 

Future Plans 

Improvements will continue to be made in the model. When 

the simulation of Jupiter is satisfactory, the other giant planets 

will be simulated. 

Publications 

Glatzmaier, Gary A. "3D Global Numerical Simulations of Convection and Magnetic Field Generation in Jupiter." Bull. 

American Astronomical Soc. 21 (1 989): 752. 

Simulation of temperatures and velocities In the equator~al plane of Jupiter 

50 

CR:GIF:!i!- PAGE 

COLO3 PH3TQ1C;RAPH 
Hypersonic Flows in Chemical and Thermal Nonequilibrium 

Peter A. Gnoffo, Principal Investigator 

NASA Langley Research Center 

Research Objective 

To make possible the simulation of hypersonic flow fields in 

chemical and thermal nonequilibrium over realistic geometries, 

with particular emphasis on Aeroassisted Orbital Transfer 

Vehicle and Mars-return applications. 

Approach 

The three-dimensional Navier-Stokes equations, 1 1 species 

continuity equations, a total energy equation, and a vibrational 

energy equation are solved in a fully coupled, point implicit, 

symmetric-total-variation-diminishing algorithm. 

Accomplishment Description 

Aeroassist Flight Experiment (AFE) trajectory points at three 

altitudes and two or three angles of attack per point were 

computed and used to define aerodynamic coefficients of the 

complete configuration. Generally good comparisons were 

obtained with several ground-based and in-flight experiments, 

including Project FIRE (heat transfer), RAM-C (electron 

number density), shock tunnel (interferogram), ballistic range 

(shock shape), and Mach 10 wind tunnel (pressure and heat 

transfer). The first four tests made possible a limited evaluation 

of the nonequilibrium physics modeled in the code. The last 

test provided initial confirmation of the ability of the code to 

predict shear-layer impingement heating on the payload 

behind an aerobrake. Impingement-heating studies on the 

AFE carrier are ongoing, with emphasis placed on the worstcase scenario at a -5" angle of attack (see accompanying 

figure). Finite-catalytic-wall boundary conditions were added 

to the code. Preliminary studies were completed that used 

reduced chemical kinetic models, as defined by the computational singular perturbation (CSP) method for the AFE shock 

layer, to enhance code efficiency in the presence of complex 

chemical kinetic models. A preliminary evaluation of the code 

for higher velocity entries characteristic of return from Mars 

was prepared. 

Significance 

The present algorithm, coupled with improved physical 

models, will be used to benchmark design future Aeroassisted 

Orbital Transfer Vehicles, lunar- and Mars-return aerobrakes, 

and aerospace planes. It is now being used in the design of 

the AFE vehicle, scheduled for flight in 1994. 

Future Plans 

The code will be restructured to permit more efficient use of 

parallel processing and to facilitate the implementation of the 

CSP procedure. The matrix of cases for the AFE flight project 

will be updated to include the effects of finite-rate wall catalysis, with emphasis on heating predictions on the forebody and 

impingement points on the carrier. Parameter studies of kinetic 

models and their effects on uncoupled, nonequilibrium radiation and electron number density will be conducted in support 

of AFE flight experiments. 

Publications 

1. Gnoffo, Peter A. "Upwind-Biased, Point-Implicit Relaxation 

Strategies for Viscous, Hypersonics Flows." AlAA Paper 89- 

1972-CP, 1989. 

2. Gnoffo, Peter A. "An Upwind-Biased, Point-Implicit 

Relaxation Algorithm for Viscous, Compressible Perfect-Gas 

Flows." NASA TP-2953, Feb. 1990. 

3. Gnoffo, Peter A. "A Code Calibration Program in Support 

of the Aeroassist Flight Experiment." J. Spacecraft and 

Rockets 27, no. 2 (Mar.-Apr. 1990). 

AFE surface heating;,\/, = 9.3 kmls, h = 75 km, a = -5". 
Flow-Field Simulation Around Different Rotor Planforms 

Robert A. Golub, Principal Investigator 

Co-investigator: Forooz F. Badavi 

NASA Langley Research CenterILockheed Engineering and Sciences Company 

Research Objective 

To develop computational methods for the aerodynamic and 

aeroacoustic comparison of transonic flow around different 

rotor planforms. 

Approach 

The transonic flow around a helicopter rotor in forward flight is 

calculated on a body-conformed grid around a rectangular 

and a swept-back rotor planform by coupling a recently 

developed three-dimensional Navier-Stokes solver with the 

wake analysis code CAMRAD. The Navier-Stokes solver is 

developed using an implicit, upwind-biased, finite-volume 

scheme that uses the Van Leer flux vector splitting and BeamWarming approximate factorization techniques. 

Accomplishment Description 

Detailed profiles were obtained of surface pressure as a 

function of azimuth at different chord locations, and of local 

Mach numbers at the leading edges of rotors as a function of 

radial location at different azimuths. Comparisons of these 

profiles indicate that the performance of the swept-back rotor 

is better than that of the rectangular rotor at transonic tip Mach 

numbers. These comparisons show that the primary contribution of the swept-back rotor is the delay of shock-induced 

separation. The figures on the left compare the surface pressures of two rotors, and the figures on the right compare the 

leading-edge local Mach numbers. 

Significance 

With the current push toward high-speed-rotorcraft research, 

the present algorithm, with its demonstrated capability, 

supplies a method for studying either the global or detailed 

boundary-layer features of different rotor planforms at 

transonic tip Mach numbers. 

Future Plans 

The future plans for the present algorithm are to make the grid 

topology more efficient, to extend the spatial accuracy of the 

scheme to higher order to resolve the attenuation of propagating acoustics waves in the far field, and to implement a more 

accurate turbulence model. 

- Rectangular 

---- Sweptback 

Correlation of numerical results for nonlifting rotors in forward flight; M, = 0.630, p = 0.39. (Left) Surface pressure. (Right) Leadingedge local Mach number. 
A Supersonic Computational Fluid Dynamic Analysis of a Generic Fighter 

Aga M. Goodsell, Principal Investigator 

NASA Ames Research Center 

Research Objective 

To evaluate the solutions, obtained from an Euler code, of 

supersonic flow fields about a generic fighter, in order to 

determine their validity over a wide range of angles of attack. 

Approach 

The Euler computations are performed using FL057, a three- 

'dimensional finite-volume code, originally written by Antony 

Jameson and modified by several users in order to accommodate an 0-H grid topology. Computed surface-pressure distributions, forces, and moments are compared to experimental 

data. 

Accomplishment Description 

The FL057 solutions were obtained at Mach numbers of 1.2, 

1.4, and 1.6 for angles of attack between 4" and 20". Two 

configurations were studied, a winglbody and a winglbodyl 

chine. The FL057 code predicted pressure distributions, 

forces, and moments well at low angles of attack, at which the 

flow was fully attached. The agreement between Euler and 

experimental results were not as good when the vortex was 

just beginning to form, but the agreement improved when the 

vortex was well established. The addition of the chine did not 

create a marked change in the pressure distributions on the 

wing. The main effect of the chine was to push the leadingedge vortex outboard. 

Significance 

The validity of flow solutions about complex configurations is 

critical to the successful computational analysis of current and 

future aircraft geometries. The only method of determining the 

validity is to compute and analyze numerous solutions over a 

broad range of conditions and compare them with experimental results. 

Future Plans 

Navier-Stokes computations using LANS3D will be obtained. 

First the winglbody configuration will be analyzed; then the 

computations will include the winglbodylchine. 

Publications 

1. Goodsell, Aga M.; Madson, Michael D.; and Melton, 

John E. "TranAir and Euler Computations of a Generic Fighter 

Including Comparisons with Experimental Data." AlAA 

Paper 89-0263, Jan. 1989. 

2. "Visualization of Vortex Flows about Chine-Delta Configurations." Video, Feb. 1989. 

3. Goodsell, Aga M.; Melton, John E.; and Madson, 

Michael D. "A Transonic/Supersonic CFD Analysis of a 

Generic Fighter." Presented at the 17th ICAS Congress 6.4.2., 

Sept. 1990. 

Normalized stagnation pressure. 
Simulation of Compressible, Spatially Evolving, Reactive Planar Shear Flows 

Fernando F. Grinstein, Principal Investigator 

Naval Research Laboratory 

Research Objective 

To understand the dynamics and topology of the large-scale 

coherent structures controlling the development of the mixing 

layers in transitional, reactive, free shear flows. 

tion. This particular 3000-step simulation of the plane wake 

was performed on the Cray Y-MP on a 170 x 120 x 60 grid, 

using 8 megawords of storage and about 20 (single processor) CPU hours. 

Significance 

The simulations provide insight into the physics of large-scale 

coherent structures in planar shear flows and the mechanisms' 

affecting the growth of mixing layers and the transition to turbulence. The effort advances the state of the art of transitional 

shear flow simulations, which may also be useful in developing 

the technology base for the National Aero-Space Plane. 

Future Plans 

Three-dimensional effects of compressibility and energy 

release will be investigated in simulations that have improved 

modeling of the chemistry and diffusive transport. 

Publications 

1. Grinstein, F. F.; Oran, k. S.; and Boris, J. P. "Reinitiation 

and Feedback in Global Instabilities of Subsonic Spatially 

Developing Mixing Layers." Phys. Rev. Lett. 64 (1990): 870. 

2. Grinstein, F. F.; Hussain, F.; and Oran, E. S. "A Numerical 

Study of Mixing Control in Spatially Evolving Shear Flows." 

AlAA Paper 89-0977, 1989. 

3. Grinstein, F. F.; Boris, J. P.; Griffin, 0. M.; Hussain, F.; and 

Oran, E. S. "Coherent Structure Dynamics in Spatially Evolving 

Near Wake Flows." AlAA Paper 90-057, 1990. 

Approach 

The approach is to solve numerically the three-dimensional, 

time-dependent, compressible-flow equations on structured 

grids using a fourth-order, phase-accurate flux-corrected 

transport (FCT) algorithm with directional time-step-splitting 

techniques, and appropriate inflow and outflow boundary 

conditions. No subgrid modeling other than that provided by 

the FCT high-frequency filter is included in the numerical 

model. Reactive flows are modeled using fast, one-step, 

irreversible chemical reactions. 

Accomplishment Description 

(1) The existence of global, self-sustaining instabilities in compressible (subsonic) mixing layers was demonstrated. (2) The 

effects of spanwise excitation, chemical reaction, and energy 

release on the development of free mixing layers were studied. 

(3) The three-dimensional coherent structures in the nonreactive plane jet and plane wake were investigated. The figure 

includes a typical instantaneous flow visualization from a 

numerical simulation of a nonreactive three-dimensional plane 

wake, showing the formation of unconnected, closed vortex 

loops in the high-strain saddle regions between rollers of 

opposite sign, in response to cross-stream spanwise excita1 THREE-DIMENSIONALITY 

IN BLUFF-BODY WAKE 

U=2 x lo2 nzls 

170 x 120 x 60 grid points 

solid : k streamwise vorticity 

wire : k spanwise vorticity I 

Three-dimensionality in bluff-body wake; U = 2 x lo2 mls, grid size 170 x 120 x 60. 

54 
Three-Dimensional Atmospheric Simulation Model 

W. L. Grose, Principal Investigator 

Co-investigators: W. T. Blackshear, R. W. Turner, and R. S. Eckman 

NASA Langley Research Center 

Research Objective 

To conduct a three-dimensional simulation of the evolving 

atmospheric circulation and trace-constituent distributions 

over a multi-year cycle, in order to better understand stratospheric dynamics, transport, and photochemistry and to apply 

this knowledge in support of the Upper Atmospheric Research 

Satellite (UARS) program. 

Approach 

A three-dimensional, spectral, primitive-equation, atmospheric 

model incorporating chemistry has been developed. The 

model consists of two components: a module that calculates 

the winds and temperatures to describe the global atmospheric dynamics and a separate transport/chemistry module 

(driven by the simulated dynamics) to describe the transport 

of photochemically active trace constituents. 

Accomplishment Description 

A one-year simulation investigating aspects of the Antarctic 

ozone hole and its subsequent recovery following the breakup 

of the polar vortex was performed. Analysis of the results 

yielded information on the possible impact of the mixing of 

ozone-poor air into the midlatitudes in the southern hemisphere. In addition, a multi-year simulation to examine the 

behavior of a long-lived tracer, nitrous oxide, has been run. 

This simulation has enhanced our knowledge of aspects of 

stratospheric-tropospheric exchange processes. Analysis of a 

simulation to study the seasonal variation of the odd nitrogen 

family in the stratosphere is continuing. Typically, the model 

requires 300 CPU seconds per model day and 1.5 megawords 

of memory on the Cray Y-MP. 

Significance 

This study provides increased understanding of stratospheric 

dynamics, transport, and photochemistry, and supports the 

UARS and Earth Observing System (Eos) programs. 

Future Plans 

The transportlchemistry model is undergoing substantial revision to explicitly transport additional species, so that it will 

better represent high-latitude chemical processes. A parameterized heterogeneous chemistry scheme will be implemented 

to reflect our understanding of the importance of these processes in the stratosphere. A one-year simulation representing 

the Antarctic ozone depletion will be run to compare these 

model upgrades with our previous simulation. 

I nnn 

1000 I 1000 rn 

-00 -60 -30 0.0 30 60 90 

Latitude [deg) atit ude Idcg) 

0.D 2 4 6 8 10 12 14 18 1 I 

Miring Ratio (ppbv) 

Langley Research Center three-dimensional model; seasonal evolution of NOY. ORIGINAL PAGE 

COLOI? PHOTOGRAPH 
Simulation of FluidJStructural Interactions 

G. P. Guruswamy, Principal Investigator 

Co-investigators: S. Obayashi, N. M. Chaderjian, and P. M. Goorjian 

NASA Ames Research Center 

Research Objective 

The objective is to develop a numerical capability to couple 

EulerINavier-Stokes solutions with structural equations, for 

conducting aeroelastic analyses of complete aircraft. This 

capability is required for aircraft of national importance for 

defense, like the ATF, the F-16, and the B1 aircraft. 

Approach 

The three-dimensional EulerINavier-Stokes equations of motion 

coupled with structural equations of motion are solved by 

finite-difference schemes. 

Accomplishment Description 

A code based on the EulerINavier-Stokes equations, 

ENSAERO, is used to simulate unsteady flows over general 

wing configurations. The code uses implicit finite-difference 

methods for aerodynamic calculations based on both central 

and upwind schemes. The ability to directly couple the aerodynamic solutions from the Euler or Navier-Stokes equations 

with the structural equations for computing aeroelastic 

responses is incorporated in the code. The aeroelasticconfiguration adaptive dynamic grids with zonal capability 

are used in the analysis. This is the first time that such a 

computational capability has been developed in computational fluid dynamics using the Navier-Stokes equations. Using 

ENSAERO, vortical and transonic flows are computed over 

flexible fighter wings in unsteady motions. A typical computation of a wing in ramp motion requires about 10 hours of CPU 

time and 16 megawords of memory for a grid of size 

151 ~25x32. 

Significance 

This project demonstrates the ability of computational methods 

to simulate aeroelasticity associated with complex vortical and 

transonic flows for improving the performance of an aircraft. It * 

also serves as a major step toward developing a multidisciplinary version of ENSAERO for full-aircraft analysis. This 

development is of great national importance, particularly in 

view of the Air Force's ATF project. 

Future Plans 

Research will be continued to compute transonic and vortical 

flows over wing-body configurations and will be further 

extended to study aeroelastic responses associated with 

vortices and shock waves. In the coming years, ENSAERO 

will be developed as a multidisciplinary code to study 

fluid/structural interactions of aerospace vehicles, including 

thermal loads and controls. 

Publications 

1. Guruswamy, G. P. "Navier-Stokes Computations on 

Swept-Tapered Wings, Including Flexibility." AlAA Paper 90- 

1152-CP, Apr. 1990. 

2. Chaderjian, N. M., and Guruswamy, G. P. "Unsteady 

Transonic Navier-Stokes Computations for an Oscillating Wing 

Using Single and Multiple Zones." AlAA Paper 90-0313, Jan. 

1990. 

Navier-Stokes computations of turbulent separated flows on a flexible wing in ramp motion; AR = 4.0, TR = 0.3, leading-edge 

sweep angle = 30.0°, M, = 0.50, Re, = 2.0 x lo6, pitch rate = 0.01, a = 8.0". Contours represent velocity magnitude. Flow is 

separated near the tip, leading to buffeting. 
Vortex Dynamics in Aerodynamic Flows 

Karl E. Gustafson, Principal Investigator 

Co-investigator: Robert R. Leben 

University of Colorado, Boulder 

Research Objective 

To validate large-scale vortex-separation patterns of accelerating, plunging, and pitching laboratory flows, and conversely to 

validate the codes simulating those flows, thereby making 

possible an increased understanding of the aerodynamic 

characteristics of such flight. 

Approach 

We use a two-dimensional stream-function vorticity scheme 

Aat includes a novel grid-generation scheme in which the 

infinite physical domain is mapped to auxiliary flowcomputation domains, avoiding any truncated far-field 

boundary conditions. An orthogonal grid using a weak 

interpolation constraint is obtained by an efficient multigrid 

solver, which is used as well in the unsteady Navier-Stokes 

solver. 

Accomplishment Description 

Laboratory findings of vortex-splitting and vortex-shredding 

events in acceleration flows over airfoils were validated and, in 

most cases, reproduced exactly by our code flow simulations. 

Significant lift increase caused by such events near dynamic 

stall was exhibited. More recently we have successfully 

modeled several complex combined plunginglpitching modes 

representing hovering flight in still air. The result is a selfinduced large-thrust jet formed by matched vortical patterns 

exhibiting rotations reversed from those of a Karman street. 

The figure shows a segment of a period of such a hovering 

mode, in which laboratory visualizations indicated a vortexsevering event, seen clearly in the numerical simulation. A 

typical computation on a 65 x 65 grid required 10 megawords 

of Cray-2 memory and approximately 40 minutes of CPU time 

for four periods of a typical hovering-mode computation, 

including graphics processing. 

Significance 

Hovering-mode flight in still air, as practiced, for example, by 

dragonflies and other insects and small birds, exhibits the 

construction of dynamic stall vortices that enable the production of very high thrust. The simulation of such modes will 

make possible a considerably increased understanding of the 

unsteady aerodynamic characteristics (e.g.. lift) of such flight. 

Future Plans 

The main immediate focus will be to carefully calculate the 

aerodynamic lift to compare with the downstream thrust coefficient found in the laboratory studies. 

A vortex-severing event for an aircraft in hovering mode. 

ORIGINAL PAGE 

COLOR PHOTOGRAPH 
Parameter Study in the Driven Cavity 

Kadosa Halasi, Principal Investigator 

Co-investigator: Karl E. Gustafson 

Kansas State UniversityIUniversity of Colorado, Boulder 

Research Objective 

To investigate the effects of parameters on two-dimensional 

incompressible flow. In particular, to determine critical parameter values at which asymptotic solutions become periodic. 

Approach 

Two-dimensional, time-dependent, incompressible NavierStokes equations expressed in the biharmonic stream-function 

form are used. The convection terms are differenced with an 

Adams-Bashford scheme, and a Crank-Nicolson method is 

applied to the diffusion terms. A multigrid solver is used to 

solve the linear implicit equation at each time step. 

Accomplishment Description 

For an aspect ratio of A = widthldepth = 2, the critical Hopt 

bifurcation value of Reynolds number (Re) was sought. Measures of periodicity were introduced, and the periodicity (or 

lack of periodicity) of the flow with respect to these measures 

was followed. The effects of grid-mesh size on periodicity was 

also investigated. It was found that (I) the critical Re satisfied 

2000 < Re < 5000; (2) the time to achieve a periodic state 

increased with decreasing mesh size, and the period, itself, 

decreased on finer meshes; and (3) there existed a period of 

intermittency, during which time the flow was caught between 

a tendency toward a steady final state on one hand, and a 

periodic final state on the other. 

Significance 

The investigation will provide a better understanding of vortei 

dynamics in the face of an impending oscillatory flow regime. 

Future Plans 

We plan to continue the parameter study in both shallow anddeep cavities, and to extend the study to three-dimensional 

settings. 

Publications 

1. Goodrich, J.; Gustafson, K.; and Halasi, K. To be published in J. Computational Physics, 1990. 

2. Halasi, K.; Gustafson, K.; and Goodrich, J. "Periodicities, 

Intermittencies, and Criticalities in Driven Cavity and General 

Flows." Presented at IMACS 1 st International Conference on 

Computational Physics, Boulder, CO, June 1990. 

Stream-function c@nge:versus total kinetic energy, 6100 < t I 7100. 
Ducted Propfan Analysis 

Edward J. Hall, Principal Investigator 

Allison Gas Turbine Division, General Motors Corporation 

Research Objective 

The ultimate objective of this research is to develop an 

advanced aerodynamic analysis tool for ducted-fan aircraft 

propulsion systems. This analysis will provide a detailed 

description of the flow through the fan and the external flow 

about the fan cowl and nacelle. Special attention is given to 

he accurate prediction of the flow near the fan-cowl leading 

edge. 

Approach 

A three-dimensional, time-marching, finite-volume Euler analysis is applied to predict the steady flow about ducted propfan 

geometries. The Euler analysis is based on a multiple-gridblock solution scheme that uses a cylindrical coordinate 

system that rotates with the fan. The multiple-grid-block solution technique permits a number of convenient grid arrangements, to enhance the accuracy of the calculated results. 

Accomplishment Description 

An explicit Runge-Kutta Euler code was modified to utilize a 

multiple grid-block strategy for the prediction of high-speed 

ducted-fan flows. Calculations were performed on both an 

H-type grid system incorporating a branch-cut-opening representation for the cowl, and a multiple-block structured grid 

using a C-type mesh about the cowl leading edge. The 

multiple grid blocks were numerically coupled through the 

mutual specification of boundary conditions along the interface between adjacent blocks. The H-grid analysis was 

extended to permit the prediction of counter-rotating flows 

through the use of the average-passage solution technique. 

Both single-rotation and counter-rotation calculations were 

performed. Predicted results were compared with numerical 

and experimental data for several ducted-fan geometries. A 

typical solution required 1 CPU hour and 2 megawords of 

memory. 

Significance 

The principal benefit realized by the very high bypass ratio 

(VHBPR) turbofan engine is a substantial improvement in 

propulsive efficiency over current high-bypass-ratio engines. 

However, VHBPR engines impose stringent demands on the 

aerodynamic and structural integration of large, variable-pitch 

airfoils in minimum-length, low-drag cowls. This program is the 

initial step in developing a complete aerodynamic model of 

the flow field through a ducted fan and the external flow over 

the engine nacelle and fan cowl. 

Future Plans 

The multiple-block Euler analysis will be modified to include a 

Navier-Stokes solution capability. Following the incorporation 

of time-accurate boundary conditions, the time-marching 

scheme will be applied to predict the unsteady flow resulting 

from ducted propfans operating at angle of attack. 

Publications 

1. Hall, Edward J.; Delaney, Robert A.; and Bettner, 

James L. "Investigation of Advanced Counterrotation Blade 

Configuration Concepts for High Speed Turboprop Systems: 

Task 1 - Ducted Propfan Analysis." NASA CR-185217, Apr. 

1990. 

2. Hall, Edward J.; and Delaney, Robert A. "3D Euler Analysis of Ducted Propfan Flowfields." Presented at the AlAA 

Applied Aerodynamics Conference, Portland, OR, Aug. 1990. 

Predicted static pressure ratio for an Allison ducted propfan; M = 0.75. 
Evaluation of the CAP-TSD Computer Code Using an F-16 Study Case 

Richard L. Haller, Principal Investigator 

Co-investigators: Kevin Penning and Lam-son Vinh 

General Dynamics, Fort Worth Division 

Research Objective 

To determine if the computer code CAP-TSD can predict limit 

cycle oscillations for an F-16. 

Approach 

The unsteady aerodynamics code CAP-TSD will be used to 

model the F-16 aircraft. The CAP-TSD results will be compared 

with available test data. The CAP-TSD code will then be used 

to analyze a store loading that experiences limit cycle 

oscillations. 

Accomplishment Description 

Steady-state CAP-TSD results have been Cbmpated with wind 

tunnel test data for Mach numbers 0.85, 0.95, and 1.2 at 

angles of attack of 2" and 4". The comparisons were good and 

the work is continuing into unsteady aerodynamics. Oscillatory 

pressures are not available for the F-16 so comparisons will be 

made between the predicted and measured flutter speeds. 

Because of our lack of experience with the CAP-TSD code and 

the long turnaround time on the NAS computers, only 10 hours 

of Cray-2 time and 32 megawords of memory were used. 

Significance 

The CAP-TSD code is presently the only computer code avail-' 

able to industry to analyze the unsteady aerodynamics of 

three-dimensional aircraft in transonic flight. It represents a 

large step forward from the doublet-lattice and kernel-function, 

codes that are in use today. In order to bring this code into 

use in industry, CAP-TSD must be evaluated and guidelines 

for its use developed. 

Future Plans 

The CAP-TSD code will be used to analyze a store loading that 

experiences limit cycle oscillation. 

The CAP-TSD upper surface pressure coefficients and deflection for an F-16 aircraft at M = 0.8 and a = 2". (Deflections magnified 

by a factor of 10.) 

I L 
Supersonic LaminarcFlow-Control Computational Fluid Dynamics 

Julius E. Harris, Principal Investigator 

Co-investigators: Venkit lyer and Robert E. Spall 

NASA Langley Research Center 

Research Objective 

To develop numerics and related software for threedimensional transition prediction (TP) and laminar flow control 

(LFC) for high-speed aircraft. 

Approach 

Two three-dimensional compressible boundary layer (3DBL) 

codes have been developed and are being verified. The 

general TPLFC software package includes (1) the 3DBL packages, (2) two Euler solvers (ES), (3) grid generations for the 

3DBL and ES packages, and (4) an interfaceloutput package 

for the existing stabilityltransition routines (COSAL, EMALIK). 

Three-dimensional Navier-Stokes solutions are also required in 

order to verify the TPRFC software and determine problems 

associated with non-boundary layer equation regions (wingbody, for example). Current emphasis is being placed on 

obtaining Euler and Navier-Stokes solutions for the F16xL configuration. The pressure field from the Euler solutions will be 

used as input for the 3DBL software. The output from the 

Navier-Stokes solution will be used in the validation of the 

Euler plus 3DBL solutions. Mach number contours using the 

CFL3DE Euler solver contours for the upper surface of the 

F16xL wing at an angle of attack of 4" for a free-stream Mach 

number of 2 is presented in the figure. Typical system 

requirements per converged case are as follows: 3DBL 

(0.5 megawords of memory, 10 minutes CPU time), Euler 

(8 megawords of memory per block, 6 blocks, 4 hours CPU 

time), Navier-Stokes (16 megawords of memory per block, 

6 blocks, 40 hours CPU time). 

Significance 

This work has a direct impact on high-speed LFC and transition prediction and control. 

Publications 

1. lyer, V., and Harris, J. E. "Fourth-Order Accurate ThreeDimensional Compressible Boundary-Layer Calculations." J. 

Aircraft 27, no. 3 (Mar. 1990): 253-261. 

2. Wie, Yong-Sun, and Harris, J. E. "Numerical Solution of 

the Boundary-Layer Equations for a General Aviation Fuselage." AlAA Paper 90-0305, 1990. 

3, lyer, Venkit. 'Computation of Three-Dimensional Compressible Boundary Layers to Fourth-Order Accuracy on 

Wings and Fuselages." NASA CR-4269,1990. 

CUNIUUH LFUtI S 

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1.80000 

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1.90Oflfl 

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. 

Mach number contours for the Fl6xL wing upper surface, from the CFL3DE Euler solver; M = 2.0, a = 4". 
General, Fast, Accurate Floating Shock 

Unadapted Meshes 

Peter M. Hartwich, Principal Investigator 

ViGYAN, Inc.1NASA Langley Research Center 

Research Objective 

To develop an accurate and efficient method for computing 

shocked flows on relatively crude, unadapted meshes. 

Approach 

A time-implicit upwind Euler solver is constructed. Code 

development is expedited by relying as much as possible on 

proven numerical techniques and by initially focusing on twodimensional flows. For computational speed, the upwinding is 

based on the nonconservative split-coefficient-matrix method, 

and for accuracy across shocks, floating shock fitting is 

implemented. 

Accomplishment Description 

Results have been obtained for Riemann's problem, for a 

regular shock reflection at an inviscid wall, for supersonic 

flow past a cylinder, and for a transonic airfoil. In all these 

cases, the computed shocks are in good to excellent agreement with reference solutions. This is exemplified by the 

results shown in the accompanying figure for supercritical flow 

(M, = 0.8) over a NACA 0012 airfoil at zero incidence. These 

solutions were computed on a coarse and a standard C-type 

mesh. The standard mesh with 161 x 33 grid points is closely 

patterned after that used by Pulliam et al. (AIAA Paper 83- 

0344) for subcritical flow; the coarser grid is obtained by 

dropping every other grid point in each coordinate direction. 

For the chosen parameters, shocks develop at x/c = 0.5, which 

coincides with the coarsest chordwise resolution of the 

"subcritical" grids. The spatial step size Axlc in the neighborhood of the fitted shocks is about twice (161 x 33 grid) and 

four times (81 x 17 grid) as large as in the reference solution, 

which was computed on an adapted 161 x 33 grid with sixteen 

radial lines clustered along the shock fronts with a regular 

spacing of Mc = 0.01. Even with that handicap, the surface 

pressure distributions and the shock locations as predicted by 

the present method on both grids agree well with the accurate 

shock-capturing results on the adapted grid. (Note that 

despite their crisp appearance, the captured shocks are still 

resolved over four mesh intervals.) The surface entropy distriFitting Procedure for ~ 

butions provide another means of demonstrating the accuracy 

of the present results: (I) entropy is only gen-erated across the 

shocks, (2) away from the shocks entropy is merely convected 

and thus it remains at a constant level, and (3) the fitted 

shocks are completely devoid of any spurious oscillations. = Starting from free-stream conditions, it took about 500 to 

600 iterations to reduce the L2-norm of all residuals by at least 

four orders of magnitude and to establish asymptotic values 

for the drag, which differ by just four counts for the two cases., 

Computing these results on a single processor of the NAS 

Cray Y-MP required about 6.5 pseclnodeliteration, which 

translates to total run times of 4.5 sec-onds for the 81 x 17 grid 

and roughly 18 seconds for the 161 x 33 grid. 

Significance 

The present general shock-fitting procedure for solving the 

two-dimensional Euler equations at least matches, if not surpasses, the computational efficiency of shockcapturing 

schemes. Even more importantly, it produces highly accurate 

solutions for shocked flows which exhibit very little grid sensitivity. This brings down costs in two ways: savings in the total 

number of grid points required for a proper resolution of the 

flow translate to immediate shorter computing times, and 

reducing the need to generate adapted meshes improves 

turnaround time. 

Future Plans 

The present floating shock fitting technique is currently being 

extended to three dimensions. Further extensions will encompass the addition of viscous terms, a turbulence model, and a 

capability to handle overset grids. 

Publications 

1. Hartwich, P. M. "Fresh Look at Floating Shock Fitting." 

AlAA Paper 90-108, Jan. 1990. 

2. Hartwich, P. M. "Split Coefficient Matrix (SCM) Method 

with Floating Shock Fitting for Transonic Airfoils." Presented at 

the 12th International Conference on Numerical Methods in 

Fluid Dynamics, Oxford, UK, July 1990. 

GENERAL FAST. ACCURATE FLOATING SHOCK ITfllM PROCEDURE FOR UNADAPTED GRIDS 

I -. -- Exam~le ~o~.m: NACA 0012 airfoil. Y, . 0.a a. o0 I 

Ld Uma s1.ppinp. CFL = 10 

OM 

OrSupercritical flow over a NACA 0012 airfoil; M = 0.8, a = 0". (Top) Surface pressure distributions. 

(Bottom left) Surface entropy distribution. (Bottom right) Convergence summary. 
Navier-Stokes Solutions for Vortical Flows over a Forebody 

Peter M. Hartwich, Principal Investigator 

ViGYAN, Inc./NASA Langley Research Center 

Research Objective 

The research objective is the computational assessment of the 

effects of Reynolds number and angle of attack on vortical 

flows over a pointed slender body. 

Approach 

Steady-state solutions for vortical flows with 0.2 x 106s ReD s 

3.0 x lo6 and 20" I a s 40" over a 3.5-caliber tangent-ogive 

cylinder are computed with FMCI, a time-implicit upwind 

method for the three-dimensional, incompressible NavierStokes equations. This solver comprises flux-difference 

splitting, a TVD-like discretization of the inviscid fluxes, and 

several extensions of the algebraic turbulence model by 

Baldwin and Lomax to handle flows with massive crossflow 

separation. 

Accomplishment Description 

A rational extension of the Baldwin-Lomax turbulence model 

has been devised. That extension allows computational 

modeling of transitional crossflow separation (i.e., flows with 

three-dimensional, laminar, equatorial separation bubbles and 

subsequent transition in the separating shear layers which roll 

up into two primary vortices). In addition, it proves to be 

relatively insensitive to the choice of adjustable parameters in 

simulations of fully turbulent crossflow separations. For a 2 30" 

and ReD = 0.8 x 106, a perturbation of the geometry into a 

slightly elliptic cross section just at the nose tip eliminates 

multiple steady-state solutions with asymmetric vortex patterns 

along the forebody. A typical solution is shown in the accompanying figure, in which the major axis of an "elliptic" nose tip 

is rolled by 45" in the counterclockwise direction (pilot's view) 

out of its horizontal position. Four shedding events are shown 

by means of helicity density contours (helicity density is 

defined as the scalar product of local velocity and vorticity 

vectors). An almost perfect mirror image is produced when the 

nose tip is rolled for another 90". This supports earlier conjectures that slight imperfections in the vicinity of the apex of 

slender bodies with sharp noses control the asymmetric 

pattern along the entire body. Reynolds number effects for 

a I 30" are found to diminish for ReD 2 1.0 x lo6. All computational results compare well with experimental surface pressures and flow visualizations. Typical calculations of symmetric forebody flow are carried out on grids of about 

190,000 grid points, and they require about 1.5 Cray-2 hours 

(single processor mode). A fully converged result for asymmetric vortical flow on a standard grid of about 380,000 grid 

points is obtained after about 2500 time steps, which translates to roughly 10 Cray Y-MP hours (single processor mode). 

Significance 

Knowledge about transition and other driving mechanisms 

controlling vortex asymmetries will assist in the design of 

improved missiles and fighter aircraft forebodes. 

Future Plans 

A Navier-Stokes analysis of an FIA-18 or an F-16 forebody with 

a modified nose tip will exploit the methodology and the 

insights into the physics of vortical forebody flows. 

Publications 

1. Hartwich, P. M.; Hall, R. M.; and Hemsch, M. J. "NavierStokes Computations of Vortex Asymmetries Controlled by 

Small Surface Imperfections." AlAA Paper 90-0385, Jan. 1990. 

2. Hartwich, P. M., and Hall, R. M. "Navier-Stokes Solutions 

for Vortical Flows Over a Tangent-Ogive Cylinder." AlAA J. 28 

(July 1990). 

Helicity density contours; a = 40°, ReD = 0.8 x lo6. 
Monte Carlo Simulation of Hypersonic Flows 

H. A. Hassan, Principal Investigator 

Co-investigators: David P. Olynick and Jeff C. Taylor 

North Carolina State University 

Research Objective 

The objective of this work is to calculate nonequilibrium 

radiation for reentry vehicles. The heat load resulting from 

such radiation becomes important for reentry velocities in 

excess of 10 kmlsec. 

Approach 

Solutions of the Navier-Stokes equations for reentry flows 

break down when the local Knudsen number is 0.2 or higher. 

Moreover, when thermal nonequilibrium is important, the 

functional dependence of reaction rate on the various temperatures is not known, thus rendering Navier-Stokes solutions 

useless. As a result, an approach based on the direct simulation Monte Carlo (DSMC) method is used. 

Accomplishment Description 

All DSMC methods depend to a large extent on the physical 

model used. Traditional DSMC computations have a number 

of limitations, Internal energy partition relies on a phenomenological model, and probabilities that determine energy partition 

are assumed constant. Moreover, available dissociation rates 

seem to overpredict dissociation at high temperatures. Finally, 

when ionization is important, a consistent treatment of ambipolar diffusion is needed. All of these issues have to be 

resolved before nonequilibrium radiation can be cothe actual 

distribution for various times.a heating environment from 4,000 

to 8,000 K was undertaken. The accompanying figure shows 

that during the vibrational relaxation of rotationless N2 from 

4,000 to 8,000 K, all levels remain in equilibrium at the 

average vibrational temperature. Because of this, the bottleneck observed in continuum cal-culations is not observed 

here. A typical job requires 4 megawords of memory and 40 - 

CPU hours of run time. 

Significance 

Proposed missions to Mars and return require calculation of 

nonequilibrium flows that may not be modeled correctly by the 

Navier-Stokes equations. Therefore, it is important that an 

alternative simulation procedure be developed and perfected. 

Future Plans 

We plan to continue improving the physical models used in the 

DSMC. Moreover, there is always a need to speed up the 

simulation. 

Publications 

I. Olynick, David P.; Moss, James N.; and Hassan, H. A. 

"Influence of Afterbodies on AOTV Flows." AlAA Paper 89- 

031 1, Jan. 1989. 

2. Taylor, J. C.; Moss, J. N.; and Hassan, H. A. "Study of 

Hypersonic Flow Past Sharp Cones." AlAA Paper 89-1713, 

June 1989. 

Comparison of the equilibrium vibrational population distribution at the average vibrational temperature with 

ihe actual distribution for various times. 
Turbulence Modeling of Separated Flows 

H. A. Hassan, Principal Investigator 

Co-investigators: Robert A. Mitcheltree and Richard L. Gaffney, Jr. 

North Carolina State University 

Research Objective 

To develop turbulence models capable of predicting attached 

and separated flows for a wide range of Mach numbers. 

Approach 

Ye are developing a Navier-Stokes code that incorporates a 

turbulent stress model. The development is being carried out 

using airfoil data at various Mach numbers and angles of 

attack. The current model uses field equations for the shear 

stress and the turbulent kinetic-energy equation, and algebraic expressions for the normal stresses and the turbulent 

energy-dissipation rate. 

Accomplishment Description 

An explicit upwind code with multigrid, based on Roe's 

method, was developed. The time stepping was based on a 

four-step Runge-Kutta method. The constants in the turbulent 

model were fine-tuned for a flat plate and are being used for 

flow past airfoils. Earlier work used a one-equation eddy viscosity model and a separation model that incorporated observations made by Simpson. Unfortunately, it was not able to 

match the success of the Johnson-King model. More recently, 

a new stress was incorporated. The model is still under development. The figure shows the prediction of the stress model, 

and other models, of the pressure distribution for case 9 of the 

RAE 2822 airfoil. A job size is about 4 mega-words and 

requires 2 CPU hours to converge. 

Significance 

Designing high-performance, high-angle-of-attack aircraft 

requires the understanding of turbulent separated flows. Without such understanding, it is not possible to determine with 

confidence the aircraft's performance and characteristics. 

Future Plans 

Some of the assumptions made regarding the normal stresses 

and the rate of energy dissipation will be relaxed. An equation 

for the inverse of the turbulent time scale will be implemented 

in place of an equation for energy dissipation, because it 

appears to be more appropriate. 

Publications 

1. Mitcheltree, R. A.; Salas, M. D.; and Hassan, H. A. "A One 

Equation Turbulence Model for Transonic Airfoil Flows." AlAA 

Paper 89-0557, Jan. 1989. 

2. Gaffney, R. L., Jr.; Salas, M. D.; and Hassan, H. A. "An 

Abbreviated Reynolds Stress Turbulence Model for Airfoil 

Flows." AlAA Paper 90-1468, June 1990. 

- Present method 

Pressure distribution predictions for case 9 of theRAE 2822 airfoil. 
Turbulent Supersonic Mixing Layers 

H. A. Hassan, Principal Investigator 

Co-investigators: Dean R. Eklund, Steven H. Frankel, and Erick J. S. Gantt 

North Carolina State University 

Research Objective 

The ultimate goal of this work is to develop the computational 

capability to predict turbulent supersonic combustion in 

scramjets. The early phase of this work is restricted to mixing 

layers that simulate parallel injection of hydrogen fuel into a 

scramjet combustor. 

Approach 

An axisymmetric Reynolds-averaged Navier-Stokes code with 

nonequilibrium chemistry was developed and used to predict 

the flow field in a coaxial jet. Early work treated the source 

terms in the species conservation equations as laminar-like; 

more recent work used an assumed probability density 

function to calculate the averages of the source terms. The 

results were used to predict the results of two experiments 

involving supersonic mixing layers. 

Accomplishment Description 

Early work used an algebraic turbulence model to model 

coaxial mixing layers in the absence of combustion. The constants in the turbulence model were fine-tuned using experiments, carried out by Eggers, involving coaxial hydrogen-air 

jets. Next, two experiments involving combustion, one by 

Beach and the other by Jarrett et al., were modeled. It became 

clear that the constants developed for cold flows were not 

1.500 - - - - . - - wlout PDP -. -.- I - 

W/ Gausian PDF 

0.900 wl Bcla PDF 

suited for modeling flows with combustion. This confirms the 

importance of the coupling of mixing and combustion. The 

source terms in the calculations were evaluated at the mean 

flow properties and, as such, were treated as laminar-like. 

More recent work used two assumed probability density 

functions; one was Gaussian and the other was a beta func- ' 

tion. The figure compares some of the results with the measurements of Jarrett. A job size is about 4 mega-words and 

requires 2 CPU hours to converge. 

Significance 

The success of the National Aero-Space Plane and similar 

vehicles will depend on the availability of an efficient scramjet 

engine. Because of the lack of suitable test facilities, the 

development of the engine will have to rely on adequate 

physical and computer models. 

Publications 

1. Eklund, D. R.; Drummond, J. P.; and Hassan, H. A. 

"Numerical Modeling of Turbulent Supersonic Reacting 

Coaxial Jets." AlAA Paper 89-0660, Jan. 1989. 

2. Frankel, S. H.; Drummond, J. P.; and Hassan, H. A. "A 

Hybrid Reynolds AveragedIPDF Closure Model for Supersonic 

Turbulent Combustion." AlAA Paper 90-1593, June 1990. 

----..- w/om PDF -. 

. 

The flow field in a coaxial jet; the results of computations with and without an assumed probability density function (PDF) are 

coypared with experimental results. . t 

. . 66 

1.500- 

0.900- 

Y(N) 

0.300- 

-0.300- 

-0.900- 

- 1.500 

0 400 800 1200 1600 2000 0 400 800 1200 1600 2000 

T T 

1.500- 

------- w/ourPDF - - - - - - - w/out PDF 

- . - . - w/ Gaussian PDF -. -.- - wlBetnPDF - wIBctaPDF 

0.300 

-0.300 - 

-0.900- 

X = 2IN 

-1.500 

X = 41N 
Multiblock Solutions of the Navier-Stokes Equations 

Henry J. Haussling, Principal Investigator 

Co-investigators: Joseph J. Gorski and Roderick M. Coleman 

David Taylor Research Center 

Research Objective 

To apply and validate numerical methods for a multiblock 

solution of the Reynolds-averaged Navier-Stokes equations for 

turbulent flows about naval vehicles. 

,Approach 

The multiblock capability of the DTNS3D method and 

computer code is being developed for and tested on the 

computation of flows about submerged bodies with and withnut appendages. The grid-generation capability of the computer code NUGGET is being further developed and used to 

automate the treatment of complex geometries for input into 

DTNS3D. 

Accomplishment Description 

The DTNS series of computer codes was developed at David 

Taylor Research Center for the numerical solution of the 

Reynolds-averaged Navier-Stokes equations for incompressible flow. The equations are discretized using an upwind 

differenced, total-variation-diminishing scheme for the convective terms, along with central differencing for the diffusion 

terms. Complex geometries, which are split into multiple 

blocks, are readily computed with the codes because the 

block boundary information consists only of single-line inputs 

specifying which blocks interface with each other. During the 

1989-90 operational year the NAS facility was used in the validation of the DTNS3D code through the computation of the 

flow about several appended submarine geometries developed for the DARPA SUBOFF project. In one of the more 

complex cases, a 29-block calculation was performed for a 

submarine with a sail and four stern planes. A computation 

typical of those carried out to date used about 12 megawords 

of memory and up to 10 hours of Cray-2 time for solutions 

using about 500,000 grid points. 

Significance 

The development of the DTNS codes represents a significant 

step forward in the development of a robust capability to solve 

the flow equations for a wide variety of complicated naval 

geometries. The power of the multiblock approach has been 

demonstrated on the DARPA SUBOFF bodies. Initial progress 

toward an unsteady version brings within reach a very general 

unsteady computational capability. The emphasis on the 

usability and reliability of these codes means it is now easy to 

calculate the flow over a wide variety of geometries, and the 

codes are being used by researchers in fluid dynamics who 

are not interested in code development. 

Future Plans 

Research on boundary-fitted coordinate systems will continue 

to focus on the development of improved control mechanisms 

for coordinate representation. Improved turbulence models will 

be developed and implemented. Validation of improved flow 

codes will receive high priority, with computed and experimental results being compared. Development of methods for the 

solution of the unsteady equations will continue. 

Publications 

Haussling, H. J.; Gorski, J. J.; and Coleman, R. M. "Computation of Incompressible Fluid Flow about Bodies with Appendages." Proceedings of the International Seminar on 

Supercomputing in Fluid Flow. Lowell, MA, Oct. 1989. 

I 

fz PARTICLE TRACES 

DMPAZ unu BAIL 

DAVID TAnm RESEARCH CENTER I 

Particle traces on a DARPA2 submarine with sail. 
An Analysis of the Viscous Flow through a Compact Radial Turbine by the 

Average-Passage Approach 

James D. Heidmann, Principal Investigator 

NASA Lewis Research Center 

Research Objective 

The objective of this study is to gain an understanding of the 

complex flow physics associated with the flow through a compact radial turbine. An additional objective is to extend the use 

of the average-passage code and validate its application to 

radial turbomachinery. 

Approach 

Three-dimensional Euler and Navier-Stokes codes based on 

the average-passage set of equations for turbomachinery are 

used with H-grids to calculate the rotor flow field. Bladeclearance and hub-rotation effects are modeled in the viscous 

calculation. 

Accomplishment Description 

The three-dimensional average-passage code was modified 

for use with radial turbomachinery and was used to analyze 

the flow field in an advanced compact-radial-turbine rotor. The 

computational solutions improved progressively; they included 

an Euler solution, a Navier-Stokes solution without clearance, 

and a Navier-Stokes solution with clearance. The NavierStokes solution with clearance predicts secondary vortical 

flows, which help explain experimental trends in the rotor exitflow angle, and it also best predicts the experimental distribution of loss from hub to tip at the rotor exit. The viscous 

calculation requires about 4 Cray-2 hours and 2.5 megawords 

of memory. 

Significance 

The average-passage code allows for the interpretation of 

secondary flows. It also brings a better insight into the flow . physics of turbomachinery, which is particularly complex in 

radial machines such as the compact radial turbine. This 

insight can lead to an explanation of experimental trends, 

which makes the code a powerful new analysis tool. With 

experience, the knowledge of secondary flow patterns can 

lead to improved turbomachinery designs and improved 

engine efficiencies. 

Future Plans 

The average-passage code will be applied to the compact 

radial turbine stage to determine the effects of the upstream 

stator on the rotor flow field, and the results will be compared 

with the previous rotor calculations and experimental data. 

Publications 

Heidmann, James D., and Beach, Timothy A. "An Analysis of 

the Viscous Flow Through a Compact Radial Turbine by the 

Average Passage Approach." NASA TM-102471 and ASME 

Paper 90-GT-64, June 1990. 

blade suction surface 

- - 

Relative velocity vectors near the surface of a compact-radial-turbine rotor, viscous clearance solution; grid size 109 x 33 x 33. 

68 

-- - 
Direct Simulation of Turbulent Reacting Flows 

James C. Hill, Principal Investigator 

Co-investigators: Andy D. Leonard and Dana G. Haugli 

Iowa State University 

Research Objective 

Simple chemical reactions in three-dimensional turbulent flows 

are being studied with direct simulations of the Navier-Stokes 

equations and mass conservation equations. The long-range 

objectives of the research are twofold: (I) to gain insight into 

the physical processes of turbulent mixing and chemical 

reaction, and (2) to use this insight to improve modeling methods for reacting flows. The immediate objective is to see how 

a uniform shear flow affects the structure of the reaction zones 

:ompared with the case of decaying, homogeneous 

turbulence. 

Approach 

A pseudospectral code was used to calculate the velocity 

components and species concentrations for a second-order, 

two-species reaction of non-premixed species in incompressible, homogeneous turbulence. Either decaying, homogeneous turbulence was used or uniform mean shear with a 

deforming metric was used. 

Accomplishment Description 

For the non-premixed reaction, regions of highest reaction rate 

occur where the compressive strain rate is greatest in both 

decaying, homogeneous turbulence and uniformly sheared 

turbulence. The eigenvectors for the compressive strain rate 

are perpendicular to the reaction zone in both cases (as 

shown in figure (a) for the sheared case). Since the peak strain 

rates occur in the tails of the strain-rate probability density 

function (PDF), it appears that rare events make a significant 

contribution to the overall reaction rate. The PDF of the alignment of the concentration gradient vector with principal strain 

rates shows that for both flows the reaction-zone alignment is 

determined by the compressive strain rate, but in the shearflow case the PDF for the most extensional strain rate is flat. 

In the shear case, regions of highest reaction rate also tend to 

lie in axially strained vortices (as shown with the horseshoe 

vortex in figures (b) and (c)), contrary to the secondary role of 

vorticity in the isotropic case. Each 643 run with eight scalars 

requires about 8 megawords of memory and 3 hours of CPU 

time on the Cray-2. Shear-flow runs of size 128 x 128 x 64 

with three scalars require 16 megawords of memory and 

30 seconds per time step (8 to 10 hours per run). 

Significance 

This work has shown that rare fluid mechanics events make 

important contributions to reaction rates, and that yortices (or 

"bra~ds" in mixing layers) are the sites of high reaction rates in 

shear flows. Consequently, theories involving turbulence 

intermittency may be important for modeling reactions in 

homogeneous turbulence, and mechanistic models involving 

axially strained vortices may suffice for reactions in shear 

turbulence. 

Future Plans 

The mixing study is being continued with the development of 

forcing algorithms to decouple the time scales for reaction 

from the time scales for the decay of the turbulence. More 

extensive shear-flow calculations are also under way. In addition, new code is being developed that will enable the simulations to accommodate h~gher strain rates and reaction rates. 

Turbulence." Paper #I 1 h, American Institute of Chemical 

Engineers 1989 Annual Meeting, San Francisco, Nov. 1989. 

3. Leonard, Andy D., and Hill, James C. "Numerical Studies 

of Scalar Dissipation and Mixing in Turbulent Reacting Flows." 

Presented at the IUTAM Symposium on Fluid Mechanics of 

Stirring and Mixing. La Jolla. CA, Aug. 1990. 

4. Leonard, Andy D., and Hill, James C. "Kinematics of the 

Reaction Zone in Homogeneous Turbulence." Presented at the 

Twelfth Symposium on Turbulence, Rolla, MO, Sept. 1990. 

Publications 

1. Leonard, Andy D., and Hill, James C. "Turbulent Struc- rn 

tures and Local ~eaction Rates in Homogeneous Turbulent 

Flow." Presented at Turbulence 89: International Conference 

on Organized Structures and Turbulence in Fluid Mechanics, 

Grenoble. France, Sept. 1989. 

2. Leonard, Andy D., and Hill, James C. "The Influence of 

Local Kinematics on Chemical Reactions in Homogeneous 

Reaction rate contours (highest rate in red) for homogeneous 

turbulent shear flow and non-premixed reactants. (a) Cross 

section showing both reaction zones and the eigenvectors 

(white lines) of the most compressive principal strain rate. (b) 

and (c) Cross section in inclined plane (26") showing horseshoe-shaped structure, (b) without and (c) with vortex vectors 

superimposed. 
A Computational and Experimental Parametric Study of Three-Dimensional 

Side-Wall Compression Scramjet Inlets at Mach 10 

Scott D. Holland, Principal Investigator 

Co-investigator: John N. Perkins 

North Carolina State University 

Research Objective 

To demonstrate that computational fluid dynamics is useful as 

a design tool for supersonic combustion ramjet inlets in a 

hypersonic environment. 

Approach 

A preliminary computational parametric study is performed to 

eliminate from consideration inefficient designs; this leads to 

an "optimized" configuration. A wind tunnel model of the 

proposed configuration is then constructed to provide experimental verification of the design. The class of inlet chosen for 

the study was the three-dimensional side-wall compression 

inlet. Since there exists an experimental and computational 

data base (though sparse) in the supersonic regime, inlets of 

this class seemed the obvious choice for extension to the 

hypersonic parametric study. Additionally, the threedimensional inlet affords a relatively simple, generic geometry, 

while producing a highly complex flow field dominated by 

shock/shock and shocWboundary-layer viscous interactions. 

Accomplishment Description 

A three-dimensional Reynolds-averaged Navier-Stokes code 

was modified for the current computational parametric study 

to identify the effects of leading-edge sweep and cowl 

position. Additionally, the effects of boundary-layer state 

(laminarlturbulent) and thermal wall boundary conditions 

(adiabaticl300-K constant wall) were assessed. The code 

solves the governing equations in full conservation form using 

MacCormack's time-asymptotic, explicit, predictor-corrector 

method. This method is second-order accurate in time and 

space and yields to a high degree of vectorization. The figure 

shows a lengthwise cross section of the inlet, revealing particle traces on the side wall and forebody plane (top of figure). 

Multiple regions of shock-induced separation and reattachment demonstrate the complexity of the flow. The computation 

required approximately 4 Cray Y-MP hours and 

3 megawords of memory. 

Significance 

Proposed hypersonic vehicles will operate in flight regimes 

that impose high thermal as well as aerodynamic loads. To 

relieve some of these aerothermal loads, it is desirable to 

sweep the sharp leading edges of the inlet side wall. The 

degree to which this sweep affects the internal aerodynamics 

of the inlet was assessed. When comparisons were made of 

mass capture, throat Mach number, total pressure recovery, 

and average inlet compression ratio at different sweeps, it was 

found that the effect of sweeping the leading edge from 0° to 

30" was negligible. Further increase in sweep tends to 

degrade the mass capture and compression while improving 

the total pressure recovery and throat Mach number. A tradeoff of these parameters leads to a 45"-sweep configuration. 

Future Plans 

A project parallel to the experimental verification of these 

findings has evolved. While preparing for the experimental 

work, an opportunity arose to test a model of this class at 

Mach 6 in CF,. Since CF4 is neither calorically nor thermally 

perfect, the code will be extended to handle the virial gas 

equations, allowing benchmark comparisons with virial (realgas) data. 

Publications 

Holland, Scott D., and Perkins, John N. "A Computational 

Parametric Study of Three-Dimensional Sidewall Compression 

Scramjet Inlets at Mach 10." AlAA Paper 90-2131, July 1990. 

Particle traces on a three-dimensional side-wall compression inlet with leading-edge sweep = 30 and cowl at the throat, in 

laminar/300-K wall boundary conditions; M = 10, a = 0°, Re = 2.10 x lo6, grid size 65 x 31 x 61. 
Turbulence Modeling for Compressible/Hypersonic Flows 

C. C. Horstman, Principal Investigator 

Co-investigators: J. R. Viegas, T. J. Coakley, and P. Rodi 

NASA Ames Research Center 

Research Objective 

To develop, test, and validate turbulence models for complex 

aerodynamic flow fields at supersonic and hypersonic speeds. 

Approach 

.Three-dimensional Navier-Stokes codes with various levels of 

turbulence modeling are used to predict various flow fields 

that have been experimentally documented. 

Accomplishment Description 

Solutions were obtained for a series of three-dimensional, 

shock-wavelturbulent-boundary-layer interaction flow fields 

using several turbulence models. As the shock strength 

increased, the peak values of measured skin friction were 

underpredicted by as much as 52%. No turbulence model 

correctly predicted all the test cases. The simpler algebraic 

models outperformed the more complex two-equation eddyviscosity models. The use of wall functions caused significant 

underpredictions of the interaction size. The accompanying 

figure shows the flow geometry, along with typical results, for a 

16" sharp fin at Mach 4. A single computation needed about 

20 Cray Y-MP hours and 10 megawords of memory. 

Significance 

Proposed aerospace vehicles will sometimes operate in flight 

regimes that are beyond the accessibility of ground-based 

wind tunnels. Therefore, the vehicle design process will 

depend on computational fluid dynamics. For accurate flow 

simulation, valid turbulence models must be used. 

Future Plans 

Work will continue to improve the turbulence modeling, grid 

resolution, and boundary condition treatment. Extension to 

higher Mach numbers is also planned. 

Publications 

Kim, K.-S.; Lee, Y.; Alvi, F. S.; Settles, G. S.; and Horstman, 

C. C. "Laser Skin Friction Measurements and CFD Comparison 

of Weak-to-Strong Swept ShockIBoundary-Layer Interactions." 

AlAA Paper 90-0378, 1990. 

SHARP 

2D TURBULENT 

BOUNDARY 

LAYER 

8 r 0 EXPERIMENT 

- 

COMPUTATIONS 

K - E (WALL FUNCTION) 

6 --- --- K - E (INTEGRATE TO WALL) 

CEBECI SMITH 

Flow geometry and typical results for a 16" sharp fin; M = 4. 
Prediction of Vortical Flows Using lncompressible Navier-Stokes Equations 

C.-H. Hsu, Principal Investigator 

ViGYAN, Inc./NASA Langley Research Center 

Research Objective 

To develop a computational method for calculating low-speed, 

three-dimensional viscous flow fields. 

Approach 

A computer code VOR3Dl is developed. The code uses the 

implicit upwind-relaxation finite-difference algorithm with a 

nonsingular eigensystem to solve the preconditioned, threedimensional, incompressible Navier-Stokes equations in 

curvilinear coordinates. 

Accomplishment Description 

Steady-state Navier-Stokes solutions were carried out for 

three low-aspect-ratio wings with rounded edges. Computed 

surface-particle traces at a = 20" show the flow separation 

and attachment resulting from the generation and interaction 

of leading-edge vortices. 

Significance 

Computations for highly three-dimensional, leading-edge 

vortex flows over a delta wing, a double-delta wing, and a 

cropped double-delta wing have shown good agreement with 

experimental data. The analyses indicate that the present 

code can predict important features of complicated threedimensional vortical flow fields. 

Future Plans 

The computer code has been extended, to be able to make 

time-accurate computations. Numerical simulations of vortex 

breakdown will be performed. 

Publications 

1. Hsu. C.-H., and Liu, C. H. "Numerical Study of Vortical + 

Flow over a Sideslipping Delta Wing." AlAA Paper 90-3001- 

CP, Aug. 1990. 

2. Hsu, C.-H.; Chen, Y.-M.; and Liu, C. H. "Preconditioned 

Upwind Methods to Solve 3-0 lncompressible Navier-Stokes - 

Equations for Viscous Flows." AlAA Paper 90-1496, June 

1 990. 

3. Hsu, C.-H., and Liu, C. H. "Prediction of Vortical Flows on 

Wing Using lncompressible Navier-Stokes Equations." Proceedings of the Third International Congress of Fluid 

Mechanics, Vol. 2. Cairo, Egypt, Jan. 1990, pp. 573-586. 

4. Hsu, C.-H., and Liu, C. H. "Simulation of Leading-Edge 

Vortex Flows." To be published in Theoretical and Computational Fluid Dynamics 2 (1 990). 

5. Hsu, C.-H., and Liu, C. H. "Navier-Stokes Computation of 

Flow Around a Round-Edged Double-Delta Wing."Submitted 

to AlAA J. 28 (1 990). 

Particle traces on a delta wing, a double-delta wing, and a cropped double-delta wing; a = 20". 

72 
Turbulence Modeling for Submarine Flow Field Computation 

Thomas T. Huang, Principal Investigator 

Co-investigator: Yu-Tai Lee 

David Taylor Research Center 

Research Objective 

To examine the effect of the turbulence model on the solutions 

of the Navier-Stokes solvers and submarine flow fields. 

Approach 

.Three-dimensional, steady-state, incompressible, Reynoldsaveraged Navier-Stokes equations are solved using a finitevolume formulation based on a central-difference spatial 

discretization and an explicit Runge-Kutta time-stepping 

-scheme. Algebraic numerical grid generation is used. 

Accomplishment Description 

Laminarlturbulent flows past an axisymmetric body and a 

body of revolution with appendages in the tail region were 

predicted at a O0 angle of attack. Calculated results for 

turbulent axisymmetric flows at a Reynolds number of 

6.6 x lo6 agreed well with the experimental data. The accompanying figure shows the stern region of the computational 

grid for an appended submarine. The predicted laminar flow 

on a generic appended body of revolution at a Reynolds 

number of 0.5 x 10" shown in the figure, was found qualitatively to be in good agreement with the turbulent-flow 

measurements on a body of revolution with slightly different 

appendages. The results for the appended body of revolution 

were obtained using a coarse (43 x 13 x 13) grid for the initial 

solutions and a fine (85 x 25 x 25) grid for the final solutions. 

The running times of each iteration for the coarse and the fine 

grids are 0.097 and 0.639 Cray Y-MP seconds, respectively. 

Three thousand iterations are made on the coarse grids and 

2000 on the fine grids. The total CPU time for the case is 

27 minutes. This work was published in the proceedings of 

the Sixth International Conference on Numerical Methods in 

Laminar & Turbulent Flow, Swansea, U.K., July 1989. 

Significance 

The capability developed from this project will lead to a significant increase in the understanding of submarine hydrodynamics and to an improvement in ship design. 

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CONTOURS OF 

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MEASURED 

CONTOURS OF 

AXIAL VELOCITY 

Flow field at a submarine stern. 
Numerical Simulation of an F-16A at Angle of Attack 

Gary W. Huband, Principal Investigator 

Co-investigators: J. S. Shang and Michael J. Aftosmis 

Wright Research and Development Center 

Research Objective 

The objective of this project is to show that realistic, complex 

aircraft can be accurately simulated in flight using computational fluid dynamics methods. Specific goals are to highlight 

the current simulation capability and to identify areas that 

need improvement. 

Approach 

An F-16A fighter at an angle of attack and transonic Mach 

number was simulated by solving the mass-averaged NavierStokes equations on a single-block grid. MacCormack's 

explicit predictor-corrector algorithm was used to integrate the 

equations of motion, and a modified version of the BaldwinLomax algebraic turbulence model was used to achieve turbulent closure. 

Accomplishment Description 

A numerical simulation of a wind tunnel experiment was performed for an F-16A at a free-stream Mach number of 0.85, a 

Reynolds number of 12.75 x 10" and an angle of attack of 

16". The computed lift coefficient differed from the wind tunnel 

lift coefficient by less than 1 %, and the computed drag coefficient differed from the wind tunnel drag coefficient by 8%. The 

computed surface pressure coefficients along the body, wing, 

and empennage also matched wind tunnel data reasonably 

well. New grid generation methods were developed and used 

that ensure a smooth flow-field grid, but still accurately 

describe the body shape. These grid generation methods 

also significantly reduce the time to generate a grid about a 

complex three-dimensional shape. 

Significance 

This is a first step toward the development of an aircraft 

design tool that can provide detailed and accurate information 

about a configuration's aerodynamics. Such a tool will reduce* 

design time, wind tunnel time, and flight test time, while allowing the development of more innovative designs with lower 

risk. 

Future Plans 

Three areas are targeted for future research-increasing code 

efficiency, improving the turbulence model in separated 

regions, and improving the grid generation methods. Because 

the time to obtain a solution must be reduced as much as 

possible, an implicit code is under consideration. To ease the 

grid generation requirements, multiblock solvers and unstructured solvers are also being considered. 

Publications 

1. Huband, G. W.; Rizzetta, D. P.; and Shang, J. S. 

"Numerical Simulation of the Navier-Stokes Equations for an 

F-16A Configuration." AlAA Aircraft J. 26, no. 7 (Jul. 1989): 

634-640. 

2. Huband, G. W.; Shang, J. S.; and Aftosmis, M. J. 

"Numerical Simulation of F-16A at Angle of Attack." Presented 

at the AlAA 28th Aerospace Science Meeting, Reno, NV. 

i 

1 

1 

3 

1 

1 i 

I 

Particle Traces 

F-l6A Maek 8.85 A88 18 detg 

~ 

Particle traces on an F-16A; M = 0.85, a = 16". 
Computation of Steady Three-Dimensional Separation 

Ching-mao Hung, Principal Investigator 

NASA Ames Research Center 

Research Objective 

To study several basic issues of steady three-dimensional flow 

separation, such as open versus closed separation, the existence of secondary separation, and the accessibility of threedimensional separation. 

Approach 

The compressible Navier-Stokes equations are solved for 

supersonic flows over a sharp and a flat-faced blunt fin 

mounted on a flat plate. A finite-volume algorithm of 

JvlacCormack's explicit-implicit scheme is used. Separation of 

the boundary layer on the flat plate is investigated for various 

grid refinements and fin wedge angles. Results are compared 

with experimental measurements of surface pressure, to 

determine the accuracy of the computations. 

Accomplishment Description 

(1) The results of using the same number of grid points with 

three different grid spacings show that the origin of the line of 

separation changes from an open-type to a closed-type separation. This demonstrates that the grid resolution can affect the 

"calculated" topology. (2) Surface particle traces show that 

there is no secondary separation. Another oil-accumulation 

line is just a demarcation between regions of high and low 

UWTREAM / 

BOUNDARY LAYER \ Y 

surface skin friction. (3) A close examination of the particle 

traces near the apex shows that the flow is already separated 

on the plate before reaching the conventional criterion of 

incipient separation, which is that the turning angle of the skinfriction line is equal to the shock angle. (4) The results demonstrate that flow particles above the body are able to access 

the separation region through the attachment node and the 

spiral nature of the separation surface. 

Significance 

Some observations and new interpretations from this study 

that will have significant impacts on the understanding of the 

three-dimensional flow field are as follows: (1) Some of the 

numerically observed open-type separation is a result of insufficient grid resolution, and similarly, some of the experimentally 

observed open-type separation is the result of the low resolution of the device and facility. (2) An accumulation of oil flow 

on the surface is not necessarily a line of separation, as is 

usually inferred. (3) The conventional criterion of boundary 

separation, which involves comparing the turning angle of the 

skin-friction line to the shock angle, is not uniformly valid. 

(4) There is no steady three-dimensional separation that is 

totally closed by a separation surface as a bubble. All threedimensional separation is accessible. 

MEDIUM 

....., . I I , --. 

I >-....,... , ..... C 

COARSE FINE 

Grid refinement near the fin apex shows the simulated flow topology changes from an open-type to a closed-type separation. 

75 
Eddy-Resolving Model of the Pacific Ocean 

Harley E. Hurlburt, Principal Investigator 

Co-investigators: Alan J. Wallcraft and Jimmy L. Mitchell 

Naval Oceanographic and Atmospheric Research LaboratoryIJAYCOR 

Research Objective 

To develop, understand, and validate eddy-resolving models 

of the Pacific Ocean. This is a step in developing an eddyresolving, global ocean-monitoring and -prediction system for 

the U.S. Navy. This system will rely heavily on supercomputers 

(Class VII and greater) and on satellite data, especially altimetry from satellites like GEOSAT, TOPEWPOSEIDON, and 

ERS-1. 

Approach 

We used primitive-equation layered models with two to four 

layers and 112" to 118" resolution. The versions used were 

hydrodynamic, thermodynamic, reduced-gravity (lowest layer 

infinitely deep and at rest), finite-depth flat bottom, and finitedepth with topography. A free surface was retained by treating 

gravity waves implicitly in the finite-depth versions and solving 

the resulting Helmholtz equations using the direct capacitance 

matrix technique. The models were spun up at coarser resolution, then continued with increased resolution forced by the 

Hellerman-Rosenstein monthly wind climatology. The different 

versions of the model were used to help sort out the dynamics 

and mechanisms behind different oceanic phenomena. 

Accomplishment Description 

We developed 112" and 114" finite-depth and 118" reducedgravity models on the Cray Y-MP. The models successfully 

simulated many features of the Pacific Ocean, as illustrated in 

the figure. The figure shows the sea surface height (SSH) from 

the 114" model with realistic topography. Surface flow tends to 

parallel isolines of SSH. Some of the salient features are the 

Subarctic Front (40-45N across the Pacific) and the Kuroshio 

CurrentIKuroshio Extension (along the western boundary north 

of 14N, then eastward across the Pacific at about 35N). The 

Kuroshio bifurcates at the Shatsky rise (about 160E) and a 

contour connects to the Subarctic Front, an observed feature 

that does not occur in the flat-bottom and reduced-gravity 

models. The ribbon of blue marks the North Equatorial Current 

flowing westward at 10-15N, the Mindanao Current flowing 

southward along the Philippines coast, and the eastward North 

Equatorial Countercurrent at about 5N. The Mindanao eddy is 

simulated southeast of the Philippines. Four-layer versions of I 

the models also depict the westward equatorial surface current and eastward equatorial undercurrent, which are absent 

in the two-layer versions. We performed 24 Pacific simulations, 

integrating a total of 524 model years and using about 

550 Cray Y-MP hours. 

Significance 

The Cray Y-MP at NASA Ames permitted the highest horizontal 

resolution ever in modeling the Pacific Ocean-114" for the 

finite-depth models and 118" for a reduced-gravity model. This 

was a major step in developing an eddy-resolving, global 

ocean-prediction capability for the U.S. Navy, and it provided 

a high-impact demonstration of feasibility to the Navy. Applications include antisubmarine warfare, long-range weather prediction, climate monitoring and prediction, optimum-track ship 

routing, search and rescue, fisheries, and ice prediction. 

Future Plans 

We will continue to develop eddy-resolving, basin-scale and 

global-scale ocean models for ocean prediction using the 

Navy's Cray Y-MP 81128 scheduled for installation at the Naval 

Oceanographic Office by October 1990. 

FREE SURFACE DEVIATION N PACIFIC 13133:2: 9.3 

I)F = 12.5 CM DATE = 289/0067 

120H lOOW 

-43 437 5-25 0- 1 I 87.5100 01 15 3 NORDA 323 8-FEE-9L 

Sea-surface height anomaly (cm) on a day in mid-October, year 67 of the model integration. The model is two-layer hydrodynamic 

with 0.25" x 0.35" resolution (latitude, longitude) and realistic topography. The simulation depicts major current systems of the 

Pacific Ocean as well as current meanders and eddies caused by mesoscale flow instabilities. This simulation required 

4.5 megawords of memory, 33 megawords of SSD, 2.5 Cray Y-MP hours per model year, and 72 Cray Y-MP hours for a 72-year 

integration, including spin-up at 112". 

ORIGINAL PAGE 

COLO2 PHOTOGRAPH 
Computational Advanced Propulsion Technology Research 

Danny Hwang, Principal Investigator 

Co-investigators: John Wolter, Joe Nenni, Mark Krein, and Dave Georgevich 

NASA Lewis Research Center 

Research Objective 

To develop the ability to perform three-dimensional aerodynamic computations for high-speed nozzles and inlets. The 

verified computer codes will be used as design tools for analyzing new concepts even before a model is built. 

~pproach 

Two three-dimensional Navier-Stokes codes, PARC3D and 

DLUMSD, were used for calculations. A three-dimensional grid 

generator by Soni, McClure, and Heikkinen was applied to 

create grids for analysis. 

Accomplishment Description 

The three-dimensional viscous calculations were performed for 

the AR410 transition duct by using PARCSD and DLUM3D. To 

reduce the uneven distribution of the boundary layer, caused 

by the skewness of H-grids on the surface, the decision was 

made to use an 0-grid. The computer codes were modified to 

handle the 0-grid. The preliminary laminar results of the secondary flow near the exit of the transition duct are shown in the 

accompanying figure. The centers of the vortices obtained 

from the two codes agree fairly well. However, the vortices 

obtained from DLUMBD are stronger than those from PARCSD. 

A study is under way of turbulent flow, using the BaldwinLomax model and the k-E model. The result9 from both laminar 

and turbulent flows will be compared with experimental data. 

Most of the computations required about 20 Cray-2 hours and 

15 megawords of memory. 

Significance 

The total pressure loss, which can affect the performance of 

an advanced aircraft, can be more accurately predicted using 

viscous calculations. However, because of the long CPU time 

needed to carry out the viscous calculation, the Euler solution 

might be considered in some cases as a substitute. 

Future Plans 

The codes will be further used to study the effect of turbulence. By comparing the results with experimental data, we 

can determine the range of validity of each code. 

Preliminary laminar results of the secondary flow near the exit of the AR410 transition duct; M = 0.5. (Top) DLUM3D solution. 

(Bottom) PARCSD solution. 
Numerical Inversion of a Limited-Data X-Ray Transform 

Steven H. Izen, Principal Investigator 

Case Western Reserve University 

Research Objective 

The ultimate purpose of this research is to recover the threedimensional density profile of supersonic gas flow between 

compressor blades in a wind tunnel. The more immediate goal 

of this work is to illustrate how well three-dimensional information about density profiles can be recovered when diffuseillumination heterodyne holographic interferometry is used as 

an experimental technique, along with fully three-dimensional 

tomography for data analysis. 

Approach 

The data provided by diff use-illumination heterodyne holographic interferometry experiments are line integrals of the 

index of refraction along lines perpendicular to the viewing 

direction of the holographic plate. Since the index of refraction 

is proportional to density, the data can be interpreted as 

determining the line integrals of density, or from a mathematical point of view, the data determine the x-ray transform of the 

density. Experimental constraints severely limit the viewing 

directions, so a mathematical inversion algorithm has been 

developed that takes advantage of the parallel-beam geometry inherent in the data acquisition. The algorithm transforms 

the experimentally obtained data to data at sample points in 

three-dimensional Fourier space in accordance with the 

projection-slice theorem. Then a singular value decomposition 

is performed to find the coefficients in a polynomial expansion 

for the density. Recent tests on the imaging of a laboratory 

flask have shown that this algorithm is able to recover significant three-dimensional information. Also, the tests have 

indicated that extreme care is required in the lab to ensure 

that the data from each of the views of the hologram are 

properly registered. Each reconstruction requires 2 Cray-2 

hours and 35 megawords of memory. 

Significance 

It is of interest to understand the behavior of flows in wind , tunnel cascades. Computational fluid dynamics researchers 

have developed computer codes to model such flows. In order 

to verify these codes, experimental data are required. Current 

experimental techniques are able to supply only two- . dimensional data, which are of limited use in the verification 

of three-dimensional models. The three-dimensional density 

profiles that will be computed from the diffuse-illumination 

heterodyne holographic interferometry data will provide verification data for the three-dimensional codes. 

Future Plans 

Enhancements such as edge-detection capability are being 

explored. Also, constraints arising from data generated by 

alternate experimental techniques are being incorporated to 

improve the reconstruction quality. 

Publications 

1. Izen, Steven H., and Decker, A. J. "Fully ThreeDimensional Tomographic Reconstructions from Holographic 

Interferometry Data." In preparation. 

2. "An Application for a Limited Solid Angle X-ray Transform." Proceedings of the 1989 AMS Conference on Radon 

Transforms and Tomography. 

OMSO Fi 1 led Flask, Laboratory Data 

Degree 12 Reconstruct ion 

CONTO R LEUELS :BB~~/BB 

Laboratory data for a DMSO filled flask; degree 12 reconstruction. 
Linking Attractor Geometry to Turbulence Physics 

Laurence R. Keefe, Principal Investigator 

NASA Ames Research Center 

Research Objective 

To increase understanding of dynamical processes in turbulent shear flows by studying the structural characteristics of 

strange attractors, which have been demonstrated to underlie 

such flows. 

Approach 

Three-dimensional direct numerical simulation of lowReynolds-number channel turbulence is used to calculate 

Lyapunov vectors and exponent spectra, fractal dimension, 

and other quantities suggested by chaos theory to be useful 

in analyzing dynamical events in such flows. 

Accomplishment Description 

Calculations were completed of Lyapunov exponent spectra 

from three different spatial resolutions of the channel flow at a 

single Reynolds number. The results show that these spectra, 

when scaled by the metric entropy and the number of nonnegative exponents, have the same shape. The lowest resolution simulation yields an attractor of dimension -360, but using 

these scaling properties, we estimate that the true dimension 

of the attractor underlying flows in this computational domain 

is -780. The lack of increase in attractor dimension between 

the middle- and high-resolution cases indicates that the 

additional scales involved in the high-resolution case do not 

fundamentally affect the dynamics. Thus the effect of these 

scales should be assignable to an eddy viscosity or sub-gridscale model. The scaling properties of the Lyapunov spectra 

can be seen in the figure. Each exponent calculation required 

250 hours of CPU time and 16 megawords of memory. 

Significance 

The strange attractor is an exciting model for the mathematical 

structure of fully developed shear flows. Exploration of the 

known structural characteristics of such attractors and their 

link with the phenomenology of fully developed flows will provide new insight into the dynamics of turbulence and new 

ideas for prediction and control. 

Future Plans 

We will examine the phase-space characteristics of "coherent 

structures" found by experimenters. What is the relation 

between attractor structure and turbulence modeling? 

Publications 

Keefe, Laurence; Moin, Parviz; and Kim, John. "Application of 

Chaos Theory to Shear Turbulence." In The Ubiquity of Chaos, 

ed. Saul Krasner. Washington, DC: AAAS, 1989. 

j/N, 

Scaling properties of the Lyapunov spectra. 
Solar Dynamic Space Power-System Design and Performance Analysis 

John L. Klann, Principal Investigator 

Analex Corporation/NASA Lewis Research Center 

Research ObJoctive 

To accurately predict the performance of dynamic electric 

power modules in their intended space application and to 

evaluate the effects of design changes on such performance. 

Current emphasis is on the solar-powered Brayton cycle 

modules intended for Space Station Freedom. 

Approach 

The Closed Cycle Engine Program (CCEP) is being developed 

for the analysis of spacecraft electric power systems that use 

the Brayton thermodynamic cycle. The CCEP uses the same 

basic techniques as the NavyINASA Engine Program (NNEP), 

a widely used computer program for the design and performance analysis of aircraft jet engines. However, CCEP is 

evolving with greater depth in its component design and performance simulations. In particular, it currently includes some 

transient orbital performance capabilities. 

Accomplishment Description 

Two large matrices are needed for radiosity calculations within 

the cavity of the power module's solar heat receiver, to properly evaluate the receiver's transient operating temperatures. 

Most of the incident solar flux within the heat receiver is 

absorbed by salt canisters that surround 82 equally spaced, 

gas heat-transfer tubes around the cylindrical internal wall. 

Active gas-flow length is 8 ft, and there are 96 canisters per 

tube. During the sunlit portion of an Earth orbit, part of the heat 

is stored by melting the salt for later use during passage 

through the Earth's shadow. Thus, heat is continuously provided b the working gas. The figure shows the highest predicted surface-temperature distributions that occur with the 

best flux-tailored mirrorlreceiver arrangement. Interior surfaces 

are unwrapped; the offset aperture is shown on the left, and 

the enclosing end on the right. The peak wall temperature was' 

1546" F (the figure is in OR) and occurred at sunset under 

minimum-insolation and orbital energy-equilibrium conditions 

(third orbit). Each orbital calculation requires 1 Cray-2 hour 

and about 4 megawords of storage. 

Significance 

The CCEP is an in-house development at NASA Lewis, and its 

capabilities are unique in the Space Station Freedom program. 

The NAS capabilities are needed to examine mirrorlreceiver 

designs so that receiver spatial and time-dependent temperature variations can be minimized. The results of this effort 

should maximize the life of this critical component. 

Futuro Plans 

The CCEP will continue to be exercised for component and 

system evaluations throughout the Phase-C effort for Space 

Station Freedom. The heat receiver radiosity calculations will 

be altered to accommodate assumptions other than a graybody assumption, to evaluate the benefits of outer salt-canister 

surface treatments. 

Receiver-wall temperature profile; N = 3, increment = 54.64. 

80 

ORIGINAL PAGE 

COLOR PHOTOGRAPH 
Three-Dimensional Shock/Shock Interactions on the Inlet Side Wall 

Ajay Kumar, Principal Investigator 

Co-investigator: Dal J. Singh 

NASA Langley Research Center 

Rerearch Objective 

To numerically simulate the three-dimensional shock/shock 

interaction on the swept inlet side walls of the scramjet inlet at 

high Mach number. 

Ibpproach 

The interaction of the inlet shock with the forebody shock 

is studied by solving three-dimensional, thin-layer NavierStokes equations. The governing equations are solved using 

van Leer's finite-volume flux-splitting algorithm. The impinging 

shock is treated as a sharp discontinuity across which exact 

shock jump conditions are applied. The inlet side wall of the 

scramjet inlet is modeled by a cylindrically blunted wedge, 

and the forebody shock by the extraneous impinging shock. 

Accomplishment Description 

The effects of shock impingement on the scramjet-engine-inlet 

leading edge are investigated numerically. Type IV and Type 

V interactions are investigated. Results of the present numerical investigation are compared with the available experimental 

data. For flow at Mach 5.94 and Reynolds number 202,500, 

the peak pressure is found to be 2.2 times and the peak heating 3 times the unimpinged stagnation values. The heating 

rates and surface pressure are slightly lower for Type V interaction. The flow for Type IV interaction is found to be 

unsteady. 

Significance 

When the forebody shock interacts with the blunt inlet-leadingedge shock, a complex flow field is produced, with localized 

zones of high pressure and intense heating. The large temperature gradients cause thermal stresses that could result in 

structural failure. To determine the cooling requirements, 

pressure and heating rates on the body need to be predicted 

accurately. 

Future Plans 

Efforts are currently under way to investigate the unsteady 

behavior showed by the Type IV interaction. Also we plan to 

use multizone andlor adaptive grids to properly resolve the 

flow field. 

Publications 

Singh, D. J.; Kumar, A.; and Tiwari, S. N. "Three-Dimensional 

Shock-Shock Interactions of the Scramjet Inlet." AlAA 

Paper 90-0529, Jan. 1990. 

Type V shocklshock interaction on the inlet side wall. (Left) Numerical simulation. (Right) Experiment. 
Numerical Study of Fundamental Fluid Dynamics using Navier-Stokes 

Equations 

Geojoe Kuruvila, Principal Investigator 

NASA Langley Research Center 

Research Objective 

To study vortex breakdown and to develop the ability to 

predict it. 

Approach 

The integral forms of the complete, unsteady, compressible, 

three-dimensional Navier-Stokes equations in the conservation 

form, cast in a generalized coordinate system, are solved 

numerically to simulate vortex breakdown. The inviscid fluxes 

are spatially discretized using Roe's upwind-biased fluxdifference splitting scheme, and the viscous fluxes are 

discretized using central differencing. Time integration is 

performed using a backward Euler alternating-direction 

implicit scheme. A full approximation of multigrid is used to 

accelerate the convergence to steady state. 

Accomplishment Description 

A three-dimensional finite-volume Navier-Stokes code was 

developed to study vortex breakdown. The bubble-type 

breakdown was simulated for several sets of Reynolds 

numbers (Re), swirl velocity parameters (S), and low Mach 

numbers (M). Solutions were obtained for S = 1, M = 0.1 and 

Reynolds numbers, based on the vortex core radius, as high 

as 1000. A typical run with 65 x 33 x 33 mesh points and four 

multigrid levels required about 9 megawords of memory and 

6 Cray-2 hours to obtain a solution converged to machine 

zero. About 2500 multigrid cycles were required to obtain a 

solution. 

Significance 

The code that has been developed is robust, and its performance is good for this particular problem, in terms of both the 

rate of convergence and the use of computer resources. The 

code is a good platform from which to conduct further exten- ' 

sive numerical experiments. Since the compressible form of 

the Navier-Stokes equations is used, this code can be used to 

study the effect of Mach number, in addition to the effects of 

Reynolds number and swirl velocity parameter, on the 

breakdown. 

Future Plans 

Other types of breakdown, especially the spiral type, will be 

studied, as will the effects of boundary conditions on the type 

of breakdown. 

Publications 

A NASA Technical Memorandum detailing this work will be 

published soon. 

VORTEX BREAKDOWN 

Streamsurfaces (Re=375, S= 1.46, M=0.1) 

Vortex breakdown; Re = 375, S = 1.46, M = 0.1. 

82 

ORIGINAL PAGE 

COLOR PHOTBSRAPH 
Incompressible Navier-Stokes Calculations for the Space Shuttle Main Engine 

Dochan Kwak, Principal Investigator 

Co-investigators: Stuart Rogers, Seokkwan Yoon, Moshe Rosenfeld, and Cetin Kiris 

NASA Ames Research Center 

Researoh ObJective 

To develop numerical simulation procedures for viscous 

incompressible flows and apply them to the Space Shuttle 

main engine (SSME), high-lift aerodynamic configurations, and 

$n artificial heart. 

Approach 

The three-dimensional, incompressible Navier-Stokes 

equations in generalized coordinates are solved by two 

different methods (pseudocompressibility and a fractionalstep method) using different numerical algorithms. 

Accomplishment Description 

One of the primary areas in which the performance of the 

SSME can be improved is the flow in the high-energy liquidoxygen and fuel pumps. The INS3D-LU code, which is based 

on the lower-upper, symmetric, Gauss-Seidel implicit algorithm, was used to study the effect of tip clearance in the 

inducer of the SSME high-pressure oxidizer turbopump. The 

time-accurate incompressible code, INS3D-UP, was used to 

study the unsteady flow during the opening and closing of a 

tilting disk valve. This is an idealized problem for an artificial 

heart valve, although the same code can be used to simulate 

the start-up or the shut-down procedure of the SSME. The total 

allocated time of 300 hours was used, and over 200 deferred 

hours were also used. An average run for the SSME inducer 

was kept small during this period, requiring approximately 

15 megawords and 1 hour of run time. A finer resolution study 

and a more complete inducerhmpeller geometry will require at 

least 3 to 5 times more mesh points and run time. An unsteady 

case of valve flow requires 5 megawords of memory and 

10 hours of run time per cycle, using 100,000 mesh points. 

Significance 

The speed and accuracy of the incompressible Navier-Stokes 

codes developed are demonstrated by computing the SSME 

inducer and a tilting disk valve. By multi-tasking the INS3D-LU 

code on eight processors of the Cray Y-MP, 1.07 GFLOPs was 

achieved using 1 million grid points. This is a major step 

toward developing a highly efficient computational fluid 

dynamics design procedure. 

Future Plans 

A full simulation of the entire SSME power head will be 

continued. The numerical simulation of high-lift aerodynamic 

configurations will be performed. During the next period, an 

average job will require 10 to 20 megawords of memory and 

10 to 40 hours of Cray-2 time. 

The Space Shuttle main-engine turbopump (left) with tip clearance, and (right) without tip clearance. 

ORIGINAL PAGS 

COLOR PHOTOSRAPH 
Computation of Single-Expansion=Ramp and Scramjet Nozzles 

H. T. Lai, Principal Investigator 

Sverdrup Technology, Inc. 

Research Objective 

To obtain three-dimensional numerical flow fields for the 

nonaxisymmetric single-expansion-ramp and scramjet nozzles 

at test conditions in the supersonic regimes. 

Approach 

The existing PARC code is used to compute the solutions of 

laminar and turbulent thin-layer Navier-Stokes equations for a 

perfect gas. 

Accomplishment Description 

Converged turbulent results for the single-expansion-ramp 

nozzle were computed for a nozzle pressure ratio of 4. In this 

case, the flow at a stagnation reservoir expands subsonically 

along the converging section, becomes sonic at the throat and 

supersonic in the diverging section, and then exhausts supersonically into a quiescent environment. The internal expansion 

and the external exhaust plume were both simulated. A grid of 

95 x 90 x 50 and a total of 45 Cray-2 hours were used. Converged laminar results for the scramjet nozzle were also 

obtained for an external Mach number of 6 and an internal 

Mach number of 1.62. The flow field is characterized by strong 

supersonic expansions in both streamwise and spanwise 

directions. Only a portion of the exhaust plume was simulated 

in this case. A grid of 90 x 90 x 95 and a total of 18 Cray-2 " 

hours were used. 

Significance 

Streamwise vortices are present in the exhaust flow of the , single-expansion-ramp nozzle and on the ramp surface of the 

scramjet nozzle. 

Publications 

Lai, H. T. '3D Computation of Single-Expansion-Ramp and 

Scramjet Nozzles." Presented at the CFD Symposium on 

Aeropropulsion, Cleveland, OH, Apr. 1990. 

Flow-field calculation; M = 1.000, a = O.OOO, Re = 2.25 x lo6, grid size 95 x 90 x 27. 

ORIGINAL P,9CZ 

COLOR PHOTOSRAPH 
Numerical Investigation of NASP-Like Vehicles 

C. C. Lee, Principal Investigator 

Co-investigators: William Bower, Shawn Hagmeier, Scott Van Horn, Pat Vogel, and Darrell Weber 

McDonnell Douglas Corporation 

Research Objective 

The objective of this research is to calibrate National AeroSpace Plane (NASP) -related computational fluid dynamics 

(CFD) codes using the most recent test data from the 

McDonnell Douglas Corporation (MDC) -NASP project and 

'the NASP Technology Maturation Plan (TMP). The calibrated 

CFD codes will then be used to produce design guidelines for 

NASP-like vehicles. 

APproach 

Three-dimensional Navier-Stokes codes developed by 

government agencies were selected for code calibration, 

including the CFLBDE and CNS codes. Reliable experimental 

data were extracted from the MDC-NASP project and the TMP. 

The code calibration included a grid density study, conservation error checks, and evaluation of physical modeling. 

Accomplishment hscription 

In order to increase confidence in the CFL3DE code, an 

extensive calibration for flow-field and forcelmoment predictions was performed. It included calibrations against detailed 

flow-field data from wind tunnel and flight tests over a range of 

Mach numbers from 6 to 20. Configurations selected for this 

study included blended wing-body, noncircular-body, reentry 

F, advanced manned interceptor, and NASA Ames all-body. A 

typical example of the computed flow fields is shown in the 

figure, which is for the all-body vehicle with Mach = 7.4. For 

this case. 49 radial, 49 circumferential, and 72 axial points 

were used. It was run in parabolized Navier-Stokes mode and 

took 25 CPU minutes on the Cray-2. Computed pitot pressure 

showed excellent agreement with the test data. Surface pressure and heat transfer rates showed the same agreement. 

Significance 

The CFD calculations are needed to predict flow fields for the 

NASP design in flight regimes beyond those in which current 

wind tunnels can operate. The accuracy of these predictions 

must be quantified using available data. All sources of errors 

present in the computation methods. post-processing rnethods, and experimental data must be quantified to reduce 

design risk. The calibrated CFD codes are necessary tools for 

the NASP design. 

Future Plans 

Code calibration for external and internal flows will continue. 

Grid density studies will be performed with all codes at different Mach ranges, to obtain grid-independent solutions. The 

calibrated codes will be used to perform parametric studies to 

define the critical geometric parameters that drive vehicle 

design. 

MDC-CFL3DE Flowfield Solution 

for NASA Ames All-Body 

Mach 7.4 

a = 0.0 

I 

Single Zoae r 

(7ex49x4L, I 

The MDC-CFL3DE flow-field solution for the NASA Ames all-body hypersonic vehicle; M = 7.4, a = O.OO, single-zone grid 

size 72 x 49 x 49. 
Nonlinear Instability of Shear Layers 

S. J. Leib, Principal Investigator 

Sverdrup Technology, Inc./NASA Lewis Research Center 

Research Objective 

To study the nonlinear spatial evolution of instability waves on 

compressible shear flows. 

Approach 

A combination of asymptotic and numerical methods is used. 

Nonlinear effects first become important in the "critical layer" 

when the wave amplitude becomes large enough while the 

dynamics outside this region are still linear. An asymptotic 

analysis yields a nonlinear integro-differential equation for the 

instability wave amplitude, with the linear solution as an initial 

condition. The cubic nonlinearity has the form of a convolution 

integral over the entire history of the solution. 

Accomplishment Description 

A code was written to obtain numerical solutions to this nonlinear evolution equation. A fourth-order predictor-corrector 

scheme was used to advance the solution in the downstream 

direction. The trapezoidal rule was used to compute the 

integral term, and the upstream tails were evaluated analytically from the linear solution. Typical runs required from 4 to 

6 megawords of memory and approximately 2 hours of CPU 

time. 

Significance 

The numerical results showed that inviscid solutions ended in 

a singularity at a finite downstream distance. Equilibrium solutions were possible when the viscous effects were large 

enough, but only for certain parameter ranges. These results 

indicate that nonlinearity can lead to explosive growth of the 

instability wave for a compressible shear layer, in contrast to - 

the incompressible case. 

Future Plans 

Similar evolution equations can be derived for other types of . shear flows, and their numerical solutions will be pursued in 

the future. 

Publications 

1. Goldstein, M. E., and Leib, S. J. "Nonlinear Evolution of 

Oblique Waves on Compressible Free Shear Layers." J. Fluid 

Mechanics 207 (1989): 73-96. 

2. Leib, S. J., and Goldstein, M. E. "Nonlinear Evolution of 3D 

Instability Waves on Compressible Shear Layers." Presented 

at the American Physical Society Division of Fluid Dynamics 

Meeting, Palo Alto, CA, 1989. 

3. Leib, S. J. "Nonlinear Evolution of Subsonic and 

Supersonic Disturbances on a Compressible Free Shear 

Layer." Submitted to J. Fluid Mechanics, 1990. 

Normalized instability wave amplitude vs. scaled downstream distance. Solid lines are numerical solutions, dashed lines are 

asymptotic. (Left) lnviscid solutions. (Right) Solutions for various values of the viscous parameter. 
Computational Fluid Dynamics Analysis of Space Shuttle Main Engine 

Turbopump RotorIStator Flows in Two and Three Dimensions 

S. J. Lin, Principal Investigator 

Co-investigator: R. J. Yang 

Rockwell International, Rocketdyne Division 

Research Objective 

The objective of the present research is to utilize and extend 

the rotor family codes developed by Dr. M. M. Rai at NASA 

pmes to calculate dynamic loading on various Space Shuttle 

main engine (SSME) turbine blades. Extensive flow data were 

obtained and then reduced to provide inputs for the dynamic 

and structural analysis of the turbine blade cracking problem 

in the SSME. 

Approach 

The rotor codes developed by Dr. Rai were applied in this 

project. The code was also extended to have multistage 

capability. The code solves the two- and three-dimensional, 

compressible, unsteady, thin-layer Navier-Stokes equations 

on a system of patched and overlaid grids. 

Accomplishment Description 

The Rotor-2 code developed by Dr. Rai was extended to have 

multistage capability. The code was also modified to compute 

steady-state subsonic and supersonic isolated airfoils. The 

resulting code was used to compute dynamic loading on 

turbine blades for a single-stage and a multistage highpressure fuel turbopump, a multistage low-pressure oxidizer 

turbopump, and a single-stage single-crystal turbine blade. 

Good agreement was obtained between calculated results 

and SSME balance data. Extensive data were also obtained 

and input to dynamic and structural codes for fatigue crack 

analysis. The calculations took about 4 to 30 Cray-2 hours for 

a single run, depending on the number of stages included. It 

required about 2 to 15 megawords of run time memory. 

Significance 

Turbopump blade cracks have been identified in the SSME. 

The life of these turbine blades is limited by high cycle fatigue 

cracks. Successful simulations of rotorlstator flows will provide 

accurate predictions of rotorlstator blade dynamic loading, 

which will help improve the performance and design of 

turbopumps. 

Futun, Plans 

The rotor code will be further developed to calculate dynamic 

loading and thermal characteristics of turbine blades in two 

and three dimensions. The data will then be used in dynamic 

and stress analysis codes for turbine crack analysis. 

Publications 

1. "Navier-Stokes flow Simulations of Multi-Stage and MultiBlade Turbines in SSME Turbopumps." Presented at the 8th 

CFD Working Group Meeting, Marshall Space Flight Center, 

AL, Apr. 1990. 

2. "Rotor Code Applications to Turbine Analysis." Presented 

at the 8th CFD Working Group Meeting, Marshall Space Flight 

Center, AL, Apr. 1990. 

Entropy contours for a two-stage, multistator/multirotor, high-pressure fuel turbopump. 

OZIC!fdj!L P/?GE 

COLOR Pi40 iOGRAPH 
Application of Computational Fluid Dynamics Methods to Radar Cross Section 

Computations 

Rung T. Ling, Principal Investigator 

Northrop Aircraft Division 

Research Objective 

The long-term objective of this project is to provide an integrated approach to solving aerodynamics and electro-magnetics problems in aircraft design. The short-term objective is to 

apply computational fluid dynamics (CFD) methods to radar 

cross section (RCS) computations. 

Approach 

A differential-equation approach was developed for the 

solution of the Maxwell/Helmholtz equations encountered in 

electromagnetic scattering. This approach is based on mathematical similarities between aerodynamics and electromagnetics problems. It takes advantage of progress made in 

CFD and incorporates appropriate innovative modifications 

necessary for electromagnetics problems. 

Accomplishment Description 

A time-dependent method for the numerical solution of the 

frequency-domain Helmholtz equation was developed. This 

method involves the reversion of the Helmholtz equation to the 

wave equation, and the introduction of time dependence into 

the generalized scattering amplitude. The scattering problem 

thus reverts from an elliptic boundary-value problem to a 

hyperbolic initial-value problem. The hyperbolic nature of the 

wave equation allows a time-dependent method to be 

incorporated so that solutions can be obtained by forward 

marching in time. This time-dependent formulation has been 

applied to scattering by long cylinders and spheres. The 

accompanying figure shows the evolution history of the profiles of the time-dependent generalized scattering amplitude in 

the scattering by a metallic circular cylinder. An explicit finitedifference scheme based on the Lax-Wendroff method is now 

being used in the three-dimensional RCS prediction code. The 

RCS computation for a three-dimensional object approximately 

one wavelength in each dimension needs 5 Cray-2 hours and 

20 megawords of memory. 

Significance 

The time-marching method developed under this project for 

the solution of the frequency-domain Helmholtz equation is ,- similar to using time-marching schemes to solve timedependent fluid dynamic equations as a means of obtaining 

the steady-state solution in steady flow problems. The memory 

requirement is minimized by using an explicit time-marching 

scheme to allow three-dimensional electromagnetic scattering 

phenomena in the resonance and high-frequency regions to 

be accurately simulated. 

Future Plans 

The three-dimensional computational electromagnetics code 

will be further developed, validated, and applied to simple, 

nonspherical, three-dimensional objects. 

Publications 

"A Time-Dependent Method for the Numerical Solution of 

Wave Equations in Electromagnetic Scattering Problems." 

Invited paper, presented at the IEEEIURSI Meeting, San Jose, 

CA, June 1989. (Also to be published in a special issue of 

Computer Physics Communications on computational 

electromagnetics.) 

-1.5 1 Initial Condition, 0 At 

Nondimensional Radial Distance, kr 

Scattering by a metallic circular cylinder with ka = 3.1 and E-polarization; the time-dependent generalized scattering amplitude at 

various time steps (8 = 0, real part). 
Computational Prediction and Control of Steady and Unsteady Asymmetric 

Vortex Flows around Cones 

C. H. Liu, Principal Investigator 

Co-investigator: Osama A. Kandil 

NASA Langley Research CenterIOld Dominion University 

Research Objective 

The major objective of the present research is to simulate, 

analyze, and control steady and unsteady asymmetric vortex 

flows around cones. The influential flow asymmetry parameters, such as the relative incidence, Mach number, Reynolds 

number, and shape of cross-sectional area, are considered in 

this work. Control of flow asymmetry is also studied. 

Approach 

The unsteady, compressible Navier-Stokes equations were 

solved in this study. Two computational schemes were used to 

solve the equations. The first, which was the main scheme, 

was an implicit, upwind, flux-difference splitting finite-volume 

scheme. The second, which was used to validate certain solutions of the upwind scheme, was an implicit, approximately 

factored, central-difference finite-volume scheme. Pseudotime stepping was used for unsteady-flow solutions. Locally 

conical flow solutions were considered at a chord station of 

unity. 

Accomplishment Description 

The figure shows sample solutions for unsteady, asymmetric, 

vortex-shedding flow. A grid of 161 x 81 points in the circumferential and normal directions was used for this application. 

The cone semi-apex was 5". A modified Joukowski transformation with a clustering geometric series was used to generate the grid, and the smallest grid length at the solid boundary 

was lo4. The figure shows snapshots of the time history of the 

solution for the total-pressure loss contours. The time step 

from 15,000 to 15,700 represents one-half of the cycle of the 

periodic flow response. At the time step of 15,000, the asymmetric flow is seen with the shed vortex on the right side. As 

time progresses, the shed vortex is convected in the flow field 

and the primary vortex on the left side stretches upward, while 

the primary vortex on the right gets stronger and expands to 

the left side of the free-shear layer. At the time step of 15,600, 

the left side of the free-shear layer shows two vortices; one 

at the top and another one below it. The upper part of the freeshear layer is moving upward and is about to be shed in the 

flow field. The solutions at time steps 15,000 and 15,700 are 

mirror images of each other, and the shedding frequency is 

4.49. 

Significance 

Results from the current investigation demonstrate the ability 

to simulate steady and unsteady asymmetric vortical flows 

around symmetric cones at zero side slip. This research 

shows, for the first time, that unsteady asymmetric vortex 

shedding is predicted. 

Future Plans 

Three-dimensional asymmetric flows are being considered for 

analysis and control. Several turbulence models are also 

being considered in this investigation to simulate other mechanisms of flow asymmetry. 

Images of unsteady asymmetric vortex shedding; M, = 1.8, 

a = 30", Re = lo5, At = 76. 
Transonic Navier-Stokes Solutions about a Complex High-Speed Accelerator 

Configuration 

James M. Luckring, Principal Investigator 

Co-investigators: Farhad Ghaffari, James L. Thomas, and Brent L. Bates 

NASA Langley Research Center 

Research Objective 

To apply advanced Navier-Stokes methods to complex 

National Aero-Space Plane (NASP) -type configurations at 

transonic speeds. 

A~proach 

An accelerator configuration recently tested in the Langley 

Research Center (LaRC) 18F00t Transonic Tunnel was 

selected for the study. This model was composed of a 

cone-cylinder-frustum body, a wrap-around engine nacelle, 

forebody and aft-body engine fillets, and a 70°'delta wing at 

incidence. The entire configuration surface was modeled 

analytically; this included faired-over engine inlet and 

exhaust faces. A blocked flow-field domain of approximately 

373,000 grid points was then constructed with hybrid topologies, using transfinite interpolation methods. Steady-state 

solutions to the compressible, thin-layer Navier-Stokes equations were obtained with an implicit finite-volume algorithm 

developed at LaRC (CFL3D). These solutions were achieved 

using van Leer's upwind-biased, flux-vector-splitting technique 

and an extended version of the Baldwin-Lomax algebraic 

turbulence model. 

Accomplishment Description 

Turbulent results have been obtained at a = 2O, RL = 30 x lo6 

and M, = 0.9, which correspond to flow conditions included 

in the recent wind tunnel tests mentioned above. The Mach 

contours on the surface and in the plane of symmetry, shown 

in the accompanying figure, demonstrate a smooth solution 

across various longitudinally blocked interfaces. After a subsonic and mainly attached forebody flow, the flow accelerates - 

supersonically over the engine cowl and subsequently shocks 

down at the exhaust cowl lip. (The sonic line is represented by 

a white contour line in the plane of symmetry to highlight the 

supersonic flow region.) The presence of the shock, as well as, 

the slanted exhaust face, causes the flow to separate and 

envelop the entire boattail region. This separation appears to 

be the principal cause for the excessive number of iterations 

(4610) needed to achieve a three-order-of-magnitude reduction of the residuals. The solution required approximately 

25 hours of Cray-2 time and 12 megawords of memory. 

Significance 

The design of proposed NASP vehicles will inevitably rely 

heavily on computational fluid dynamics to complement and 

extend information obtained in current ground-test facilities. 

Future Plans 

Efforts are under way to develop and implement a simple 

algorithm for simulating propulsion-induced effects. 

Publications 

Ghaffari, F.; Luckring, J. M.; Thomas, J. L.; and Bates, B. L. 

"Transonic Navier-Stokes About a Complex High-Speed 

Accelerator Configuration." AlAA Paper 90-0430, 1990. 

>.

LaRC 

Navier-Stokes Mach contours; M, = 0.9, a = 2", RL = 30 x lo6. 

ORIGiPJAL FA22 

COLOR PHOTQTOZRAPH 
Earthquake-Cycle Stress Simulations 

Gregory A. Lyzenga, Principal Investigator 

Co-investigators: Arthur Raefsky and Stephanie G. Mulligan 

Jet Propulsion Laboratorylcalifornia Institute of Technology 

Research Objective 

This work is aimed at understanding the spatial and temporal 

variations in stress and strain in the Earth's crust and upper 

mantle, at plate tectonic boundaries where relative motion is 

jxcommodated by recurrent great earthquakes. The resolution 

of outstanding questions regarding the driving forces of plate 

tectonics and seismic rupture requires a quantitative understanding of the processes operating in the transitional regime 

between elasticlbrittle rock behavior and plasticlducti~e flow. 

Approach 

Two-dimensional finite-element simulations of viscoplastic 

deformation were used to investigate the time evolution and 

distribution of stress near an infinitely long strike-slip fault in a 

layered Earth model. Special-purpose stress-activated fault 

elements were developed to simulate the stress-driven seismic 

rupture initiation. 

Accomplishment Description 

A systematic examination of a suite of candidate Earth models 

was conducted. The variable parameters included the far-field 

plate driving rate, the fault-failure strength criterion (either 

strong at -100 MPa, or weak at -10 MPa), and the crustal 

rheology law (either Maxwell-Newtonian or power-law nonNewtonian). The results of the study consist of calculated 

earthquake recurrence times, stress distributions, and 

stresslstrain histories, which may be compared with available 

field observations from the San Andreas fault region. These 

model results include the prediction that the crustal stress field 

is characterized by a local minimum in shear stress at shallow 

depths centered on the fault trace. At greater depths, below 

the elastic/plastic transition, the stress distribution is inverted, 

with locally hinh stress in the immediate neighborhood of the 

down-dip iaufi extension. - 

SigniRcame 

The results of simulations to date have lent support to the view 

that faults like the San Andreas fault generally sustain shear 

stresses an order of magnitude lower than those that would be 

expected on the basis of laboratory rock-strength measurements. The stress distribution features emerging from some of 

the current series of models are consistent with available 

experimental data, but also indicate areas in which additional 

measurements could be important. These results provide significant new details about the physical processes by which 

steady plate motion results from large episodic slip events on 

plate tectonic boundaries. 

Future Plans 

The existing finite-element code can be used to simulate 

deformations with three-dimensional displacement degrees of 

freedom on the two-dimensional grid. This capability will be 

used to simulate earthquake motions, including nonzero dipslip components. Such models will be useful for the study of 

events like the October 1989 Loma Prieta, California, earthquake as well as convergent and divergent plate boundaries. 

Publications 

Lyzenga, Gregory A.; Raefsky, Arthur; and Mulligan, 

Stephanie G. "Models of Recurrent Strike-Slip Earthquake 

Cycles and the State of Crustal Stress." Submitted to J. 

Geophysical Research, Apr. 1990. 

distance 1 to fault 

Shfifir Stress Maqni tilde 

Plot of shear-stress total magnitude for the power-law non-Newtonian rheology model, high-stress fault case, showing the stress 

field at year 108 of the 220-year earthquake cycle. The stress distribution is qualitatively similar to that of the Newtonian case, 

except in the details of the brittlelductile transition region. c;;:;/, -. .-, , - - - 4 - 

CSL;,T: Ftic: .-: ;I;;;"?), 
Numerical Investigation of a Space Shuttle Orbiter Contingency Abort 

Edward C. Ma, Principal Investigator 

Co-investigator: Thomas C. Wey 

Lockheed Engineering and Sciences Company 

Research Objective 

To investigate the contingency-abort longitudinal aerodynamic 

characteristics of the Space Shuttle orbiter and to compare the 

computational fluid dynamics results with experimental data. 

Approach 

A three-dimensional Euler code with a perfect-gas model is 

used to simulate high-angle-of-attack flow fields around the 

Space Shuttle orbiter. 

Accomplishment Description 

To integrate the Euler equations, three implicit methods are 

implemented; they are the two-factor alternating-direction 

implicit method, the blocked-line Gauss-Seidel scheme, and 

the hybrid time-marching scheme. A generalized upwindbiased interpolation scheme, which is basically an extension 

of van Leer's MUSCL scheme, was derived to achieve 

second- or third-order-accurate solutions. This new interpolation scheme was implemented in Steger-Warming and 

van Leer's flux-vector splitting methods and also in Roe's fluxdifference splitting method. As shown in the planform-view 

plot, the bow shock from the nose impinges on the wing near 

the side fuselage. As the angle of attack gets higher, the wing 

shock spreads outward and the interaction point moves off 

from the wing leading edge. The perfect-gas computation 

needed 2 Cray Y-MP hours and 3.9 megawords of memory. 

Significance 

If a contingency abort is required during the ascent, the orbiter 

will have to fly at a very high angle of attack (45" or above) 

and a relatively low Mach number (between 1 and 4). Successful simulation of these high-angle-of-attack cases provides an indispensable tool in the decision-making during an 

abort entry. 

Future Plans 

The codes will be further used to predict the aerodynamic 

characteristics of a complete Space Shuttle orbiter. 

-Shuttle Orbiter Mach Number Distribution 

Space Shuttle orbiter Mach number (top), and pressure distributions (bottom); M = 10.0, grid size 80 x 35 x 65. 
Nonlinear Evolution of Supersonic Disturbances in Mixing Layers 

M. G. Macaraeg, Principal Investigator 

NASA Langley Research Center 

Research Objective 

To understand the nonlinear evolution of supersonic disturbances that dominate the instability processes of high-speed 

mixing layers. 

Appraach 

Linearized and fully nonlinear compressible Navier-Stokes 

codes were written to study the linear stability and nonlinear 

evolution of high-speed mixing layers. The flow is considered 

to be temporally evolving and the solution schemes are a fully 

implicit spectral algorithm and an explicit algorithm, both 

written to study the nonlinear evolution. 

Accomplishment Description 

The fully implicit spectral algorithm uses a central finitedifference preconditioner. Discretization involves a Chebyshev 

series in the normal direction and a Fourier series in the 

streamwise direction. An order-of-magnitude increase in the 

allowable time step is attainable relative to an explicit formulation. Linear stability analysis identified the dominant instability 

modes associated with high-speed mixing layers to be supersonic. Studies of these disturbances in the nonlinear simulation show a resistance to subharmonic growth-a necessary 

precursor for mixin enhancement. Running the explicit code 2 requires 3.66 x 10- seconds per time step per grid point and 

15 megawords of memory for a typical grid. The implicit code 

is competitive in total time required to reach a desired time 

level. Further work is under way to speed up the finitedifference preconditioner, which presently requires the 

largest block of time in this code. 

Significance 

Enhanced mixing between the fuel stream and airstream is a 

major issue in scramjet engine design. Experiment and theory 

have shown that increases in Mach number produce lower 

levels of mixing efficiency. The current study shows how the 

growth of primary disturbances at low Mach number (left-hand 

figure) evolves into a strong subharmonic disturbance (i.e.. 

vortex pairingka mechanism responsible for mixing 

enhancement. This situation is sharply contrasted with that in 

the right-hand figure, which shows the time evolution of a 

supersonic disturbance. No subharmonic growth occurs; 

instead, there is a spectral broadening, as evidenced by the 

development of small-scale structures. 

Future Plans 

To study the complex nonlinear interactions of supersonic 

disturbances, secondary stability analysis will be used in conjunction with the nonlinear simulation. The secondary analysis 

will provide insight into the types of interactions these modes 

may undergo to promote higher harmonic growth and thus 

enhanced mixing. These studies will be pursued in the full 

nonlinear simulation study. 

Publications 

1. Macaraeg, M. G., and Streett, C. L. "New Instability 

Modes for Bounded, Free Shear Flows." Physics of Fluids A 1, 

no. 8 (Aug. 1989). 

2. "Bounded Free Shear Flows: Linear and Nonlinear 

Growth." Proceedings of the ICASffNASA Langley Workshop 

on Stability and Transition, June 1989. 

Subharmonic growth of a Mach 0.5 free-shear flow shearing Growth of a supersonic "kinking" mode; M, = 2. 

mode as time progresses. 
Simulation of Highly Ionized Flows 

Robert W. MacCormack, Principal Investigator 

Co-investigator: Philippe Rostand 

Stanford University/Analatom, Inc. 

Research Objective 

The ultimate objective is to obtain the capability to predict the 

flow of a moderately ionized nitrogen plasma in the different 

components of an arc-heated wind tunnel. The techniques 

developed will also be useful for the design of electric plasma 

thrusters. As a first step, we derived a computational fluid 

dynamics program capable of simulating the recombination of 

the plasma in an expansion chamber. 

Approach 

A generic program for the simulation of an axisymmetric flow 

of nitrogen in thermochemical nonequilibrium at high enthalpy 

and high speed is used to investigate the behavior of the jets 

of interest. The electric effects are accounted for in the socalled weak ionization approximation. The numerical method 

chosen is a finite-volume, upwind implicit scheme. 

Accomplishment Description 

Our program was developed and its results compared with 

experiment to obtain preliminary validation. The program uses 

five species, three temperatures, and the two components of 

the speed vector to represent the media. The internal energy 

model includes vibration of molecules, electronic excitation of 

atoms, and thermal agitation of electrons. The chemical model 

consists of six two-body and three-body reactions; the influence of the thermal nonequilibrium on the rates of reaction is 

accounted for. The electric effects introduce a nonconservative term in the equations, which is the source of numerical 

difficulties. The time integration to steady state is done through 

a fully coupled, fully implicit nonfactored scheme. A typical 

calculation takes 10 minutes on the Cray-2 and uses 3 megawords of memory. The accompanying figure shows the mass 

fraction of atomic nitrogen in the mixture, in the calculation that 

was used for validation. It illustrates the fact that the stiffness - 

problem and its associated numerical difficulties have been 

overcome. 

Significance 

Arc-jets are one of the few means by which high-enthalpy 

flows can be investigated experimentally. Their numerical 

simulation is important for two related reasons: to help in their 

design, and to improve and validate the models of the numerous phenomena they host (dissociation, ionization, thermal 

nonequilibrium, and radiation are the main ones). 

Future Plans 

A more extensive validation of the code will have to include 

simulation of nozzle expansions, in which rapid cooling is 

usually a challenge to the therrnochemical model. A natural 

extension of our work would be the simulation of the arc itself, 

which would need the inclusion of an electrical current model 

and a radiation model. 

Publications 

Rostand, P., and McCormack, R. W. "Nonequilibrium Flow in 

an Arc-Jet." Presented at the Workshop on Hypersonic Flows 

for Reentry Problems, Antibes, 1990. 

Mass fraction of atomic nitrogen; grid size 120 x 65. 
Computer Simulation of Ion Transport across Membranes 

Robert D. MacElroy, Principal Investigator 

Co-investigator: Andrew Pohorille 

NASA Ames Research Center 

Research Objective 

The objective of this research is to provide a molecular-level 

description of protobiological processes. In particular, our 

goal is to explain phenomena occurring at interfaces between 

water and nonpolar media (such as a membrane interior), and 

to understand how ubiquitous biological processes could 

occur in the absence of the complex, specialized enzymes 

that mediate these processes in currently existing organisms. 

bproach 

Our approach is to simulate the behavior of all the atoms in 

the system by molecular dynamics (numerical integration of 

Newton's equations of motion). This method allows us to 

obtain a molecularly detailed description of the system and to 

calculate its thermodynamic and structural properties. The 

system consists of biochemically important molecules in their 

natural environment (water and/or membranes). 

Accomplishment Description 

(1) Interactions of positive (sodium) and negative (chloride 

and fluoride) ions with a water liquidlair interface were studied. 

It was shown that the water at the interface with nonpolar 

media is significantly different from that in the bulk. As a result, 

negative ions can approach the interface more easily than 

positive ions (30 CPU hours, 4 megawords of memory). 

(2) First simulations of molecules at water surfaces were performed. Amphiphilic molecules assume rigid orientations in 

which polar groups are buried in water while hydrocarbon 

parts are located in the nonpolar environment (20 CPU hours, 

4 megawords of memory). (3) Large-scale simulations of DNA 

fragments in an aqueous solution were performed in order to 

study the opening of the DNA double helix. Two distinctly 

different pathways of opening were found (50 CPU hours, 

8 megawords of memory). 

Significance 

Our studies showed that interfaces between water and 

nonpolar media are uniquely suitable for promoting protobiological evolution. They can (1) selectively attract organic 

material and mediate its transport, (2) serve as simple catalysts for chemical reactions, and (3) promote the formation of 

electrical and chemical gradients, which could provide energy 

sources for protocells. Simulations of DNA yield information on 

the opening of the double helix-the critical step in protobiological, nonenzymatic DNA replication. 

Future Plans 

We will continue using computer simulations to study 

membranetwater interfaces, chemical reactions at those 

interfaces, and the transport of ions and small molecules 

across membranes. 

Publications 

1. "DNA Dynamics in Aqueous Solution: Opening the Double 

Helix." To be published in Int. J. of Supercomp. Applications, 

1990. 

2. Pohorille, A., and Pratt, L. R. "Cavities in Molecular Liquids 

and the Theory of Hydrophobic Interactions." J. Am. Chem. 

Soc,, 1990. 

3. Wilson, M. A.; Pohorille, A.; and Pratt, L. R. "Comment on: 

Study on the Liquid-Vapor Interface in Water. I. Simulation 

Results of Thermodynamic Properties and Orientational 

Structure." J. Chem. Phys. 90 (1989): 521 1. 

A fragment of the DNA double helix with the terminal adenine-thymine base pair opened. For clarity, water molecules and 

counterions, present in the calculation, were removed. Oxygen atoms are red, nitrogen atoms are light blue, hydrogen atoms are 

white, phosphorus atoms are yellow, carbon atoms of the bases are dark blue, and carbon atoms of the sugar-phosphate backbone are green. Note that both hydrogen bonds between thymine and adenine are broken and adenine moved away from its 

original position in the double helix. In contrast, the position of thymine remains almost unchanged. 

ORtGiNAL PAGE 

COLOR PtiOTOSRRPH 
Transonic Analysis About the F-16A and Other Complex Configurations 

Michael D. Madson, Principal Investigator 

Co-investigators: Alex C. Woo, Ralph L. Carmichael, F. T. Johnson, S. S. Samant, D. P. Young, R. G. Melvin, 

M. B. Bieterman, and J. E. Bussoletti 

NASA Ames Research CenterlBoeing Advanced Systems 

Research Objective 

To develop and validate a computational method that eliminates the use of surface-conforming grids in the analysis of 

complex aircraft configurations in the transonic flow regime. 

Approach 

The TranAir full-potential code was developed by Boeing 

under NASA contract. The code embeds accurately defined 

surface-panel models of very general and complex configurations such as the F-16A in a rectangular array of flow-field grid 

points. The grid is adaptively refined based on local error 

estimates, in order to more accurately resolve the local flow 

field. A system of nonlinear algebraic equations is constructed 

from the finite-element operators on the grid; the equations are 

solved in an iterative fashion. 

Accomplishment Description 

The final version of the code was delivered during the operational year. The two most significant enhancements to the 

code were a solution-adaptive grid-refinement capability and 

the ability to solve supersonic free-stream problems. The 

solution-adaptive capability helps the user determine where 

denser grid definitions are needed. The refinement in regions 

of secondary interest can be controlled by the user so that the 

grid-point distribution is clustered in regions of primary interest. The ability to solve problems in the supersonic flow regime 

allows engineers to obtain solutions for complex fighter configurations as well as for commercial high-speed transports. 

The figure shows a vertical cut of the refined grid through the 

wing and chine of the generic fighter geometry. This grid was 

generated for a case in which M = 1.2 and a = 4". The solution 

about a complex configuration in transonic flow using about 

300,000 flow-field grid points takes about 5000 CPU seconds 

on a Cray Y-MP and uses less than 4 megawords of central 

memory. 

Significance 

TranAir has the unique ability to obtain solutions about arbitrary and complex configurations in subsonic, transonic, and 

supersonic flow regimes. The use of surface panels for the 

geometry definition, and the use of unstructured Cartesian 

flow-field grids allow the engineer to quickly and easily obtain 

aerodynamic solutions for a wide range of configur~t' Ions. 

Future Plans 

This project was not granted a continuation for operational 

year 1990-91. Work will continue on the ACF Cray Y-MP. The 

code is scheduled to be delivered to several requesters in 

government, industry, and academia. 

Publications 

1. Madson, M. D.; Carmichael, R. L.; and Mendoza, J. P. 

"Aerodynamic Analysis of Three Advanced Configurations 

Using the TranAir Full-Potential Code." NASA CP-3020, vol. 1, 

part 2, Apr. 1989, pp. 437-452. 

2. Johnson, F. T.; Samant, S. S.; Bieterman, M. B.; Melvin, 

R. G.; Young, D. P.; Bussoletti, J. E.; and Madson, M. D. 

"Application of the TranAir Rectangular Grid Approach to the 

Aerodynamic Analysis of Complex Configurations." AGARD 

CP-464, May 1989, chap. 21. 

A vertical cut of the refined grid through the wing and chine of a generic fighter geometry. 

96 
Radiation and Control of the Acoustic Field Caused by a Wave Packet Evolving 

along a Concave-Convex Surface 

L. Maestrello, Principal Investigator 

Co-investigator: N. M. El-Hady 

NASA Langley Research CenterIAnalytical Services and Materials, Inc. 

Research Objective 

This research is an engineering application of flow through a 

wind tunnel contraction. The objective is to investigate the 

acoustic field and the control of the acoustic radiation resulting 

from the evolution of a wave packet in an unstable boundary 

layer over a concave-convex surface. Numerical experiments 

were conducted to study the behavior of a wave packet with 

iegard to the stability, sound radiation, and control of the 

radiation in the boundary layer. 

Approach 

The analysis is based on the numerical solution of twodimensional, nonlinear Navier-Stokes equations; a fourthorder-accurate operator-split algorithm is used. An initial 

steady solution is obtained, and an unsteady disturbance 

of finite duration is introduced in the form of a TollmienSchlichting wave and its subharmonic. Hence, a wave packet 

is created that grows and decays as it passes through the 

region of curvature. The acoustic radiation resulting from the 

evolution of the packet is evaluated by solving the linearized 

Euler equations, using the pressure computer from the NavierStokes equations as a time-dependent boundary condition. A 

fixed control algorithm is used in which the attenuated signal is 

0 

instantaneus 

total 

vorticity 

Instantaneous total vorticity. 

Acoustic 

pressure o 

at 60" 

synthesized by a filter that actively adapts itself to the 

amplitude-time response of the outgoing acoustic waves. 

Accomplishment Description 

The character of the wave packet is illustrated by the instantaneous total vorticity, plotted in terms of nondimensional time. 

The total vorticity was initially amplified on the flat portion, and 

additional amplification come on the concave curvature due to 

unfavorable pressure at 60" angle show a strong beaming, an 

equivalent weaker beaming occurs at 135". The control is 

applied to the far field to adjust the amplitude of the interference signal at different angles. The filters compensate for the 

amplitude and bandwidths, and the controllers produce an 

interference field. The effectiveness of the control is shown by 

a reduction in acoustic intensity corresponding to a 6-dB 

change in amplitude. 

Significance 

lnhomogeneity of the source field over a finite time has been 

identified as an important source of sound radiation and can 

be regarded as typical wind tunnel contraction noise. 

Future Plans 

A model wind tunnel is being constructed using a new contraction geometry such that disturbances propagating into the 

contraction can effectively decay exponentially with distance. 

Sound control system. 

- Uncontrolled ---- Controlled 

Acoustic 

far field 

intensity 

Acoustic pressure at 60". Acoustic far-field intensity. 

Control of the acoustic field caused by a wave packet evolving over a concave-convex surface. 
Transition in Hypersonic and Three-Dimensional Boundary Layers 

Mujeeb R. Malik, Principal Investigator 

Co-investigators: C.-L. Chang and R. E. Spall 

High Technology CorporationINASA Langley Research Center 

Research Objective 

The long-term goal of this research is to develop the capability 

to predict the onset of boundary layer transition in high-speed 

and three-dimensional boundary layers. Understanding the 

transition process in these flows is an essential prerequisite for 

the development of reliable transition-region models for computational fluid dynamics applications. This understanding and 

the prediction capability can only be achieved through studies 

involving internalization of disturbances (receptivity), linear 

and nonlinear development of various disturbances (TollmienSchlichting, crossflow, Gt)rtler), and their possible interaction. 

For high-speed flows, such effects as bluntness, shocklwave 

interactions, and crossflow instability need to be studied. 

Approach 

For high-speed applications, Navier-Stokes and parabolized 

Navier-Stokes (PNS) codes are used for computation of the 

basic flow, which is analyzed using linear stability theory. 

Time-accurate Navier-Stokes codes are used for the direct 

numerical simulation of the nonlinear development of disturbances and final breakdown. 

Accomplishment Description 

(1) Linear stability analysis of the Mach 8 flow past a 7" semivertex blunt cone (nose Reynolds number = 31,250) was performed. Results indicated that nose bluntness caused the 

critical Reynolds number for the onset of instability to increase 

an order of magnitude (from about 2.25 x lO" for the sharp 

cone to 3.3 x lo6 for the blunt cone). The predicted critical 

Reynolds number, the disturbance frequency, and the growth 

rates were in agreement with the experiment of Stetson et al. 

(1984). Calculations were also performed for reentry-F cone 

data (M, = 20,s" semi-vertex cone) using an equilibrium-gas 

model. These stability calculations required that the basic flow 

and its first and second derivatives be computed accurately. 

CONTOUR LEVELS 

0. OOODO 

0.05000 

0.10000 

u.15000 

u. 211000 

11. ')sflull 

0.30000 

0.351000 

O.4OQOlJ 

0,45000 

0.50000 

fl .5500CI 

0. bllUUU 

a. 65000 

0.70000 

0.75000 

0.75000 

About 240 grid points were used across the shock layer in the 

PNS calculation. A complete run (Navier-Stokes solution for 

the nose, PNS solution, stability analysis, and application of 

the eN method) requires about 3 to 12 hours of Cray Y-MP 

time, depending on Mach number and gas chemistry. The 

maximum memory requirement is about 1.5 megawords for 

the axisymmetric version. (2) In order to understand the breakdown of a crossflow vortex (present in three-dimensional 

boundary layers because of inflectional crossflow velocity 

profiles), a Navier-Stokes simulation of a crossflow vortex in a - 

three-dimensional boundary layer was performed. The resultant velocity field is shown in the figure. Because of the nonlinear crossflow vortex, low velocity regions appear within the 

boundary layer; this results in "wake-like" profiles subject to 

secondary instabilities. This would provide at least one route to 

transition in a three-dimensional boundary layer. 

Significance 

Transition prediction is crucial for the design of aerospace 

vehicles such as the National Aero-Space Plane, and for 

supersonic laminar flow control for High Speed Civil Transport. 

The agreement of our stability results for hypersonic flow with 

experimental data gives confidence in the theory and in its 

usefulness for transition prediction. 

Future Plans 

The codes will be used to study instabilities in threedimensional boundary layers at supersonic and hypersonic 

Mach numbers for bodies at angle of attack. In addition, 

shock-wave effects on the instability will be studied and 

numerical simulations of transition will be performed. 

Publications 

"Effect of Nose Bluntness on Boundary Layer Stability and 

Transition." AlAA Paper 90-01 12, 1990. 

Nonlinear crossflow vortex in a three-dimensional boundary layer. The computed velocity component along the axis of the vortex 

is shown. 
Navier-Stokes Analysis of the Air Force Vortex Flap Model and the F/A-18 

John Mangus, Principal Investigator 

Co-investigators: Shreekant Agrawal, Robert Lowrie, and Brian Robinson 

Northrop Aircraft DivisionIMcDonnell Aircraft Company 

Research Objective 

The objective of this work is to investigate vortical flows about 

the Air Force Vortex Flap Model (AFVFM) and the FIA-18 aircraft at high angles of attack. The intent of these investigations 

js to analyze the actual geometries, to verify computational 

fluid dynamics codes for high-angle-of-attack flows, and to 

gain a better understanding of the physics of these flows. 

Approach 

Because of the complex geometries and the nature of the flow, 

three-dimensional Navier-Stokes codes were used to predict 

the flow fields. The thin-layer Navier Stokes code was used to 

compute the flow about the AFVFM geometry, and the CFL3D 

code was used to compute the flow about the FIA-18 ForebodyLEX geometry. 

Accomplishment Description 

Navier-Stokes solutions were obtained about the AFVFM 

and FIA-18 geometries. The AFVFM was modeled using a 

193 x 49 x 81 C-0 topology mesh. This grid was found to be 

too coarse in the normal direction to adequately resolve the 

boundary layer. Both single-zone and two-zone grids were 

used to model the FIA-18 Forebody-LEX geometry. 

Zone 1: 35 x 51 x 50 

The single-zone grid had 406,617 points, and the two-zone 

grid had 234,500 points. Laminar and turbulent (BaldwinLomax turbulence model) viscous flow fields were considered. Pressure-coefficient results for the M = 0.24, a = 30.3", 

and 

Relft = 885,000 case compared well with flight test data. 

These cases required approximately 4 Cray-2 hours and 

40 megawords of memory. 

Significance 

Future fighter aircraft will be required to maneuver within 

broader flight envelopes. The computational prediction of 

flows past complex geometries at high angles of attack will 

not only enhance the design of future aircraft but will aid in 

under-standing the physics of such flows. The results obtained in this study are a significant step toward the NavierStokes analysis of full aircraft geometries at high angles of 

attack. 

Future Plans 

The AFVFM will be modeled with a grid that will adequately 

resolve the boundary layer. The FIA-18 geometry will be 

extended to include the wing. Comparisons with flight test 

data will continue. 

I 

FIA-18 Surface Cp Distribution, FS 184 

Zone 2: 35 x 83 x 50 

0 

8 - deg 

Stagnation pressure contours for the FIA-18 Forebody-LEX geometry, two-zone grid; M, = 0.24, a = 30.3", Re/ft = 885,000. 

ORIG~NAL P/:.GE 

COLOR PWTOGHAPH 
Direct Simulation of Compressible Turbulent Flows 

Nagi N. Mansour, Principal Investigator 

Co-investigators: J. Chen and G. Blaisdell 

NASA Ames Research Center 

Research Objective 

To develop an understanding of the effects of compressibility 

on turbulent flows, and to develop a data base for compressible turbulent flows using direct simulation methods. 

Approach 

Three-dimensional time-dependent simulations of compressible turbulent flows are carried out using spectral methods. 

The effects of compressibility on the growth of wakes are 

studied by solving the compressible Navier-Stokes equations 

using Fourier methods in the streamwise and spanwise directions, and solving a mapped spectral in the cross-stream 

direction. The development of compressible homogeneous 

turbulent flows is studied by solving the Navier-Stokes equations using Fourier methods in all directions, in a moving grid. 

Accomplishment Description 

We found that the baroclinic and dilatational terms prevent the 

roll-up of vorticity at high Mach numbers, and thus reduce the 

growth rate of the wake. We found that vortex loops may or 

may not form, depending on the phase between the initial twodimensional wave and the oblique wave perturbations. The 

turbulence energy in homogeneous flows under mean shear 

was found to decrease with increasing high Mach numbers. 

We found that the streamwise component of the solenoidal 

part of the field grows as in the case of incompressible flows, 

while for the dilatational part of the field, the cross-stream 

component grows. This may be caused by the radiation of 

acoustic waves in the cross-stream direction. 

Significance 

At high Mach numbers the effects of compressibility on the 

turbulence are felt through the dilational part of the field and 

the baroclinic terms. The existing turbulence models that do . not take the dilational effects into account will fail for high 

Mach numbers. Data bases are available for testing modeling 

hypothesis and formulations. 

Future Plans 

We will continue to work on the development of wakes by 

studying the effects of random initial perturbations on the 

development of the large structures. Homogeneous flows 

under mean compression will be simulated using spectral 

methods. 

Publications 

Chen, J. H.; Cantwell, B. J.; and Mansour, N. N. "The Effect of 

Mach Number on the Stability of a Plane Supersonic Wake." 

Physics of Fluids A, June 1990. 

Vortex lines in a plane wake, revealing the formation of vortex loops; M = 1.000, a = O.OOO, Re = 1 .OO x lo2, time = 98.0, grid size 

24 x 128 x 12. 
Space Shuttle Flow Field 

Fred W. Martin, Jr., Principal Investigator 

Co-investigators: Joseph Steger, Pieter Buning, Steve Labbe, Ray Gomez, Phil Stuart, Jeff Slotnick, Steve Parks, and 

Stan Johnson 

NASA Johnson Space Flight CenterINASA Ames Research Center 

Research Objective 

To enhance the fidelity of the Space Shuttle ascent geometry 

by including additional components of the aft attach hardware 

between the orbiter and the external tank. 

'Approach 

The F3D-Chimera scheme is used to obtain flow fields about 

the Shuttle launch vehicle in the Mach number range from 

0.6 to 4.5, with particular emphasis in the transonic range. 

Accomplishment Description 

Two additional components of the orbiter-to-external-tank aft 

attach interface were added to the Shuttle launch vehicle grid 

system. The first item was a high-fidelity representation of the 

orbiter-to-external-tank vertical strut, and the second was an 

ellipsoid designed to approximate the frontal area of the 

17-in.-diameter propellant feed lines. These features brought 

the modeled aft attach blockage to 85% of the blockage on 

the launch vehicle. An M = 1.25, a = -4.0 solution was 

obtained with the new grid system. Integrated wing loads 

were slightly lower than, but compared favorably with, the 

Shuttle's IVBC-3 aeroloads data base for wing-root shear and 

bending. However, large discrepancies existed in the wing 

torsion comparison. 

Significance 

The Shuttle orbiter wing loads are adversely affected by the 

attach hardware between the Shuttle components. As a result, 

zero wing lift occurs on the negative-a side of the transonicascent flight envelope, instead of at the more benign center of 

the envelope. The correct modeling of the ascent vehicle's 

blockage and protuberances is instrumental to obtaining 

accurate simulations of the Shuttle ascent aerodynamic loads. 

Future Plans 

The fidelity of the aft attach hardware will be further improved 

by including the asymmetries caused by the liquid oxygen and 

liquid H2 feed lines. Unfortunately, the corresponding calculations will not be able to take advantage of the plane-ofsymmetry boundary condition, thus doubling the required 

computer resources. 

Publications 

Martin, F.; and Slotnick, J.; in collaboration with the Ames 

Space Shuttle Flow Field Simulation Group: Steger, J.; Buning, 

P.; Chiu, I.; Meakin, R.; Obayashi, S.; Rizk, Y.; and Yarrow, M. 

"Flow Computations for the Space Shuttle in Ascent Mode 

Using Thin Layer Navier-Stokes Equations." To be published in 

the AlAA Progress Series volume Applied Computational 

Aerodynamics. 

1 Pressure coefficient for the Space Shuttle flow field; M = 1.25, u = -4.0' 

!I i RAP H 

101 
Solution of the Steady State Navier-Stokes Equations on Unstructured and 

Adaptive Meshes 

Dimitri J. Mavriplis, Principal Investigator 

NASA Langley Research CenterIlCASE 

Research Objective 

To develop an accurate and efficient method for computing 

turbulent compressible flow about complex configurations. 

Approach 

The steady-state Navier-Stokes equations are solved on an 

unstructured triangular mesh with highly stretched elements in 

the boundary-layer and wake regions. Mesh adaptivity is used 

to enhance solution accuracy, and an unstructured multigrid 

technique is used to accelerate the convergence to steady 

state. An algebraic turbulence model specifically devised for 

use with multiple-body geometries and unstructured meshes is 

used. 

Accomplishment Description 

An accurate and efficient method for computing turbulent 

compressible flows has been devised. Accuracy is achieved 

by extensive use of adaptive meshing techniques. Efficiency is 

obtained by using a multigrid acceleration method and a relatively inexpensive algebraic turbulence model, both suitable 

for use on unstructured meshes. The multigrid algorithm 

accelerates the convergence to steady state by repeatedly 

time stepping on a sequence of coarse and fine unstructured 

meshes, each generated either globally or by adaptive refinement, and interpolating the flow variables back and forth 

between these meshes. The algebraic turbulence model 

operates on a set of local background structured meshes (one 

about each wall or wake boundary). At each time step, the 

flow variables are interpolated onto the background meshes, 

and the resulting eddy viscosities are interpolated back to the 

global unstructured mesh. The interpolation patterns for both 

the multigrid and the turbulence model are determined in a 

preprocessing step, where an efficient tree-search algorithm is 

used. The turbulent compressible flow over a four-element 

airfoil configuration was computed using 62,000 grid points. A solution converged to engineering accuracy was obtained in * 

100 multigrid cycles, requiring approximately 40 minutes of 

Cray-2 CPU time and 16 megawords of memory. A total of 

70 Cray-2 hours were used in the development and validation 

of this code. 

Significance 

The ability to predict turbulent compressible flows about 

complex geometries such as high-lift multi-element airfoil 

configurations in two dimensions and full aircraft configurations in three dimensions is important to the aircraft industry. 

Future Plans 

Future work will study the effect of more sophisticated turbulence models on the solution accuracy and efficiency. The 

extension of these ideas to three dimensions is also under 

way. 

Publications 

1. Mavriplis, D. J., and Jameson, A. "Multigrid Solution of the 

Navier-Stokes Equations on Triangular Meshes." To be published in AlAA J., 1990. 

2. Mavriplis, D. J. "Euler and Navier-Stokes Computations for 

Two-Dimensional Geometries Using Unstructured Meshes." 

CASE Rep No. 90-3, NASA CR-181977, Jan. 1990. 

Solution of the steady state Navier-Stokes equations on unstructured and adaptive meshes. 
Numerical Study of Planetary Atmospheres 

Hans G. Mayr, Principal Investigator 

Co-investigator: Kwing L. Chan 

NASA Goddard Space Flight Center 

Research Objective 

The ultimate objective of this work is to understand the 

dynamics of the prevailing atmospheric circulations of the 

planets in the solar system. The questions of concern are: 

What mechanisms generate the alternating wind bands on 

Jupiter, Saturn, and Neptune? Is there a common origin? What 

generates the extremely large super-rotation of the atmosphere of Venus (60 times the rotation rate of the planet)? 

What are the differences and links among the atmospheres of 

the terrestrial planets and the outer planets? At first sight, 

these questions seem to address too broad a subject. In fact, 

some unifying principles that provide answers to these 

questions have been worked out, but mostly based on a 

quasi-linear theory (Mayr and Harris, Astron. Astroph. 121 

(1983): 124; Mayr, Harris, and Chan, Earth Moon and Planets 

30 (1984): 245; Mayr et at., Adv. Space Sci. 5 (1985): 63). Our 

numerical computations advance this theory into the nonlinear 

regime and check for the validity of some basic theoretical 

assumptions. The most important among them concerns the 

behavior of the Reynolds stresses in a rotating fluid. Numerical 

computation is the only viable way to study such problems. 

Approach 

Two- and three-dimensional codes are used to solve the 

Navier-Stokes equations for a compressible, stratified fluid. An 

alternating-direction implicit spectral code was developed to 

run on the Crays. This code describes the spherical geometry 

naturally and is extremely efficient for low-Mach number flows. 

Accomplishment Description 

An axisymmetric version of the spectral code was used to 

study the spin-up of the super-rotating Venusian atmosphere. 

This problem was chosen as a first step in our program 

because it is easier than the other problems and it can provide 

us with valuable experience in adapting our codes to planetary applications. Since the problem is axisymmetric, the 

demand on memory is so far not high (about 10 megawords). 

However, the CPU requirement is already substantial. The 

difficulty lies in the extremely long physical relaxation time. The 

Venusian atmosphere needs a few hundred years to spin up. 

Even running at a CFL number of 103, the code needs about 

one million steps to converge; that takes about 2 hours on the 

Cray Y-MP. 

Significance 

The resulting zonal wind from the numerical model is within a 

factor of two of that observed on Venus. Since there are still 

many uncertainties about the atmospheric conditions of 

Venus, and some parameters can be adjusted, this calculation 

demonstrates that the super-rotation of the Venusian atmosphere can in principle be explained. The parametric behavior 

of the model is in line with the expectation from the quasilinear theory. Numerically, it shows that more realistic threedimensional simulations are feasible. 

Future Plans 

We plan to carry out three-dimensional calculations to study 

the behavior of the Reynolds stresses (especially the horizontal ones) in order to check whether they are diffusive as 

assumed in the axisymmetric model and whether they are 

large enough to transport sufficient angular momentum from 

high latitudes to the equatorial region, where large zonal winds 

are observed. 

Publications 

Chan, K. L., and Mayr, H. G. "Modeling the Circulation in a 

Venus-like Atmosphere." Presented at the 1990 Spring AGU 

Meeting, Baltimore, MD, May 1990. 

40 km - Altitude pole 

Venus-like atmospheric super-rotation. 
National Aero-Space Plane Propulsion Flow-Path Analysis and Code Certification 

Charles R. McClinton, Principal Investigator 

Co-investigators: R. Bittner, G. Bobskill, R. Hawkins, T. Jentink, P. Kamath, M. Mao, G. Mekkes, and D. Riggins 

NASA Langley Research Center 

Research Objective 

To certify computer codes for National Aero-Space Plane 

(NASP) scramjet flow-field evaluation and test support. 

Approach 

The SPARKBD, CFL3D, and GASP codes are applied to 

selected "unit" and "component" experimental problems 

identified as typical of NASP inlet, combustor, and nozzle 

flows. Calculated performance parameters and flow fields are 

compared with experimental results to obtain confidence in 

the ability of computational fluid dynamics to model largescale flight conditions. 

Accomplishment Description 

Numerical analysis of three simulated scramjet nozzle 

experiments, nine transverse fuel injectors with no reaction, 

one direct connect combustor experiment (illustrated in the 

figure) and two inlet experiments provided an enhanced 

understanding of engine flow fields, a direct comparison with 

experimental measurements, an understanding of solution grid 

density and computer memory and CPU requirements, and an 

estimate of numerically generated engine thrust performance 

accuracy. The photograph illustrates the hydrogen mass 

fraction distribution in a direct connect combustor, just downstream of a swept-ramp fuel injector. Calculated wall pressures over the entire 1.3-m length of the direct connect 

experiment are in reasonable agreement with experimental 

measurements, and the calculated combustion efficiency is 

within 5 to 10% of the experimentally determined value. Other 

performance prediction accuracies are discussed in the 

publications. 

Significance 

The capability developed under this project has provided an 

understanding of the capabilities and limitations of numerical 

analysis of large-scale scramjet flow fields and has clearly 

demonstrated the value of this numerical analysis in providing 

design support for hypersonic air-breathing vehicles. 

Future Plans 

We will continue more complex and higher speed inlet, 

combustor, nozzle, and complete airframe integrated enginevehicle analysis using and supporting ground and flight tests. 

Publications 

1. Drummond et al. Paper 17, 6th NASP Symposium, Apr. 

1989. 

2. Riggins et al. Paper 25, 6th NASP Symposium, Apr. 1989. 

3. Mekkes et al. Paper 55, 6th NASP Symposium, Apr. 1989. 

4. Drummond et al. AlAA Paper 89-2794, 1989. 

5. Richardson et al. SAE Paper 89-2313, 1989. 

6. Riggins et al. NASP CR-1043, Apr. 1989. 

7. Riggins et al. Paper 56, 7th NASP Symposium, Oct. 1989. 

8. Riggins et al. AlAA Paper 90-0203, 1990. 

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104 
Aerodynamic Flows about High-Performance Rotor Blade Tips 

W. J. McCroskey, Principal Investigator 

Co-investigators: J. D. Baeder, G. R. Srinivasan, and E. P. N. Duque 

U. S. Army Aeroflightdynamics Directorate-AVSCOM/NASA Ames Research Center 

Research Objective 

The objective of this research is to develop and validate 

accurate, user-oriented, viscous computational fluid dynamics 

(CFD) codes for three-dimensional, unsteady aerodynamic 

flows about advanced-geometry rotor blade tips. These codes 

are then used to study the fluid physics of tip vortex formation 

and roll-up from complex tips, and to develop improved tip 

shapes for high-performance rotorcraft. 

+iccomplishment Description 

Thin-layer Navier-Stokes solutions were used to further analyze 

the nonrotating aerodynamic characteristics of the British 

Experimental Rotor Program (BERP) blade. In all flow regimes 

explored, the computations predicted that the blade had many 

favorable aerodynamic characteristics in comparison with 

conventional helicopter rotor blades. The computed results 

exhibited a good qualitative comparison with the wind tunnel 

tests performed by Westland Helicopters Ltd., as shown in the 

accompanying figure. The solutions required approximately 

25 megawords of memory and 25 hours of Cray-2 CPU time 

per solution. 

Significance 

This work provides a source of aerodynamic data for the BERP 

blade. It demonstrates the ability to predict the viscous threedimensional effects of complex helicopter blade tips. It also 

illustrates the ability of CFD to provide a better understanding 

of complex aerodynamic geometries, not easily attained by 

experiment, and it provides a new tool the rotorcraft community can use to analyze and design new blade tips. 

Future Plans 

The group will continue to develop more accurate and efficient 

flow simulation codes. Future computations will include computations of other advanced helicopter blade tips in both 

hover and forward flight. These studies will allow new tips to 

be designed that will improve helicopter performance. 

Publications 

1. Duque, E. P. N. "A Numerical Analysis of the British 

Experimental Rotor Program Blade." NASA TM-102247, Nov. 

1989. 

2. Brocklehurst, A,, and Duque, E. P. N. "Experimental and 

Numerical Study of the British Experimental Rotor Program 

Blade." AlAA Paper 90-3008, Aug. 1990. 

Computed Experiment 

Comparison of computed results with wind tunnel tests; a = 20°, M = 0.20, Re = 1.5 x lo6. 
Airloads and Acoustics of Rotorcraft 

W. J. McCroskey, Principal Investigator 

Co-investigators: J. D. Baeder, E. P. Duque, and G. R. Srinivasan 

U. S. Army Aeroflightdynamics Directorate-AVSCOMINASA Ames Research Center 

Research Objective 

To develop and validate accurate, user-oriented, viscous 

computational fluid dynamics (CFD) codes (with inviscid 

options) for three-dimensional, unsteady aerodynamic flows 

about arbitrary rotorcraft configurations; developing the 

capability to calculate the associated acoustic field is 

included. 

Approach 

Unsteady Euler and thin-layer Navier-Stokes codes are being 

developed, adapted, and extended to simultaneously capture 

the aerodynamics and the acoustics of rotorcraft. Accuracy 

and stability are achieved by utilizing Roe upwind-biasing with 

third-order-accurate in space MUSCL-type limiting. Efficiency 

is obtained with an LU-SGS implicit operator on the left-hand 

side, combined with Newton iterations. In order to properly 

capture the acoustics, the grid is extended to a distance 

several rotor radii away from the center of rotation. 

Accomplishment Description 

The previous investigation of the aerodynamics of isolated 

rotor blades in hover was extended to capture the high-speed 

impulsive (HSI) noise of a nonlifting rotor. The accompanying 

figure shows the pressure contours and grid in the plane of 

the rotor for a tip Mach number of 0.92. The time history of the 

pressure disturbance at a location 2.18 rotor radii from the 

center of rotation is shown in the inset; the agreement with 

experimental data is excellent. Fine-grid Euler computations, 

using over 400,000 grid points, required about 20 megawords 

of central memory and 5 Cray-2 hours of CPU time per 

solution. Similar agreement with experiment was shown for a 

range of Mach numbers, out to a distance of 3 rotor radii (over 

42 chord lengths). A second code was developed to capture 

the vortical structure of the rotor wake without ad hoc modeling, thus facilitating the viscous simulation of multiple lifting 

blades in hover. Preliminary coarse-grid Navier-Stokes 

calculations, using about 100,000 grid points, required about 

10 megawords of central memory and 3 Cray-2 hours of CPU 

time per solution. The computed near-wake effects of the 

vortical wake show good agreement with experimental data. I 

Significance 

The ability to simulate accurately the aerodynamics and 

acoustics of rotorcraft will enable significantly better and 

quieter vehicles to be designed at lower cost, with less 

expensive testing and less risk. This is the first time that a 

purely CFD method has been used to calculate HSI noise; it 

has resulted in agreement with experiment that is vastly 

improved compared with previous analytical methods, which 

are usually off by almost a factor of two in predicting the peak 

negative pressures. 

Future Plans 

The research will continue in order to develop more accurate 

and efficient simulations of rotor aerodynamics and acoustics. 

with particular emphasis given to combining the above 

capabilities to investigate the rotor wake and its influence on 

blade airloads and acoustics for various blade planform and 

airfoil shapes. This will necessitate the development of 

multizones and/or adaptive grids, especially for forward flight. 

Publications 

1. "The Computation and Analysis of Acoustic Waves in 

Transonic Airfoil-Vortex Interactions." Ph.D. Thesis, Stanford 

Univ., Sept. 1989. 

2. "Computational Analysis of Transonic Airfoil-Vortex Interaction Acoustics and Rotorcraft CFD." NASA 7th Annual 

Review of Helicopter Noise Reduction Program, Oct. 1989. 

3. "Unsteady Interaction of a Rotor with a Vortex." AlAA 

Paper 89-1848, June 1989. 

Noise resulting from thickness for a nonlifting hovering rotor, Euler solution; Mtip = 0.92. 

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Tilt-Rotor Aerodynamic Interactions 

W. J. McCroskey, Principal Investigator 

Co-investigators: V. Raghavan and S. Stanaway 

NASA Ames Research Center 

Research Objective 

To apply Reynolds-averaged Navier-Stokes codes to interactional aerodynamic problems associated with high-speed 

rotorcraft, including tilt-rotor aircraft. 

~ccomplishment Description 

Proposed designs for a high-speed rotorcraft involve some 

hybrid of a helicopter and an airplane-for example, a tilt rotor. 

One unique aspect of this application is the presence of a 

rotating grid around the rotor blades combined with a fixed 

grid about a wing and fuselage. The approach taken was to 

validate the Navier-Stokes codes for individual vehicle elements (a fuselage andlor a wing at 90" angle of attack), place 

these elements in the presence of a modeled rotor on a fixed 

grid, and compute the flow for the combined rotor and body. 

The full-scale interactional aerodynamic test, whose set-up is 

shown in the accompanying figure, was chosen as a test case 

for code validation. The results of a Reynolds-averaged 

Navier-Stokes calculation is also shown; the color mapping 

depicts the pressure distribution on the body, and the lines 

indicate the surface skin friction vectors on the isolated body. 

Another component studied extensively was the tilt-rotor wing 

airfoil at an angle of attack of -90°, showing high-frequency 

shedding for laminar and turbulent flows. The rotor was 

modeled initially by an actuator disk, which was treated 

implicitly in the Navier-Stokes environment as an internal 

boundary condition in a cylindrical grid, using the fortified 

Navier-Stokes technique. Preliminary calculations for the 

fuselage body used 210,000 points, requiring about 4 hours 

of Cray-2 time, and typical bluff-body calculations used 

20,000 points, requiring 30 minutes of Cray-2 time per 

solution. 

Significance 

Three-dimensional fuselage calculations have shown skin 

friction patterns similar to experimental results. The twodimensional bluff-body predictions showed some success and 

also pointed to the areas that need further study, namely, 

turbulence models for unsteady shear flows. The actuator disk 

was implemented successfully in the Navier-Stokes environment. This work demonstrates the usefulness of Reynoldsaveraged Navier-Stokes equations for complex viscous 

environments, and lays the groundwork for interactive aerodynamic calculations. 

Future Plans 

Future plans include more extensive code validation for the 

isolated body, followed by rotorlbody interaction calculations 

for a fuselage and actuator disk. Similarly, we will compute the 

three-dimensional wing at 90" and combine it with an actuator 

disk to predict the tilt-rotor download in the take-off configuration. Although the actuator disk model assumes a uniform disk 

loading, this is not necessary in our approach, and the next 

step will be to include a nonuniform disk-loading model. The 

potentially complex grid generation task typically involved for 

a complex geometry such as the rotor and body combination 

will be simplified by using the overset grid technique, 

Chimera. Other work in progress includes better turbulence 

modeling of massively separated flow, and code performance 

improvements. 

Publications 

Raghavan, V.; McCroskey, W. J.; Van Dalsem, W. R.; and 

Baeder, J. D. "Calculations of the Flow Past Bluff Bodies, 

Including Tilt-Rotor Wing Sections at Alpha = -90 degrees." 

AlAA Paper 90-0032, Jan. 1990. 

Turbulent flow; M = 0.18, a = 17", Re = 27.0 x lo6. 
Incipient Leading-Edge Separation 

S. Naomi McMillin, Principal Investigator 

NASA Langley Research Center 

Research Objective 

To computationally determine the effect of leading-edge 

radius and camber on the formation of incipient leading-edge 

separation over the lee side of delta wings at supersonic 

speeds. 

Approach 

A computational parametric study is conducted on a 

65"-swept, conical delta wing at M = 1.6, using CFL3Da Navier-Stokes computational code. 

Accomplishment Description 

The conical geometries examined in this study were three 

uncambered 65"-swept delta wings that varied in leadingedge radius only and three 65"-swept rounded-leading-edge 

delta wings that varied in spanwise camber. In the previous 

year, conical Navier-Stokes solutions were obtained using the 

turbulent boundary-layer model at M = 1.6 and Re = 1.0 x lo6, 

2 x 10" and 5 x lo6. The results showed that applying leadingedge radius andlor camber on a delta wing can delay the 

onset of leading-edge separation such that leading-edge separation occurs at a higher angle of attack. These computations 

have been repeated using the laminar-boundary-layer model 

in order to study the effect of boundary-layer model on the 

incipient separation characteristics of these geometries. A 

typical solution needed approximately 0.6 hours of Cray-2 time 

and 4 megawords of memory. Typical results are presented in 

the figures in the form of crossflow Mach number contours. 

The solution in the left-hand figure is the turbulent-boundarylayer solution for the 10" camber wing at 8O angle of attack. 

The code predicted attached flow with an isentropic compression occurring inboard of the leading edge. The laminarboundary-layer solution presented on the right predicts a 

leading-edge separation bubble. This comparison between - 

laminar- and turbulent-boundary-layer solutions suggests that 

the effect of leading-edge radius and/or camber in delaying 

the onset of leading-edge separation is less effective with a 

laminar-boundary-layer condition on the surface of the wing. 

Significance 

The code CFL3D has been used to quantify the effects of 

leading-edge radius, camber, Reynolds number, and possibly 

boundary-layer condition on incipient leading-edge separation 

over delta wings. 

Future Plans 

Wind tunnel models will be tested and experimental data will 

be compared with computational results. Then the computational study will be extended to further investigate the effect of 

boundary-layer model on incipient separation. 

Publications 

"A Computational Study of lncipient Leading-Edge Separation 

at M = 1.60." Presented at the AlAA Applied Aerodynamics 

Conference, Portland, OR, Aug. 1990. 

Turbulent boundary layer. Laminar boundary layer. 

Crossflow Mach number contours, showing the effect of the boundary-layer model on computational results; M = 1.6, a = 8", 

Re = 1 x lo6. 
Multiblock, Multigrid Met hod for the Solution of the Three-Dimensional 

Euler Equations 

N. Duane Melson, Principal Investigator 

Co-investigators: Frank E. Cannizzaro, Alaa Elmiligui, and E. von Lavante 

NASA Langley Research Center 

Research Objective 

To develop a computer program that would aid in the study of 

rectangular noule flows exhausting into different free-stream 

conditions. - 

Approach 

An explicit upwind method was used to solve the finite-volume 

formulation of the Euler equations. Multigrid acceleration was 

implemented to increase the rate of convergence. The computer program was transformed into a multiblock structure to 

provide flexibility for analyzing different geometric configurations. 

Accomplishment Description 

Two types of upwind methods were investigated to solve the 

body-fitted finite-volume formulation of the Euler equations: 

van Leer's flux vector splitting and Roe's flux difference 

splitting. Both used MUSCL-type differencing. A modified 

Runge-Kutta time-stepping scheme was used to advance the 

solution. A multiblock capability was used to compute the 

nozzle flow shown in the accompanying figure. The flow 

conditions were M, = 3.0, Miet = 1.99, Pjet/P, = 8.96, and 

Tjet/T, = 3.55. 

Significance 

The multiblock structure provides a computer program that is 

independent of grid topology. Thus, the same computer program can be used to solve internal flows (such as noule 

flows, which may be an H-H grid topology) and external flows 

(such as flow over a wing, which may be a C-H, a C-0, or an 

0-0 grid topology) without requiring changes to the program. 

Inputs to the computer program require that boundary and 

interface conditions of each face of each block be specified, 

therefore allowing any type of grid topology to be handled. 

Future Plans 

We plan to increase the range of nozzle flow conditions that 

can be solved, improve the computational efficiency of the 

computer program by investigating various types of residual 

smoothing, and include viscous terms in the governing 

equations. 

Publications 

Canniuaro, Frank E.; Elmiligui, Alaa; Melson, N. Duane; 

and von Lavante, E. "A Multiblock Multigrid Method for the 

Solution of the Three-Dimensional Euler Equations." AlAA 

Paper 90-0105, Jan. 1990. 

Density Contours 

Mach Contours On Computational Grid 

(Top) Nozzle-flow Mach contours on a computational grid. (Bottom) Nozzle-flow density contours. 
Computational Fluid Dynamics Analysis of Advanced Turboprop Configurations 

John E. Melton, Principal Investigator 

Co-investigators: Ronald G. Langhi and Brian A. Nishida 

NASA Ames Research Center 

Research Objective 

To develop advanced computational fluid dynamics tools for 

the design and analysis of transport aircraft configurations that 

use advanced turboprop or propfan propulsion systems. 

Approach 

Advanced grid-generation techniques and a modified Euler 

flow solver are used to model complex winglnacelle geometries and to predict accurately the effects of the propeller slipstream on the aerodynamic performance of the configuration. 

Accomplishment Description 

A three-dimensional elliptic grid-generation program was used 

on the Cray-2, Navier, to produce volume grids up to 1.2 million points in size about various fuselage/wing/nacelle transport aircraft configurations where the point density in regions 

of interest and the orthogonality of grid lines intersecting the 

geometry surface were especially critical. Typical CPU time 

and memory requirements were on the order of 2400 seconds 

and 15 megawords, respectively. To study the effects of the 

propeller slipstream, an actuator disk algorithm was incorporated into Jameson's multistage scheme for the Euler 

equations. Calculated velocities over a propellerlnacelle 

test rig were computed and found to be in good agreement 

with laser Doppler velocimeter data from a NASA Lewis 

experiment. More detailed computations over a winglbodyl 

nacelle/propeller were done, and the results compared well 

with NASA Ames I I-Foot Wind Tunnel data. Further improvements in the Euler code included multiple-block capabilities 

that enabled the program to handle general, complex geometries; exploit the fast inputloutput of Reynold's SSD; and take - 

advantage of the multiple-block grid-generation packages 

now available. An unstructured, hexahedral-based Euler code 

that used grid enrichment was also developed and tested on a 

variety of complex configurations. 

Significance 

Future advanced turboprop aircraft will require a high degree 

of aerodynamic integration in order to fully exploit the fuel 

efficiency of the propfan propulsion systems. Computational 

analysis can provide additional understanding of important 

flow-field phenomena and insights that are difficult to obtain 

experimentally about design considerations. 

Future Plans 

More testing and verification of the Euler codes is currently 

under way so that they can be routinely used as design tools. 

The grid-generation package is mature and is being used on a 

variety of other programs. 

Grid for a multiblock Ames fuselage1UTW-nacellelwing-with-LEX configuration; midchord I = 114. 

110 
Vortex-Induced Nonlinearities on Submarines 

Michael R. Mendenhall, Principal Investigator 

Co-investigator: Stanley C. Perkins, Jr. 

Nielsen Engineering & Research, Inc. 

Research Objective 

The objective of this work is to investigate an analytical 

procedure to predict the nonlinear fluid mechanics characteristics of modern attack submarines in steady and unsteady 

-maneuvers involving high incidence angles and high angular 

rates. Effects of flow separation and shed vorticity are to be 

included, and the resulting method is to be applicable to 

generic submarine configurations for a wide range of flow 

conditions and Reynolds numbers. 

Approach 

A hydrodynamic prediction method is coupled with a sixdegree-of-freedom (6-DOF) equation-of-motion solver to 

calculate the motion of a submarine configuration. The 

calculation requires only the submarine geometry and mass 

characteristics, initial flow conditions, and time histories of 

propeller rotation rate and fin deflections. Components of the 

submarine are modeled with potential flow models; specifically, the axisymmetric hull is represented by axis singularities 

and the lifting surfaces are represented by a panel method. 

Flow separation from the hull is calculated using modified 

Stratford criteria, and hull shed vortices are modeled by 

clouds of discrete vortices. Trailing vortices from the lifting 

surfaces are treated as free vortices aft of the trailing edge of 

the surface. Starting at an initial time with a given set of flow 

conditions, a marching procedure is used to calculate pressures, flow separation, and forces and moments on the 

submarine components. The resulting total submarine forces 

and moments are used in conjunction with a 6-DOF equationof-motion solver to calculate the motion of the submarine over 

a small time interval, in order to produce a new orientation of 

the vehicle and new flow conditions. The vortex wake is 

allowed to move under the influence of the changing flow 

conditions during the time interval, and the modified vortex 

field influences the pressure distribution on the vehicle and 

thus affects subsequent separation characteristics. New 

vortices are added to the flow field, new forces and moments 

are calculated, and the submarine motion is predicted for 

another time interval. The procedure is continued for a 

specified time or maneuver. 

Accomplishment Description 

The above code and prediction methods were applied to a 

modern attack submarine configuration under various maneuvering conditions, and the predicted results were compared 

with available sea trial results. The calculation procedure 

worked well and a number of detailed results were obtained. 

For example, the vortex lag caused by the delay between a 

vortex being shed from the hull and its later influence on tail 

control surfaces proved to be a critical component of the flow 

phenomena that dictate the behavior of the maneuvering 

submarine. For one maneuver condition, the time history of the 

forces on the four tail fins showed a vortex-induced imbalance 

that created a rolling moment on the submarine and influenced the calculated motion. A typical maneuver lasting 

approximately 25 seconds required between 0.5 and 1 .O Cray 

Y-MP hours and 2 megawords of memory. The accompanying 

figure shows traces of vortex centroids from the sail, sailplanes, and deck of a generic submarine configuration in 

steady flow conditions. The keel side vorticity cannot be seen 

in this view. 

Significance 

Modern attack submarines in steady and unsteady maneuvers 

involving high incidence angles and high angular rates have 

fluid mechanic characteristics dominated by flow separation, 

vorticity, and unsteady lag effects. The design and analysis of 

advanced submarines requires computational methods that 

can represent these complex flow phenomena, to produce the 

highly nonlinear forces and moments acting on maneuvering 

submarines. An improved analytical capability will provide a 

means to investigate stability and control effects, particularly in 

regions of vortex-dominated flows. One use of this capability is 

to provide insight into the complex problem of vortex interference on control surfaces, especially in a time-dependent flow 

field. 

Future Plans 

The objective of the second phase of this computational effort 

is to study further the direct calculation simulation approach 

for submarines and to continue to apply the method to the 

prediction of submarine trajectories in unsteady maneuvers. A 

number of computational and physical problems became evident as a result of the first phase of this study. For example, it 

is now apparent that the unsteady character of the separation 

line on the hull may be different from the known separation line 

in steady flow. This is one important area requiring further 

study. 

Traces of vortex centroids from the sail, sailplanes, and deck of a generic submarine configuration in steady flow. r- --I-,,.- 

-> - 

LOLL,; ri .C . t.: ;;ii.FH 
Standing Oblique Detonation Waves 

Gene P. Menees, Principal Investigator 

Co-investigators: Henry G. Adelman and Jean-Luc Cambier 

NASA Ames Research Center 

Research Objective 

The ultimate objective of this work was to demonstrate the 

proof-of-concept of an oblique detonation wave engine 

(ODWE) for hypersonic air-breathing propulsion. The work 

included an experimental study performed in an arc-heated 

wind tunnel, and a series of analytical studies. The development and validation of a numerical capability for the timeaccurate simulation of detonations and supersonic combustion 

was an essential part of the program. 

Approach 

Two- and three-dimensional Navier-Stokes codes were 

developed that used a second-order, upwind (total-variationdiminishing) scheme. The code used multiple-species convection coupled with detailed chemical kinetics in a time-accurate 

fashion, along with an explicit, operator-splitting approach. 

Fickian and laminar diffusion processes were also incorporated. The codes used a fully conservative grid-patching 

algorithm to allow the modeling of complex geometries and to 

increase the computational efficiency for steady-state as well 

as unsteady calculations. 

Accomplishment Description 

The code was used to successfully simulate oblique detonation waves attached to a ramp, and the results were in accord 

with analytical expectations. It was also used to model the 

standing detonation waves in various mixing conditions and to 

study the wave patterns expected in the experiment. It was 

seen that in the limit of low mixing, the detonation reduces to 

shock-induced combustion, with a flame anchored at the primary shock. It was also seen that the combustion can strongly 

amplify initial perturbations in the shock curvature, thereby 

possibly leading to a bootstrap effect of enhanced mixing and 

combustion. The code was also used to model the fuel injection from struts, according to the experimental design, in order 

to estimate the positions of shock impingements and fuel 

penetration and mixing. Finally, the code was validated by 

comparing the results with previous experimental studies of 

shocklflame interactions done in a ballistic range. The exact 

reproduction of the position of flamelshock decoupling, as 

indicated in the accompanying figures, is a critical test of the 

accuracy of the coupling between chemistry and convection 

algorithms in the code. This calculation was done on 

36,000 grid points, with 9 chemical species and 44 elementary 

(one-step) chemical reactions, and required 12 hours of 

Cray-2 time and less than 10 megawords of memory. 

Significance 

The ODWE represents an alternative concept to the scramjet . for hypersonic air-breathing propulsion. Theoretical advantages of this design have been estimated and are effective in 

the high-Mach number range. The practical realization of this 

engine concept is critically dependent on the degree of mixing . attainable at high velocities and is therefore difficult to assess 

without long and intensive studies. Some "spin-offs" from this 

concept can be of importance in more conventional scramjet 

designs; notably, the interactions between shock waves of 

various strengths, turbulent mixing, and combustion deserve 

special detailed study. 

Future Plans 

The ODWE program was terminated at the end of FY89. The 

experimental program showed partial success and would 

have required additional measurements for unambiguous 

answers. The numerical program was a complete success, 

with the important validation of the code against previous 

ballistic experiments. The code has been used as a launch 

platform for the development of other, more sophisticated 

codes for nonequilibrium flows. Extensions to multipletemperature and strongly ionized flows have been done and 

are being pursued further by one of the co-investigators (JLC). 

Publications 

1. Adelman, H. G.; Cambier, J. L.; and Menees, G. P. 

"Experimental and Analytical Investigations of Wave Enhanced 

Supersonic Combustors." AlAA Paper 89-2787, July 1989. 

2. Menees, G. P.; Adelman, H. G.; Cambier, J. L.; and 

Bowles, J. V. "Wave Combustors for Trans-Atmospheric 

Vehicles." Presented at the 9th Int. Symposium on AirBreathing Engines, Greece, Sept. 1989. 

3. Menees, G. P.; Adelman, H. G.; and Cambier, J. L. 

"Analytical & Experimental Validation of the Oblique Detonation Wave Engine Concept." Presented at the 75th AGARD 

Symposium on Hypersonic Combined Cycle Propulsion, 

Madrid, Spain, May 1990. 

The position of flamelshock decoupling. The color figure shows temperature contours in Hrair; M = 6.46. 
Large-Eddy Simulations of Ramjet Combustion Instability 

Suresh Menon, Principal Investigator 

Co-investigator: Wen-Huei Jou 

QUEST Integrated, Inc. 

Research Objective 

The objective of this research is to study, through large-eddy 

simulations, the complex interactions among acoustic waves, 

vortex motion, and combustion heat release in a ramjet combustor. These interactions often lead to combustion instability 

in such a device. 

Approach 

The unsteady compressible Navier-Stokes equations, together 

with a thin-flame model for a premixed combustion, are solved 

using MacCormack's explicit finite-volume scheme. The 

enthalpy in the energy equation contains a heat-of-formation 

term that can be varied to reflect the effects of the equivalence 

ratio of a fuel mixture. The turbulent flame speed appears 

explicitly in the combustion model as a function of the laminar 

flame speed and the subgrid turbulence kinetic energy. 

Accomplishment Description 

Large-eddy simulations of premixed combustion in an 

axisymmetric ramjet combustor were carried out. Both "stable" 

and "unstable" combustion were simulated numerically. The 

stable combustion flow field is characterized by low-level 

(15% of mean pressure) pressure fluctuations and vortex 

roll-uplpairing processes occurring in the shear layer. The 

flame is entrained by the vortical structures as it propagates 

downstream. In the unstable combustion flow field, largeamplitude, low-frequency pressure fluctuations occur at levels 

as high as 50% of the mean pressure, and a large, hooked 

vortexlflame structure propagates through the combustor at 

the low frequency. The computed flame structure, the phase 

relation between the pressure and velocity fluctuations, and 

the fluctuation levels in the combustor for unstable combustion 

are in remarkable agreement with experimental results (e.g., 

Smith and Zukoski, AlAA Paper 85-1248). Each simulation of 

combustion instability in the ramjet using a grid of 256 x 64 

points required around 24 Cray-2 hours and about 5 megawords of memory. 

Significance 

The numerical simulation of combustion instability has provided, for the first time, detailed information on an unstable 

flow field in a ramjet. This capability will be exploited in a 

theoretical framework to analyze the results of simulations for 

practical applications, such as developing strategies for 

actively controlling the instability. 

Future Plans 

A new research study has been initiated to further improve the 

large-eddy simulation model and to study numerically active 

control techniques for controlling ramjet combustion instability. 

Publications 

Menon, S., and Jou, W.-H. "Large-Eddy Simulation of Combustion Instability in an Axisymmetric Ramjet Combustor." 

AlAA Paper 90-0267, Jan. 1990. 

I) Unstable Combustion 

Typical flow fields for (left) stable and (right) unstable combustion. (Experimental visualization from Smith and Zukoski, AlAA 

Paper 85-1 248.) 
Mixing Enhancement for Scramjet Flameholders 

Suresh Menon, Principal Investigator 

Co-investigator: Emerick Fernando 

QUEST Integrated, Inc. 

Research Objective 

The primary objective of this research is to investigate the 

unsteady mixing processes between a supersonic air stream 

and tangentially injected fuel near three-dimensional flameholders. The numerical work is being carried out in parallel 

with an experimental study of similar flameholder 

configurations. 

Approach 

The compressible, three-dimensional Navier-Stokes 

equations are solved using a finite-volume scheme based on 

MacCormack's technique. A fully implicit scheme is used for 

steady-state calculations, and a large-eddy simulation code is 

being developed for unsteady simulations. To resolve shocks 

in the flow field, the Roe-averaged flux difference splitting 

scheme is used. 

Accomplishment Description 

The research is being carried out in two phases. In the first 

phase, an explicit three-dimensional version of the code was 

used to carry out direct simulations of temporally evolving 

compressible mixing layers, to study the effect of compressibility on secondary instability in the mixing layer. The evolution 

of three-dimensional modes and the subsequent formation of 

streamwise vortices for various convective Mach numbers 

were numerically simulated. For a 643 grid resolution, approximately 12 megawords of memory and 4 Cray-2 hours were 

required for each simulation. In the second phase, a fully 

implicit version of the code was used to obtain steady-state 

turbulent supersonic flows past rearward-facing steps with 

and without spanwise modification to the flameholder. Using a 

74 x 64 x 32 grid and the implicit scheme, steady-state solutions required about 8 Cray-2 hours and 14 megawords of 

memory. The steady-state solution will be used to initialize the 

flow field for the unsteady simulations, which are currently 

being initiated. 

Significance 

In the Mach number regime from 2 to 4, stability analysis . indicates that the most unstable mode is three-dimensional. 

Enhancing three-dimensional instability may lead to an 

increase in streamwise vorticity in the mixing layer, which 

could result in increased fuellair mixing. Mixing enhancement 

is essential for improving the combustion efficiency of the 

scramjet engine. 

Future Plans 

Steady-state solutions for supersonic flow past a flameholder 

geometry identical to the experimental configuration will be 

carried out for code validation. Tangential fuel injection near 

the flameholder will be included. Large-eddy simulations will 

be carried out to investigate the unsteady aspects of fuellair 

mixing near three-dimensional flameholders. 

Publications 

Menon, S., and Fernando, E. "A Numerical Study of Mixing 

and Chemical Heat Release in Supersonic Mixing Layers." 

AlAA Paper 89-0152, Jan. 1990. 

Streamwise vorticity (ax) downstream of a sawtooth flameholder; M, = 3.0, Re = 1 x I@. 
Absorption of Microwave Energy in a Flowing Gas 

Charles L. Merkle, Principal Investigator 

Co-investigator: S. Venkateswaran 

The Pennsylvania State University 

Research Objective 

To develop a comprehensive computational model to investigate the physics and dynamics of the microwave/gas-dynamic 

interaction in microwave plasma discharges. 

.Approach 

The full Navier-Stokes equations in axisymmetric form are 

solved for the gas, coupled simultaneously to Maxwell's equations for the microwave field. An implicit algorithm that had 

-been developed for low-Mach number flows is incorporated in 

the Navier-Stokes code, and an explicit time-accurate method 

is used for Maxwell's equations. 

Accomplishment Description 

A coupled Navier-Stokes/MaxwelI solver was developed to 

model the absorption of microwave energy in helium gas. 

Flow-field solutions were obtained for various geometries, 

including the configuration used in the companion experimental program. The effects of several parameters (such as discharge pressure, gas velocity, incident microwave power, and 

location of a microwave waveguide) on the size, shape, and 

location of the plasma were investigated. Comparison with 

experiments showed that except for the threshold powers of 

the plasma, the trends were predicted accurately. The one 

discrepancy seemed to be due to the assumption of local 

thermal equilibrium between electrons and heavy particles in 

the plasma. Nonequilibrium effects are being included to 

enhance the present model and improve predictions. 

Significance 

Microwave propulsion appears to be a promising new concept 

for space applications such as orbital transfer vehicles. These 

devices provide moderate thrust levels at high specific 

impulses. Several experimental programs in the country are 

studying microwave plasma discharges and their application 

to rocket propulsion. So far, however, theoretical modeling of 

the problem has received very little attention. Theoretical 

analysis aided by numerical computations can be very useful 

in the understanding of the complex interaction between the 

microwave and gas-dynamic fields. 

Future Plans 

The present model will be enhanced by the inclusion of 

nonequilibrium effects. This involves the solution of additional 

transport equations for the electron number density and electron energy. Validation of the model with experimental data will 

continue. Future calculations will consider more practical configurations and larger power levels. Further, calculations will 

be extended to include the rocket nozzle as well as to estimate 

thrust and overall efficiencies. 

Publications 

1. Venkateswaran, S.; Merkle, Charles L.; and Micci, 

Michael M. "Analytical Modeling of Microwave Absorption in a 

Flowing Gas." Presented at the AlAA 21st Fluid Dynamics 

Plasmadynamics and Lasers Conference, Seattle, WA, June 

1990. 

2. Venkateswaran, S., and Merkle, Charles L. "Coupled 

Navier-Stokes Maxwell Solutions for Microwave Propulsion." 

Presented at the 12th International Conference on Numerical 

Methods in Fluid Dynamics, Oxford, England, July 1990. 

Temperature contours (drawn at intervals of 500 K) for three different flow geometries: (left) a straight duct, Tpeak = 9335 K; 

(center) an intermediate sphere-cylinder, Tpeak = 9060 K; and (right) the sphere-cylinder used in experiments, Tpeak = 9200 K. 
Numerical Simulation of Advanced Propellers 

Christopher J. Miller, Principal Investigator 

Co-investigator: Saif A. Warsi 

NASA Lewis Research CenterISverdru p Technology, Inc. 

Research Objective 

Euler and Navier-Stokes codes for predicting high-speed 

propfan flow fields have been developed, but need to be 

verified with experimental data. The objectives for this year 

involved validation comparisons for both a single-rotation 

propfan at an off-design condition and a counter-rotation 

propfan at a design condition. There was also an effort to 

evaluate a counter-rotation propfan for the highly viscous 

unsteady flow field at the back of a generic cruise missile 

body. 

Approach 

The Euler and Navier-Stokes codes used in this research were 

developed at the NASA Lewis Research Center by Dr. John 

Adamczyk. These are finite-volume codes using a four-stage 

Runge-Kutta integration scheme. An algebraic eddy-viscosity 

turbulence model is used in the Navier-Stokes code. The wind 

tunnel test data used for comparison are primarily the overall 

performance data of a blade row (thrust, power, efficiency). 

For the counter-rotation propfan at cruise, laser Doppler 

anemometer data were also compared with the predicted flow 

field. 

Accompiishment bscription 

Surface static-pressure data are available for a single-rotation, 

9-ft-diameter SR-7 propfan that was tested in Modane, France. 

For the takeoff condition, Euler code predictions capture most 

of the flow physics, including a leading-edge vortex, and the 

calculated surface pressures are similar to the test data. The 

Navier-Stokes code captures the same flow phenomena with 

fewer mesh points. The calculated surface pressures, 

although similar to the test data and Euler predictions, show 

the need for further code improvement. The prediction of the 

flow field around a counter-rotating propeller for comparison 

with laser Doppler velocimeter data is not complete. The preliminary results show a general agreement with test data. The 

Eular predictions do not show the velocity jump across the 

blade wake that persists in the test data a chord length down- * 

stream of the trailing edge. This potential flow feature should 

be present, and the problem is being investigated. Finally, the 

Navier-Stokes code was used to predict the performance of a 

counter-rotation pusher propfan designed to operate on a 

simulated cruise missile. Because of the thick boundary layer 

coming off the body and the sharp boat-tail angle ahead of 

the propeller, this calculation can only be done with a viscous 

three-dimensional propeller code. There are three basic 

results: (I) there is a small separation region ahead of the 

propeller. (2) the propeller accelerates the boundary layer and 

almost removes the velocity deficit, and (3) the efficiency is 

roughly 80%. All three results are favorable for the design. 

Significance 

The validation work has shown that the Euler and NavierStokes codes are reliable methods for predicting propfan performance at cruise conditions. For takeoff conditions, the Euler 

code is qualitatively correct, and the Navier-Stokes code 

shows promise but needs additional work in the turbulence 

model. 

Future Plans 

Continued improvement and validation of the Navier-Stokes 

code is the highest priority. Both codes will be used to explore 

new concepts in high-speed propfan propulsion. 

Leading-edge vortex, imaged using density, for an LAP SR-7 two-bladed case (%), computed with the Adamczyk Euler code; 

640 cycles, CFL = -4, Ct = 0.1697, Cp = 0.2156, Eta = 0.6926, M = 0.200, a = O.OOO, time = 2.60 x lo3, grid size 107 x 35 x 45. 
Quantum Mechanical Reactive Scattering 

William H. Miller, Principal Investigator 

Co-investigator: John Z. H. Zhang 

University of California, Berkeley 

Research Objective Specific plans include the development of various basis set 

TO develop new, more efficient methods for carrying out rigor- contraction schemes, in order to be able to treat more than 

OUS quantum mechanical reactive-scattering ~al~~lati~n~ for three-atom reactive systems. chemical reactions, and to apply these methods to interesting . . - dynamical problems. 

'Approach I I 

The coupled-channel Schr6dinger equation for reactive scattering (i.e., chemical reactions) is solved by the S-matrix 

version of the Kohn variational principle. - Accomplishment Description 

The S-matrix version of the Kohn variational principle is 

proving to be an extremely powerful and straightforward way g O." 

to solve the integro-differential coupled-channel SchrBdinger F 

equation for reactive scattering of atoms and molecules. It was - 

shown this year how the method can be readily applied to 

determine photodissociation and photodetachment cross 

sections, and also continuum resonance Raman-scattering - cross sections. Specific calculations for H2F- + h, + H2+F, 

HF+H + e- were carried out. 

Significance 

Quantum reactive scattering provides the most rigorous I I 

possible description of a chemical reaction. The present 0.26 0.30 0.34 0.38 0.42 0.46 0.50 0.54 0.58 

method based on the S-matrix version of the Kohn variational E (eV) 

principle is by far the most powerful that has yet been developed for carrying out these~calculations. ~ecause of a new 

generation of experimental studies of these elementary reac- Photodetachment Cross sections (unnormalized) for H~F- + h, 

tions, there is an unprecedented opportunity for detailed + He15 HF+H + e-(E). The energy on the horizontal axis is 

comparisons of theory and experiment. the energy in the neutral scattering system, which is related to 

Future Plans the ejected electron energy E by E = 1.27 eV - E. 

There are a number of opportunities for application of the 

current method, and there are many avenues for enhancing it 

to make it applicable to an even wider class of chemical reactions. 
Multi-Tasked Numerical Simulation of Complex Configurations in 

Hypersonic Flow 

Joseph H. Morrison, Principal Investigator 

Co-investigator: David L. Whitaker 

NASA Langley Research Center 

Research Objective 

The primary objective of this research is to develop the 

capability to compute high-speed flows about general hypersonic vehicle configurations. It is necessary to develop the 

ability to numerically simulate hypersonic flows, both inviscid 

and viscous, about general configurations to evaluate the 

design of hypersonic configurations such as that of the 

National Aero-Space Plane. 

Approach 

Two- and three-dimensional Navier-Stokes codes, using zonal 

structured and unstructured meshes, are used to predict highMach number flows about hypersonic-flight vehicles. Adaptive 

grids can easily be generated for the unstructured meshes to 

improve the accuracy of the calculation. 

Accomplishment Description 

A two-dimensional flux-difference splitting scheme based on a 

triangular discretization of the computational domain was 

developed. The full Navier-Stokes equations can be solved for 

a laminar flow on a triangular mesh, and an extension of a 

Cebeci and Smith algebraic turbulence model to the unstructured mesh is under development. The convergence rate of 

the upwind scheme on an unstructured mesh of triangles, 

using a pointwise explicit scheme, was found to be very slow. 

An implicit scheme was implemented using flux-vector splitting to drive the higher order flux-difference split method. 

Current sparse matrix solution technology was used to obtain, 

quickly, approximate solutions to the series of sparse linear 

systems. The figure shows the solution in the P8 inlet using the 

unstructured solver. Also, a three-dimensional Navier-Stokes 

zonal structured code was used to solve flows about general 

hypersonic configurations and inlets. The code can predict 

both laminar and turbulent viscous flows using either'a timedependent procedure or a marching procedure. A threedimensional inlet model required 5 Cray-2 minutes to run in the , marching calculation and about 2 Cray-2 hours for a timedependent solution, using about 5 megawords of storage. 

Autotasking was used to evaluate the multi-tasking characteristics of the codes. No dedicated processor time was avail- - 

able, so the level of success of these efforts is not known. 

Slgnlflcance 

Proposed hypersonic vehicles will operate in flight regimes 

that are beyond the capability of current wind tunnels to test. 

Therefore, much of the aerodynamics work will have to be 

done using numerical simulation. The geometric complexity of 

the configurations, especially the engines with multiple struts, 

require either zonal structured grids or unstructured grids. 

Future Plans 

The unstructured-grid code will be extended to threedimensional meshes composed of tetrahedrons. The use of 

grid enhancement through mesh adaptivity will also be 

explored. Further investigation of implicit methods and the use 

of sparse matrix solvers will be conducted. The zonal structured code will be extended to include a two-equation turbulence model in order to calculate more accurately the flow field 

about configurations and inlets in hypersonic flow. The 

efficiency of the multi-tasking will be evaluated. 

Publications 

Whitaker, D. L.; Slack, David C.; and Walters, Robert W. 

"Solution Algorithms for the Two-Dimensional Euler Equations 

on Unstructured Meshes." AlAA Paper 90-0697. Jan. 1990. 

(Top) Pressure contours and (bottom) mesh of triangles for a P8 inlet. 
Wall-Bounded Turbulent Flows 

Robert 0. Moser, Principal Investigator 

Co-investigator: John Kim 

NASA Ames Research Center 

Research Objective 

To study the physics of wall-bounded turbulent shear flows, 

including the effects of flow complications (e.g., curvature), 

flow control, and coherent structures. 

Approach 

Direct numerical simulations are performed of turbulent flows 

in simple geometries (plane and curved channels), and the 

resulting fields are analyzed. 

~ccokplishment Description 

Three major direct numerical simulations were completed to 

study three specific questions. First, a high-Reynolds number 

(Red = 8000) channel flow was computed to investigate 

Reynolds number effects. Near-wall statistics were found to be 

dependent on Reynolds number, in agreement with boundary 

layer computations of Spalart. These results are being used to 

develop improved turbulence models. Second, a plane channel with active control was simulated, and control methods 

were improved by the use of spanwise andlor normal velocity 

control at the wall, resulting in a 30% reduction in drag. The 

mechanisms of this drag reduction are being investigated. 

Finally, a strongly curved turbulent channel was computed. 

It was found that large-scale Gortler vortices are not twodimensional as they are with weak curvature. 

Significance 

The numerical simulations allow access to information about 

the flow that is not available by other means. Both curvature 

and turbulent drag reduction are of great technological importance in aeronautics and other applications. 

Future Plans 

The simulations are being analyzed. It is expected that the 

curvature simulations will be used to evaluate and develop 

turbulence models that include curvature effects, and future 

simulations with more realistic and improved drag reduction 

algorithms are being planned. 

Vortex pair impinging on a wall without control (top) and with control (bottom). 

Note that with-control vortices behave as on a wall with slip. 
Electronic Structure of Superconductors 

Wolfgang Mueller, Principal Investigator 

Analatom, Inc./NASA Lewis Research Center 

Research Objective 

To investigate the electronic structure of high-temperature 

superconductors with the quantum chemical cluster approach, 

perform theoretical analyses for critical materials properties, 

and contribute to a better understanding of the mechanism 

responsible for high-temperature superconductivity. 

Approach 

Large-cluster calculations are carried out using the selfconsistent, relativistic scattered-wave method, which is based 

on the Dirac wave equation. The method uses the multiple 

scattering technique and Slater's statistical approximation for 

electron exchange and correlation. 

Accomplishment Description 

Fully relativistic calculations have been performed for 

Y-Ba-Cu-0 using two different clusters: Y2Ba2Cul2OI8 with 

three Cu-0 layers, and YBa2C~16020 with four CU-0 layers. 

The accompanying figure shows the valence and conduction 

electronic structure per YBa2Cu307 cell as derived from the 

two clusters, and a decomposition into atomic contributions. 

The prominent double peak just below the Fermi level, and 

other features that are observed in photoemission experiments, are clearly resolved. For Y2Ba2CuI2Ol8, final-state 

photoemission relaxation contributions have been calculated 

DENSITY OF STATES FOR Y2 Ba2Cu 18 

-b-bi-ioi4i8m 

ENERGY RELATIVE TO THE FERMl LEVEL (eV) 

DENSrrY OF STATES FOR YBa2Cu l6 020 

-. -a-02-i o i 4 a ato 

ENERGY RELATIVE TO THE FERMl LEVEL (eV) 

Density of states for (top) Y2Ba2CuI2Ol8 and (bottom) 

YBa2c~16020. ' 

l#qf!~ ,: . .- 

for about 25 valence and core states. Final-state effects 

(relative to the cluster Fermi level) are found to be small within 

the valence band, but significantly affect the core levels, 

where the remaining errors are 1 to 5 eV. A typical calculation 

requires about 5 Cray-2 hours and 2 megawords of memory. 

Significance 

The investigation of spin-orbit, relaxation, and correlation 

effects in cluster calculations is important for understanding 

the discrepancies between band structure results and 

photoemission data. Large clusters are shown to provide a 

good description of the electronic structure of these materials'. 

Future Plans 

Extended cluster and plane-wave calculations will be performed for thin films of Y-Ba-Cu-0 on various substrates. 

Publications 

1. Mueller, W. "Relativistic Cluster Results for YBa2Cu307." 

Physica C 162-1 64 (1 989): 1357. 

2. Mueller, W. "Valence and Core Electronic Structure of the 

90K Superconductor Y-Ba-Cu-0." Presented at the 10th 

Canadian Symposium on Theoretical Chemistry, Banff, 

Alberta, Aug. 1989. 

ENERGY RELATIVE TO THE FERMl LEVEL (eV) 

Atomic contributions to the density of states. 
Transonic Potential Flow about Transport Aircraft 

D. A. Naik, Principal Investigator 

Co-investigators: A. M. Ingraldi, R. G. Jorstad, T. A. Reyhner, and S. F. Yaros 

ViGYAN, Inc./NASA Langley Research Centerme Boeing Company 

Research Objective 

To analyze transonic flow about different transport airplane 

configurations. 

Approach 

A transonic full-potential code was used in the analysis. 

Considerable flexibility is possible in the choice of the airplane 

configuration because the code uses Cartesian or cylindrical 

grids that intersect, rather than fit, the complex body. The 

code uses a multigrid scheme to accelerate convergence and 

is vectorized for optimum performance on a Cray-2 supercomputer. An unstructured-grid post-processing code was 

used to analyze flow solver output. 

Accomplishment Desciiption 

Three different airplane configurations were analyzed: (I) a 

generic high-wing transport, (2) a generic low-wing transport, 

and (3) a High Speed Civil Transport (HSCT). The first two 

transports are based on existing wind-tunnel models that are 

being experimentally evaluated in the NASA Langley 164 

transonic tunnel. The accompanying figure shows upper- and 

lower-surface Mach contours for the HSCT when it is operating 

in the transonic regime. The original HSCT geometry is shown 

in silhouette. This analysis involved 18,000 surface intersections within a Cartesian mesh of 4 million grid points. Four 

levels of multigrid cycling were used. This computation took 

843 CPU seconds and 12 megawords of memory onlhe 

Cray-2. A total of 17 hours of CPU time was used during the 

198990 operational period. 

Significance 

This work is part of an ongoing study at NASA Langley 

Research Center about the optimum reduction of the adverse 

installation effects of the propulsion systems of transport 

aircraft. 

Future Plans 

This project has been moved to the supercomputer network 

system at the NASA Langley central-site computers. 

Mach 

9.459E-01 

9.491E-Dl 

9.403E-01 

9.37SE-01 

9.345E-01 

9.31s-01 

9.291E-01 

9.zWE-u l 

9 I 

Full Potential Solution 

Lowr Surface 

ORIGINAL PAGE 

COLOR PHOTOGRWH 

Full-potential solution for the Mach contours for the High Speed Civil Transport; M = 0.9, a = 2.0". 
Unsteady Flow Field on an Advanced Propeller 

R. M. Nallasamy, Principal Investigator 

Sverdrup Technology. Inc./NASA Lewis Research Center 

Research Objective 

The objective of this investigation is to understand the 

aerodynamics and acoustics of an advanced propeller at an 

angle of attack. A detailed numerical study of the unsteady 

flow field of the propeller at different operating conditions 

(cruise and takeoff) is attempted. 

Approach 

Unsteady three-dimensional Euler equations are solved for the 

case of an advanced propeller at an angle of attack. The flow 

field is represented by multiblock composite grids. The solution at each time step is updated by having only one block in 

memory while other blocks are stored in solid-state storage 

devices. Fine-grid representation of the blade surface and 

regions near the blade surface is used to capture the leadingedge vortex. 

Accomplishment Description 

The three-dimensional Euler code capable of handling 

unsteady flow fields, developed by Prof. Whitfield of 

Mississippi State University, was used. The flow field was 

represented by multiblock composite grids. Solutions were 

obtained for cruise conditions of the eight-blade flight test 

configuration. A fine-grid solution was obtained for takeoff 

conditions of the two-blade wind tunnel test configuration. This 

solution indicated the presence of a leading-edge vortex on 

the blade throughout the revolution of the propeller. The size, 

strength, and chordwise location of the vortex depended on 

the azimuthal position of the blade. The accompanying figure 

shows the pressure contours indicating the leading-edge 

vortex on the suction surfaces of the two blades. Note the 

difference in size of the vortex between the two blades-the 

vortex is larger on the blade going down. The multiblock 

composite grid computations use 4 megawords of memory 

and 12 hours on the Cray Y-MP for one revolution of the 

propeller. 

Significance 

The cruise-condition solutions of the eight-blade configuration, 

indicate that significant azimuthal variations of blade loading 

occur with changes in the angle of attack. A shock appearing 

near the trailing edge on the suction surface of the blade 

extends across the passage to the pressure surface of the 

successive blade during the highly loaded part of the 

revolution. Such details of shocks and shock motion are of 

great importance in understanding the advanced propeller 

performance and acoustics. 

Future Plans 

The unsteady solution will be obtained for different operating 

conditions and Mach numbers in order to make detailed 

comparisons with test data. A higher spatial resolution 

throughout the flow field will facilitate the direct computation of 

acoustic levels from the flow solutions. 

Pressure contours indicating the leading-edge vortex on the blades of a two-blade wind tunnel test configuration. 

122 cRlG:[: - '- j;E 

COLOR P1.i~-. ../ ,..iAPH 
PegasusTM Aerodynamic Analyses 

David Nixon, Principal Investigator 

Co-investigators: Gary D. Kuhn, Steven Caruso, and Michael R. Mendenhall 

Nielsen Engineering & Research, Inc. 

Research Objective 

The objective of this work is the prediction of hypersonic aerodynamic and thermodynamic characteristics of PegasusTM, the 

world's first air-launched satellite launch vehicle. Of particular 

interest is the wing-fuselage-fairing region, where the flow may 

be dominated by shock-wavelboundary-layer interactions, and 

the tail region, where the control effectiveness may be influenced by the wing wake and forebody vorticity. 

Approach 

Three-dimensional Navier-Stokes codes are used to predict 

the flow characteristics around the Pegasus wing, fuselage, 

and tail for a range of Mach numbers and angles of attack that 

correspond to a typical flight profile. 

Accomplishment Description 

In the previous year, the NASA Ames F3D code was used to 

predict the flow characteristics of the Pegasus wing and 

fuselage. In the current year, calculations were extended to 

include the fuselage-tail region, using the Chimera compositegrid scheme developed at NASA Ames to couple the tail grid 

with the wing-fuselage-fairing grid. The results provided 

information on the complexity of the flow field in the wingfuselage-fairing region and in the tail region. The results for 

M = 5, cx = 5" indicate that the wing leading-edge shock wave 

does not impinge directly onto the fuselage or the fairing for 

this flight condition because of the complicated interaction 

with the flow around the fuselage. The results also indicate 

flow separation under the wing and over the wing-fuselagefairing aft of the wing trailing edge. This separation requires 

further study to determine how it may change with different 

flight conditions. The aerodynamic characteristics from these 

predictions are in good agreement with simpler engineering 

h PRESSURE 

methods, further verifying the predicted aerodynamic loads 

used for the preliminary design analyses. A typical calculation 

of the full configuration required about 35 Cray-2 hours and 

15 megawords of memory. 

Significance 

Pegasus, a winged vehicle with flexible operations permitting 

launch into orbit, NASP trajectories, and ICBM trajectories is 

the first major hypersonic vehicle to go from concept to flight 

with its design based solely on computational fluid dynamics 

(CFD), without wind tunnel tests. Aerodynamic characteristics 

for flight control and trajectory optimization are available from 

standard codes, but several complex problems, critical to 

successful vehicle design and operation, are beyond the 

capability of these codes. Results from the 1989-90 effort on 

NAS have demonstrated that available CFD codes have the 

ability to predict the fluid dynamic properties in complex threedimensional flow regimes to assist in design analyses of new 

flight vehicles. 

Future Plans 

The aerodynamic characteristics of the Pegasus full configuration will be predicted at three or four additional flow conditions in a typical flight trajectory, to complement the results 

obtained in 1989 (M = 5, a = 5"). These results will identify 

locations of possible high heating rates and possible loss of 

control effectiveness and will provide guidance for modification of the thermal protection and control systems. The grid 

resolution in the wing-fuselage-fairing region will be refined to 

increase the accuracy of the heat transfer calculations. Predicted local heat-transfer rates on the fairing and wing will be 

compared with flight test data from the first Pegasus flight. 

Pressure contours for Pegasus. 
Navier-Stokes Simulation of Separated Turbulent Flow around a Generic 

Fighter Aircraft 

Charles R. Olling, Principal Investigator 

Co-investigators: Pradeep Raj and Josef S. Sikora 

Lockheed Aeronautical Systems Company 

Research Objective 

To numerically simulate separated turbulent flow around a 

complete generic fighter aircraft with powered nacelles at high 

angles of attack, and to investigate the applicability of different 

turbulence models to this problem. 

Approach 

The three-dimensional Reynolds-averaged Navier-Stokes 

equations are solved with a finite-volume Runge-Kutta tirnpstepping method, TRANSAM. 

Accomplishment Description 

Flow was computed around a supersonic V/STOL fighter 

aircraft with powered nacelles. The free-stream Mach number 

was 1 .I9 and the angle of attack was 15'. A 27-zone grid with 

378,000 cells was generated by a method optimizing a measure of uniformity and orthogonality. The full Navier-Stokes 

equations with the Chien two-equation k-E turbulence model 

were solved in the zones surrounding the wing, and the Euler 

equations were solved elsewhere. About 15 points were 

located inside the boundary layer. The results were compared 

with those obtained using the Baldwin-Lomax turbulence 

model on the same grid. The figure illustrates the surface 

pressure coefficient. High values are blue and low values 

are magenta. A total of about 20 Cray-2 hours and about 

17 megawords of memory were used for an average case. 

Grid points were added in the streamwise direction toward 

the wing trailing edge and in the spanwise direction toward 

the wing root and tip. The resulting grid had a total of 

434.924 cells and 36 zones. The full Navier-Stokes equations 

with the Baldwin-Lomax turbulence model as modified by . Degani and Schiff were solved in the zones surrounding the 

wing, and the Euler equations were solved elsewhere. The 

results were compared with those previously obtained using 

the Baldwin-Lomax model without the Degani-Schiff 

modification on a coarser grid. 

Significance 

The study is applicable to the design of advanced fighter 

aircraft. 

Future Plans 

A grid will be generated for the complete FIA-18 aircraft with 

clustering suitable for viscous computations near all solid 

surfaces. Navier-Stokes computations will be performed with 

the Johnson-King turbulence model on the wing and the 

Baldwin-Lomax turbulence model with the Degani-Schiff 

modification elsewhere. 

Publicat ions 

Olling, C. R.; Raj, P.; and Miranda, L. R. "Aerodynamic 

Analysis Using EulerINavier-Stokes Equations." To be published in Advances in Computational Fluid Dynamics, ed. 

W. G. Habashi and M. M. Hafez, 1990. 

Computed surface pressures for a supersonic V/STOL fighter aircraft with powered nacelles. 

1 24 
Navier-Stokes Simulation of Turbulent Flow over Rectangular Cavities 

Containing Stores 

Charles R. Olling, Principal Investigator 

Co-investigators: Pradeep Raj and James E. Brennan 

Lockheed Aeronautical Systems Company 

Research Objective 

To numerically simulate turbulent flow over three-dimensional 

rectangular cavities containing generic missile stores, and to 

investigate the applicability of different turbulence models to 

this problem. 

Approach 

The three-dimensional Reynolds-averaged Navier-Stokes 

-equations are solved with a finite-volume Runge-Kutta timestepping method, TRANSAM. 

Accomplishment Description 

Time-dependent flow over an empty cavity was computed with 

the Chien two-equation k-E turbulence model. The free-stream 

Mach number was 1.5. For the cavity, the length-to-depth ratio 

UD was 5.1, and the width-to-depth ratio WID was 2.6. The 

grid had a total of about 169,000 cells and was broken up into 

two zones. Time-averaged pressures along the centerline of 

the cavity floor were compared with the experimental values. 

The figure shows the evolution of the pressure coefficient in 

the longitudinal symmetry plane during the time interval 

5.33 msec to 6.23 msec. A total of about 85 Cray-2 hours 

and about 7 megawords of memory were used. A grid was 

generated for an AIM-9C-SF store model inside a threedimensional cavity with UD = 4.5 and a free-stream Mach 

number of 0.95. The grid had a total of about 370,000 cells 

and was broken up into 40 zones. An H-H-type grid was used 

outside the cavity and an 0-0-type grid around the missile 

inside the cavity. The grid had a clustering suitable for viscous 

computations toward all solid surfaces. Time-dependent computations with a CFL number of 1.7 were carried out, requiring 

about 4 megawords of memory. The Baldwin-Lomax turbulence model with the Degani-Schiff modification was used. The 

flow was initialized to be stagnant inside the cavity. A total of 

10,550 time steps were completed (corresponding to a time of 

0.158 msec) at the end of the operational year. 

Significance 

The study is applicable to understanding supersonic flow over 

weapon bay cavities. 

Publications 

1. Olling, C. R. "Navier-Stokes Computations of Turbulent 

Flow Over a Rectangular Cavity." Presented at 1989 SAE 

Aerospace Technology Conference, Anaheim, Sept. 1989. 

2. Olling, C. R.; Raj, P.; and Miranda, L. R. "Aerodynamic 

Analysis Using EulerINavier-Stokes Equations." To be published in Advances in Computational Fluid Dynamics, ed. 

W. G. Habashi and M. M. Hafez, 1990. 

Pressure distribution at the cavity symmetry plane. 
Unsteady Diffusion Flames 

Elaine S. Oran, Principal Investigator 

Co-investigator: Janet L. Ellzey 

Naval Research LaboratoryIBerkeley Research Associates 

Research Objective 

Experiments on jet diffusion flames have shown that two types 

of instabilities form in the flow field. High-frequency instabilities 

form between the high-velocity and the low-velocity streams. 

Low-frequency instabilities form outside the flame zone. The 

purpose of this study is to investigate the importance of various physical processes to the formation and evolution of these 

structures. 

Approach 

The two-dimensional representation of the compressible 

Navier-Stokes equations with chemical reaction is used to 

simulate fluctuating H2-N2 diffusion flames. The convection 

terms are solved using the Barely Implicit Correction to FluxCorrected Transport (BIC-FCT) algorithm. The effects of conductivity, mass diffusivity, and viscosity are included through 

explicit finite-difference formulations. 

Accomplishment Description 

An initial study of a confined, steady, laminar flame (BurkeSchumann flame) has shown that the computations agree with 

the theoretical predictions for flame location. In addition, computations of diffusion flames at velocities of 10 mlsec have 

shown the effects of viscosity, heat release, and gravity on the 

two types of instabilities. These results indicate that viscosity 

and heat release dampen the high-frequency instabilities. 

In addition, the computations show that low-frequency 

instabilities in the low-velocity region outside the flame zone 

are induced when gravity is included in the calculations. 

These computations require from 4 to 10 megawords of 

memory and 10 to 30 hours of CPU time, depending on the 

resolution. 

Significance 

Although numerous experiments on jet diffusion have been 

conducted, highly resolved time-dependent experimental 

data on reacting flows are often difficult to obtain. Computa- - 

tions provide detailed data; this is not practical in an experiment. In addition, the effects of individual processes can be 

examined separately. From the computations at NAS, the . effects of heat release, viscosity, and gravity have been 

examined individually. 

Future Plans 

The computations will be compared with experiments on jet 

diffusion flames to further validate the approach. In addition, 

the importance of multistep chemistry will be investigated. 

Publications 

1. "Dynamics of Unsteady Diffusion Flames: Effects of Heat 

Release and Viscosity." Presented at the 12th International 

Colloquium on the Dynamics of Explosions and Reactive 

Systems, Ann Arbor, MI, July 1989. 

2. "Effects of Heat Release on a H2-N2 Diffusion Flame." 

Presented at the 42nd Annual Meeting of the Division of Fluid 

Dynamics of the American Physical Society, Palo Alto, CA, 

Nov. 1989. 

3. "Effects of Heat Release and Gravity on an Unsteady 

Diffusion Flame." Presented at the 23rd International Symposium on Combustion, Orleans, France, July 1990. 

Contours of H20 mole fraction for a hydrogen diffusion flame. This figure shows the formation of low-frequency structures induced 

by the gravitational field. The time interval between each pair of frames is 11.25 msec. 

126 
Flux-Based Finite-Element Formulation Reduces CPU Time for ThermalStructural Analysis 

Ajay K. Pandey, Principal Investigator 

Lockheed Engineering and Sciences CompanyINASA Langley Research Center 

Research Objective 

To improve the efficiency and accuracy of finite-element 

thermal-structural analysis using a flux-based formulation. 

Approach 

The thermal-structural response of structures is obtained by 

solving the heat transfer and quasi-static structural equilibrium 

equations, subject to specified boundary conditions. These 

equations are written in the conservation form in terms of the 

conservation variable u and the flux components E, F, and G, 

as ~OIIOWS: a{u)/at + ~{E)I~x + a(Fj/ay + ~{G)I~z = H. BY 

expressing these equations in the conservation form, the 

approach provides simplicity in handling different types of 

boundary conditions, such as applied aerodynamic heat flux 

and radiation flux. To simplify the nonlinearities of these 

equations, the fluxes are interpolated linearly over an element. 

The resulting finite-element equations are in the same form as 

those obtained from'the conventional finite-element technique, 

as follows: [K](u) = {R), where [K] is the finite element stiffness 

matrix, {u) is the vector of nodal unknowns, and {R) is the 

vector of nodal forces. The stiffness matrix [K] obtained from 

the flux-based formulation is different from that obtained from 

the conventional approach and can be evaluated in closed 

form; i.e., numerical integration is not required. A CPU time 

saving of 80% is achieved in evaluating one three-dimensional 

stiffness matrix using the flux-based formulation rather than 

the conventional finite-element formulation. To validate the 

flux-based finite-element formulation, thermal and structural 

analyses are performed of a three-dimensional leading-edge 

Conventional 

Relative CPU time for computing [K]. 

model subjected to a prescribed aerodynamic loading from 

Mach 5 flow (shown in the upper right figure). The predicted 

axial stresses are shown on the deformed shape of the 

leading edge in the lower right figure. The results obtained 

from the flux-based approach are in excellent agreement with 

those predicted by the conventional finite-element approach, 

but have significant CPU time savings. 

Accomplishment Description 

A thermal-structural analysis approach was developed using 

the flux-based formulation. The thermal-structural analysis of a 

three-dimensional leading-edge model subjected to aerodynamic loading was performed and compared with the 

conventional finite-element solution. 

Significance 

The flux-based formulation yields comparable solution 

accuracy but provides significant CPU time savings. 

Future Plans 

The flux-based formulation for predicting high-temperature 

structural response will be extended using unified 

viscoplasticity theory. 

Publications 

1. Pandey, A. K.; Dechaumphai, P.; and Wieting, A. R. 

"Thermal-structural Finite Element Analysis Using Linear Flux 

Formulation." AlAA Paper 89-1224-CP, Apr. 1989. 

2. Dechaumphai, P.; Wieting, A. R.; and Pandey, A. K. 

"Fluid-Thermal-Structural Interaction of Aerodynamically 

Heated Leading Edges." AlAA Paper 89-1227-CP, Apr. 1989. 

Aeropressure 4 

Three-dimensional, leading-edge finite-element model. 

p2=" dia r Deformed f ksi - 

.03" \ 

Deflection '--8 ksi \;. -3 ksi 

'Wndeformed 

Stress on deformed leading edge. 
Hydrodynamics of Self-Propelled Bodies 

V. C. Patel, Principal Investigator 

Co-investigator: F. Stern 

lowa Institute of Hydraulic Research/University of lowa 

Research Objective 

To extend the lowa Institute of Hydraulic Research (IIHR) 

numerical method of solving the Reynolds-averaged NavierStokes equations in order to simulate the flow around complete hydrodynamic vehicles, including appendages and 

propulsors. 

Approach 

The IlHR numerical method solves the complete Reynoldsaveraged Navier-Stokes equations in numerically generated, 

body-fitted, nonorthogonal coordinates for unsteady, threedimensional turbulent flows. No approximations are made 

other than those implied by the two-equation turbulence 

model that is used. Several basic numerical and physical 

problems are being addressed (including grid generation for 

complex shapes and moving boundaries, time accuracy of 

the numerical scheme, and turbulence model development) 

through studies of model problems; some examples of the 

model problems are (I) the flow around bodies at incidence, 

to study the topology of three-dimensional flow attachment 

and separation and to evaluate turbulence models; (2) the 

flow around a propeller, to resolve the viscous flow over the 

blades as well as the flow around it; and (3) the flow over 

bodies with appendages and/or propellers. 

Accomplishment Description 

Programs developed at IlHR were first implemented on NAS 

facilities in late 1989. Since then, calculations have been 

performed for (1) laminar flow on a body of revolution over a 

range of incidences to study the various types of flow separation that arise as the incidence is varied; (2) turbulent flow 

over a self-propelled appended body to study propeller/hull 

interaction; (3) turbulent flow for a two-dimensional cascade to 

evaluate the performance of a two-layer turbulence model; 

and (4) laminar flow over the SR-7 turboprop to study the 

details of the complex blade-to-blade flow. 

Significance 

Despite the impressive strides made in computational fluid 

dynamics, a numerical method that can predict the viscous 

flow around a complete marine vehicle does not exist, even 

for the relatively simple case of a submerged body in steady 

motion along a straight path. Neither do methods that can 

calculate the flow on and around a marine propeller. This 

research is being carried out with the sponsorship of ONR, 

and in support of the DARPA Subtech Program, to advance 

the technology base for the design of marine vehicles and 

propulsors. 

Future Plans 

We plan to continue the development of numerical methods 

that can calculate the flow on and around a marine propeller 

and predict the viscous flow around a complete marine 

vehicle. This research is being carried out with the sponsorship of ONR, and in support of the DARPA Subtech Program. 

Navier-Stokes solution for SR-7 turboprop. 
Generic National Aero-Space Plane Afterbody 

James L. Pittman, Principal Investigator 

Co-investigators: Kenneth E. Tatum and Mohamed E. El-Eshaky 

NASA Langley Research Center 

Research Objective 

The ultimate goal of this study is to develop procedures for the 

analysis and design of generic hypersonic afterbody geometries. The prime immediate goal is to determine the optimum 

aumerical algorithms and codes for analyzing diffusive, 

multiple-species, hypersonic, three-dimensional flow fields. 

Approach 

Several Navier-StokesIEuler codes, using different numerical 

%Igorithms, are exercised to analyze flow about a generic 

scramjet nozzlelafterbody model. The calculated results, twoand three-dimensional Euler and viscous, are compared with 

measured surface (static) and flow-field (pitot) pressures for 

several single- and multiple-species flows. 

Accomplishment Description 

An explicit parabolized Navier-Stokes (PNS) code with 

multiple-gaseous-species capability was modified to allow 

solid-wall boundary conditions internal to the grid in order to 

define a cowl separating a jet flow from a free-stream flow. 

Calculations in the Euler mode were made to determine the 

accuracy obtainable with inviscid calculations. The generic 

scramjet nozzlelafterbody model was modeled in two and 

three dimensions and the computed results compared with 

measured pressures from the NASA Langley 20-Inch Mach 6 

Wind Tunnel. The jet fluid was modeled as air (perfect gas), a 

mixture of nitrogen and oxygen, and two mixtures of argon and 

freon-12 to simulate the ratio of specific heats of actual hot 

scramjet exhaust gases. The implicit GASP code was subsequently exercised in the same fashion and proved to be the 

more robust code for high jet pressures. The GASP 2D PNS 

calculations showed improved agreement with experiment 

over Euler solutions, both in surface pressures and flow-field 

details around the cowl trailing edge. A three-dimensional, 

explicit, marching Euler calculation on a cross-plane grid of 

2100 points required 700 Cray Y-MP seconds, and a twodimensional, implicit PNS calculation required about 

9300 Cray Y-MP seconds on a 17,000-point grid. A threedimensional, explicit, elliptic full Navier-Stokes code was 

modified to accept block-structured grids, and two multiplespecies, half-span nozzle calculations were performed, each 

requiring 24.4 Cray-2 CPU hours. A total of 95 NAS hours were 

used during the 1989-90 operational year. 

Significance 

Proposed hypersonic vehicles will operate in flight regimes 

beyond the accessibility of ground-based test facilities. The 

ability to numerically analyze and design scramjetlafterbody 

components for such vehicles is crucial for efficient, integrated, interdisciplinary design. 

Future Plans 

A full three-dimensional hypersonic vehicle will be modeled, 

including a precisely defined scramjet nozzle and afterbody. 

Parametric studies will be conducted on families of twodimensional afterbody shapes. The GASP code will be 

coupled with an iterative optimizationldesign code. 

Euler scramjet exhaust calculation compared with measured flow-field pitot pressures; argonlfreon-12 

simulant gas jet ejecting into a Mach 6 air free stream. '-.,'. ... 0- --. T.3 .OO-.# . 5 - , . , . .L 

CCLCR Pt-!.L~::i:,~,A?j-/ 
NASP-TMP Forebodyflnlet Integration 

James L. Pittman, Principal Investigator 

Co-investigator: Lawrence D. Huebner 

NASA Langley Research Center 

Research Objective 

To computationally analyze the flow field for hypersonic 

forebodylinletlafterbody regions as part of the overall National 

Aero-Space Plane (NASP) technology maturation plan (TMP) 

effort in the area of propulsionlairframe integration (PAI). 

Approach 

An EulerlNavier-Stokes computational fluid dynamics (CFD) 

code is used to compute the three-dimensional flow about a 

hypersonic forebody-alone, a full body, a forebody with 

blocked inlet, and a forebody with inlet fairing, and the twodimensional flow about a "powered" hypersonic vehicle. The 

CFD solutions are compared with surface and pitot pressure 

data, as well as with Schlieren and oil-flow photographs. 

Accomplishment Description 

Pitot pressure measurements made at the inlet plane of the 

forebody-alone showed very good agreement with pitot 

pressures calculated from parabolized Navier-Stokes (PNS) 

solutions. At four different conditions the computational results 

accurately predicted boundary-layer thickness and the extent 

of the classic boundary-layer accumulation on the centerline. 

Each of these solutions took about 12 megawords of memory 

and 40 Cray-2 minutes of CPU time, The PNS solutions for a 

NASP-type full body at Mach 20 in helium also showed good 

agreement of centerline surface pressures. These solutions 

took about 16 megawords and one Cray-2 hour. Thin-layer 

Navier-Stokes (TLNS) solutions of the forebody with blocked 

inlet and with faired inlet were performed with expectations of 

predicting massive flow separation on the forebody undersurface. Comparison of computational surface particle traces 

with oil-flow photographs showed excellent agreement of the 

extent of separation, flow patterns with the separated region, 

and the location of flow reattachment on the blocked- and 

faired-inlet surfaces. These solutions required 21 megawords 

and the CPU time varied from 5 to 18 Cray-2 hours. Finally, a 

two-dimensional study was undertaken to analyze flow-field 

features associated with a simulated powered hypersonic 

vehicle. Euler and PNS solutions were performed for four 

different test conditions. Under one condition, an additional 

shock was seen underneath the cowl trailing edge and was 

anticipated to be from boundary-layer separation caused by 

localized recirculation. An effort was made to compute this 

using the code as a TLNS solver, and as shown in the figure, ' 

accurate prediction of the salient flow-field features was 

achieved. All two-dimensional solutions took about 8 megawords of memory. The Euler solution required about 5 Cray 

Y-MP minutes, the PNS solutions required about 52 Cray Y-MP 

minutes, and the TLNS solution required 18 Cray Y-MP hours. 

Significance 

The ability of computational methods to accurately predict 

flow phenomena associated with NASP PA1 is critical to the 

design of the NASP vehicle. The accurate comparison of CFD 

results with wind tunnel data provides confidence and the first 

step in the code's ability to predict the flow about NASP-type 

vehicles at full-scale flight conditions. 

Future Plans 

Computations on the simulated powered configuration will be 

expanded to three dimensions and will be executed with a 

turbulence model. This effort will eventually result in tip-to-tail, 

three-dimensional Navier-Stokes solutions on the entire NASP 

configuration. 

Publications 

1. Huebner, Lawrence D. "Computational Investigation of 

LaRC Test Technique Demonstrator Reentry Configurations 

(U)." Paper 36, 7th NASP Technology Symposium, Cleveland, 

OH. Oct. 1989. 

2. Woods, William C.; Huebner, Lawrence D.; and Everhart, 

Joel L. "Measured and Predicted Pressure Distributions on the 

Langley Test Technique Demonstrator at M=20 in Helium (U)." 

Paper 33,7th NASP Technology Symposium, Cleveland, OH, 

Oct. 1989. 

Nozzle flow-field prediction for a hypersonic air-breathing vehicle. 
Development and Evaluation of Computational Methods for Turbomachinery 

Applications 

Richard H. Pletcher, Principal Investigator 

Co-investigator: Edward J. Hall 

Iowa State University/Allison Gas Turbine Division, General Motors Corporation 

Research Objective Future Plans 

To develop and evaluate advanced numerical methods for Plans include the development and evaluation of timethe simulation of unsteady viscous flows occurring in turbo- accurate algorithms for three-dimensional flows, along with 

machinery applications. some improvements in the efficiency of the upwind scheme. 

Approach 

Three traditional central-difference algorithms and a new 

upwind-biased, generalized conjugate gradient, total- 

?ariation-diminishing (GCG-TVD) scheme have been used to 

solve the two-dimensional, time-dependent Navier-Stokes 

equations for steady and unsteady flows. 

Accomplishment Description 

Unsteady Navier-Stokes flow simulations were carried out on 

a fine (361 x 99) grid for an impulsively started cylinder at 

Reynolds numbers of 3000 and 9500. The results from four 

algorithms were compared with experimental data. The purpose was to compare the accuracy and efficiency of the 

schemes for complex time-dependent flow. Three of the algorithms used central differences, the explicit hopscotch and 

Runge-Kutta schemes, and an approximately factored, linearized block implicit scheme. The fourth scheme was a new 

upwind-biased algorithm utilizing an implicit time-marching 

relaxation procedure based on Newton iteration. This upwind 

scheme utilizes a TVD formulation and a GCG minimal residual 

descent matrix relaxation procedure. The accompanying 

figure compares the streamline pattern predicted by the 

upwind scheme with flow visualization results after the cylinder 

had moved two diameters from rest at a Reynolds number of 

9500. Such a calculation requires about one hour of Cray-2 

time and 4 megawords of memory. 

Significance 

Current turbomachinery design analyses are generally based 

on steady flow calculations although most real turbomachinery 

flows are unsteady. With recent advances in computer archi- A GCG-nID-~redicted streamline Pattern for the flow of an 

tecture it is becoming feasible to simulate increasingly com- impulsively started cylinder; Re = 9500, t = 2.0. 

plex flows. The capabilities and limitations of algorithms for 

time-dependent calculations need to be understood so that 

time-accurate calculations can ultimately be used to guide the 

design of more efficient turbomachines. 
Vapor-Phase Growth of Crystals in Microgravity 

Andrew Pohorille, Principal Investigator 

University of California, Berkeley 

Research Objective 

The objective of this research is to explore the factors that 

influence the structure of thin films grown by molecular deposition from the vapor phase. The ultimate goal is to explain the 

results of experiments conducted in space by the 3M Corporation, which showed that thin films of copper phthalocyanine 

formed in microgravity are different from those formed in the 

presence of gravity. 

Approach 

Deposition of particles on the substrate and their diffusion on 

the surface was simulated by a molecular dynamics method. 

New particles were introduced to the system in the direction 

perpendicular to the deposition surface and moving toward 

this surface. The velocities of the molecules at the deposition 

surface were reset periodically to a Maxwellian distribution 

corresponding to the desired temperature of the substrate. 

Accomplishment Description 

(1) Deposition of the spherical particles with the LennardJones potential of interactions led to well-layered crystalline 

growth. This regular growth was perturbed only when new 

particles were introduced to the systems in very short succession. In those conditions particles reaching the substrate did 

not have time to relax on the surface, and disordered, but 

uniform, growth was observed. (40 CPU hours, 4 megawords 

memory) (2) Six-membered ring molecules interacting via 

Lennard-Jones potentials tended to form regular crystal-like 

structures if sufficient time was permitted for surface diffusion. 

(50 CPU hours, 8 megawords memory) (3) Spherical particles* 

introduced with nonuniform spacial distributions and nonMaxwellian velocity distribution~ also exhibited crystalline 

growth if the deposition rate was low. (60 CPU hours, 4 megawords memory) 

Significance 

Our studies on simple model systems showed that (I) molecular dynamics is a very good tool for detailed studies of vaporphase deposition, (2) the main factor influencing thin film 

growth is the relaxation time on the surface, and (3) changes 

in the deposition parameters that can be attributed to convective flow appear not to change the structure of thin films. 

Future Plans 

We will apply molecular dynamics to simulate deposition and 

diffusion on the surface of copper phthalocyanine using 

recently developed, realistic intermolecular potential functions. 

Atoms deposited on tl "urface from the vapor F, ,,;e form crystalline-like strut,,, ,.,,,,, , ,, ,,,, , ,, "hange l, ,, , I orange (top) to 

green (bottom) with their depth in the sample. For better visibility, atomic radii were reduced by 50%. 7.. ..- o~~~;::,";- ; : L 

1 32 COLOR PttL ~<~vII,APH 
Finite-Element Analysis of Equilibrium and Nonequilibrium Flows 

Ramadas K. Prabhu, Principal Investigator 

NASA Langley Research CenterILockheed Engineering and Sciences Company 

Research Objective 

To develop a capability to predict aerothermal loads experienced by bodies in high-speed flight. 

Approach 

Navier-Stokes equations in two and three dimensions will be 

_solved by the finite-element method on meshes generated 

with an adaptive remeshing technique. The gas properties will 

be modeled with the assumptions of ideal gas as well as those 

of thermal and chemical equilibrium and nonequilibrium. 

 accomplishment Description 

A two-dimensional finite-element Navier-Stokes solver developed for ideal gases was modified to include equilibrium 

flows. The adaptive remeshing procedure proved to be an 

excellent method for capturing sharp flow features. This code 

was applied successfully to solve several hypersonic flows 

involving shock interference at Mach 8 and Mach 16 past a 

circular cylinder. (The cylinder is the typical shape of a 

leading edge of a winglike body.) Results compared well with 

1, 111 

(a) ' ' "- 

available experimental data. Depending on the size of the 

mesh, it took about 5 megawords of memory and 2 to 3 hours 

of computing time for convergence on each mesh. Extension 

of this code to chemical nonequilibrium flows is in progress. 

Significance 

Flight conditions of hypersonic vehicles are such that the 

classical ideal-gas assumption is not valid. During extreme 

cases, thermal and chemical nonequilibrium effects play a 

significant role. Under these conditions the vehicles experience high aerodyriamic and thermal loads. Knowledge of 

these loads and design options to alleviate them is necessary 

for a successful design. 

Future Plans 

The existing computer codes will be extended to include 

thermal and chemical nonequilibrium flows and effects of 

turbulence. Several problems of interest, including the cooling 

of a cylindrical leading edge by blowing into the stream, will 

be studied. 

Computational domain and finite-element meshes used for a Type IV shock interference problem on a cylinder: (a) computational 

domain, (b) initial mesh, (c) adaptively generated second mesh, (d) adaptively generated third mesh-7614 nodes, 4224 

triangles, 6449 quads. 

Results for a Type IV shock interference problem; M = 16, Re = 1.45 x lo5: (a) velocity contours, (b) pressure contours, 

(c) Schlieren photograph. 

133 
Chaotic, Unsteady, Low-Reynolds Number Navier-Stokes Flow 

Thomas H. Pulliam, Principal Investigator 

NASA Ames Research Center 

Research Objective 

To investigate unsteady computations of low-Reynolds 

number flow past a realistic (two-dimensional airfoil) geometry, 

and to study the physics of the flow using nonlinear dynamics. 

Approach 

The two-dimensional full Navier-Stokes equations were solved 

using either explicit or implicit time differencing and second-, 

fourth-, or sixth-order-accurate space differences. Long-term 

time integrations were performed in which hundreds of 

thousands of time steps were obtained for analysis. 

Accomplishment Description 

Standard nonlinear dynamics analysis tools were applied to 

the unsteady characteristics of numerically computed lowReynolds number flow past a two-dimensional airfoil. Numerical results were generated using ARC2D and other NavierStokes codes. Results for a NACA 0012 airfoil at M, = 0.2, 

a = 20°, and Re = 800 to 3000 exhibit a progression from 

single-period vortex shedding to chaotic unsteadiness via a 

sequence of period doublings. Between Re = 1600 and 

Re = 2200 periodic windows are observed, with subsequent 

doublings back to chaos. Time-delay reconstructions, 

Poincar6 sections, frequency decompositions, Lyapunov 

exponent calculations, and dimension calculations are used 

to characterize the flow. 

Future Plans 

A more detailed analysis of the mechanisms associated with 

the bifurcation sequence to chaos will be carried out. Local 

Lyapunov analysis will be used to characterize the critical 

physical events responsible for the cascade. 

Publications 

Pulliam, T. H., and Vastano, J. A. "Numerical Simulation of 

Chaotic Flows: Measures of Chaos." Presented at the 3rd Joint 

ASCEIASME Mechanics Conference Forum on Chaotic Flows, 

La Jolla, CA, 1989. 

<l) 

Re = 800, Period 1 

v(1) 

Re = 1075, Period 2 

V(1) 

Re = 1400, Period 4 

+ .... 

42 4 0.0 0.1 02 0.3 42 4.1 0.0 0.1 0.2 0.3 42 I 0.0 0.1 02 0.3 

v([) ~(1) V(1) 

Re = 1600, Low D Chaotic Re = 1825, Period 6 Re = 3000, Chaotic 

Time-delay reconstructions of the vertical velocity near the trailing edge of a NACA.0012 airfoil, showing the period-doubling 

sequence to chaos; M, = 0.2, a = 20". 
A Finite-Difference Approach to Direct Simulations and Large-Eddy Simulations 

of Turbulent Flow 

Man Mohan Rai, Principal Investigator 

NASA Ames Research Center 

Research Objective 

To develop finite-difference methods that can be used for 

direct and large-eddy simulations of compressible turbulent 

flow. 

Approach 

The principle obstacle to using existing finite-difference 

schemes for direct and large-eddy simulations of turbulent 

flow is the inadequate accuracy levels of such schemes. In 

'ihis study the use of high-order-accurate finite-difference 

methods is investigated. 

Accomplishment Description 

A fifth-order-accurate upwind finite-difference method was 

developed for direct and large-eddy simulations of compressible, turbulent flow. The truncation error of this scheme is 

sufficiently small to yield accurate simulations of turbulent flow 

with a reasonable number of grid points. A variant of this 

method that is applicable to incompressible flows was used to 

simulate low-Reynolds number, fully developed, turbulent 

channel flow. The results thus obtained compare well with the 

results of earlier simulations using the spectral method. The 

version of the method for compressible flows was used to 

develop a code to compute transitional/turbulent flow over a 

flat plate. Preliminary results were obtained on a coarse grid 

for a free-stream Mach number of 0.1 and Reynolds number of 

50,000.0/in. The figure shows the skin friction distribution on 

the plate as a function of the distance along the plate. The 

computed data appears "noisy" because it has not been 

averaged in time. The transition region compares well with the 

experimental data. The skin friction values in the turbulent 

region are a little lower than the data. Grid refinement studies 

indicate that a computation on a finer grid will yield the right 

distribution of skin friction. A fine-grid computation will require 

about 15 million grid points (which translates into 16 megawords of run-time memory) and about 3000 hours of Cray-2 

single-processor hours. 

Significance 

To date the most successful direct simulations have been 

performed with spectral methods because of the very high 

accuracies that these methods possess. However, spectral 

methods are difficult to use for complex geometries. The highorder-accurate finite-difference method developed in this 

study can, with modifications, be used in a straightforward 

manner for complex geometries. In addition, the direct 

simulation of transition on a flat plate being attempted in this 

study represents a first-of-a-kind effort in computational fluid 

dynamics. 

Future Plans 

The flat-plate computation will be performed on a more refined 

mesh. 

,White (turbulent) I 

Skin friction distribution on a flat plate; M = 0. 1, Re = 50,000/ 

in., number of grid points = 10,875,385. 
Three-Dimensional Multi-Airfoil Navier-Stokes Simulations of RotorIStator Interaction in Turbines 

Man Mohan Rai, Principal Investigator 

Co-investigators: Nateri K. Madavan and Akil A. Rangwalla 

NASA Ames Research Center 

Research Objective 

To develop and validate a three-dimensional Navier-Stokes 

code (ROTOR-4) to simulate flows through single-stage 

turbomachinery with an arbitrary number of blades or vanes 

in each row. 

Approach 

The ROTOR4 code incorporates multiple-zone technology 

and an implicit, high-order-accurate upwind scheme for the 

time-accurate solution of the thin-layer Navier-Stokes 

equations. 

Accomplishment Description 

The development of the ROTOR-4 code was completed and 

validation studies for an axial turbine configuration with three 

stator and four rotor airfoils are in their final stage. Mesh 

refinement studies were also carried out. The stator:rotor airfoil 

count (3:4, which is equivalent to 21 :28) in the calculation 

closely approximates that of the experimental configuration 

(22:28). The accompanying photograph shows the instantaneous static pressure distribution in this turbine stage from 

inlet (left) to exit (right). The multi-airfoil calculation requires 

approximately 150 Cray Y-MP single-processor hours; it 

requires under 4 megawords of core memory and 27 megawords of auxiliary memory (SSD). 

Significance 

The ROTOR-4 code is the only code of its kind and is of 

extreme importance to the turbomachinery community in 

understanding the unsteady aerodynamics of turbomachinery 

The validation studies conducted represent the most comprehensive numerical simulation to date of a single-stage turbine. 

Future Plans 

Efforts are under way to develop a multistage, multi-airfoil 

code (STAGE-3) using ROTOR-4 as the base code. 

Publications 

Madavan, N. K.; Kelaita, P.; and Gavali, S. "Supercomputer 

Applications in Gas Turbine Flowfield Simulation." To be 

published in The international Journal of Supercomputer 

Applications 4.2 ( 1 990). 

MULTIBLADE SIMULATION OF A SINGLE STAGE TURBINE 

- [NSTANTANEOUS PRESSURE DISTRIBUTION 

Multiblade simulation 

w;.. 

of a single-stage turbine; instantaneous pressure distribution. 

. 

v,.-.7... - ..-- 0,: . - r . 

COLOR P~:;L--OL~ iAPW 
Unsteady Flow in a Multistage Compressor 

Man Mohan Rai, Principal Investigator 

Co-investigators: Karen L. Gundy-Burlet and Akil Rangwalla 

NASA Ames Research Center 

Research Objective 

To develop a two-dimensional Navier-Stokes zonal code 

(STAGE-2) to simulate the unsteady flow within multistage 

turbomachines. 

Approach 

The unsteady, thin-layer Navier-Stokes equations are solved 

using an implicit, third-order-accurate, upwind-biased finitedifference scheme and a multiple-zone methodology. 

Accomplishment Description 

A two-dimensional multistage turbomachinery code (STAGE-2) 

was developed and validated. Results from the code compare 

well with experimental data for both a multistage compressor 

and a single-stage turbine. Several calculations, including grid 

and time-stop refinement studies, were run on the Cray Y-MP 

and the Cray-2. The results of these investigations can be 

found in publications 1 and 2. The accompanying photograph 

shows instantaneous entropy contours within a 2 IM-stage 

compressor. Features of interest include waketwake and 

wakelairfoil interactions. A typical calculation requires 

2 megawords of run-time memory, 5 megawords of SSD, and 

between 5 and 40 hours of Cray-2 single-processor hours, 

depending on the level of convergence required. 

Significance 

The development of STAGE-2 represents a major step in 

computing flows through multistage turbomachines. As seen 

in the photograph, the flow increases in complexity as it 

moves downstream through the compressor. Therefore, in 

order to simulate the flow in a downstream stage using a 

single-stage or cascade code, complex boundary conditions 

would have to be applied at the stage inlet. Hence, multistage 

turbomachinery codes are required in order to understand the 

aerodynamic processes in multistage turbomachines. 

Future Plans 

A three-dimensional multistage turbomachinery code, 

STAGE-3, will be developed and validated during the 1990-91 

NAS operational year. 

Publications 

1. Gundy-Burlet, K. L.; Rai, M. M.; and Dring, R. P. "TwoDimensional Computations of Multi-Stage Compressor Flows 

Using a Zonal Approach." AlAA Paper 89-2452, July 1989. 

2. Gundy-Burlet, K. L.; Rai, M. M.; Stauter, R. C.; and Dring, 

R. P. "Temporally and Spatially Resolved Flow in a Two-Stage 

Axial Compressor, Part 2 - Computational Assessment." ASME 

Paper 90-GT-299, June 1990. 

. MSTANTANEOUS ENTROPY CONTOURS 

Instantaneous entropy contours in a 2 112-stage compressor. 
Analysis of Rotary Engine Processes and Computer Codes 

M. S. Raju, Principal Investigator 

Sverdrup Technology. Inc. 

Research Objective 

The direct-injection stratified-charge rotary combustion engine 

(DISC-RCE) would be a desirable powerplant for light aircraft 

and drones (including high-altitude applications) if its efficiency could be made closer to that of reciprocating engines. 

Continuing research and development sponsored by NASA is 

aimed at reducing the cruise brake-specific fuel consumption 

from the current value of 0.42 Ibtbhp-hp to 0.35 or less by the 

end of 1992. 

Approach 

Much of the expected improvement in RCE performance will 

be facilitated by computational fluid dynamics-driven fuelinjection, spray, and nozzle optimization; rotor pocket and 

nozzle relocations; and related modifications. 

Accomplishment Description 

A new computer code was developed for predicting the 

turbulent and chemically reacting flows occurring inside a 

DISC-RCE. The solution procedure is based on an EulerianLagrangian approach in which the unsteady, threedimensional Navier-Stokes equations for a perfect-gas mixture 

with variable properties are solved in generalized, Eulerian 

coordinates on a moving grid by making use of an implicit, 

finite-volume, Steger-Warming flux-vector-splitting scheme, 

and the liquid-phase equations are solved in Lagrangian 

coordinates. Numerical predictions of the pressure and temperature histories, the torque generated by non-uniform pressure distribution within the chamber, energy release rates, and 

various flow-related phenomena were obtained and compared 

with experimental data. The code takes about 10 CPU hours 

and 5 megawords of memory when the calculations are 

performed on a grid with a mesh size of 31 x 16 x 20 on a 

Cray Y-MP for one entire cycle. 

Future Plans 

The computer code will be modified with the incorporation of a 

k-& turbulence model and an eddy break-up model to account* 

for some of the effect of turbulence on the combustion model. 

The spray model may also be improved with the inclusion of 

submodels associated with the droplet collision, droplet 

break-up, and droplet dispersion resulting from turbulence. 

Publications 

1. Raju, M. S., and Willis, E. A. "Analysis of Rotary Engine 

Combustion Processes Based on Unsteady. ThreeDimensional Computations." AlAA Paper 90-0643, 1989. 

2. Raju, M. S., and Willis, E. A. "Computational Experience 

with a 3-D Rotary Engine Combustion Model." Proceedings of 

the 1990 Joint AIAAIFAA Symposium on General Aviation 

Systems. Ocean City, NJ, Apr. 1990. 

Analysis of rotary combustion engine processes. 

138 

ORlGii.JA?- TRGE 

COLOR PHOTOGRAPH 
An Adaptation Procedure Combining Mesh Refinement with Mesh Movement for 

Compressible Flows 

R. Ramakrishnan, Principal Investigator 

NASA Langley Research Center 

Research Objective 

To use a mesh adaptation scheme that combines mesh 

refinement and derefinement with mesh movement to capture 

sharp gradients such as shocks by using an upwind finiteslement formulation. 

Approach 

A mesh adaptation scheme that uses both triangular and 

quadrilateral elements to enrich and coarsen elements based 

'dn refinement indicators has found an application in modeling 

inviscid and viscous flows. To minimize the number of elements used in the analysis, this adaptive mesh-refinement 

procedure is complimented by a mesh movement scheme. 

Mesh movement is accomplished by using the concept of a 

spring-mass system centered on each node. Stiffness coefficients for these springs are related to element errors, which 

are computed from normalized second derivatives of a key 

variable such as density. To demonstrate the adaptation 

scheme, Mach 6 inviscid flow over a cylindrical leading edge 

is modeled. A node-based, upwind finite-element algorithm 

with higher order extensions is used to solve the compressible 

Euler equations. The finite-element mesh obtained after two 

levels of refinement contains 3769 nodes, and the density 

contours on this mesh appear on the left side of the figure. The 

mesh obtained after one refinement with mesh movements at 

s~ecified intervals contains 1587 nodes. This mesh and the 

The surface pressure distributions along the right boundary of 

the computational domain compare well for the two cases. The 

inclusion of mesh movement produces a crisper definition of 

the bow shock. A closer look at the elements in the vicinity of 

the bow shock shows the mesh being aligned and stretched 

along the shock when adaptive refinement is combined with 

mesh movement. 

Accomplishment Description 

An adaptation procedure that combines mesh refinement with 

mesh movement is coupled with an upwind, higher order 

finite-element algorithm to model high-speed compressible 

flow. 

Significance 

The mesh refinement procedure augmented by nodal relocation orients the elements along the shocks or flow discontinuities. Nodal density across such high gradients is increased, 

resulting in excellent shock resolution. The number of elements needed to model the domain is reduced substantially 

and no a priori knowledge of the flow field is required. 

Future Plans 

Future plans include developing accurate indicators for mesh 

movements in the boundary layer for viscous flows and 

extending the adaptation procedure for three-dimensional 

applications. 

density contours on it appear on the right side of the figure. 

Refinement only. Surface pressure distributions. Refinement plus movement. 

la2I -- refinement only 

- refinement i movement 

Mesh refinement for inviscid flow over a cylindrical leading edge. 

! ., ,;I: 
Modeling Global Cloudiness 

David A. Randall, Principal Investigator 

Colorado State University 

Research Objective 

To numerically simulate the global distribution of cloudiness 

in the Earth's atmosphere and the effects of the clouds 

on climate-specifically, the effects of the clouds on 

C02-induced climate change. 

Approach 

A three-dimensional atmospheric general circulation model is 

used in low-resolution simulations of several annual cycles 

and in high-resolution simulations of individual seasons. 

Accomplishment Description 

A five-year low-resolution simulation was completed, and the 

model is now being run with increased resolution, using both 

Navier-Stokes and Reynolds codes. Runs require 12 megawords of memory and about 36 CPU hours per simulated 

year. This year we established, among other things, that the 

observed diurnal variation of precipitation over the oceans 

is due primarily to the radiative effects of clouds. This is 

illustrated in the accompanying figure. We have continued 

our participation in a comparison of results from 18 climate 

models from around the world. 

Significance 

Climate change resulting from increasing atmospheric carbon' 

dioxide cannot be understood or predicted without taking into 

account the effects of the clouds. 

Future Plans 

The high-resolution model will be run through 18 simulated 

months, about 6 months of which have already been completed. Results will be analyzed with special attention to the 

simulated cloudiness and surface energy budget. 

TOTAL PRECIPITATION (MINUS THE TIME MEAN) 

SEAWORLD WITH CLOUDS 

90. 

70. 

50. 

10. I 

-1 0. 

I 

u. 14. 10. 

Local tlmm. hrm 

Total precipitation (minus.the time mean) 

! +..' 

140 

ORIGINAL ?;!.SE 

COLOR PHCTOGXAPH 
Computation of ASTOVL Flow Fields 

James A. Rhodes, Principal Investigator 

McDonnell Aircraft Company 

Research Objective 

The objective of this research is to compute flow fields related 

to the design of Advanced Short Takeoff and Vertical Landing 

(ASTOVL) aircraft. In particular, the computation of threedimensional jets exiting from a wall into a low subsonic cross- 

!low and the computation of three-dimensional impinging jets 

are of high interest. Our 1989 objective was to apply the 

MCAlR upwind scheme NASTD to the above two problems 

and evaluate the results. 

approach 

The approach in 1989 was first to attack the problem of a 

three-dimensional jet in a subsonic crossflow and then to 

proceed to the more complicated problem of the threedimensional impinging jet. The first problem is one of the 

simplest jet-in-crossflow problems and yet is rich in interesting 

fluid dynamics. A two-zone grid was developed, which we 

believed to be adequate for resolving the key flow-field features. The flow solver was applied and run in a sequenced 

mode on a coarse version of the grid. A preliminary solution 

was obtained and examined. 

Accomplishment Description 

A grid was developed with a reflection boundary aligned 

parallel to the crossflow and normal to the wall. The 

PARTICLE TRACES 

65 x 33 x 65 rectangular zone 1 is where the jet interacts with 

the crossflow, and the semicircular 25 x 13 x 9 "nozzle" zone 2 

sets up the jet and is coupled using a point-matching interface. The grid was developed using elliptic methods so that 

the grid in the hole is a Cartesian subset of the wall boundary. 

The flow solver was run on a coarse grid to obtain an initial 

solution, which is shown in the figure. This solution will be 

refined in the future. 

Significance 

A solution of a jet exiting from a wall into a low subsonic crossflow was obtained using a code that solves the full Reynoldsaveraged Navier-Stokes equations using a finite-volume 

upwind scheme with an algebraic turbulence model. The 

solution shows many of the physical features that are characteristic of such flows. 

Future Plans 

This work will continue in 1990. Grid modifications will be 

attempted, to reduce the boundary layer thickness of the jet 

as it exits from the noule zone below the wall. Adaptive 

gridding will be used and the flow solver will be run using a 

two-equation low-Reynolds number turbulence model. We will 

also compute the flow inside the lift noule return "cactus" 

duct of an ASTOVL vehicle. 

A three-dimensional jet in a subsonic crossflow. 
Kinetic Theory Model for the Flow of a Simple Gas from a Three-Dimensional 

Axisymmetric Nozzle 

Ben R. Riley, Principal Investigator 

University of Evansville 

Research Objective 

The objective is to develop a model to predict the flow field of 

exhaust plumes for small low-thrust nozzles. In particular, the 

effect of the assumptions about the boundary layer along the 

inside wall, especially near the nozzle lip, on the flow fields 

external to the nozzle is of interest. 

Approach 

The mathematical framework for the description of the gas 

flow is the time-independent Boltzmann equation for binary 

collision. The complete scattering term is replaced by a Krooktype (collision relaxation) approximation to simplify the 

collision calculations. Starting with a zeroth-iteration set of 

flow-field parameters for temperature, number density, and 

mean velocity at each grid point, the method of characteristics 

is used to numerically solve the Boltzmann equation in order to 

find the first iteration values for temperature, number density, 

and mean velocity. This iteration procedure is repeated until a 

reasonable convergence is obtained. A major concern in this 

technique is the proper number and location of grid points, 

especially near the nozzle lip. The accompanying figure shows 

the number density in a half-plane through the centerline. 

Each solution required about 10 hours of Cray Y-MP time and 

2 megawords of memory. 

Significance 

Self-induced molecular contamination around a spacecraft 

can limit its usefulness, because the contaminants may 

adversely affect components or experiments being performed 

on or near the spacecraft. Since it is difficult to perform 

ground-based experiments because of low-vacuum requirements, computer models are needed to help design the 

nozzles. 

Future Plans 

The code will be used to study the plume flow fields with 

different nozzle conditions. At the same time, work is being 

done on the code to further vectorize it and to decrease the 

run time. 

Publications 

Riley, Ben. "Kinetic Theory Model for the Flow of a Simple Gas 

from a Three-Dimensional Axisymmetric Nozzle." Presented at 

the 17th International Conference for Rarefied Gas Dynamics, 

Aachen, Germany, July 1990. 

Three-dimensional plot of number density. The number-density 

axis is marked in powers of 10, and the shaded area is inside 

the 20"-half-angle nozzle. The angle is measured in degrees 

from the centerline, the nozzle-lip grid point is marked L, and 

the distance from the nozzle throat to the exit plane is -0.01 m. 
Scattering from Ocean Surfaces and Near-Surface Objects 

Charles L. Rino, Principal Investigator 

Co-investigators: Hoc D. Ngo and Thomas L. Crystal 

Vista Research, Inc. 

Research Objective 

To develop the capability to simulate electromagnetic and 

acoustic scattering from dynamically evolving nonlinear ocean 

surfaces and near-surface objects. 

Approach 

Linear ocean-surface realizations are generated by allowing 

noninteracting Fourier modes to propagate according to the 

:inear dispersion relation for surface waves. The linear surfaces are then converted to their nonlinear form by using an 

efficient procedure based on Hilbert transforms. Scatter is 

simulated by solving the surface boundary-value problem 

numerically. Scatter from a nearby object is accommodated 

by a new technique, which we call the mutual interaction 

method. 

Accomplishment Description 

We have been able to simulate, for the first time, Doppler 

spectra from nonlinear ocean-surface realizations, as well as 

scatter from objects near rough surfaces. The simulations 

have revealed differences between acoustic bottomside cross 

sections and radar cross sections at the same wavelength. 

Our simulations have also been used to study the effects of 

subsurface bubble clouds. 

Significance 

The complexities of nonlinear hydrodynamics, rough-surface 

scattering, and mutual interaction are sufficiently complex in 

their own right that few analytic results are available. Combining these effects via numerical simulation is presently the only 

way to model the full range of observable ocean-surface 

scatter phenomena. 

Future Plans 

At the present time, our simulations have been restricted to 

one-dimensional surface realizations. Although there is much 

to be learned from such models, we will be implementing 

some promising schemes that may be fast enough to allow 

realistic two-dimensional simulations. 

Publications 

1. Rino, Charles L., and Ngo, Hoc D. "Numerical Simulation 

of Acoustic Scatter from Subsurface Bubble Clouds." 

ONTIDARPA Technical Report NO001 4-87-C-0437, 1989. 

2. Rino, Charles L.; Crystal, Thomas L.; Koide, Alan K.; Ngo, 

Hoc D.; and Guthart, Harold. "Numerical Simulation of Acoustic and EM Scattering from Linear and Nonlinear Ocean 

Surfaces." Submitted to Radio Science, 1990. 

(a) Nonlinear Surface Height -- 700/5 pls. U = 15 rn/s 

4',,,,I'.',I.,.,l,'., ,," ,,', ,,,, 

Distance - rn 

(b) Differential Scolter Coefficient -- O,,, = 60 deg l,l.,l..,.,l,,,.. ..,,. ,,.., ,,,,, 

I 

(1) SURF ALONE - NUMERICAL 

(2) CYL UNDER SURF - NUMERICAL 

-90 -60 -30 0 30 60 90 

Theta - deg 

Simulation of acoustic bistatic scatter for an isolated nonlinear 

surface and a cylinder 10 m below the surface reference level. 

The wavelength is 7.5 m and the source field is incident at 6(P 

from vertical. The surface realization is shown in the top frame. 

The peaked crests and more rounded troughs are characteristics of ocean surface waves. Note the bistatic enhancements 

above the level that would be observed for a smooth surface, 

which is the dotted curve. The mutual interaction method was 

used to obtain the exact analytic result for an isotropic 

scatterer above a smooth surface. 
Turbulent Reacting Flows 

Michael M. Rogers, Principal Investigator 

Co-investigators: Robert Moser and Chris Rutland 

NASA Ames Research Center 

Research Objective 

The objective is to generate a direct numerical simulation data 

base for reacting turbulent flows that will aid in the study of 

combustion problems by providing an understanding of the 

effects of turbulence on reaction. Early work will focus on the 

low-heat-release limit of reaction in incompressible turbulence. 

Approach 

A direct numerical simulation of the full three-dimensional 

Navier-Stokes equations is performed with resolution adequate 

to resolve both the turbulence and the flame zone. Early work 

is based on reacting passive scalars in an incompressible 

turbulence, using pseudospectral numerical methods. 

Accomplishment Description 

Several three-dimensional numerical simulations of temporally 

evolving, plane mixing layers were generated. The effect of 

streamwise "rib" vortices on the "rollers" of spanwise vorticity 

formed by the Kelvin-Helmholtz instability was studied for a 

variety of low-wave-number initial disturbances. The flows 

were simulated for up to two pairings of the spanwise rollers 

with a spanwise domain containing up to four unequalstrength pairs of counter-rotating rib vortices. It was found that 

despite the lack of any broadband initial disturbances, some 

of the simulated flows undergo a transition to turbulence. This 

"mixing transition" is marked by a significant increase in smallscale vortical structures of a highly disorganized nature. The 

enhanced mixing associated with such a flow results in 

increased product production, the amount of which is in 

agreement with that seen experimentally. The figure shows 

product concentration at one spanwise location of a mixing 

layer at completion of the second pairing. The instantaneous 

flame surface is indicated by the black line. The roughly 

uniform product concentration in the roller core (figure center) 

is in line with experimental observations. Simulations require& 

up to 400 Cray Y-MP CPU hours and 70 megawords of 

memory. 

Significance 

These direct numerical simulations are the first to simulate thi 

transition to turbulence in a plane mixing layer. The mechanisms of this transition are under study and should provide 

insight into the control of mixing and combustion in free shear 

flows. 

Future Plans 

We plan further postprocessing of the numerical data base in 

an effort to better understand the mechanisms of mixing transition. The effects of a reduced chemical reaction rate will be 

studied. Long-term goals include simulating reactions with 

heat release. 

Publications 

1. Presented at the 1989 Turbulent Shear Flows conference. 

2. Presented at the 1990 IUTAM Symposium on Fluid 

Mechanics of Stirring and Mixing. 

3. In preparation for submission to J. Fluid Mechanics. 

Product concentration at one spanwise location of a mixing layer at completion of the second pairing. 
Hydrogen-Air Combustion Simulation in a Pulse Facility 

R. Clayton Rogers, Principal Investigator 

Co-investigator: Elizabeth H. Weidner 

NASA Langley Research Center 

Research Objective 

To use computational fluid dynamics (CFD) codes to model 

the supersonic/hypersonic mixing and combustion of hydrogen in an air flow that is entering a scramjet at conditions that 

correspond to hypervelocity atmospheric flight. 

Approach 

Two- and three-dimensional Navier-Stokes solvers (SPARK) 

with turbulence, and a full eighteen-reaction, nine-species, 

;-I2-air, finite-rate combustion model are used to compute the 

flow through simple combustor configurations that have been 

tested in the T4 Shock Tunnel at the University of Queensland, 

Australia. Both full and parabolic versions of the CFD codes 

are applied, depending on the flow geometry. 

Accomplishment Description 

The accomplishment during this year's project consisted 

primarily of calculations made with the parabolized NavierStokes (PNS) version of the SPARK code for a combustor 

configuration, shown schematically in the upper left figure. 

Some effort was spent learning the PNS code and the techniques for applying it to the quasi-steady flow from a pulse 

facility. The total duct flow was computed in two parts: from 

the leading edge of the fuel strut to the strut base; and then 

patching this flow to begin the solution, with added fuel injection from the strut base, to the duct exit. Results are shown for 

one test condition with inflow velocity, pressure, and temperature of 3670 mlsec, 21.5 kPa, and 1165 K, respectively. Fuel 

is injected parallel to the flow at the upper computational 

lcm ////////////////////////////I/ 

shock tunnel 

Schematic of experimental combustion duct. 

Laminar 

Pressure contours, reacting flow. 

boundary. The lower left figure shows the static pressure field 

for the reacting flow case for laminar and turbulent flow. The 

upper computational boundary is the duct centerline from the 

strut base. The effect of turbulence is to increase the mixing 

and therefore the combustion, resulting in higher pressures 

and increased wave angles. This result is also evident in the 

pressure distributions along the lower wall shown in the figure 

on the right. The data are from recent tests in the T4 Shock 

Tunnel at the University of Queensland. In general the agreement is good, considering the uncertainty in some of the data 

and the turbulence modeling needed for the reacting flow 

case. These results are preliminary using the PNS code, and 

the computations are continuing in this year's effort. 

Significance 

Although preliminary, these results add to our mixing and 

combustion computational data base for flows at conditions 

corresponding to hypervelocity flight, and the method provides an alternate means, using the PNS codes, to obtain 

more rapid calculations. 

Future Plans 

The use of the SPARK family of codes to analyze and interpret 

experimental results acquired in pulse facilities at hype~elocity conditions will continue, with the focus on relating the computed results to combustor design parameters of scramjets. 

These results will be published when a complete set of cases 

has been computed. 

$ Data, T4 Shock tunnel 

- SPARK-PNS, laminar 

--- SPARK-PNS, turbulent 

- Fuel-on, reacting 

Fuel-on, no reaction 

I I I I I I I 

0 20 40 60 80 100 120 140 

Distance from duct inflow, cm 

Pressure distributions. 
National Aero-Space Plane Inlet Boundary Layer Control, Phase I1 

William C. Rose, Principal Investigator 

NASA Lewis Research CenterIRose Engineering & Research, Inc. 

Research Objective 

To compute inlet flow fields with novel boundary-layer-removal 

simulations using the three-dimensional Navier-Stokes 

equations. 

Approach 

A modified version of the three-dimensional Kumar internal 

flow code is run on the Cray-2 with boundary conditions 

applied to the inlet surface that are representative of those 

expected to occur from both porous surfaces and portions of 

surfaces removed. 

Accomplishment Description 

The code was modified to calculate the flow internal and 

external to the inlet. A four-block grid using two overlap points 

at the multiblock interfaces was used to examine the effects of 

the "correct" interaction between the internal and external 

flows. Approximately 100 hours of single-processor CPU time 

was expended, with an average of 16 megawords of run-time 

memory. Solutions were obtained for the Mach 5 configuration 

for conditions representative of those that occur in the NASA 

Lewis 10- by 10-foot wind tunnel. The figure shows the shaded 

Mach number contours for half of the inlet on the symmetry 

plane and four selected crossflow planes. The ramp surface is 

at the bottom and the cowl is at the top. The multiblock grid is 

depicted at the last crossflow plane. The side-wall vortical flow' 

spills over the cowl lip as indicated at the third crossflow 

plane. 

Significance 

Significant interaction between the captured internal flow and 

the flow that spills over the side walls and cowl lip (external 

flow) is expected to occur. The code is now capable of 

accounting for these interactions. 

Future Plans 

The multigrid capability will be used to investigate the effect of 

flow passing through porous and/or cutaway surfaces. 

CO\TOllM I FIIFI 

I IIO 

Mach number contours for half of the NASP inlet. 
National AeromSpace Plane Inlet Flow Fields 

William C. Rose, Principal Investigator 

Co-investigator: Edward W. Perkins 

NASA Ames Research CenterIRose Engineering & Research, Inc. 

Research Objective 

To compute the fully three-dimensional flow field within inlets 

typical of those expected to be used on the National AeroSpace Plane (NASP). 

Approach 

The existing Kumar three-dimensional internal flow code is run 

on the Cray-2. 

Accomplishment Description 

.Approximately 300 hours of single-processor CPU time were 

expended with an average of 16 megawords of run-time 

memory. Solutions were obtained for a representative Mach 8 

inlet model on a grid that was 201 x 23 x 61 for half of the 

symmetric inlet. The flow conditions were those characteristic 

of flight with a cool wall. The Mach contours are shown in the 

figure for the entire flow field and an enlargement. Contours 

are shown on the symmetry plane (nearest plane) and two offcenter planes. Crossflow planes at the cowl lip, near the 

throat, and near the exit are shown. Near the center, the flow 

appears two-dimensional, while near the side wall (far plane) 

the flow becomes highly three-dimensional. This threedimensional flow causes significant nonuniformities at the 

entrance to the combustor. 

Significance 

The flow in the two-dimensional models can be computed with 

a three-dimensional code to quantify the effects imposed on 

the flow by the addition of the side walls. 

Future Plans 

Currently this code is being used to solve other threedimensional inlet and nozzle flow fields expected to be 

applicable to the NASP vehicle. 

Publications 

"Comparison of CFD Results and Experimental Data for 

Scramjet Inlets at M = 8 and 18." Paper 46, the 7th NASP 

Symposium, Oct. 1989. 

7.970 MACH 

O.OmEG ALPHR 

6.71x10**6Re 

1.90x10**-3IME 

201YL361 GR I0 

Mach number contours for the NASP inlet; M = 7.970, a = O.OOO, Re = 6.71 x lo6, time=1.90 x grid size 201 x 23 x 61. 
Three-Dimensional Viscous Flow in High-Speed Inlets 

William C. Rose, Principal Investigator 

Co-investigator: Edward W. Perkins 

NASA Ames Research CenterIRose Engineering & Research, Inc. 

Research Objective 

To compute inlet flow fields with three-dimensional NavierStokes equations in order to investigate fully three-dimensional 

flows and shock-wave effects on inlet distortion. 

Approach 

The existing three-dimensional Kumar code is run on the 

Cray-2. 

Accomplishment Description 

Approximately 50 hours of single-processor CPU time were 

expended, with an average of 16 megawords of run-time 

memory. Solutions were obtained on a 101 x 63 x 41 grid for a 

three-dimensional side-wall compression inlet that had a contraction causing swept shock waves to exist within the inlet in 

the presence of a thick, oncoming boundary layer. The results 

indicate a distorted outflow condition with large variations in 

Mach number, as shown in the attached figure. 

Significance 

With the large run-time memory available, solutions to internal 

flow problems representative of generic high-speed inlets can. 

be obtained with sufficient resolution to demonstrate the 

potential for distorted flow fields exiting the inlet. 

Future Plans 

The code is being used to solve other fully three-dimensional. 

inlet flow fields with swept shock-wavelboundary-layer interactions applicable to high-Mach number flows. 

Publications 

"Analysis of the Flow in Sidewall Compression Inlets at Hypersonic Mach Numbers." NASP Contractor Report 1064, Oct. 

1 989. 

17.700 MACH 

O.OmEG ALPHA 

9.3Sx10*+8Re 

1.34x10**-3IME 

1Ofikll GRID 

Mach number contours for an SWC inlet on a 4" wedge; M = 17.700, a = O.OOO, Re = 0.35 x lo8, time = 1.34 x 10". grid size 

101 x 63 x 41. 
Advanced Computational Materials 

M. B. Salamon, Principal Investigator 

Co-investigators: R. Averback, Y.-C. Chang, J. Kogut, R. Martin, 

University of Illinois, Urbana-Champaign 

Research Objective 

The program seeks new algorithmic approaches to problems 

in materials research. New methods for quantum problems 

and new approaches to statistical mechanics problems are 

the main focuses of the NAS work. This effort is sponsored by 

-the Materials Laboratory Program of the National Science 

Foundation. 

Approach 

monte Carlo methods, a combination of local-density and 

molecular dynamics techniques, and the embedded atom 

method are among the approaches used. 

Accomplishment Description 

Martin's group developed new local-density methods that, 

combined with molecular dynamics, are providing a description of liquid carbon at high temperatures and pressures. 

Renken, with Kogut, applied scaling laws to the specific heat, 

which has a peak as a function of surface curvature, to confirm that the crumpling transition is of second order with a 

correlation-length exponent of 0.78(2). The band structure of 

semiconductor wires was studied by Chang's group. This 

study has just begun at Ames. Averback simulated the collision of 13- and 92-atom clusters with crystal surfaces. He 

found that when the cluster velocity exceeds the sound velocity of the crystal, the collisions approximate individual atom 

collisions, while at lower velocities macroscopic descriptions 

are adequate. 

and P. Wolynes 

Future Plans 

The researchers on the project plan to extend the development work to actual production runs, but find the turn-around 

time excessive. Renken will try to compute the central charge 

of his two-dimensional critical theory. Averback will study 

clusters with larger energies to investigate "thermal spiken 

effects. Chang's preliminary work on quantum wires and 

multilayers will continue. 

Publications 

1. Averback, R. S. "Ion Beam Mixing at Metal Surfaces." 

lnvited paper, presented at the American Physical Society 

Spring Meeting, 1990. 

2. Hsieh, H., and Averback, R. S. "Molecular Dynamics 

Investigation of Cluster Beam Deposition." To be submitted to 

Phys. Rev. B. 

3. Averback, R. S.; Hsieh, H.; Diaz de la Rubia, T.; and 

Benedek, R. "Interactions of Energetic Particles and Clusters 

with Solids." lnvited paper, presented at the 7th International 

Conference on Ion Beam Modifications of Materials, Knoxville, 

TN, Oct. 1990. 

4. Renken, Ray L., and Kogut, John B. "Scaling Behavior at 

the Crumpling Transition." 

5. Renken, Ray L., and Kogut, John B. "The Central Charge 

of the Crumpling Transition." 

The specific heat as a function of the extrinsic curvature coupling for L = 8 (x), L = 12 (triangles), L = 16 (squares), L = 24 (empty 

circles), L = 32 (filled circles). 
Computational Methods for Rotor-Blade Drag Prediction 

Matthew T. Scott, Principal Investigator 

Bell Helicopter Textron, Inc. 

Research Objective 

The objective of this project is to examine the predictive 

capabilities of a hierarchical assortment of numerical methods 

for the computation of airflows about helicopter rotor blades. 

In particular, measurement of the various components of drag 

on rotor blades is being emphasized. 

Approach 

Three-dimensional Navier-Stokes codes utilizing both rotating 

and nonrotating coordinate frames attached to the rotor blade 

are used to predict drag levels along rotor blades. An 

unsteady three-dimensional full-potential code in rotating 

coordinates is used to provide inviscid drag levels. A comparison of results from the codes allows an assessment of the 

relative magnitudes of the drag components that are due to 

viscosity, wake induction, and algorithm. 

Accomplishment Description 

Existing three-dimensional viscous codes were modified to 

facilitate computations of rotor blades in nonrotating coordinate systems as well as rotating ones. Boundary conditions for 

one viscous solver were rewritten so the results could be 

compared with existing wind tunnel data. Another viscous 

code was modified to disable rotational motion of the coordinates and thus to provide algorithmic correlation with the first 

solver. The inviscid rotor code was used to provide baseline 

spanwise drag levels on both proprietary and general-use 

rotor planforms and also to provide insight into unsteady 

shock collapse on the advancing part of the disk. The accompanying figure shows some correlations made on a solution 

for a NACA 001 2 rotor at transonic conditions and yawed 

relative to the free stream. Away from the tip region, this code 

shows a shock location approximately 12% forward of that 

shown by two-dimensional test data. Other test data (Harris, 

NASA TM-81927, 1981) show the shock location to be 

between these two values, at 46% chord. Drag values differ 

by 14 counts; this is mostly attributable to the difference in - 

shock location. At the tip, the shock has moved forward on the 

blade. In nonrotating coordinates, this movement results in a 

net thrust on that section. However, inviscid results in rotating . coordinates show that the shock is almost nonexistent and 

that the section still produces drag. Further research tested 

the effect of yaw angle on shock location and wake model on 

required rotor power. 

Significance 

Requirements for modern high-speed helicopters include fast 

rates of climb, improved performance, and high degrees of 

maneuverability. By reducing the levels of certain components 

of drag on the blade, more power is made available to the 

rotor for these tasks. Accurate assessment of blade drag in 

maneuvers, transonic flight, or at high a is crucial to rotorcraft 

predictive and analytic methodology. 

Future Plans 

Analyses of the drag components that are due to azimuthal 

blade position, wake induction, and three-dimensional effects 

will be continued. Viscous solutions will be provided to correlate with wind tunnel tests of high-speed tip planforms. 

#-0 VISCOUS. NOW-ROtATlWG ICA-0 016) 

Pressure contours on a NACA 0012 rotor blade; M = 0.80, a = 2.40°, yaw angle = 20" forward, Re = 3.7 x lo6. 
Direct Simulation of High-Speed Mixing Layers With and Without Chemical 

Heat Release 

Balu Sekar, Principal Investigator 

Co-investigators: H. S. Mukunda and Mark H. Carpenter 

NASA Langley Research Center 

Research Objective 

To examine the effects of convective Mach number, disturbance levels, initial profiles, Reynolds number, and chemical 

heat release on the structure of a high-speed mixing layer. 

Approach 

The SPARK2D code is used to perform a direct numerical 

simulation of the high-speed two-dimensional mixing layer. 

The numerical algorithm used is the dissipative compact 

parameter scheme, which has a formal accuracy of 

O(A~~,AX~). 

Accomplishment Description 

High-speed mixing-layer calculations were made at convective Mach numbers of 0.38 and 0.76 for a number of initial 

disturbance levels, for two initial profiles, and for a range of 

Reynolds numbers, using the SPARK2D code. Fine grids were 

used to ensure that all the relevant length scales were 

resolved. From the calculations, the following conclusions 

were drawn: (1) Assumed hyperbolic tangent profiles need 

large disturbance levels to make the flow transitional. (2) The 

concept of a convective Mach number needs review at high 

convective Mach numbers because the structures dilate 

significantly. (3) The growth rates obtained from the timeaveraged data compare reasonably well with existing experimental data, illustrating the compressibility effects. (4) The 

significant role of heat release is to reduce the growth rate of 

the mixing layer by about 5 to 7% and to reduce the convective speed of the structures by about 10% at M, = 0.38. 

Preliminary results indicate that increasing the convective 

Mach number will reduce the effect of heat release. 

(5) Changes in density in the flow result from temperature, 

pressure, and composition variations in the compressible 

case, unlike those in incompressible flows, in which temperature and composition are the dominating factors. (6) The 

reduction in Reynolds stresses and kinetic energy of fluctuations, as well as the reduction of entrainment with heat 

release, are akin to those in incompressible flows, but to a 

much lesser extent. In view of the weaker role of heat release, 

it is reasonable to conclude that it is useful to concentrate on 

nonreacting flows for the mixing-related issues. Heat release is 

likely to provide only a small perturbation to many nonreacting 

flows. 

Significance 

Direct numerical simulation of high-speed mixing layers has 

improved the understanding of fuel-air mixing in scramjet 

combustors. Current studies have facilitated the determination 

of several important techniques for producing high levels of 

mixing and combustion efficiency in a scramjet combustor. 

Future Plans 

Flow conditions exist for which the above conclusions may be 

only partially valid. Further study of these issues as well as a 

complete study of three-dimensional nonreacting and chemically reacting mixing layers is necessary. 

Publications 

Sekar, Balu; Mukunda, H. S.; and Carpenter, M. H. "The Direct 

Simulation of High Speed Mixing Layer Without and With 

Chemical Heat Release." Presented at the Computational 

Fluid Dynamics Symposium on Aeropropulsion, NASA Lewis 

Research Center, Cleveland, OH, Apr. 1990. 

CMlTOllR LFUCI S 

Non Reacting 

- 

0 I I I I I I I I 5b CONTOUR LEVELS 10C 

-s,ll.llll 

- IIIII 11111 

-150 no1 

-7110 O Reacting -2511 11" 

- 1011 11 IVorticity contours for a nonreacting and a reacting H2-air mixing layer; M, = 0.38, domain size 100 x 50 rnm, grid size 201 x 125. 
Ionized Flow Around a Reentry Vehicle 

John V. Shebalin, Principal Investigator 

NASA Langley Research Center 

Research Objective 

The objective of this work is to numerically simulate plasma 

electrodynamic processes in the ionized flow that occurs 

around an aerospace vehicle during high-Mach number 

reentry. This will provide the ability to study the effects of 

electromagnetic (EM) stresses on spacecraft design and 

performance, on flow-field modeling, and on EM wave propagation through the plasma surrounding a hypewelocity reentry 

vehicle. 

Approach 

A two-dimensional, compressible magnetohydrodynamic 

(MHD) spectral code, with a polytropic isentropic equation of 

state, was used to study the growth and homogeneous 

dynamics of the self-magnetic field. A Fourier collocation time 

domain (FCTD) method was created to study EM propagation 

in a plasma medium. 

Accomplishment Description 

(1) A Fourier spectral transform method code was used to 

study magnetic field amplification in forced MHD turbulence. 

Initial conditions consisted of an external mean magnetic field 

and a negligible turbulent magnetic field; it was found that 

although the final energy in the turbulent magnetic field 

depended directly on the initial external mean field strength, 

the actual amplification of the turbulent magnetic field varied 

inversely with the mean field strength. Also, compressibility 

appeared to have only a marginal effect in mediating the 

transfer of kinetic into magnetic energy. (2) A new, twodimensional, EM propagation code using an FCTD method 

was created. The advantage of this method over the popular 

finite-difference time domain (FDTD) method lies in an 

accuracy that is greatly increased for a relatively small 

increase in computation time, while the ease of use of FDTD is 

maintained. In these initial investigations, both of these efforts 

traded relatively small grid sizes (64 x 64 and 128 x 128) for 

several dozen separate simulations, each separate simulation 

lasting 3 to 4 CPU hours and using 1 to 2 megawords of 

memory. 

Significance 

As NASA moves further into the realm of hypersonic flight, the 

need to adequately understand ionized aerodynamic flow (i.e., 

plasma electrodynamics) in addition to aerothermodynamics 

becomes more critical. Such flow, and the novel features it 

may contain, is associated with atmospheric reentry, flight, 

and aeromaneuvering. Aerospace systems that generate 

ionized flows include the planned Aeroassist Flight Experiment 

vehicle, future aeroassisted orbital transfer vehicles, the 

National Aero-Space Plane, and tethered satellites. Furthermore, an understanding of ionized flow fields may shed some 

light on those unexpected phenomena encountered during 

shuttle reentry: hypersonic pitching moment and jet-aileron 

interactions. Plasma processes are also expected to be 

important in hypervelocity shocks. 

Future Plans 

In the coming year (NAS 1990-91), the primary planned 

objectives are an investigation into magnetic field and electric 

current generation occurring in plasma shock fronts, and . 

further investigations into EM wave propagation in inhomogeneous plasmas. Three-dimensional simulations are planned. 

Regional energy = 0.082 = 0.171 = 0.053 

Total energy = 0.306 at 0.32 nsec 

A 12.5-GHz single-wavelength sinusoidal pulse propagating 

out of a microwave horn, through a thermal tile, and into an 

over-dense (reentry) plasma; total energy = 0.306 at 0.32 

nsec. 
Afterbody Aerothermodynamic Studies for the Hypersonic Glide Vehicle 

Peter K. Shih, Principal Investigator 

Co-investigator: Che-Shing Kang 

General Dynamics, Convair Division 

Research Objective 

To develop a computational fluid dynamics (CFD)-based 

analytical method for the calculation of the aerothermodynamic environments of the Hypersonic Glide Vehicle (HGV), 

with the emphasis on the aftbody flow field. 

Approach 

The technical approach to this study is to validate existing 

%FD techniques against the HGV test data. In 1986, heat 

transfer and pressure data were obtained from the Calspan 

shock tunnel for a 0.3-scale model of the HGV. These data 

were compared with the PARC3D results. The 0.3-scale model 

was heavily instrumented in the aftbody region, which consisted of the fuselage, wing, tip fin and elevon surface. A good 

test case was thus provided for the PARC3D code. 

Accomplishment Description 

The full Navier-Stokes (FNS) solutions for the 0.3-scale HGV 

model were obtained using the PARC3D code under various 

Calspan test conditions, including both laminar and turbulent 

flows at zero or moderate angles of attack. In general, both 

laminar and turbulent FNS results agreed well with Calspan 

test data. To demonstrate the results, the turbulent FNS 

solutions, using the Baldwin-Lomax turbulence model, are 

presented in the accompanying figure. A heat flux comparison 

along the periphery of two axial locations of the HGV model is 

shown for 0" and 8.0" angle of attack. At Station 45, both 

laminar and turbulent results are plotted since the test data 

show the characteristic of boundary layer transition, whereas 

at Station 63.6, the fully turbulent solutions seem to fit the test 

data satisfactorily. A typical PARC3D computation for the HGV 

whole-body takes 20 Cray-2 hours and 10 megawords of 

memory. 

Significance 

The design of future hypersonic vehicles requires a complete 

understanding of the aerothermodynamic environment, which 

is especially severe because of the long endoatmospheric 

mission durations desired and the high lift-to-drag ratio 

necessary for maneuvers. Because of the lack of applicable 

test facilities, CFD solutions are particularly required in 

designing these vehicles. 

Future Plans 

The 1990 objectives are to (1) develop dynamic gridding 

techniques for PARC3D applications, (2) compare turbulent 

models to determine the effects on heating data prediction, 

and (3) model the flow field near a deflected elevon in 

-y-:~--?; +++ 

STA 45.0 STA 63.6 

Placement of the instrumentation on the 0.3-scale HGV model. 

- PARC3D -Turbulent 

- - - PARCBD - Laminar 

A Calspan test data 

Comparison of heat transfer data from the PARC3D code and 

the Calspan wind tunnel tests; M = 1 1.5, Re = 10.0 x 106/ft. 

(a) Station 45.0, a = 0.0"; (b) Station 45.0, a = 8.0"; 

(c) Station 63.6, a = 0.0"; (d) Station 63.6, a = 8.0". 
Advanced Numerical Algorithms for Chemically Reacting Flows 

Jian-Shun Shuen, Principal Investigator 

Sverdrup Technology, Inc./NASA Lewis Research Center 

Research Objective 

The objective of this work is to develop a new procedure that 

combines the accuracy of modern upwind schemes and the 

efficiency of the lower-upper (LU) factorization scheme for 

high-speed reacting flows. The resulting code has to be 

efficient and robust for flows involving high Mach numbers, 

strong shocks, and large zones of flow separation. 

Approach 

An efficient upwind method for solving the Navier-Stokes 

equations with nonequilibrium, frozen, and perfect-gas 

chemistry models is developed to calculate high-Mach 

number, high-enthalpy flows. The method uses either Roe or 

van Leer flux splitting for inviscid terms and central differencing for viscous terms in the explicit operator, and StegerWarming splitting and LU factorization for the implicit operator. 

Accomplishment Description 

An implicit, upwind, two-dimensional Navier-Stokes code was 

developed for high-speed reacting flow calculations. The 

code uses upwind, flux-splitting total-variation-diminishing 

schemes and LU factorization. The flow and chemistry are 

fully implicit and fully coupled to achieve efficiency and 

robustness. Sophisticated thermodynamic and transport 

property models are used for realistic evaluation of thermophysical properties at high temperatures. A series of numerical tests for a variety of flow configurations at varying Mach 

numbers and total temperatures was conducted to study the 

effects of real-gas chemistry on the structure of these flow 

fields. The test cases demonstrate the good shock-capturing 

capability as well as the efficiency and robustness of the 

code. The accompanying figure shows the species mass 

fraction contours for flows over a half-cylinder at free-stream 

T = 600 K and M = 7.0. A typical chemical nonequilibrium 

calculation with a 100 x 100 grid needs about 1.5 Cray Y-MP 

hours and 3 megawords of memory. 

Significance 

The numerical method and computer code developed in this 

work can be used to simulate both external and internal flows 

for the proposed aerospace vehicles in actual flight 

conditions. 

Future Plans 

The code currently uses an air dissociation model for the 

nonequilibrium chemistry. It is planned to extend the chemical 

kinetics to include both the air disassociation/ionization and 

hydrogen-air reactors. - 

Species mass fraction contours for flow over a half-cylinder; 

M- = 7.0. 
Ignition and Flame Spread above Liquid Fuel Pools: Gravity Effects 

William A. Sirignano, Principal Investigator 

Co-investigators: Fanghei Tsau and David N. Schiller 

University of California, lrvine 

Research Objective 

The objective of this research is to understand the basic 

mechanisms of buoyancy and/or surface-tension-driven flows 

and thereby provide adequate engineering scaling laws to 

guide experimental designs for reduced-gravity environments. 

Both two- and three-dimensional computational capabilities 

are required to simulate numerically an unevenly heated 

two-phase flow inside a cylindrical enclosure. The threedimensional study is needed when a variable acceleration 

field is present. 

Approach 

Two- and three-dimensional Navier-Stokes computer codes 

with variable fluid properties are used to predict the temperature and flow fields inside the cylindrical enclosure. The 

numerical codes use a hybrid differencing scheme and a 

semi-implicit solution procedure. 

Accomplishment Description 

The Cray hours allocated were used for three-dimensional 

studies, so the current discussion focuses on the results 

gained from them. Numerical simulations were conducted for 

a single-phase flow with a prescribed periodic acceleration 

field. The conventional Boussinesq approximation for changes 

of fluid properties was found to overpredict the heat transfer 

rate and to have a stronger tendency to respond to external 

agitations. The variable acceleration field (the so-called 

g-jitter) alters the heat transfer and flow characteristics significantly. For example, the heat transfer rate becomes periodic 

and the interaction between the thermal field and the flow field 

also becomes stronger. Strong three-dimensional effects result 

in complicated cellular flow structure and larger advection 

speed. The study also finds that reducing the total gravity level 

is better than just terminating the external g-jittering to restore 

8.0 

- - - - : WTHOVT C-IITIER. VARIABLE PROPERTY 

- : Wml C-JllTER VARIABLE PROPERTY 

6.0 - 

s 4.0 - w 

I; sec. 

a perturbed system. Different fluids have different post-jitter 

responses closely related to the viscosities of the working 

fluids. The external acceleration components that are perpendicular to the imposed thermal gradient have positive effects 

in increasing the heat transfer, but the role of the component 

parallel to the imposed thermal gradient is somewhat ambiguous. A typical variable-property run with simulation of up to 

two cycles of gravity modulation requires 10 Cray-2 hours and 

5 megawords of memory. 

Significance 

This research relates to hazardous fire at Earth-gravity 

conditions and aboard space vehicles at reduced-gravity 

conditions where a pool of flammable fuel is in the vicinity of 

an initial fire. Understanding the interaction between the 

buoyancy and the surface tension (along the surface of the 

fuel pool as a result of nonuniform heating) in various gravitational conditions can lead to the understanding of mechanisms 

for ignition and flame spread. Preventative measures can then 

be set up to avoid irreversible damages. Knowledge of the gjitter effects can also be beneficial to material processes and 

can increase the success rate of space experiments. 

Future Plans 

The three-dimensional code will be further implemented to 

conduct two-phase calculations. Thermal-capillary motions will 

be studied first under different gravity levels with various 

fluids. The knowledge and capabilities accumulated will then 

be used to investigate the two-phase flow with g-jitter effects. 

Publications 

Tsau, F.; Elghobashi, S.; and Sirignano, W. A. "Effects of 

G-Jitter on a Thermal, Buoyant Flow." Presented in the 28th 

Aerospace Sciences Meeting, Reno, NV, Jan. 1990. 

- - - - : rnomc-Irn. VARIABLE AlORRTY 

- : Wml G-ITEP. VARIABLE PROPERTY 

4 1.5 

9 

Y s 1.0 

.w . 

---------___ -----_____- 

0.5 

0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 

Thermal energy and its rate histories for the variable-property cases with and without g-jitter. 
Transition and Turbulence in Three-Dimensional Flows 

Philippe R. Spalart, Principal Investigator 

NASA Ames Research Center 

Research Objective 

The objective is to use direct numerical simulations of selected 

transitional and turbulent boundary layers to contribute to the 

understanding and prediction of aerodynamic flows. Recent 

efforts cover a range of more complex flows-for instance, 

spatially developing, three-dimensional, and separating flows. 

Approach 

We use a well-established spectral solver of the incompressible, three-dimensional, time-dependent, unaveraged NavierStokes equations over a flat plate. It can now treat spatially 

developing flows thanks to the "fringe" method. Each study 

involves choices of boundary conditions (pressure gradient), 

initial disturbances, and analysis procedures. 

Accomplishment Description 

(1) Direct simulations of crossflow vortices in a truly spatially 

developing, laminar boundary layer were conducted for the 

first time. (2) Direct simulations of a truly spatially developing, 

turbulent boundary layer were conducted for the first time and 

compared with a companion experiment conducted at Ames 

by Watmuff. 

Significance 

ltem (1) accurately provides the growth rates of vortices, 

which often cause transition on swept wings, without the 

controversial parallel-flow approximation. ltem (2) includes all 

effects of the pressure gradient on the turbulence; experiment 

and simulation are closely matched, including the pressure 

distribution and the Reynolds number, and the results compared in depth, resulting in a high level of confidence (see 

figure). 

Future Plans 

For the Watmuff flow we will obtain statistics, analyze the 

results from a theoretical and modeling point of view, and 

publish it. We are also simulating a three-dimensional boundary layer with pressure gradient, and a separation bubble. 

Pressure and skin friction for a spatially developing, turbulent 

boundary layer; experiment, -simulation. 
Magma Chamber Convection 

Frank J. Spera, Principal Investigator 

University of California, Santa Barbara 

Research Objective 

The goal of this work is to understand the dynamics of viscous 

flows in which two sources of buoyancy (chemical and thermal) are present. Nonlinearities inherent in the convectiondiffusion transport equations as well as in the rheological 

constitutive law give rise to complex flows in time and space. 

We wish to understand the dynamical basis of these 

complexities. 

Approach 

Jwo codes, a finite-element one and a primitive variable one 

valid for both two- and three-dimensional situations, were used 

to study single-phase and multiple-phase (e.g., solidification 

plus convection) mass and energy transport in doubly 

diffusive systems. 

Accomplishment Description 

A parametric study was used to determine the conditions in 

parameter space (Ra, Rs, Le, Pr) with and without crystallization, such that the computational domain becomes chemically 

heterogeneous starting from a constant composition field. 

Significance 

Magma chambers within the Earth's crust commonly show 

evidence of in situ compositional zonations. These simulations 

show in detail how chemical heterogeneity can develop from 

magma bodies that initially are unzoned but that mix actively 

by buoyancy-driven convection. 

Future Plans 

The codes will be further altered to incorporate more realistically the physics of convection with phase change. Specifically, more attention will be focused on the two-phase region 

(the mush). 

Publications 

1. Spera, Frank J.; Oldenburg, Curtis M.; and Yuen, David A. 

"Magma Zonation: Effects of Chemical Buoyancy and Diffusion." Geophysical Research Letters 16, no. 1 2 (1 989): 1 387- 

1390. 

2. Trial, Alain F., and Spera, Frank J. "Mechanisms for the 

Generation of Compositional Heterogeneities in Magma 

Chambers." Geological Society of America Bulletin 102 (1 990): 

353-367. 

Magma chamber convection. 
National Aero-Space Plane Engine Corner-Flow 

B. M. Steinetz, Principal Investigator 

Co-investigators: W. J. Coirier and Mike Tong 

NASA Lewis Research CenterlSverdrup Technology Inc. 

Research Objective 

The objective of this work is to determine the flow field and 

heat transfer in a panel-edge seal system of advanced 

hypersonic engines such as the National Aero-Space Plane 

(NASP). These seals must prevent the extremely hot, pressurized, engine flow-path gases from escaping through the 

interfaces between the articulating engine panels and the 

stationary splitter walls. Accurately estimating the seal heat 

fluxes and the ambient seal channel temperatures is a key to 

determining the seal-coolant resources that are required to 

prevent seal over-temperatures. Three-dimensional flow 

analyses are required in this study to assess the effects of the 

engine corner and the seal recess depth on the actual heat 

flux into the seal. 

Approach 

A three-dimensional Navier-Stokes code, PARC3D, was used 

to investigate the flow field and heat transfer in a panel-edge 

seal configuration. To improve the convergence rate for these 

studies, a hybrid lower-upper symmetric Gauss-Seidel 

(LU-SGS) algorithm was implemented. 

Accomplishment Description 

An example of the type of simulations possible with this 

advanced capability is shown in the accompanying figures. In 

this study, Mach 10 air is flowing in the engine inlet, which is 

modeled by horizontal and vertical engine panels. The paneledge seal is slightly recessed below the horizontal panel. The 

figure on the left shows the flow velocities at four engine-inlet 

positions; pink is the high-speed flow and blue is the lowspeed flow. Note that the seal-channel flow quickly decelerates as the boundary layer grows, limiting the heat flux into the 

seal. The three-dimensional character of the flow is demonstrated by the particle traces shown in the right-hand figure. 

Based on the flow calculations made, heat fluxes to the seal 

were determined and subsequently used for thermal stress 

analyses of the panel-edge seal system. To improve overall 

efficiency of the code, an LU-SGS algorithm was implemented 

for the approximate Newton iterations; this also required less 

user interaction to achieve acceptable convergence rates. An 

efficient method to account for limited real-gas effects was 

- 

also made available to PARC-3D. A typical computer run 

required 8 megawords of memory and 2 CPU hours on the 

Cray-2. 

Significance 

The panel-edge seal system is a critical mechanical system in 

an advanced hypersonic engine. These seals must prevent 

the extremely hot, pressurized, engine flow-path gases from 

escaping past the movable panels. Successful simulation of 

the fluid dynamic and heat transfer phenomena in and around 

the seal system is crucial to the design of the hypersonic 

engine. 

Future Plans 

Future work will investigate the fluid dynamic and heat transfer 

phenomena of the seal system with various gap aspect ratios 

(e.g., exposed seal-widthlrecess-depth). 

Publications 

Coirier, W. J. "High Speed Corner and Gap-Seal Computations 

Using an LU-SGS Scheme." AlAA Paper 89-2669, July 1989. 

Hypersonic gap seal simulation (Left) Flow velocities at four engine-inlet positions. (Right) Particle flows. 

a ,4.' ,- \. 'd -. . . jr8 -,,-.-<- 81,. .t,.. '- , >, ::- 

COLOR Pti3?.CGi?kPH 
Computational Fluid Dynamics Prediction of Advanced Rotor Performance 

Roger C. Strawn, Principal Investigator 

Co-investigators: John Bridgeman, K. Ramachandran, and Frank Caradonna 

U.S. Army Aeroflightdynamics Directorate-AVSCOMINASA Ames Research Center 

Research Objective 

This project is aimed at developing methods for predicting the 

aerodynamic loads on helicopter rotor blades. Primary areas 

of investigation are unsteady transonic flow, viscous contributions to drag and pitching moment, and the influence of the 

iotor wake. The development of computational fluid dynamics 

codes for immediate use as rotor design tools is emphasized. 

Approach 

Jhree-dimensional unsteady potential codes are used to 

compute the inviscid flow. The full-potential code is modified 

with an entropy correction term to give Euler shock-jump 

behavior. A three-dimensional, unsteady boundary layer code 

is coupled to the inviscid solution to compute viscous drag. 

The rotor wake is modeled with a combined EulerianLagrangian scheme to compute the rotor and free-wake 

solutions simultaneously. 

Accomplishment Description 

The Helix-1 hover performance prediction code was extended 

to obtain the compressible free-wake flow about a lifting rotorbody. The method is an extension of a unique vorticity 

embedded full-potential method. It was used to predict the 

performance of a full-scale rotor in partial ground effect with 

the rotor mounted on a large pylon. In a separate investigation, a three-dimensional, finite-difference boundary layer 

scheme was coupled to the full-potential rotor code (FPR) to 

predict drag and torque for rectangular and swept-tip rotor 

blades. Also, the FPR code was coupled to the CAMRADIJA 

rotor performance code to model a swept-tip Puma helicopter 

rotor in high-speed forward flight. Results compared well with 

extensive flight-test measurements. Typical runs with the 

HELIX-1 code required 4 hours of CPU time and 4 megawords 

of memory on the Cray-2 computer. 

Significance 

All of the crucial rotorcraft performance limitations stem from 

aerodynamic flow phenomena. The recent success of the 

British Experimental Rotor Program showed that significant 

gains in performance can be obtained by designing nonrectangular rotor planforms. Prediction capabilities for 

transonic effects on drag and pitching moment, and wakeinduced blade-vortex interactions, are important tools for 

future designs of this type. A specific application for this work 

is the Army's LHX helicopter program, which will put new 

helicopter designs into the field in approximately 10 years. 

Future Plans 

Development of rotor drag and pitching-moment prediction 

capabilities will continue with an emphasis on forward-flight 

cases and three-dimensional tip shapes. The Helix-1 rotorbody prediction method will be extended to more complex 

geometries. 

Publications 

1. Bridgeman, J. 0.; Strawn, R. C.; Caradonna, F. X.; and 

Chen, C. S. "Advanced Rotor Computations with a Corrected 

Potential Method." Presented at the 45th Annual Forum of the 

American Helicopter Society, Boston, MA, May 1989. 

2. Strawn, R. C.; Desopper, A.; Miller, J.; and Jones, A. 

"Correlation of Puma Airloads - Evaluation of CFD Prediction 

Methods." Presented at the 15th European Rotorcraft Forum, 

Amsterdam, The Netherlands, Sept. 1989. (See also NASA 

TM-102226, Au~. 1989.) 

PUWA swtr i - i ir LASL 3 

Mtipt0.62, Advance ratio=0.38 

CMIRAD/JA PRESCRIBED WAKE 

FPR SURFACE MACH CONTOURS 

CAMRADIJA-FPR rotor blade and wake solution. 

.dnic:?,\!~ t, -,*,P. i' ,., - 

COLGi? PHO r'GG3APH 

159 
Numerical Simulation of Wave Interactions Related to Transition 

Craig L. Streett, Principal Investigator 

Co-investigator: S. Balachandar 

NASA Langley Research Center 

Research Objective 

To clarify the role of instability-wave interactions in the middle 

to late stages of transition in three-dimensional boundary 

layers. 

Approach 

The similarity solution for the boundary-layer flow on a rotating 

disk is used as a prototype for three-dimensional boundary 

layers that exhibit inflection instabilities known as crossflow 

modes. These low-frequency disturbances are observed on 

swept wings as vortices nearly aligned with the potential-flow 

direction, and are a mechanism for transition in favorable 

pressure gradient regions on such wings. The rotating-disk 

model flow has been investigated through hot-wire and flowvisualization experiments, and using linear stability theory. It 

has been conjectured in the literature that the breakdown of 

these disturbances is the result of nonlinear interaction of 

these linear modes; in this study, this interaction is to be 

elucidated via direct simulation and weakly nonlinear theory. 

Accomplishment Description 

A spectral temporal direct simulation code, written for a 

preliminary investigation by Malik and Zang, was extensively 

modified to improve efficiency; a factor-of-seven speedup was 

achieved. Simulations were carried out using a distribution of 

primary linear disturbances as initial conditions; the expected 

nonlinear interactions were not observed. Secondary parametric instability analysis revealed a robust, broadband, 

Floquet-type instability, appearing at a primary disturbance 

magnitude threshold of about 4%. The accompanying figure 

shows a comparison of experimental and theoretical time 

histories and flow-field visualizations. A new simulation code 

was written for further improved efficiency; another factor-offive speedup was achieved. The current code runs at about 

40 psec/pt/set on a 64 x 64 x 65 mesh, at a maximum Courant 

number of about 0.8. Simulations including energy in the 

spectral region of the secondary modes confirmed the 

presence of this instability mechanism; analysis of this wellresolved late-stage simulation is ongoing. 

Sisnificance 

understanding the stages of breakdown of crossflow disturbances is crucial for developing engineering criteria for 

(Top) Hot-wire history (Wilkinson et al.). (Bottom) Streamwise 

velocity vs. 4, secondary instability theory. 

- - transition in flows dominated by these distu;bances. 

Future Plans (Top) Smoke flow visualization (Kohama). (Bottom) Lagrangian The secondary instability theory is being applied to the particle distribution, secondary instability theory. nonsimilar three-dimensional boundary layer computed for the 

swept-wing experiment in the ASU transition wind tunnel; corn- Secondary parametric instability of crossflow disturbance, 

parisons will be made with detailed hot-wire measurements rotating-disk model flow. 

taken there. Spatial simulations are planned to assess the 

effects of pressure gradient and nonparallel mean flow on the 

current (temporal) simulations. 
Transition Simulations in Nonhomogeneous Geometries 

Craig L. Streett, Principal Investigator 

NASA Langley Research Center 

Research Objective 

To develop accurate and efficient methods for the direct 

simulation of transition in incompressible and compressible 

flow and in geometries more realistic than hitherto treated; 

also, to carry out simulations of fundamental transition 

phenomena. 

Approach 

Spectral collocation algorithms are developed and utilized for 

the incompressible and compressible Navier-Stokes equaiions; nonhomogeneous basis function sets and innovative 

implementation of boundary treatments are used. The 

incompressible simulation studies focused on the use of the 

buffer-domain outflow boundary treatment (developed last 

operating period) and spectral multidomain methods to 

improve the accuracy and efficiency of spatial simulations of 

transition. Multi-tasking techniques were also investigated to 

improve the efficiency of these simulations. The compressible 

work involved the development of high-order, fully implicit 

time-stepping schemes for the compressible Navier-Stokes 

equations with spectral discretizations. 

Accomplishment Description 

The spectral, incompressible, spatial simulation code 

was verified for a number of test cases. These included 

(1) Poiseuille flow and Blasius boundary layer flow, for which 

comparisons with linear theory were made; (2) propagation of 

a vortex in a channel for PoiseuilleIBernard flow in a channel, 

for which the flow demonstrates a global instability; and 

(3) interaction of Tollmien-Schlichting waves in a nonparallel 

boundary layer with a small wall roughness element. Final 

algorithmic refinements are in progress for the case of nonparallel, nonlinear propagation of interacting disturbances in 

a growing boundary layer. The accompanying figure shows 

vorticity contours for the vortex-in-channel problem, demonstrating the clear lack of reflection when the vortex passes 

from the domain. One code developed during this ongoing 

project was successfully modified to run in a muti-task mode; 

a speed of 1.6 GFLOPs was achieved on the Cray Y-MP, 

winning a Cray Gigaflop performance award. 

Significance 

Virtually all simulations of transition phenomena to date have 

used the temporal assumption to avoid the requirement of an 

outflow boundary condition and to simplify the numerics. The 

present developments permit the use of highly accurate 

spectral methods for carrying out true spatial simulations of 

these sensitive flow fields. 

Future Plans 

Simulations of the effect of pressure gradient and distributed 

roughness on transition will be carried out in their proper, 

spatially developing setting. Transition in a separation bubble 

will also be studied, as will the middle-to-late stages of breakdown of crossflow disturbances. A version of the incompressible spatial code, using high-order finite differences in the 

streamwise direction, is under development; it will allow the 

incorporation of geometric complexity. A spectral, fully implicit 

time-stepping algorithm for the compressible Navier-Stokes 

equations is being refined, to allow the efficient simulation of 

compressible boundary-layer and free-shear layer transition. 

Incompressible vortex in a channel. 
Mars RoverISample Return Aerocapture Vehicle 

Phil C. Stuart. Principal Investigator 

Co-investigator: Chien-Peng Li 

NASA Johnson Space Center 

Research Objective 

The objective is to develop the capability to compute hypersonic flow fields about blunt-nosed bodies traveling at high 

speeds in a C02 atmosphere. This will be used to simulate 

flows about vehicles performing aerocapture maneuvers at 

Mars. 

Approach 

A three-dimensional Navier-Stokes code with ideal-gas and 

chemical nonequilibrium options is used to predict high-Mach 

number flows around slender flight vehicles, especially 

biconics. Initially the Martian atmosphere is modeled as 100% 

C02 dissociating into five species. 

Accomplishment Description 

An existing, implicit, central-differenced Navier-Stokes code 

developed at Johnson Space Center was modified to allow the 

calculation of flows of any dissociating gas. Finite-rate chemistry is modeled by a loosely coupled set of equations. The 

code has been partially verified for C02. Pressure distributions 

showed good comparison with data from a low-enthalpy wind 

tunnel test. Species concentrations at the stagnation point of a 

sphere showed good agreement with equilibrium values. 

Calculations were also done on a full-scale Mars aerocapture 

vehicle. The figure shows a computational grid, pressure 

distribution, and mass fraction of carbon monoxide on the 

body surface and in parts of the flow field around a biconic 

vehicle. The calculation involves free-stream conditions 

typical of the maximum heating point during an aerocapture 

maneuver at Mars. The nonequilibrium gas calculations 

require about 4 Cray-2 hours and 4 megawords of memory 

when viscosity is not considered. 

Significance 

Several future missions to Mars are being considered, with 

at least one in the early design phase. These include both 

unmanned and manned missions designed to return Martian - 

rock and soil samples to Earth. Because the required landing 

accuracy is significantly greater than that needed by the 

Viking landers in 1976, the flight characteristics of the vehicle 

must be known to a high order of accuracy to ensure mission 

success. Nonequilibrium C02 calculations represent a 

significant improvement in modeling over what was available 

in the past. 

Future Plans 

Our immediate plans are to perform a more comprehensive 

verification of the code when using C02. The code, with some 

further modification, will then be used to study the effects of 

thermal as well as chemical nonequilibrium in a C02 atmosphere. In addition, studies of a variety of vehicle shapes will 

be continued in support of the Mars RoverISample Return 

mission. 

1 

Grid Pressure CO concentrotion 

Mars RoverISample Return aerocapture vehicle in a C02 atmosphere. 
Numerical Study of Three-Dimensional Viscous Reacting Flows with Application to Scramjet Propulsion 

Sundaresa V. Subramanian, Principal Investigator 

Co-investigators: Michael J. Epstein 

General Electric Aircraft Engines 

Research Objective 

To optimize and apply existing three-dimensional computer 

codes for the design and performance improvement of critical 

.hypersonic vehicle components such as inlets, supersonic 

combustors, and nozzles. 

Approach 

The three-dimensional, time-dependent, compressible Navier- 

'Stokes equations are solved with an appropriate turbulence 

model and a physically realistic chemical kinetics model. to 

describe combustion phenomena occurring in the component 

of interest. 

Accomplishment Description 

The computer code RPLUS that was developed at NASA 

Lewis Research Center was used to successfully predict the 

complex, three-dimensional, turbulent reacting flows in a 

supersonic combustor that was also experimentally investigated. Computations were performed for different fuel equivalence ratios (ER) to investigate the extent of fuel penetration, 

mixing, and reaction. The accompanying figure shows the 

predicted Mach number distribution at different axial locations 

of the combustor for an ER value of 0.76. The fuel is injected 

normally at three step heights downstream of the step face 

into the Mach 2.86 free-stream air. In this configuration, the 

fuellair interaction produces two distinct counter-rotating 

vortices that travel the entire length of the combustors, 

enhancing mixing and reaction. Using an 81 x 31 x 21 grid 

and nine-species, eighteen-stop, finite-rate chemistry, convergence was obtained after 2600 iterations that required nearly 

15 hours and 8 megawords of memory on the Cray Y-MP. 

Significance 

Enhanced flow prediction methods and codes are beneficial 

for the design of all air-breathing hypersonic propulsion 

systems and are essential for the design and development of 

supersonic combustors that are characterized by a high 

degree of mixing, reaction, and overall combustion efficiency. 

Future Plans 

Research is now under way, placing particular emphasis on 

understanding the mechanisms that are crucial for high-speed 

mixing and supersonic combustion, such as injector configurations, shock excitation, and turbulence effects. 

Mach number distribution at different axial locations of a supersonic combustor; ER = 0.76. 
Microwave Hyperthermia Computer Modeling 

Dennis Sullivan, Principal Investigator 

Co-investigator: Bryan James 

Stanford University School of Medicine 

Research Objective 

The objective is to develop better equipment and methods for 

deep regional microwave hyperthermia, a relatively new form 

of cancer therapy that uses microwave heat. Computer 

simulation is used to design new microwave applicators and 

to simulate treatments on existing equipment, to increase 

effectiveness. Specifically, a method has been developed to 

simulate treatments of patients in an annular phased array, the 

most commonly used device in the treatment of deep-seated 

cancer tumors. 

Approach 

The three-dimensional finite-difference time-domain (FDTD) 

method is being used to accurately determine the near field of 

microwave applicators and the body being heated. This 

method solves the time-dependent Maxwell's equations in 

difference equation form. 

Accomplishment Description 

The annular phased array consists of four applicators 

arranged in an annulus around the patient to be treated. Each 

applicator is powered by its own linear class A power amplifier, which allows each applicator to have a different amplitude 

and phase setting. It is this capability that allows the energy to 

be "steered" within the patient. Using CAT scans, the patient 

is characterized by the dielectric constants and the conductivities of the various tissue types at 1-cm resolution, creating a 

model that generally consists of 25,000 to 35,000 cells. The 

FDTD method is used to determine the energy deposition at 

every point in the patient model. Such runs require 16 megawords of memory and 500 CPU seconds on the Cray Y-MP. A 

new technique has been developed to determine the optimum 

treatment, i.e., maximum tumor heating versus minimum 

normal-tissue heating. The following procedure is used: With 

only one quadrant activated, the magnitude and phase of the 

dominant E-field is saved on disk. This is repeated for all four 

quadrants at intervals of 10 MHz between 60 and 120 MHz. 

With this information stored, the magnitude of the E-field at any' 

point in the patient for any combination of amplitude and 

phase settings of the quadrants at any frequency is determined by the vector sum of the previously stored values, usino, 

the principles of superposition and linearity. The resulting 

energy distribution at the 25,000 to 35,000 points of the 

patient model is calculated as fast as the operator can type a 

new set of amplitude and phase settings. 

Significance 

The problem of treating patients with deep regional hyperthermia has been quantified so that the feasibility of treating 

different tumor sites can be studied and the optimum phase 

and amplitude settings can be anticipated. 

Future Plans 

Determining the best amplitude and phase settings at a given 

frequency is fundamentally that of optimizing seven independent parameters: four independent amplitude and three 

independent phase settings (any one phase may arbitrarily be 

set to zero). With the technique described above, optimization 

methods may be brought to bear on the problem. However, it 

is recognized that the annular phased array will always be 

limited in its ability to localize the energy to the tumor site. For 

this reason, more effort will be channeled to using the same 

FDTD to develop a more effective deep-heating applicator. 

(Top left) Input to the FDTD program-the model of a patient Output of the FDTD program-a s~mulation of the energy distribution of the patient in the annular phased array, show~ng the transverse (top right), coronal (bottom left), and sagittal (bottom right) 

views through the body. 

,. ___. 
Naval Applications of Computational Fluid Dynamics 

Chao-Ho Sung, Principal Investigator 

Co-investigator: Michael J. Griffin 

David Taylor Research Center 

Research Objective 

The objective is to develop the capability to predict the flow 

fields about naval ships in order to understand the physics of 

the flow field. This understanding can then be applied to the 

innovative design of naval ships. 

Approach 

The three-dimensional, incompressible, Reynolds-averaged 

Navier-Stokes equations supplemented by an appropriate 

.turbulence model are to be solved. At present, a scheme 

based on central-difference, finite-volume, spatial discretization and explicit, one-step, multistage, Runge-Kutta time 

stepping has been developed. An artificial dissipation model 

and the Baldwin-Lomax turbulence model are used. Both a 

local time-stepping and an implicit residual smoothing technique have been used to accelerate the convergence. 

Accomplishment Description 

Efforts to improve both the accuracy and efficiency of the 

algorithm continued. During the current operational period, the 

implementation of a multigrid scheme and the modifications of 

the artificial dissipation model and the implicit residual 

smoothing technique were completed. The multigrid scheme 

increased the convergence rate of three-dimensional turbulent 

flow computations by three times, at about a 15% increase in 

CPU time. The nonisotropic characteristics of the wave propagation were accounted for in the modified artificial dissipation 

model and in the implicit residual smoothing technique. This 

modification is essential for very high Reynolds number computations since the aspect ratio is expected to be high. 

Application to the evaluation of several flow control devices 

considered for future naval use was also completed. A typical 

juncture configuration with a 97 x 25 x 25 grid at an angle of 

attack of 6" requires about 3 megawords and 100 CPU minutes 

in a single-grid computation for the vorticity to converge. 

Significance 

The implementation of an efficient multigrid scheme and the 

development of techniques to improve accuracy for a highaspect-ratio grid are steps toward large-scale computations 

with over a million grid points and a very high Reynolds 

number. 

Future Plans 

A multizone scheme with emphasis on the stability of abruptly 

changed grid interfaces will be implemented. Computer codes 

for the solution of the time-dependent, Reynolds-averaged 

Navier-Stokes equations will be developed. Both the twotimes-scales approach and the projection method will be 

considered. 

7 

PART1 E TRACES 

DAVID lAYLOk kEYEARCH LtNltk 

JUNCTURE FLOW STRAKE 

FLOW CODE IFLOWS 

REYNOL 620,000 

Particle traces for strake juncture flow, calculated using the IFLOWS code; a = O.OO, Re = 6.2 x lo5. 
Development of Algorithms for Solving the Three-Dimensional Navier-Stokes 

Equations 

R. C. Swanson, Principal Investigator 

Co-investigator: M. Sanetrik 

NASA Langley Research Center 

Research Objective 

To develop accurate, efficient, and reliable algorithms for 

solving the three-dimensional Navier-Stokes equations for all 

speed regimes. 

Approach 

Cell-centered and cell-vertex finite-volume spatial discretization (yielding central differencing), a numerical dissipation 

model, and a multistage time-stepping scheme with acceleration techniques for steady-state calculations are used. 

Accomplishment Description 

The following elements of the three-dimensional Navier-Stokes 

solvers have been investigated: (I) variable coefficient implicit 

residual smoothing, (2) multigrid strategy, and (3) a numerical 

dissipation model. Transonic flow over an ONERA M6 wing 

was considered for evaluating the numerics. Alternate forms of 

residual smoothing were considered, and some improvement 

in convergence rate was obtained. Modifications in the basic 

multigrid strategy improved the robustness of the threedimensional solvers; that is, problems that presented numerical difficulties previously can now be readily solved. A 10 to 

15% reduction in computer time was achieved from changes 

in these two elements of the schemes. Often, the performance 

of a scheme is not maintained when fine meshes are used. 

Therefore, some high-density mesh calculations were performed to confirm the initial evaluation of the improvements to . the three-dimensional codes. For the computations, roughly 

2 to 50 megawords of storage were required, and the computer time ranged generally from 0.5 to 2.5 hours. 

Significance 

This project has provided significant contributions in the 

development of the elements currently being used in an 

efficient generation of Navier-Stokes codes. Much more robust 

algorithms for three-dimensional viscous flow computations 

have been constructed. 

Future Plans 

We plan to develop effective and accurate algorithms for 

solving high-speed flows, and to obtain complete validation of 

the domain-partitioning procedure. 

Publications 

"An Efficient Cell-Vertex Multigrid Scheme for the ThreeDimensional Navier-Stokes Equations." Presented at the AlAA 

9th Computational Fluid Dynamics Conference, Buffalo, NY. 

Domain decomposition for a two-element airfo~~. 

Karrnan-Tr&fftz, M,=0.125, a=O.O, lnviscid 

(-'-:' .=,I r * - -, - 

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COLCR Pti ~Tc(L;i?ri:~!i 

-3 

-2 

"&l 

0 

t 

0 

- 0 Moin Airfoil Lower Surface 

A Main Airfoil Upper Surface 

+ Flap Upper Surface 

x Flap Lower Surface 

- - Exact soin. for Main Airfoil 

- Exact soln. for Flap 

- 

- 

- 
Hydrodynamic Prediction Methods for Advanced Submarine Configurations 

Tsze C. Tai, Principal Investigator 

Co-investigators: Steven C. Fisher, Cheng-Wen Lin, and Gerald D. Smith 

David Taylor Research Center 

Research Objective 

To develop a computational fluid dynamics (CFD) method for 

the analysis and design of submarine hulliappendage configurations, and to apply the method together with numerical 

optimization techniques to design novel submarine shapes 

?hat are based on specified mission requirements. 

Approach 

The basic tool is a three-dimensional, full or thin-layer, 

Reynolds stress-averaged Navier-Stokes solver subject to 

steady and unsteady free-stream conditions. A research code 

for incompressible flow was developed to determine the 

subject submarine flow field. A zonal approach was used 

whereby the flow field was subdivided into smaller zones. 

Steady and unsteady flows over a submarine hulliappendage 

configuration at straight-ahead even keel and also at moderate turning will be considered. The approach will then be 

extended to high-speed maneuvering conditions with flow 

separation and free vortex flows. 

Accomplishment Description 

A multiblock grid-generation code (based on the algebraic 

method) was developed and used to generate surface and 

volume grids for submarine geometries. An incompressible, 

steady Navier-Stokes code with multizonal capability was used 

to compute the viscous flow around several complex configurations, including a fully appended submarine. In addition, 

flow computations were conducted to simulate experimental 

conditions for a submarine model in a wind tunnel. Results of 

these computations illustrate the effects of the supporting 

struts and wind tunnel walls on the experimental data. Computed velocity contours for a fully appended submarine model 

in a wind tunnel are illustrated in the accompanying figure. 

This solution required 250,000 grid points, took approximately 

2.5 hours of computing time on the Cray-2, and used 

20 megawords of memory. 

Significance 

The ability to predict the flow field around real submarine 

geometries is an indispensable tool for naval designers. In 

addition, pretest analysis and planning can be enhanced by 

applying the developed computational techniques to experimental conditions. The understanding of the physical phenomena on novel hull shapes or control surfaces can be 

enhanced and numerical computational results can be 

obtained with a reasonable turnaround time. 

Future Plans 

A more interactive grid generator will be used and the flow 

solver will be further improved in numerical accuracy and 

robustness. The flow solver will also be made more interactive 

and user-friendly. In addition, computational speed and 

memory usage are targeted for improvement so that a more 

practical computational design tool can be achieved. 

Publications 

1. Lin, Cheng-Wen; Smith, Gerald D.; and Fisher, Steven C. 

"Numerical Flow Simulations on the DARPA SUBOFF Configurations." David Taylor Research CenterIShip Hydromechanics 

Department Report, Apr. 1990. 

2. Lin, Cheng-Wen; Smith, Gerald D.; and Fisher, Steven C. 

"Validation of Numerical Wind Tunnel Flow Simulation on the 

DARPA Bare Body." David Taylor Research Centeriship 

Hydromechanics Department Report, Apr. 1990. 

Ll Velocity 

Contour Levels 

-U. U.1UOU 

0.00000 

0.04UqO 

8.68000 

u. 17UUU 

By Chenp Wen lin, Gerald D Smith, and Steven C Firhe! 

08IGl?lfiL Pi',;: 

COLGR PHOTOGRAPH 

Computed velocity contours for a submarine model in a wind tunnel. 
Low-Speed Maneuver Aerodynamics in a Nonuniform Free Stream 

Tsze C. Tai, Principal Investigator 

David Taylor Research Center 

Research Objective 

The objective is to develop a computational method for 

determining the nonlinear aerodynamics of an aircrawship 

interface environment. Of particular interest to the Navy is the 

ability to analyze the effects of the airwake, crosswind, windspeed fluctuation, and gust on the lift characteristics of an 

aircraft during a landing maneuver. Steady and unsteady flow 

conditions will be considered. 

Approach 

The three-dimensional, thin-layer Reynolds stress-averaged 

Navier-Stokes equations will be solved subject to a low-speed 

nonuniform free stream. A zonal approach will be adopted 

whereby the flow field is subdivided into smaller zones. This 

approach allows suitable grids to be generated for different 

zones with moderate memory requirements. A fast-convergent 

diagonal algorithm of the Beam-Warming type will be used to 

solve the discretized equations. The NASA Ames ARC3D 

code and its zonal-version transonic and compressible NavierStokes (TNS and CNS) codes will be used as the basic program, with necessary modifications. Steady flows, with a 

nonuniform free stream, of a ship wake or a crosswind will be 

considered first. The approach will be extended to unsteady 

conditions by considering wind-speed fluctuations and/or a 

sudden gust. 

Accomplishment Description 

Computational results for flow over an F-14A wing based on a 

thin-layer Navier-Stokes method are examined, and resulting 

flow separation patterns investigated. The wing is fixed with a 

sweep of 20" and travels at an altitude of 45,000 ft above sea 

level at Mach 0.6, and at sea level at Mach 0.1, at various 

angles of attack. These conditions, which yield a Reynolds 

number of 8.95 x lo6, allow evaluation of the effect of Mach 

number on flow separation patterns with fixed Reynolds 

number. Massive flow separation occurs at Mach 0.6 at an 

angle of attack of 10". At Mach 0.1, with the same Reynolds 

number, the rear-region massive separation is replaced by a 

moderate leading-edge separation. Consequently, the lift and 

drag values are far more stable as the angle of attack 

increases. A typical case that used a four-zone grid for the 

flow over a wing took approximately 2 hours of CPU time on ' 

the Cray-2 with 10 to 15 megawords of memory. These results, 

mainly based on the Ames TNS code with some modifications 

for low-speed flow conditions, are summarized in AIM 

Paper 90-0596. The nonuniform stream effect was evaluated 

by imposing an analytical defective function representing the 

free stream. A small decrease in lift resulted. An overall grid 

for the F-14A wing-fuselage-tail configuration was generated 

using the Ames 3DGRAPE code; it is shown in the accompanying figure. Implementation of zonal techniques based on 

the Ames CNS code is in progress. 

Significance 

A need for enhanced fighter maneuver (EFM) has been 

identified in the Naval Aviation Plan. Although the EFM concept is applicable to any fighter aircraft, the Navy operation is 

unique in that it requires aircraft to be able to maneuver under 

nonuniform free-stream conditions, such as a crosswind or a 

gust near a ship deck. In developing the EFM technology, this 

research will focus on problems specific to naval aviation. 

Future Plans 

The Ames CNS and BDGRAPE codes will be modified to 

handle a complete F-14A aircraft solution. Steady flow with 

uniform and nonuniform free-stream conditions will be 

considered in the NAS 1990-91 operational year. 

Publications 

Tai, T. C. "Flow Separation Patterns Over an F-14A Aircraft 

Wing." AIM Paper 90-0596, Jan. 1990. 

Grid geometry for an F-14A wing-fuselage-tail configuration. G~~;C~~,~~,L F>,;:c 

COLOR PHOTOGRAPH 
Unsteady Euler Analysis of the Redistribution of an Inlet Temperature 

Distortion in a Turbine 

Ronald K. Takahashi, Principal Investigator 

Co-investigator: Ron-Ho Ni 

United Technologies, Pratt & Whitney 

Research Objective 

To analyze the effects of three-dimensional inflow temperature 

and pressure distortions on the local gas temperatures in rotor 

gassages of turbine stages. 

Approach 

A time-accurate three-dimensional Euler code with surface 

shear modeling was used to simulate a low-speed experimen- 

'tal turbine rig. An inlet high-temperature "jet" was modeled to 

simulate turbine-engine combustor exit conditions. 

Accomplishment Description 

The results showed dramatic effects of secondary flow on 

three-dimensional temperature migration, the process by 

which the hot combustor gas redistributes within the rotor 

passage. The accompanying figure is an instantaneous image 

of the hot gas as it impacts the rotor pressure side, where it 

lingers and spreads out toward the end walls because of 

secondary flow. The calculations match the heating patterns 

observed both in experiments and on actual engine parts. 

especially on the rotor suction and pressure sides, the platform, and the outer air seals. This good agreement gives 

confidence that even the coarse mesh is resolving at least the 

first-order physics controlling the temperature migration process. Calculations using a finer computational grid showed 

that the temperature migration process is very sensitive to grid 

density in the range of the present grid sizes, and further work 

is required to quantify the effects of grid size. Coarse grid 

calculations require about 7 Cray-2 hours per run, and the fine 

grid requires about 25 Cray-2 hours and 8 megawords of 

memory. 

Significance 

The redistribution of inlet temperature distortions in the rotor 

passages is believed to be a major cause of localized overheating of rotor airfoils and passage end walls. The computations have added to the understanding of the physics controlling the temperature migration process, and the unsteady 

code may prove to be a useful design tool for increasing the 

lives of turbine parts. 

Future Plans 

Continuation of this work in 1990 will focus on grid sensitivity 

and the effects of tip leakage on temperature migration. 

Publications 

Takahashi, R. K., and Ni, R. H. "Unsteady Euler Analysis of the 

Redistribution of an Inlet Temperature Distortion in a Turbine." 

Presented at the AIAAlASME/SAE/ASEE 26th Joint Propulsion 

Conference, Orlando, FL, July 1990. 

Rotors 

Inlet Hot Gas 1 

Stators 

Instantaneous image of an isotherm contour illustrating the interaction of the hot gas with the passing rotors. 
Thermochemical and Radiative Nonequilibrium Flow Simulation for the 

Aeroassist Flight Experiment 

Luen T. Tam, Principal Investigator 

Co-investigator: Chien P. Li 

Lockheed Engineering and Sciences CompanyINASA Johnson Space Center 

Research Objective 

To develop and validate a three-dimensional thermochemical 

and radiative nonequilibrium model for the inviscidlviscous 

flow simulation of the Aeroassist Flight Experiment (AFE) 

vehicle. 

Approach 

Two- and three-dimensional flow fields were obtained from the 

Navier-Stokes equations coupled with conservation of chemical species, overall energy, electron translational energy, and 

molecular-vibrational energy. The method includes generating 

grids that are adaptive to the shock and body, and controlling 

numerical dissipation by using local flow gradients and total 

enthalpy. 

Accomplishment Description 

A two-temperature thermal nonequilibrium model was developed and incorporated into the viscous reactive flow (VRFLO) 

code. Preliminary results indicated that strong dissociation 

and weak ionization take place at the forebody and that 

vibrational freezing occurs in the afterbody expansion region, 

where the vibrational temperature is even higher than the 

translational temperature. The accompanying figure shows the 

electron number density contours obtained from two thermal 

models at the AFE trajectory point corresponding to the 

maximum aerodynamic heating. This comparison suggests 

that a 7-species kinetic model fails to predict the electron 

number density accurately. Typically, 20 Cray-2 CPU hours 

were required for a three-dimensional AFE complete-body 

viscous-flow solution with 2000 iterations, calculated from a 

two-temperature, 11-species, 30-reaction model on a grid of . 30 x 60 x 19. The memory requirement was close to 

3.8 megawords. 

Significance 

The AFE flight data related to surface properties, heating, 

electron number density, and AFE wake characteristics will be 

used to validate the VRFLO code. 

Future Plans 

Although the two-temperature model is being used to assess 

the AFE complete-body viscous flows, a radiation model also 

needs to be incorporated into the study since the radiative 

heat transfer from the forebody could be of importance as well 

as that from the wake. 

Publications 

1. Tam, L. T., and Li, C. P. "Three-Dimensional Thermochemical Nonequilibrium Flow Modeling for Hypersonic 

Flows." AlAA Paper 89-1860, June 1989. 

2. Tam, L. T., and Li, C. P. "Comparisons of Thermochemical 

Nonequilibrium Viscous Flowfield Predictions for AFE Vehicle." 

AlAA Paper 90-0141, Jan. 1990. 

CONTOUR LEVELS 

31.673 MACH 

-17.00 DEG ALPHA 

2-TEMPERATURE MODEL WITH 11 SPECIES AND 30 REACTIONS 5.75~ l0**3 Re 

29x61~37 GRID 

1-TEMPERATURE MODEL WITH 7 SPECIES AND 19 REACTIONS 

, . ....., , .. ., ".: ': , ' , .' 

~lk&on numb& de"sityCont6urs. A . log,&electron number density)lCM3; M = 31.673. a = -17.00°. Re = 5.75 x lo3, grid size 

29 x 61 x 37. (Left) Two-temperature model with 11 species and 30 reactions. (Right) One-temperature model with 7 species and 

19 reactions. c;!,z';.!:>; F,,-..;;z 
Development of a Robust Parabolized Navier-Stokes Code for Computing 

Three-Dimensional, Chemically Reacting Flow Fields 

John C. Tannehill, Principal Investigator 

Co-investigators: Phil E. Buelow and John 0. levalts 

Iowa State University 

Research Objective 

To develop a robust computer code to compute the threedimensional, viscous, chemically reacting flow around 

.hypersonic vehicles. 

Approach 

The three-dimensional parabolized Navier-Stokes (PNS) 

equations for chemically reacting flows are solved using an 

tpwind total-variation-diminishing (TVD) finite-difference 

scheme. 

Accomplishment Description 

A new upwind PNS code was developed to compute the 

three-dimensional flow of chemically reacting air around 

hypersonic vehicles. The code is a modification of the perfectgas, three-dimensional UPS code of Lawrence et al., which 

was extended in the current study to permit the calculation of 

hypersonic, viscous flows in chemical nonequilibrium. The 

algorithm solves the PNS equations using a finite-volume. 

upwind TVD method based on Roe's approximate Riemann 

solver, which was modified to account for real-gas effects. The 

current code solves the fluid dynamic and species continuity 

equations in a loosely coupled manner. The fluid medium is 

assumed to be a chemically reacting mixture of thermally 

perfect (but calorically imperfect) gases in thermal equilibrium. 

If desired, perfect-gas or equilibrium-air calculations can also 

be performed with the same code. Results were obtained for 

the hypersonic laminar flow over cones at various angles of 

attack and over the McDonnell Douglas Generic Option 

hypersonic vehicle. 

Significance 

This code provides the ability to compute the chemically 

reacting flow field about the National Aero-Space Plane. 

Future Plans 

The code is currently being extended to permit the calculation 

of internal flows with hydrogen-air chemistry. The code will 

then be able to compute aerodynamic and propulsive flow 

fields simultaneously. 

Publications 

1. Tannehill, J. C.; levalts, J. 0.; Buelow, P. E.; Prabhu, 

D. K.; and Lawrence, S. L. "Upwind Parabolized Navier-Stokes 

Code for Chemically Reacting Flows." J. Thermophysics and 

Heat Transfer 4, no. 2 (Apr. 1990): 149-1 56. 

2. Tannehill, J. C.; Buelow, P. E.; levalts, J. 0.; and 

Lawrence, S. L. "Three-Dimensional Upwind Parabolized 

Navier-Stokes Code for Real Gas Flows." J. Spacecraft and 

Rockets 27, no. 2 (Mar.-Apr. 1990): 150-1 59. 

Computed atomic oxygen levels for the McDonnell Douglas Generic Option II BWB Aerothermal Model; a PNS solution with finiterate air chemistry: M, = 25.3, a = OD, altitude = 61 km. 

(-,,:>:::. a,, .4,ts-:!',L 

COLGR PHOTOGRAPH 
Computation of Three-Dimensional Flows Using Unstructured Grids 

Rajiv Thareja, Principal Investigator 

Co-investigators: Ken Morgan, Jaime Peraire, Obey Hassan, and Joaquin Peiro 

NASA Langley Research Center 

Research Objective 

To develop a general method for automatically discretizing 

into unstructured assemblies of tetrahedra the threedimensional solution domain of complex shapes, and to obtain 

a solution to transonic and hypersonic flows over realistic 

configurations. 

Approach 

An advancing front mesh generator was coupled with a 

higher-order-accurate Taylor-Galerkin flow solver to compute 

flows over arbitrary complex geometries. Considerable benefits were achieved because the mesh was adapted in an optimal manner. The method was used to benchmark a solution 

for transonic flow at a Mach number of 0.84 and 3.06" angle of 

attack over an ONERA M6 wing against several other solution 

methods in a workshop held at NASA Langley Research 

Center in January 1990. The computation was performed 

on a grid provided for the participants and consisted of 

231,507 tetrahedral elements and 42,410 points. Views of the 

discretization of the upper and lower surfaces of the wing, 

along with the computed pressure contours, are shown in the 

figure. Even though the mesh is relatively coarse, a lambda 

shock is captured on the upper surface. The adaptive feature 

of the scheme is also demonstrated in the computation of 

internal flow in an engine inlet with a free-stream Mach number 

of 6. The computational domain is a region bounded by planar 

compression surfaces along three sides. The initial mesh 

consists of 11,478 triangular surface elements, 155,702 tetrahedra, and 29,531 mesh points. Mach number contours on 

this mesh show the complex shock interactions and reflections. Using this solution and an error indicator that uses the 

second derivatives of density and Mach number, a second 

mesh consisting of 11,290 triangular surface elements, 

181,292 tetrahedra, and 33,786 points was generated as 

shown, along with the computed Mach number contours. The 

improvement in the definition of the flow features on the . adapted mesh is apparent. It should be noted that the resolution on this mesh was increased by a factor of 2.5 although 

the number of mesh points increased only slightly. 

Accomplishment Description F 

An automatic procedure that combines adaptive mesh 

generation using unstructured grids with a flow solution for 

complex geometries was benchmarked against several 

competing solution methods, with very favorable agreement. 

Significance 

The method can be used to model hypersonic flows over 

arbitrary, complex, three-dimensional geometries. Very good 

performance in terms of accuracy and efficiency has been 

achieved. Mesh resolution can be achieved with only a minimal increase in the number of points in the computational 

domain. 

Future Plans 

Future plans include developing higher-order-accurate finitevolume algorithms and higher vectorization of these codes. 

Publications 

Morgan, K.; Peraire, J.; Peiro, J.; and Hassan, 0. "The 

Computation of Three Dimensional Flows Using Unstructured 

Grids." Presented at the Computational Fluid Dynamics 

Conference, Minneapolis, Apr. 1990. 

UPPER SURFACE INITIAL MESH ADAPTED MESH 

LOWER SURFACE 

Meshes and Mach number contours for hypersonic flow in an 

engine inlet. 

Meshes and pressure contours for transonic flow over an 

ONERA M6 wing. 
Viscous Hypersonic Flow over a 24-Degree Compression Corner 

Rajiv Thareja, Principal Investigator 

Co-investigators: Ken Morgan and Jaime Peraire 

NASA Langley Research Center 

Research Objective 

To study the effect of mesh adaptivity on the solution of Mach 

14.1 viscous flow over a 24" compression corner, and to 

compare the solutions from a higher order, unstructured-grid 

upwind code with other numerical results and with experiment. 

Approach 

A higher order, adaptive unstructured-mesh generator and 

flow solver called LARCNESS was developed and used to 

compute viscous Mach 14.1 flow over a 24" compression 

corner with a Reynolds number of 72,000lft. The solutions 

show good overall agreement with CFL3D solutions on a 

structured 101 x 101 mesh (denoted as mesh SM), but the 

calculations do not compare well with experiment. An earlier 

study had concluded that the flow has significant threedimensional effects, and a two-dimensional solution is not able 

to provide agreement with experiment. However, refining the 

leading-edge mesh while retaining the structure of the mesh 

by moving the computational domain closer to the wall 

(denoted as mesh MSM) leads to significantly improved 

comparison with experiment. Very good agreement with 

CFL3D results was also observed for this mesh. Because of 

the refined mesh, the leading-edge shock moves closer to the 

body, resulting in an impingement location significantly 

upstream of the SM solution. An adaptively generated mesh 

aligns the mesh with the leading-edge shock and the reflected 

shock, resulting in improved shock definition and a slight 

improvement in the predictions of flow separation and 

reattachment, as compared with experiment and CFL3D flow 

solutions. The computed v-velocity contours for the three 

meshes show the effect of the mesh in improving the flow 

features. Although the adapted mesh has about the same 

HEATING RATE SKIN FRICTION 

. . . 3.0 - z".Y;L _ 1 .) ..'" s15y 

g o.o! \-...- 

D i 

number of nodes as the structured meshes, it has finer mesh 

resolution where required, resulting in an optimal number of 

nodes. 

Accomplishment Description 

The effect of mesh size near the leading edge of a compression corner was shown to significantly influence the downstream features. An automatic procedure that combines 

adaptive mesh generation using unstructured grids with a flow 

solution for complex geometries was benchmarked against 

several competing solution methods, with very favorable 

agreement. 

Significance 

The method shows that mesh resolution at the leading edge 

has a significant impact on the location of the leading-edge 

shock and the resulting locations of peak pressure and heating rates, and on the location of separation and reattachment 

points. Mesh adaptivity can be used to place elements 

aligned with the principal features of the flow. Substantial 

mesh resolution can be achieved with only a minimal increase 

in the number of points in the computational domain. 

Future Plans 

Future plans include computing an adapted unstructured-grid 

solution over the three-dimensional model of the compression 

corner. 

V-VELOCITY CONTOURS / I 

Mesh MSM 

Adapted Mesh 

AM2 

A schematic of the flow, comparisons of computed and experimental heating rate and skin friction, and v-velocity contours for 

three different mesh types. 
Scattering Theory and Calculations for Chemical Reactions and Molecular Energy Transfer 

Donald G. Truhlar, Principal Investigator 

Co-investigators: David C. Chatfield, Philippe Halvick, David W. Schwenke, Thanh N. Truong, Michael J. Unekis, and 

Meishan Zhao 

University of Minnesota 

Research Objective 

The objectives of this work are to develop and implement 

efficient and accurate methods for calculating the quantum 

mechanical dynamics of reactive and inelastic collisions of 

atoms and molecules, and to use them to carry out benchmark calculations that can be compared with experiment. 

Both atom-diatom reactions and diatom-diatom energy 

transfer collisions are under study. 

Approach 

The quantum mechanical equations governing the collision 

processes are solved by algebraic variational methods and 

propagation techniques. All calculations are highly vectorized. 

Accomplishment Description 

We have developed very efficient codes, as described above. 

In one study of reactive collisions, we obtained evidence that 

the accurate quantum mechanical probability of the reaction 

of H with H2 is globally controlled by quantized transition 

states up to very high energies. The quantized transition 

states produce steplike features in the cumulative reaction 

probability curves that are analyzed, up to energies of 1.6 eV; 

the analysis clearly associates these steps (or "thresholds") 

with quantized dynamical bottlenecks that control the passage 

of reactive flux to products. We have assigned bend and 

stretch quantum numbers to the modes orthogonal to the 

reaction coordinate for all these transition states, based on 

threshold energies of semiclassical, vibrationally adiabatic 

potential-energy curves and on vibrationally specific, cumulative reaction probability densities. 

Significance 

These studies lead to a deeper understanding of fundamental 

collision processes in chemical kinetics and of quantum 

effects in kinetics and energy transfer. 

Future Plans 

Future work will include calculations of atom-diatom reactions 

and HF-HF energy transfer collisions. 

0 

0.5 0.7 0.9 1.1 1.3 1.5 1.7 

Energy (eV) 

Density of reactive states for fixed-energy, fixed-total-angularmomentum ensembles as a function of energy E, for total 

angular momentum J = 0. The solid curve was obtained by 

differentiating the calculated accurate quantum mechnical 

cumulative reaction probability (summed over all initial and 

final states open at the given E). The dashed curve is a fit 

based on ten quantized thresh-olds treated as one-dimensional effective parabolic barriers. The feature numbers 

correspond to quantized transition states. This figure shows 

that the suprathreshold reactivity is globally controlled by 

quantized transition states up to very high energies. 
Hot Gas Ingestion by STOVL Aircraft 

Pratap Vanka, Principal Investigator 

Co-investigators: D. K. Tafti and W. Pegeus 

University of Illinois, Urbana-Champaign 

Research Objective 

The goal of this research project is to develop an efficient 

computational capability to study hot gas ingestion by short 

takeoff and vertical landing (STOVL) aircraft during hover and 

landing in ground proximity. The computational procedure is 

based on using multigrid techniques to provide efficient 

convergence to a steady-state flow field. 

Approach 

The three-dimensional steady form of the Navier-Stokes equations is solved by a finite-volume technique using a multigridbased solution procedure. The momentum and continuity 

equations are solved in a coupled manner. A k-E model is 

used for modeling the turbulent fluxes. 

Accomplishment Description 

A previously developed multigrid-based code was extended 

to handle embedded obstacles and mass and momentum 

injections in order to simulate the aircraft fuselage and the lift 

jets. An equation for enthalpy was added to calculate the 

temperature field. Several validation calculations were 

completed, to assess the code and the turbulence model. 

Initially the impingement of a vertical single jet was calculated 

and the results compared with experiment. Subsequently, the 

impingement of twin jets and the formation of an upwash 

fountain were calculated and the results compared with data 

from McDonnell Research Laboratories. Finally, the code was 

used to simulate the fuselage of an aircraft and the lift jets. 

Four test calculations were completed, with variations in the 

height of the lift jets from the ground and in the headwind 

speed. The results were compared with previous calculations 

from NASA Lewis. In all these calculations, a fine grid with up 

to 210,000 cells was used. The final calculation converged in 

approximately 140 iterations and required approximately 

35 minutes on a Cray-2 and 14 megawords of memory. 

Compared with a previously used single-grid method, the 

CPU time was reduced by a factor of 10. 

Significance 

The proposed computational procedure is useful in understanding hot gas ingestion by STOVL aircraft and in conducting parametric studies to modify the design of the inlets. 

Parametric studies are in progress to investigate the effects 

of jet height, jet Mach number, and headwind speed. 

Future Plans 

The computer program is currently being extended to 

nonorthogonal grids. After this extension, realistic shapes of 

the aircraft can be simulated and more accurate parametric 

tests can be conducted. 

Publications 

1. Tafti, D. K., and Vanka, S. P. "Hot Gas Environment 

Around STOVL Aircraft in Ground Proximity, Part 2: Numerical 

Study." Presented at the 26th AIAAIASMEIASEE Joint Propulsion Conference, Orlando, FL, July 1990. 

2. Pegeus, W. J., and Vanka, S. P. "Numerical Study of TwinJet Impingement Upwash Flow." Presented at the ASME 

Forum on Turbulent Flows, Toronto, Canada, June 1990. 

Ground-plane temperature distribution for HIDj = 4.0 and U/Vj = 0.03. 
Calculation of Hypersonic Flows with Strong Surface Blowing 

Bram vanleer, Principal Investigator 

Co-investigators: T. C. Adamson, A. F. Messiter, N. D. Carter, and M. D. Matarrese 

The University of Michigan 

Research Objective 

A possible method of controlling hypersonic flight vehicles is 

to generate the required control forces by modifying the 

surface pressure distribution through the use of boundarylayer blowing. The ultimate objective of our work is to produce 

a computer code that can accurately predict the resulting 

pressure distribution for a given injection pattern. 

Approach 

A higher order Godunov-type finite-volume approach is used 

to discretize the two-dimensional Navier-Stokes equations. 

Interface values of the state quantities are reconstructed using 

a monotone interpolation technique suggested by Koren, 

based on van Leer's kappa scheme. The interface inviscid 

fluxes are computed using Roe's upwind-biased fluxdifference splitting techniques. Viscous fluxes are calculated 

using central differencing. Proper treatment of the downstream 

boundary condition is achieved using a modified form of 

Hedstrom's (1970) time-dependent characteristic conditions. 

The time-differencing algorithm is an explicit multistage 

scheme with optimized short-wave damping. 

Accomplishment Description 

Analytical similarity solutions exist for strong blowing along a 

flat plate and along a wedge with a continuous inversesquare-root injection-velocity distribution. Such solutions were 

used to validate the computer code during its development. 

The computer code produced results that compared very well 

with the analytical predictions for cases in which viscous 

effects were negligible. The accompanying figure shows a 

density contour plot for a case in which free-stream-density air 

is uniformly injected along a wedge from X = 0.25 to .5. The 

code is currently being validated for flows in which viscous 

effects are important. It has also been modified to handle 

nonreacting multicomponent flow so that the effects of foreign* 

gas injection can be studied. A typical viscous multicomponent 

flow calculation requires about 50 Cray Y-MP minutes and 

one megaword of memory. 

Significance 

The generic problem of boundary-layer blowing in hypersonic 

flows has many applications beyond vehicle control. Similar 

flow fields are found in the areas of transpiration cooling of 

hypersonic vehicles and the introduction of fuel into the 

combustion region of a scramjet. Successful simulation of 

such flow fields is vital to the understanding and efficient 

application of boundary-layer blowing in hypersonic flows. 

Future Plans 

Once the computer code has been verified to accurately 

calculate viscous flow fields for which analytical solutions are 

known, it will be used to model flows for various complex 

injection distributions. Also, it will be extended to handle realgas effects and equilibrium flow. 

Density contours for a wedge along which free-stream-density air is uniformly injected from X = 0.25 to 0.5; M = 20, a = 10" 

Re = 0.0, time = 0.0. 

f---.,-,,:,,;# P .-...- ..?l., :, I,., ,- >-,'.,::- 
High Reynolds Number, Transonic, Viscous Flow over Aircraft Components 

Veer N. Vatsa, Principal Investigator 

Co-investigator: Bruce W. Wedan 

NASA Langley Research Center 

Significance 

A numerical procedure of the type described here can be 

used to obtain accurate and reliable solutions to viscous flow 

problems of interest, since it will produce essentially gridconverged solutions in a timely manner. 

Future Plans 

The method described here will be generalized to accommodate block-structured grids so that flow over complex aircraft 

configurations can be computed. 

Publications 

Vatsa, V. N., and Wedan, 6. W. "Development of an Efficient 

Multigrid Code for 3-D Navier-Stokes Equations." AlAA 

Paper 89-1 791, 1989. 

Research Objective 

To develop an efficient and robust numerical procedure for 

computing high-Reynolds number, viscous flows over aircraft 

components. 

:Approach lo1 

A multistage Runge-Kutta time-stepping scheme with a 

multigrid acceleration technique is used for computing the 

steady-state solutions of the thin-layer Navier-Stokes equations. Baldwin-Lomax and Johnson-King models are used for 

turbulence closure. 

Accomplishment Description 

A finite-volume numerical scheme was developed for computing high-Reynolds number viscous flows over aircraft 

components. The efficiency of the scheme was enhanced 

significantly through a multigrid acceleration technique. An 

order-of-magnitude reduction in computational time was 100 

achieved because of the multigrid technique. The code was 

used to solve flow over transport wings, fighter wings, wingsin-tunnel, and winglfuselage configurations. An exhaustive 

grid-refinement study was conducted for flow over a transporttype wing, namely, the ONERA M6 wing. Because of the 

improved efficiency of the code, essentially grid-converged 

solutions for transonic flows were obtained for the first time 

using the thin-layer Navier-Stokes equations. The computational time required for obtaining a converged solution was 

found to vary linearly with the number of mesh points used, 1 0-I 

- 

- 

I I 1 11 1111 I 1 1 111111 

which indicated that the multigrid algorithm was working as 1 o-~ 1 o-~ 1 0-I 

expected. The error estimates for force coefficients (lift, drag, 

and pitching-moment) based on extrapolated infinite mesh 'I 'Kwins 

solutions are shown in the accompanying figure. Note that the 

drag coefficient would require the most resolution for a 

specified level of accuracy. The effect of tangential grid spacing on force coefficients. 
Tactical Missile Aero-Propulsion Interaction 

Bill J. Walker, Principal Investigator 

Co-investigators: C. D. Mikkelsen, K. D. Kennedy, K. L. Cornelius, and M. E. Vaughn, Jr. 

U.S. Army Missile Command-Redstone Arsenal 

Research Objective 

To develop the capability to model (1) missile plume flow 

fields, including aerodynamic flow separation of the missile 

afterbody boundary layer, which is caused by the high 

pressures at the rocket nozzle exit plane; (2) the recirculation, 

mixing, and chemical reaction in the base region; (3) the 

mixing, shock structure, and afterburning of the fuel-rich 

rocket exhaust in the near-plume region; and (4) the mixing in 

the far-plume region. 

Approach 

The technical approach entailed the simultaneous solution of 

the fluid-dynamic conservation equations; the turbulence 

model equations; the two-phase, gas-particle interaction 

equations; and the chemical kinetics equations, using proven 

numerical methods of computational fluid dynamics. 

Accomplishment Description 

A full, three-dimensional, Navier-Stokes flow-field solver 

complete with two-equation turbulence models, finite-rate 

chemistry, and a two-phase flow capability was developed 

and demonstrated for a realistic, three-dimensional, tacticalmissile aero-propulsion interaction case. The accompanying 

figure shows the flow-field velocity magnitude for a subsonic 

missile with bifurcated propulsive nozzles and a large blunt 

base. The case was run using blocking to handle high- * 

resolution grids for the forebody, the aftbody with bifurcated 

nozzles, and the wake region. This case required 13.5 Cray 

hours and 40 megawords of CPU memory. 

Significance 

The basic method now exists to numerically model and predict 

the complex, chemically reacting and two-phase flow fields for 

missiles with propulsive rocket exhaust plumes. This method, 

when validated, will provide invaluable missile design information that cannot be acquired in wind tunnels because of 

capability, safety, or cost. 

Future Plans 

Efforts will focus on validation of the model with known 

experimental data. 

The flow-field velocity magnitude for a subsonic missile. 

" ,. 
Development of Unstructured and Nonequilibrium Chemistry Upwind 

Algorithms for Hypersonic Flows 

Robert W. Walters, Principal Investigator 

Co-investigators: Bernard Grossman, P. Cinnella, Andrew S. Godfrey, William D. McGrory, and David C. Slack 

Virginia Polytechnic Institute and State University 

Research Objective 

The objective of this work is the prediction of hypersonic flow 

fields, including the effects of finite-rate chemistry and non- 

'equilibrium thermodynamics. In addition, unstructured flow 

solvers for complex geometry modeling and automatic mesh 

adaptation are being developed. 

&proach 

A three-dimensional, implicit, upwind Navier-Stokes code with 

generalized chemistry and vibrational nonequilibrium thermodynamics models is used to predict the flow field about 

hypersonic vehicles in propulsion systems. 

Accomplishment Description 

In the previous operational year, we developed a threedimensional, explicit Euler code with finite-rate chemistry. This 

year we significantly extended the General Aerodynamic 

Simulation Program (GASP) and performed code validation 

experiments. The most significant enhancements included the 

extension to the full Navier-Stokes equations, the thin-layer 

Navier-Stokes equations, and the parabolized Navier-Stokes 

equations. Space-marching was added so that the user can 

partition a domain into "elliptic" and "parabolic" regions. 

Implicit time-integration schemes with fully coupled chemistry 

were added with several options (e.g., re-use of the Jacobian 

matrices and vectorization over planes), and a multiblock 

capability was included for running on composite grids. 

Several chemistry models were added and tested during this 

operational year. Many code validation experiments were 

performed over a wide range of Mach numbers and flight 

conditions in order to test the features of GASP. A typical 

calculation with GASP is 10 hours of Cray Y-MP time with 

20 megawords of memory. In October, a beta version was 

released to the National Aero-Space Plane contractors for 

testing and feedback. In addition, work on high-order-accurate 

EN0 schemes and unstructured flow solvers continued. 

Automatic mesh adaptation and unstructured space-marching 

algorithms were developed during this period. The figure 

shows an example of a space-marching calculation on a 

hybrid structured1unstructured grid. Pressure contours in the 

symmetry planes and the exit plane of an experimentally 

tested analytic forebody are shown in the figure along with the 

grid topology. These emerging technologies will be included 

in a later release of GASP. 

Significance 

The design of hypersonic vehicles relies heavily on computational fluid dynamic simulations. The need to accurately model 

the complex chemistry and physics in these high-enthalpy 

external and internal flow fields requires the development and 

refinement of three-dimensional Navier-Stokes codes. Run 

fimes for these complex codes for realistic configurations are 

large; thus mesh adaptation is likely to play an increasing role. 

since it offers the hope of efficient placement of elements. 

Future Plans 

The GASP code will be extended to include a generalized 

indexing scheme such that calculations on both structured 

and unstructured grids can be performed. Characteristicbased algorithm development, including multiple translational 

temperatures for more accurate modeling of free-electron 

transport, will be completed and implemented. Nose-to-tail 

calculations, including the simultaneous simulation of both 

internal and external flows, will be performed. 

Grid topology and pressure contours of a space-marching 

calculation. 

ORIGINAL PAGE 

COLOR PHOTOGRAPH 
Navier-Stokes Predictions of Hypersonic Chemically Reacting Flows 

Jong H. Wang, Principal Investigator 

Co-Investigators: David Yeh and Mike George 

Rockwell International, North American Aircraft Division 

Research Objective 

To validate Navier-Stokes methods for predicting hypersonic 

chemically reacting flows. 

Approach 

Rockwell's unified solution algorithms (USA) code is applied to 

existing combustor-flow test cases to validate the code and to 

provide direction for future code development. 

Accomplishment Description 

A two-dimensional hypersonic-combustor-flow test with 

tangential hydrogen injection was investigated numerically. A 

mixing-length turbulence model and 1- and 18-step chemistry 

models were used to simulate the flow. A grid system containing 23,215 points was used. Solution times of 3.1 and 8.4 seconds on the Cray Y-MP computer were required per iteration 

for the 1- and 18-step models, respectively. The required 

memory was slightly over 2 megawords for the 18-step model 

and the solution took about 3000 to 5000 iterations for convergence. Solution strategies for speeding up the convergence 

rate were established. Also, it was concluded that the 

numerical results were very sensitive to the combustor-inlet 

flow profiles. The predicted wall static pressure, heat transfer 

rate, and combustor-exit pitot pressure profiles were in good 

accord with experimental data, as was the location of the 

ignition point (which is indicated by the sudden rise of the 

combustor pressure). The predicted contours for pressure, 

temperature, H20 mass fraction, H2 mass fraction, and 

particle traces (adjacent to the hydrogen injection inlet) are 

shown in the accompanying figure. rn 

Significance 

The design of an efficient hypersonic combustor is essential 

to the success of the National AeroSpace Plane and airbreathing hypersonic vehicles. The complexity of the flow 

physics and the need to obtain efficient mixing and combustion require an accurate and robust computational tool. 

Future Plans 

This research will be extended to study realistic threedimensional combustor flows with various hydrogen injection 

angles. 

(a) Pressure 

(b) Temperature 

(c) H20 Mass Fraction 

(d) H2 Mass Fraction 

(e) Particle Traces Behind Backward Facing Step 

a, 

" ~~~'~re.di~ti6nij& 9 gcramjet test case. 

t7;Ji;:. k ' . t , -.-if.?,. Oi?lG!NP,L PP.,: 

COLOR PHOTOGRAPd , 
Simulation of Three-Dimensional Flow in a Transonic Fan Rotor 

Kurt F. Weber, Principal Investigator 

Co-investigator: Dale W. Thoe 

Allison Gas Turbine Division, General Motors Corporation 

Research Objective 

The objective of this work is to develop and validate a threedimensional Navier-Stokes code that includes tip clearance 

modeling, for prediction of turbomachinery flows. The analysis 

will provide a detailed description of the flow through compressor rotors. Special emphasis is placed on the simulation 

of the flow field for the NASA transonic fan rotor designated 

Rotor 67. 

Approach 

A modified version of the NASA Ames finite-difference code 

ARC3D is applied to the solution of compressor and fan-rotor 

flow fields using body-conforming 0-type grids in the blade 

passage and an embedded H-type grid in the tip-clearance 

region. Code-validation and grid-independence studies are 

performed for Rotor 67. 

Accomplishment Doscdption 

An operational, three-dimensional, Navier-Stokes turbomachinery code was developed for use with 0- and C-type 

grids. Modifications were made to ARC3D to include internal 

turbomachinery boundary conditions. Terms were added to 

the code to account for blade-row rotation, and to account for 

local metric invariant errors that arise when the strong conservation form of the equations is used. Fully viscous solutions on 

a fine 0-type grid (376,309 points) were obtained for Rotor 67 

at the peak-efficiency and near-stall operating points. These 

solutions show good agreement with laser Doppler anemometer measurements. The accompanying figure shows the static 

pressure contours for the 0-grid solution at the near-stall 

operating point. This solution used 18 megawords of storage 

and required 4.4 Cray-2 hours for 1000 iterations. 

Significance 

Historically, aerodynamic design improvements to aircraft gasturbine-engine compressors and fans have depended on 

empirical correlations derived from extensive testing. Although 

this has produced lighter, more efficient compressors, it is 

unlikely that major improvements in performance can be 

achieved without great expense using this approach. Accurate 

modeling of the flow field within compressor blade rows will 

provide the information currently needed to improve compressor performance. It is also an important step toward develop 

ing a model to simulate the complete compressor flow field. 

Future Plans 

The 0-grid code will be used as a starting point for a NavierStokes code that includes tipclearance modeling. A fine 

H-type grid will be embedded in the tipclearance region. The 

blade-passage and tip-clearance flow will be solved simultaneously using the Chimera composite grid scheme. This 

scheme involves the PEGASUS and F3D codes developed at 

NASA Ames and Arnold Engineering Development Center to 

solve the flow fields about complex geometries with multiple 

grids. 

Publications 

Weber, Kurt F.; Thoe, D. W.; and Delaney, R. A. "Analysis of 

Three-Dimensional Turbomachinery Flows on C-type Grids 

Using an Implicit Euler Solver." ASME Paper 89-GT-85, 1989. 

Static pressure contours on the NASA Rotor 67 at the near-stall operating point. 

ORIGINAL PAGE 

COLOR PHOTOGRAPH 
Winged Entry Vehicle Computations 

Kenneth J. Weilmuenster, Principal Investigator 

Co-investigator: Francis A. Greene 

NASA Langley Research Center 

Research Objective 

The objective of this work is to develop an integrated and 

systematic approach to the analysis of the aerothermal 

environment of a winged entry vehicle using state-of-the-art 

grid generation and computational fluid dynamics software. 

This analysis will extend over the hypersonic flight regime and 

require analysis that models the reacting-gas chemistry 

associated with hypersonic flight. 

Approach 

The three-dimensional Euler equations written in generalized 

coordinates and including perfect-gas as well as reacting-gas 

chemistry models are solved on a volume grid generated 

using software developed at the Langley Research Center. 

Accomplishment Description 

An existing three-dimensional, total-variation-diminishing 

(TVD), Navier-Stokes code was modified to create an Euler 

solver. Also, the TVD aspects of the code were modified to 

take into account the thermodynamics of a general chemically 

reacting gas. Currently, the code includes the Tannehill and 

Vinokur descriptions of equilibrium air chemistry and the thermodynamics of CF4--a wind tunnel test gas and a perfect-gas 

option. The code was used to determine the aerodynamics of 

a proposed personnel launch system (PLS) configuration, for 

comparison with wind tunnel data at Mach numbers of 6 

and 10. In addition, the code was used to determine the PLS 

aerodynamics at several points along the hypersonic portion 

of the nominal PLS entry trajectory. Each solution of the PLS 

flow field requires 12 Cray-2 hours and 40 megawords of 

memory. During the NAS 198490 operational year, 448 Cray-2 

hours were used for this project. 

Significance 

Computed and measured aerodynamics data at Mach 

numbers of 6 and 10 for a perfect-gas flow were in good 

agreement, as were the measured and computed aerodynam-, 

ics data for Mach 6 flow using a CF4 test gas. Based on the 

good agreement with measured data from ground-based 

facilities, computations were made at points along a nominal 

PLS trajectory. As a result of these computations, it has been 

determined that the PLS aerodynamics are only slightly 

affected by reacting-gas chemistry and that the vehicle trims 

at its maximum UD in the hypersonic flight regime. 

Future Plans 

The NAS facility will continue to be used to support Euler 

computations for the PLS configuration. During the 1990-91 

operational year, viscous solutions for flow over the PLS will be 

generated at selected wind tunnel and flight conditions. 

Publications 

Weilmuenster, K. J.; Smith, R. E.; and Greene, F. A. 'Assured 

Crew Return Vehicle Flowfield and Aerodynamic Characteristics." AlAA Paper 90-0229, Jan. 1990. 

Mach number contour plots for a personnel launch system vehicle; M, = 10, a = 25", y = 1.4. 
Optical Properties of Nonspherical Particles in Planetary Atmospheres 

Robert A. West, Principal Investigator 

Jet Propulsion Laboratory/California Institute of Technology 

Research Objective 

The ultimate objective of this work is to interpret spacecraft 

and ground-based observations of the radiometric and 

polarimetric properties of the atmospheres of the planets and 

comets. Although previous analyses relied on Mie scattering 

for spherical particles, Mie scattering calculations are inappropriate for many applications, especially for studies of the 

polarization of the nonspherical ice crystals and photochemical haze particles that form the clouds and aerosol 

layers of the outer planet atmospheres. 

Approach 

The optical properties (extinction, absorption, and scattering 

cross sections, and all elements of the phase matrix) are 

calculated with a discrete dipole approximation code, in which 

an arbitrarily shaped particle is modeled as an array of point 

dipoles on a lattice grid. A matrix equation describing the 

interaction of each dipole with the incident electromagnetic 

wave and with the fields of all the other dipoles is solved with a 

steepest-descent conjugate gradient method, to produce the 

radiated field of the particle. 

Accomplishment Description 

During the past year I completed a study of the optical 

properties of colloidal particles grown by diffusion-limited 

aggregation (DLA). This study was motivated by observations 

of the forward-scattering intensity of aerosols in Titan's 

atmosphere, made by the Voyager 1 imaging instrument, and 

by observations of the polarization of light scattered from the 

atmosphere, made by the Pioneer and Voyager photopolarimeter instruments. Early attempts to fit both the high polarization 

near a scattering angle of 90" and the strong forward scattering of Titan's haze particles with distributions of spheres failed. 

The strong polarization required the particle radius to be 

approximately 0.1 pm or smaller, while the phase function 

asymmetry required the particle radius to be about 0.3 pm. 

Significance 

Aggregate particles were found to be abundant in a recent 

laboratory simulation of Titan's haze particles by Bar-Nun et al. 

(J. Geophys. Res. 93 (1 988): 8383-8387). The calculations 

showed that these particles do indeed have both strong 

polarization and strong forward scattering as observed for 

Titan's particles, and thus a long-standing puzzle was solved. 

The implications of this finding are relevant to particle 

microphysical models and chemical evolutionary models of 

Titan's haze and surface composition. The aggregate particles 

have a much smaller density than equivalent-radius spheres, 

and their sedimentation velocity is smaller because of their 

larger geometric cross section for a given mass. Particle mass 

fluxes estimated from equivalent-radius spheres are about a 

factor of five or more larger than for aggregate particles. 

Microphysical models use this mass flux as a primary constraint on particle formation rates and surface deposition 

rates, and will have to be revised by the same factor. These 

results also have implications for experiments planned for the 

Huygens probe. Experiments that rely on Mie theory to relate 

scattered intensity to particle size, as some optical particle 

spectrometers do, will give erroneous values for particle size 

since the scattering efficiency of colloidal particles differs by a 

large factor from the scattering efficiency of equivalent-radius 

spheres. A paper is being prepared for submission to Nature. 

Future Plans 

Investigation of the optical properties of DLA particles will 

continue, with emphasis on understanding how the microstructure of the particle affects its optical properties. Studies 

of simulated comet grains are also under way, directed by 

collaborator Martha Hanner of JPL. 

/ sph= 

\ 

\ 

- -. \ ' . 

-- - 

DLA particre- ' - - - 

I I 

Scattering Angle Scattering Angle h(~m) 

The optical properties of spheres are compared with those of particles formed by DLA. The left-hand figure shows the forwardscattering part of the phase function. The solid curves are for spheres of different radii, and the dashed curve is for a DLA particle 

with a projected cross-sectional area approximately equal to that of a sphere with radius 0.3 pm. The shape of the forwardscattering peak provides a sensitive diagnostic of the particle projected area and is insensitive to particle shape. Other optical 

properties, such as the linear polarization and extinction efficiency, are sensitive to particle shape, as the center and right-hand 

figures demonstrate. Measurements of the optical properties of aerosols in Titan's atmosphere show modest forward scattering, 

and strong polarization near a scattering angle of 90°, which is indicative of DLA particles, not of spheres. 
Application of Unstructured Grids to Shuttle Computational Fluid Dynamics 

Thomas C. Wey, Principal Investigator 

Co-investigator: Chien-Peng Li 

Lockheed Engineering and Sciences CompanyINASA Johnson Space Center 

Research Objective 

To develop a computational fluid dynamics capability to 

predict the high-speed flow around a realistic Space Shuttle 

configuration, while emphasizing the accuracy, efficiency, and 

affordability of Space Shuttle designs. 

Approach 

A three-dimensional structured/unstructured grid generation 

program and its corresponding Euler equation solver are 

coded for this project. 

Accomplishment Description 

A new and simple advancing-front technique for unstructuredgrid generation was developed. A new generalized upwindbiased interpolation scheme was derived to achieve secondor third-order accuracy of the Euler equation for the unstructured 

meshes. The computation for the flow at Mach number 7.32 

and a 35.1" angle of attack needed about 9 Cray-2 hours and 

20 megawords of memory. The computation needed about 

2400 Cray-2 seconds and 5 megawords of memory to 

generate a set of grids that consists of 109,866 nodes and 

641,276 tetrahedra. 

Significance 

The memory required for this grid generation is significantly 

smaller than that for other unstructured-grid generation 

methods. Because of the nature of the advancing-front 

scheme, a major part of the grid generation program runs in 

the scalar mode. Therefore the grid can be generated using a - 

less powerful scalar computer, such as a VAX computer. 

Future Plans 

It is not practical at this time to discretize the entire flow 

domain using unstructured grids. Hence the combination of 

structured and unstructured grids has been implemented in 

the flow solver. The effort to code a program to combine 

multiblock structured and unstructured grids and output the 

connectivity information between them is pending. 

Surface Mach number contours of the orbiter, calculated with unstructured grids. 
Shock Interactions in Rarefied Hypersonic Flows 

Richard G. Wilmoth, Principal Investigator 

Co-investigator: Bradford Sturtevant 

NASA Langley Research CenterICalifOrnia Institute of Technology 

Research Objective 

To provide a basic understanding of rarefied flow effects on 

shock interactions in hypersonic flows, and to enhance the 

computational capability to treat the complex shocklvehicle 

interactions that take place at reentry speeds. 

Approach 

The direct-simulation Monte Carlo (DSMC) method is used to 

model the flow about various geometries in order to study a 

-variety of shocklboundary and shocklleading-edge interactions. The simulation includes collision models that represent 

real-gas effects and nonequilibrium chemistry. An alternate 

computational approach involving finite-difference solutions of 

the Boltzmann equation using discrete-velocity models is also 

being pursued. 

Accomplishment Description 

Computational efforts for the DSMC method were focused on 

the use of multi-tasking on the Cray Y-MP and on calculations 

in support of research being conducted separately on parallel 

processing using hypercube architectures. Computations 

were up to three times faster when multi-tasking was used. 

Fine-grid solutions for a hypersonic channel flow were completed and the results used to investigate requirements for 

adaptive parallel domain decomposition on the Intel hypercube. The attached figure shows gray-shaded density 

contours for one such calculation, with the domain boundaries 

superimposed. Applications studies focused on bow-shock 

definition in transitional flows about spherical bodies representative of typical tethered satellites. For the Boltzmann 

equation studies, computations were completed for several 

one- and two-dimensional problems designed to determine 

the number of discrete velocities needed to achieve an 

adequate accuracy for each problem. Velocity models using 

from 7 to 13 discrete values per component were used to 

compute normal shock solutions to accuracies of less than 

1 %. Typical computing resources needed for DSMC applications studies range from less than 1 hour with 1 to 2 million 

words up to 20 to 30 hours for problems requiring 4 to 

8 million words. 

Significance 

Parallel processing shows tremendous potential for reducing 

the computational times required by the DSMC method. Such 

reductions will be necessary for future three-dimensional 

simulations of full-scale vehicles in the transitional flow regime. 

The Boltzmann-type solutions also provide much-needed 

fundamental information for further theoretical validation of 

the DSMC method. 

Future Plans 

Work will be expanded on the use of vectorization and 

multi-tasking for the DSMC codes. A new method for threedimensional simulations will be applied to more realistic 

geometries of full-scale vehicles. Work will continue on 

developing efficient parallel processing techniques on a 

variety of machine architectures. 

Publications 

1. Wilmoth, Richard G. "Interference Effects on the Hypersonic Rarefied Flow About a Flat Plate." Progress in Astronautics and Aeronautics 118 (1989). 

2. Wilmoth, Richard G. "Direct Simulation Monte Carlo 

Analysis on Parallel Processors." AlAA Paper 89-1666, June 

1989. 

A DSMC simulation of a shock interaction in Mach 8 channel flow; the domain boundaries for parallel decomposition are superimposed on density contours. 
Computational Fluid Dynamics Design of a LaminalcFIow Control Glove 

Chung-Jin Woan, Principal Investigator 

Co-investigator: Michael W. George 

Rockwell International, North American Aircraft Division 

Research Objective 

The current objective of continuing research involves a 

theoretical investigation of the conditions under which a single 

linear program is guaranteed to solve for the global minimum 

of a large-scale, constrained, nonlinear global-optimization 

problem. This objective arose from the discovery that the 

global optimum is very often detected after the solution of a 

single linear program, but cannot often be verified as such 

until many further iterations are completed. 

Approach 

A three-dimensional Navier-Stokes code is used in conjunction with a compressible stability-analysis code to create a 

numerical approach. The approach is being applied to a 

modified FlGxL, which will be flight-tested in April 1990. This 

NAS effort is an adjunct effort to the larger NASNRockwell 

cooperative program. 

Accomplishment Description 

A nonaligned patched-grid technique was developed and 

incorporated into an existing three-dimensional Navier-Stokes 

code to treat the wing-body-inlet combination of the modified 

FI6xL fighter. A blocked grid was generated that had 

21 blocks and a total of 759,181 grid points. A solution without 

suction was obtained. In the flow calculation, a continuingblock-solution approach was used. In this approach, the entire 

solution domain was divided into four main blocks in the 

streamwise direction, and the solution was calculated by 

marching from the most upstream block to the most downstream block. A time-marching scheme was used to compute 

the solution of each of the four main blocks. At the block 

interfaces, a supersonic outflow boundary condition was used 

for the upstream block and a supersonic inflow boundary 

condition was used for the adjacent downstream block. The 

accompanying figure shows the calculated pressurecoefficient contours on the modified F16xL surface. Also 

shown in the figure are the nonaligned grids at the block 

interface located at the middle of the canopy. The computation used 39 Cray-2 hours, and the largest block calculation 

required 18 megawords of memory. 

Significance 

The generation of a numerical ability to predict transition, and 

the extension of laminar flow control to supersonic and hypersonic regimes, would benefit several national programs, 

including the National Aero-Space Plane. 

Future Plans 

Continued effort in calculating the flow about the modified 

F16xL fighter will focus on the cases with suction and on 

validating the supersonic laminar flow control concept by 

comparing calculated results with flight test data. The modified F16xL fighter will be flight tested in April 1990. 

Publications 

"CFD Validation of a Supersonic Laminar Flow Control 

Concept." An abstract to be submitted to the AlAA 29th 

Aerospace Sciences Meeting and Exhibit, Jan. 1991. 

Pressure distribution on an F16xL fighter with a modified wing; M, = 1.6, a = 2', Re = 2,526,756.54m. 

ORIGINAL PAGE 

COLOR PHOTOGRAPH 
Numerical Simulation of Submarine Propulsion 

Cheng-l Yang, Principal Investigator 

David Taylor Research Center 

Research Objective 

To extend the capabilities of an existing Navier-Stokes code to 

compute the hull/propulsor interaction and thrust deduction of 

a submarine. 

Approach 

*Viscous flow over a submarine hull with and without a propeller in operation are simulated. Computations are performed 

with the FMCl code developed at NASA Langley Research 

Center. The method is based on an implicit high-resolution 

Scheme for the three-dimensional, incompressible NavierStokes equations. The inviscid flux is discretized with ND-like 

flux-difference splitting, and the viscous flux is discretized with 

central differencing. The computational grid is generated by a 

transfinite interpolation technique. 

Accomplishment Description 

The effect of the propeller is incorporated into the NavierStokes equation with an imbedded body-force distribution 

method; it includes both axial and tangential components. The 

differences between axial velocity components (DUxN-) with 

and without a propeller in operation at two streamwise 

locations are shown in the attached figure (x is the distance 

from the bow, L is the hull length, and r is the normal distance 

from the body surface). The propeller is located at x/L = 0.983. 

The differences in pressure distribution on the after-portion of 

the hull are also shown in the figure. The agreement between 

the computed and the measured values is very good. From 

the results of the computation, the influence of propeller 

action can be detected up to about two propeller diameters 

upstream. Typical calculations on a grid of about 

150,000 nodal points require about 1200 CPU seconds 

on a CRAY Y-MP, with 2 megawords of memory. 

Significance 

The design of an efficient propulsor system for an underwater 

vehicle requires a better understanding of hull/propeller 

interaction. It is demonstrated that essential information can 

be obtained by a computational fluid dynamics simulation. 

Future Plans 

The present method will be used to study the viscous flow 

around a compound propulsor. The method will also be used 

to study the detailed flow pattern around a propeller blade tip. 

Publications 

Yang, C.-I.; Hartwich, P.-M.; and Sundrarum, P. "Numerical 

Simulation of Three-Dimensional Viscous Flow Around a 

Submersible Body." Presented at the Fifth International 

Conference on Numerical Ship Hydrodynamics, Hiroshima, 

Japan, Sept. 1989. 

Measured and Computed Surface Pressure 

Decrease on Afterbody 1 Due to Propeller Suction 

0.06 o 0 0 Experiment 

N.S Solution 

r1L 

0.03 

0 02 

0.01 

XIL = 0.977 

00 0 Experiment 

- N.S Solut~on 

Measured and Computed Ax~al Veloc~ty Increase 

on Afterbody 1 Due to Propeller Suct~on 

(a) Submarine hull with propeller. Measured and computed (b) surface pressure decrease, (c) axial velocity increase at x/L = 

0.954, and (d) axial velocity increase at x/L = 0.977 on afterbody 1, resulting from propeller suction. 
Multistage Rotor/Stator Interaction in the Space Shuttle Main Engine 

Turbopump Turbine 

Ruey-Jen Yang, Principal Investigator 

Co-investigator: Shyi-Jang Lin 

Rockwell International, Rocketdyne Division 

Research Objective 

To develop and validate a two-dimensional Navier-Stokes 

code for predicting multistage rotorlstator unsteady flow 

interactions, with emphasis on the Space Shuttle main engine. 

Approach 

The NASA Ames ROTOR-2 code, which was developed by 

M. M. Rai, is modified. The ROTOR-2 code is a twodimensional Navier-Stokes code for single-stage turbomachinery. It uses multiple-zone technology and an iterative, 

implicit, third-order-accurate upwind algorithm. 

Accomplishment Description 

The upgraded ROTOR-2 code can handle rotorlstator interaction problems for arbitrary numbers of stages and airfoils. To 

validate the new code, a 1.5-stage, large-scale rotating rig 

(airfoil ratio 3:4:4) of the United Technology Research Center 

was simulated, and the results compared well with experimental data. For the numerical accuracy check, investigations 

were also carried out on the effect of thin-layer versus full 

viscous calculation, the effect of temporal accuracy, and the 

effect of inner subiteration of the numerical scheme. A calculation for the &stage, low-pressure oxidizer turbopump axial 

turbine of the Space Shuttle main engine was also completed. , 

Significance 

The use of multistage computations is necessary to obtain 

accurate transient flow information for multistage machines 

and, in particular, for those components along downstream 

stages. The accurate transient flow information is essential for 

providing dynamic loadings for structural model analysis. 

Future Plans 

The code will be further used to study supersonic, multistage, 

rotorlstator unsteady-flow interactions. 

Publications 

Yang, R.-J., and Lin, S.-J. "Numerical Solutions of 2-D MultiStage RotorIStator Unsteady Flow Interactions." Proceedings 

of CFD Symposium on Aeropropulsion. NASA Lewis Research 

Center, Apr. 1990. 

Calculation of a multistage rotorlstator interactiov 

188 

G"'?lr.'p-,L ,,l-j:l. P I ' .c.- .-, ' 

COLGR PHOTOGRAPH 
Tilt-Rotor Download Prediction 

Larry Young, Principal Investigator 

Co-investigator: C. S. Lee 

NASA Ames Research Center 

Research Objective 

To develop an accurate and efficient code to predict the tiltrotor download in hover. 

Approach 

,A low-order panel method is used. The rotor blades are 

modeled by an actuator disk with a known normal velocity 

distribution. The rotor wakes are simulated by a linear doublet 

in the streamwise direction. The wing is modeled by constant 

-source and doublet panels. The separated wing wake is 

represented by constant doublet panels. The separation lines 

on the wing surface are assumed to be arong the leading 

edge, wing tip, and trailing edge. The wake strength and the 

base pressure on the wing lower surface are determined by 

the Kutta condition for separated flows. Near-field correction 

in induced velocity for the close vortex/surface interaction is 

implemented to prevent the rotor wake from penetrating into 

the wing upper surface. 

Accomplishment Description 

The development of the download prediction was divided into 

stages corresponding to each component of the flow feature: 

(1) three-dimensional massive separated flow, (2) rotor 

simulation, and (3) vortex filamenttwing surface interaction. 

Progress has been made on each of the topics. For massive 

separated flows, a calculation was performed and reported for 

a wing in uniform flow with a 90" angle of attack. For unsteady 

rotor wake simulation, curved vortex elements were used for 

the rotor wake. For close vortexlsurface interaction, computational schemes such as near-field correction, wake element 

redistribution, and wake deflection near surfaces were 

developed. Each flow computation required approximately 

1 hour of Cray-2 time and 2 megawords of memory. 

Significance 

The download for a hovering tilt-rotor aircraft is typically 10 to 

15% of the total rotor thrust. Since the payload of a tilt rotor is 

25 to 30% of the gross weight, download reduction could 

mean 35 to 60% improvement on the payload. The complexity 

of the rotor and wing geometry and the flow features make the 

problem difficult to solve by a direct Navier-Stokes solver. A 

panel method can provide a relatively low-cost simulation 

without compromising too much on accuracy. 

Future Plans 

The three components of flow simulation are now being 

combined into a code capable of representing the hovering 

tilt-rotor configuration; the preliminary result is shown in the 

figure. After the code validation, the plan is to simulate the 

individual rotor blade instead of the actuator disk used in the 

present model. Since the memory required in this simulation is 

relatively small, the Cray Y-MP can support the development 

as well. Therefore, the NAS program was not applied for this 

year. 

Publications 

Lee, C. S. "Calculation of the Rotor Download on Airfoils." 

Presented at the OAST CFD Conference, NASA Ames 

Research Center, Mar. 1989. 

Flow field of a hovering tilt rotor. 
Simulation of the Climatology of the El 

Stratosphere 

Richard E. Young, Principal Investigator 

Co-investigators: Owen B. Toon and James B. Pollack 

NASA Ames Research Center 

Research Objective 

The principal objective of this project is to numerically simulate 

the behavior of the El Chichon volcanic aerosol cloud in the 

stratosphere in order to better understand stratospheric transport and aerosol microphysical processes. An associated goal 

is to assess the climatic impact of the El Chichon volcanic 

eruption on stratospheric wind and temperature fields. 

Approach 

A three-dimensional, spectral, primitive-equation model is 

used to compute wind and temperature fields in the stratosphere. This model is coupled to a three-dimensional aerosol 

transport and microphysical model that computes the dispersion of the volcanic aerosol cloud using the computed winds 

from the circulation model, accounting for such processes as 

sedimentation and coagulation of the aerosol particles. 

Accomplishment Description 

An improved balance equation was developed for initializing 

the three-dimensional circulation model wind and temperature 

fields. This effort was necessary because simulations of the 

stratosphere, typically needing about 12 Cray Y-MP hours and 

10 megawords of memory, showed two anomalous features 

that were traced to dynamical imbalances in the model initial 

conditions. One anomaly was a short-wavelength oscillation in 

temperature as a function of latitude. The second was an 

unrealistic heating in the upper troposphere and lower 

stratosphere in the polar regions. We are still testing the new 

balance procedure to ensure that no other anomalous features 

are present that are caused by initial dynamical conditions. A 

diagnostic package to calculate and display the detailed 

energy and momentum balance of the three-dimensional 

circulation model was developed. This diagnostic package 

was instrumental in tracing the above-described anomalies to 

the initial conditions. 

Significance 

Major NASA programs, such as the Upper Atmospheric 

Research Program and the NASA Ames aircraft expeditions to 

the Antarctic in 1987 and the Arctic during the winter of 1988- 

1989, as well as various Earth-orbiting satellite programs such 

as the Upper Atmospheric Research Satellite program, have 

as principal goals the study of the climatology of the stratosphere. Further, the High Speed Research Program of OAET 

is currently sponsoring research to assess the climatic impact 

of high-speed aircraft operating in the lower stratosphere. A 

unique opportunity to better understand stratospheric transport and aerosol microphysical processes occurred when the 

El Chichon volcano erupted in April 1982, injecting some 

10 million tons of aerosol particles into the stratosphere. A 

comprehensive climatology of the subsequent dispersal of the 

volcanic cloud, gathered from aircraft, satellite, and groundbased observations, has been compiled for the years immediately following the eruption. By simulating the behavior of the 

volcanic cloud we can assess and improve the theoretical 

understanding of transport and aerosol processes in the 

stratosphere, and thus make an important contribution to the 

above NASA programs. 

Chichon Volcanic Aerosol Cloud in the 

Future Plans 

Multi-year simulations of the undisturbed stratosphere will be 

carried out. The results from these calculations will be used to 

conduct passive tracer simulations of the El Chichon volcanic . cloud. Once the passive tracer computations are complete, 

fully interactive tracer simulations will be done. 

-M) -30 b 30 60 

Latitude (degrees) 

0.0 4 I I -80 -30 0 30 M) 

Latitude (degrees) 

Height-latitude cross sections of longitudinally averaged eastwest wind. Height is measured from the 300-mb pressure 

surface. The improvement resulting from the new balance - 

procedure is evident in the bottom figure. 
Development of an Euler-Based Method for Turboprop Integration 

N. J. Yu, Principal Investigator 

Co-investigators: H. C. Chen, T. J. Kao, and D. A. Naik 

The Boeing CompanylViGYAN, Inc.1NASA Langley Research Center 

Research Objective 

To develop an effective computational capability for the study 

of turboprop enginelairframe integration. 

Approach 

,Transonic, three-dimensional, inviscid, multiblock, multigrid 

Euler codes were developed for the analysis of complete 

airplane configurations with either wing-mounted or aftmounted propfans. A three-dimensional elliptic grid generation 

-code that creates the volume grid from the specified surface 

grid was also developed. The propeller power effects were 

simulated using an actuator disc; either components of force 

and work distributions, or total pressure, total temperature, 

and swirl were prescribed along the disc as boundary conditions for the flow solver. A separate embedded flow solver 

provided detailed flow characteristics in the vicinity of the 

propulsive unit. This embedded solver inherited its starting 

values from the global solution. 

Accomplishment Description 

The code was successfully applied to the NASA aft-turboprop 

model shown in the accompanying figure. For this example, 

increasing the sweep of the strut was found to significantly 

reduce the adverse installation effects of propulsion integration. A typical analysis took about 2 hours on a Cray-2, used 

295,000 grid points, and required 12 megawords of memory in 

the single-block mode or 3 megawords of memory in the 

multiblock mode. Embedded mesh solutions consumed less 

than 10 minutes of CPU time on the Cray-2. 

Significance 

The computational fluid dynamics (CFD) codes that were 

developed in this project have been used as an effective tool 

for propfan enginelairframe integration. Qualitative analysis of 

the CFD solutions have aided in the selection and modification 

of configurations for quantitative experimental analysis. 

Future Plans 

This experience is being applied to the development of a CFD 

code for turbofanlsuperfan installation. 

Mach 

0.40000 

0.43000 

0. -16000 

0.49000 

0.52000 

0.55000 

0.580flO 

0.6100ll 

6,64000 

0.67flUU 

0.7ODUD 

0.73000 

0.76000 

0.79000 

0.82000 

0. B5000 

0.88000 

0.91000 

0.Y4000 

Original Strut 

Mach number contours for the NASA aft-mounted propfan; M, = 0.77, a = 0.5". 

Swept Strut 

Freestream Mach = 0.77 

NASA AFT-PROPFAN 

G;;"';.IAL FK f 

COLOR PHQTOSfihiri 191 
Incompressible Transition to Turbulence 

T. A. Zang, Principal Investigator 

Co-investigators: S. Dinavahi, B. Singer, and U. Piomelli 

NASA Langley Research Center 

Research Objective 

The objective is to study the transition of fluid flows from 

smooth, laminar states to chaotic, turbulent states. The focus 

in 1989 was on wave interactions, on the subharmonic route to 

transition, and on modeling the final process of transition to 

turbulence. 

Approach 

Direct and large-eddy simulations of simple, low-speed 

channel and boundary-layer flows were performed under 

controlled conditions in the transitional regime. The simulations were performed for the time-dependent Navier-Stokes 

equations using highly accurate spectral methods. 

Accomplishment Description 

A weakly nonlinear theory was developed for predicting the 

effects of interaction between Gortler vortices and TollmienSchlichting waves in curved channel flow. Direct numerical 

simulations confirmed the validity of the theory. High-resolution 

direct simulations were performed of subharmonic transition in 

boundary layers. They revealed that laminar breakdown can 

occur on the large, primary scale or on smaller scales (see 

figure). Large-eddy simulations were conducted for both 

boundary-layer and channel-flow transition. They performed 

surprisingly well in predicting the peak skin friction in the 

transition zone. A total of 1540 CPU hours were used on the 

Cray-2 and Cray Y-MP during 1989-90. 

Significance 

The weakly nonlinear theory is a more economical predictive 

tool than numerical simulation, but the latter tool is essential 

for corroborating the validity of this algebraically complex 

approach. The subharmonic transition simulations indicate 

the richness of the transition process, even in simple flows. 

Large-eddy simulations of transition are far less expensive 

than direct simulations, and the use of this new technology 

can lead to the expansion of the role of numerical computations of transition. 

Future Plans 

The detailed data bases for various subharmonic transition - 

simulations will be thoroughly examined to clarify the different 

mechanisms at work. The large-eddy simulation method will 

be more thoroughly tested and then extended to spatial and 

compressible transition. 

Publications 

1. Singer, 6. A.; Zang, T. A.; and Erlebacher, G. "TS-Dean 

Interactions in Curved Channel Flow." ICASE Report No. 90-9, 

1990. 

2. Zang, T. A., and Hussaini, M. Y. "Multiple Paths to Subharmonic Laminar Breakdown in a Boundary Layer." To be 

published in Phys. Rev. Letters. 

3. Piomelli, U.; Zang, T. A,; Speziale, C. G.; and Hussaini, 

M. Y. "On the Large-Eddy Simulation of Transitional WallBounded Flows." Phys. Fluids A 2 (1990): 257-265. 

4. Zang, T. A,; Gilbert, N.; and Kleiser, L. "Direct Numerical 

Simulation of the Transitional Zone." Proceedings of the 

NASAdCASE Workshop on Instability and Transition, ed. M. Y. 

Hussaini and R. G. Voight. New York: Springer, 1990. 

Vortex lines showing laminar breakdowns in subharmonic transition. 
Index by Research Sites 

Allison Gas Turbine Division, General Motors Corporation 

Edward J. Hall Ducted Propfan Analysis .................................................................................................................. 59 

Richard H. Pletcher Development and Evaluation of Computational Methods for Turbomachinery Applications.. ...... .I31 

(with Iowa State University) 

Kurt F. Weber Simulation of Three-Dimensional Flow in a Transonic Fan Rotor ...................... ..................... 181 

Analatom, Inc. 

' Robert W. MacCormack Simulation of Highly Ionized Flows ................................................................................................... 94 

(with Stanford University) 

Wolfgang Mueller Electronic Structure of Superconductors .................................................................................... 120 

(with NASA Lewis Research Center) 

Analex Corporation 

John L. Klann Solar Dynamic Space Power-System Design and Performance Analysis ....................................... 80 

(with NASA Lewis Research Center) 

Analytical Services and Materials, Inc. 

William B. Compton Ill Transonic Navier-Stokes Solutions of Three-Dimensional Afterbody Flows ..................................... 24 

(with NASA Langley Research Center) 

N. M. El-Hady Control of the Flow Field about an Airfoil Section by Localized Surface Heating ............................ 42 

(with NASA Langley Research Center) 

L. Maestrello Radiation and Control of the Acoustic Field Caused by a Wave Packet Evolving along 

a Concave-Convex Surface ......................................................................................................... 97 

(with NASA Langley Research Center) 

Bell Helicopter Textron, Inc. 

Matthew T. Scott Computational Methods for Rotor-Blade Drag Prediction.. ........................................................... .I50 

Berkeley Research Associates 

Stephen H. Brecht Hybrid Simulations of the Global Venus/Solar Wind Interaction ............................ .. .................... 9 

Elaine S. Oran Unsteady Diffusion Flames.. .......................................................................................................... .I26 

(with Naval Research Laboratory) 

Boeing Advanced Systems 

Michael D. Madson Transonic Analysis About the F- 16A and Other Complex Configurations .................................... 96 

(with NASA Ames Research Center) 

The Boeing Company 

D. A. Naik Transonic Potential Flow about Transport Aircraft ......................................................................... 21 

(with ViGYAN Inc., NASA Langley Research Center) 

Development of an Euler-Based Method for Turboprop Integration.. ..................... ................. I 91 

(with NASA Langley Research Center, ViGYAN, Inc.) 

-California Institute of Technology 

Gregory A. Lyzenga Earthquake-Cycle Stress Simulations ............................................................................................ 91 

(with Jet Propulsion Laboratory) 

Robert A. West Optical Properties of Nonspherical Particles in Planetary Atmospheres .................... ............. .I83 

(with Jet Propulsion Laboratory) 

Richard G. Wilmoth Shock Interactions in Rarefied Hypersonic Flows.. ........................................................................ 185 

(with NASA Langley Research Center) 
Case Western Reserve University 

Steven H. lzen Numerical Inversion of a Limited-Data X-Ray Transform ................... ... ..... .... .. ............... . 78 

Clarkson University 

Nabeel A. 0. Dernerdash Finite-Element Computation of Three-Dimensional Magnetic Fields for Design 

Optimization of Generators for Space Station Solar Dynamic Power ...................................... .... 30 

Colorado State University 

David A. Randall Modeling Global Cloudiness.. . . . . . . . .. . . ... . . . . ... , . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 

David Taylor Research Center 

Henry J. Haussling Multiblock Solutions of the Navier-Stokes Equations ....... ................. ......... ..... . . . ........ .. . 67 

Thomas T. Huang Turbulence Modeling for Submarine Flow Field Computation ..................................... ... 73 

Chao-Ho Sung Naval Applications of Computational Fluid Dynamics . . . . . . . . . . .. . . . . . . . . . .. . . .. . . ... . . . . . . . . . . . . . . . . . . . . . . . . 165 

Tsze C. Tai Hydrodynamic Prediction Methods for Advanced Submarine Configurations ....................... ... . 167 

Tsze C. Tai Low-Speed Maneuver Aerodynamics in a Nonuniform Free Stream ... ........................................ 168 

Cheng-I Yang Numerical Simulation of Submarine Propulsion.. .. . . . . . . . . . . . . . . . . . . . . . . .. . . , . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 

Douglas Aircraft Company 

Lee T. Chen Calculation of Transonic and Supersonic Flows Using an Interactive Scheme Based 

on Euler and Boundary-Layer Equations ......................... ..... ..... .... . .. . .... ......... 21 

General Dynamics, Convair Division 

Adam C. Bricker Hypersonic Air-Breathing Missile Aero/Propulsion Integration .......... ..... .. ....... . . . . . . .. . . . . 1 1 

Geoffrey Butler Two-Body Hypersonic Separation Analysis . . . . . . . . . .. . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 

Peter K. Shih Afterbody Aerothermodynamic Studies for the Hypersonic Glide Vehicle.. . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 153 

General Dynamics, Fort Worth Division 

Robert DeParvine High-Angle-of-Attack Inlet Analysis and Design Using Computational Fluid 

Dynamics Methods ............................................................................................ 31 

Robert DeParvine Validation of a Computational Fluid Dynamics Code for High-Speed-Inlet Design . .. ... .. ... .. .. ......... 32 

Richard L. Haller Evaluation of the CAP-TSD Computer Code Using an F-16 Study Case ......... ... .... .. ...... ..... . ..... .. 60 

General Electric Aircraft Engines 

Sundaresa V. Subramanian Numerical Study of Three-Dimensional Viscous Reacting Flows with Application 

to Scramjet Propulsion.. . . . . . .. . . . . . .. . . . . . ... . .. . . . .. . . .... . . . , . . . . . . . . , . , . . . . . . . . . , . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 

High Technology Corporation 

Mujeeb R. Malik Transition in Hypersonic and Three-Dimensional Boundary Layers ......... ..... .................... ...... 98 

(with NASA Langley Research Center) 

EASE 

G. Erlebacher Compressible Turbulence ............................................... ,, . . ............................... . . . 44 

(with NASA Langley Research Center) 

Dimitri J. Mavriplis Solution of the Steady State Navier-Stokes Equations on Unstructured and 

Adaptive Meshes ............................ .. ..................................... ...... . ... 102 

(with NASA Langley Research Center) 

Iowa Institute of Hydraulic Research 

V. C. Pate1 Hydrodynamics of Self-Propelled Bodies. .. . . . .. . . . . . . . . . . . . .. . . . . ...... . . . , , , , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 28 
Iowa State University 

James C. Hill Direct Simulation of Turbulent Reacting Flows.. .............................................................................. .69 

Richard H. Pletcher Development and Evaluation of Computational Methods for Turbomachinery Applications.. ...... .I31 

(with Allison Gas Turbine Division, General Motors Corporation) 

John C. Tannehill Development of a Robust Parabolized Navier-Stokes Code for Computing 

Three-Dimensional, Chemically Reacting Flow Fields. .............. ..... .................................. 1 71 

- JAYCOR 

Harley E. Hurlburt Eddy-Resolving Model of the Pacific Ocean .................................................................................. 76 

(with the Naval Oceanographic and Atmospheric Research Laboratory) 

- Jet Propulsion Laboratory 

Gregory A. Lyzenga Earthquake-Cycle Stress Simulations ........................................................................................... 91 

(with California Institute of Technology) 

Robert A. West Optical Properties of Nonspherical Particles in Planetary Atmospheres ............................. .... .I83 

(with California Institute of Technology) 

Kansas State University 

Kadosa Halasi Parameter Study in the Driven Cavity.. ............ ............................................................................ .58 

(with University of Colorado at Boulder) 

Lockheed Aeronautical Systems Company 

Charles R. Olling Navier-Stokes Simulation of Separated Turbulent Flow around a Generic 

Fighter Aircraft ............................ ....................................................................................... ,124 

Charles R. Olling Navier-Stokes Simulation of Turbulent Flow over Rectangular Cavities 

Containing Stores.. ..................................................................................................................... .I25 

Lockheed Engineering and Sciences Company 

Robert A. Golub Flow-Field Simulation Around Different Rotor Planforms ............................................................. 52 

(with NASA Langley Research Center) 

Edward C. Ma Numerical Investigation of a Space Shuttle Orbiter Contingency Abort .......................................... 92 

Ajay K. Pandey Flux-Based Finite-Element Formulation Reduces CPU Time for Thermal-Structural 

Analysis.. ................................................................................................................................. .I27 

(with NASA Langley Research Center) 

Ramadas K. Prabhu Finite-Element Analysis of Equilibrium and Nonequilibrium Flows .............................................. 133 

(with NASA Langley Research Center) 

Luen T. Tam Thermochemical and Radiative Nonequilibrium Flow Simulation for the Aeroassist 

Flight Experiment.. .................................................................................................................... 1 70 

(with NASA Johnson Space Center) 

Thomas C. Wey Application of Unstructured Grids to Shuttle Computational Fluid Dynamics ................. ...... 184 

(with NASA Johnson Space Center) 

'Lockheed Missiles and Space Company, Inc. 

R. Rexford Chamberlain Three-Dimensional Calculations of Multiple Control-Jet Interactions for Defense Interceptors ....... 18 

Los Alamos National Laboratory 

Gary A. Glatzmaier Numerical Simulations of Deep Global Convection in Jupiter .............. ........................................ 50 

McDonnelI Aircraft Company 

Shreekant Agrawal Separated and Vortical Flow-Field Analysis on Fighter Wing Configurations .................................... 4 

Raymond R. Cosner Hornet 2000 Flow-Field Analysis ...................................................... .:........................................... .25 

John Mangus Navier-Stokes Analysis of the Air Force Vortex Flap Model and the F/A-18 .................................... 99 

(with Northrop Aircraft Division) 

195 
James A . Rhodes Computation of ASTOVL Flow Fields ........................................................................................... 141 

McDonnell Douglas Corporation 

C . C . Lee Numerical Investigation of NASP-Like Vehicles .............................................................................. 85 

McDonnell Douglas Research Laboratories 

Ramesh K . Agarwal Helicopter Fuselage and Rotor Flow-Field Calculations in Hover and Forward Flight ...................... 2 

(wifh NASA Ames Research Center) 

Ramesh K . Agarwal Numerical Solution of the Reynolds-Averaged Navier-Stokes Equations for Flow About 

an Almost Compete Aircraft ........................................................................................................... 3 

(with NASA Ames Research Center) 

William W . Bower Calculations of Unsteady. Supersonic-Jet Flow Fields and Acoustics .................... ..................... 6 

(with Nielsen Engineering & Research. Inc.) 

Alan B . Cain Receptivity. Eigenfunction Modeling. and Simulation of a Wall-Bounded Flow .............................. (with NASA Ames Research Center) 

NASA Ames Research Center 

Ramesh K . Agarwal Helicopter Fuselage and Rotor Flow-Field Calculations in Hover and Forward Flight ...................... 2 

(with McDonnell Douglas Research Laboratories) 

Ramesh K . Agarwal Numerical Solution of the Reynolds-Averaged Navier-Stokes Equations for Flow About 

an Almost Compete Aircraft ........................................................................................................... 3 

(with McDonnell Douglas Research Laboratories) 

Donald Baganoff Discrete Particle Simulation of Compressible Flow ................. ............................................... 5 

(with Stanford University) 

Jeffrey C . Buell Three-Dimensional Shear Layers and Wall-Bounded Compressible Turbulence ........................... 12 

Pieter G . Buning Space Shuttle Flow Field ................................................................................................................ 13 

Alan B . Cain Receptivity. Eigenfunction Modeling. and Simulation of a Wall-Bounded Flow .............................. 15 

(with McDonnell Douglas Research Laboratories) 

Denny S . Chaussee Hypersonic Flow Past Generic Lifting Bodies ................................................................................. 20 

W . J . Chyu Airframe/lnlet Aerodynamics .................................................................................... NASA Ames Research Center 

Bill Davy Three-Dimensional Aeroassist Flight Experiment Flow Simulations ....................... ................ .... 28 

Thomas A . Edwards Hypersonic Chemically Reacting Flow over Blended Wing-Body Vehicles ................................ 37 

Thomas A . Edwards Numerical Simulation of Hydrogen-Air Combustion in Hypersonic-Vehicle 

Propulsion Systems ................ ... ............................................................................................. 38 

Fort F . Felker Three-Dimensional Viscous Drag Prediction for Rotor Blades ........................................................ 45 

Jolen Flores Compressible Navier-Stokes Code Development ......... ............................................................ 48 

Aga M . Goodsell A Supersonic Computational Fluid Dynamic Analysis of a Generic Fighter ............... ............. 53 

G . P . Guruswamy Simulation of Fluid/Structural Interactions ....................................................................................... 56 

C . C . Horstman Turbulence Modeling for Compressible/Hypersonic Flows ............................................................. 71 

Ching-rnao Hung Computation of Steady Three-Dimensional Separation ......................... ............................... 75 

Laurence R . Keefe Linking Attractor Geometry to Turbulence Physics ......................................................................... 79 

Dochan Kwak lncornpressible Navier-Stokes Calculations for the Space Shuttle Main Engine ........................... 83 
Robert D. MacEIroy Computer Simulation of Ion Transport across Membranes ..............................................................95

Michael D. Madson Transonic Analysis About the F-16A and Other Complex Configurations .......................................96

(with Boeing Advanced Systems)

Nagi N. Mansour Direct Simulation of Compressible TurbulentFlows....................................................................... 100

Fred W. Martin, Jr. Space Shuttle Flow Field ................................................................................................................101

(with NASAJohnson Space Flight Center)

_N.J. McCroskey Aerodynamic Flows about High-Performance Rotor Blade Tips....................................................105

(with U. S. Army Aeroflightdynamics Directorate--AVSCOM)

_N.J. McCroskey Airloads and Acoustics of Rotorcraft ..............................................................................................106

(with U. S. Army Aeroflightdynamics Directorate--AVSCOM)

W. J. McCroskey Tilt-RotorAerodynamic Interactions ............................................................................................... 107

John E. Melton Computational Fluid Dynamics Analysis of Advanced Turboprop Configurations ........................110

Gene P. Menees Standing Oblique Detonation Waves .............................................................................................112

Robert D. Moser Wall-Bounded Turbulent Flows ......................................................................................................119

Thomas H. Pulliam Chaotic, Unsteady, Low-Reynolds Number Navier-Stokes Flow...................................................134

Man Mohan Rai A Finite-Difference Approach to Direct Simulations and Large-Eddy Simulations

of Turbulent Flow ........................................................................................................................135

Man Mohan Rai Three-DimensionalMulti-Airfoil Navier-Stokes Simulations of Rotor/Stator Interaction

in Turbines ..................................................................................................................................136

Man Mohan Rai Unsteady Flow in a Multistage Compressor................................................................................... 137

Michael M. Rogers Turbulent Reacting Flows............................................................................................................... 144

William C. Rose National Aero-Space Plane Inlet Flow Fields..................................................................................147

(with Rose Engineering & Research, Inc.)

William C. Rose Three-Dimensional Viscous Flow in High-Speed Inlets..................................................................148

(with Rose Engineering & Research, Inc.)

Philippe R. Spalart Transition and Turbulence in Three-DimensionalFlows ................................................................156

Roger C. Strawn Computational Fluid Dynamics Prediction of Advanced Rotor Performance ................................159

(with U.S.Army Aeroflightdynamics Direotorate--AVSCOM)

Larry Young Tilt-RotorDownload Prediction ...................................................................................................... 189

Richard E. Young Simulation of the Climatology of the El Chichon VolcanicAerosol Cloud in the Stratosphere....... 190

NASA Goddard Space Flight Center

David Adamec Large-Scale Ocean Modeling ............................................................................................................1

Hans G. Mayr Numerical Study of PlanetaryAtmospheres ...................................................................................103

David A. Randall Modeling Global Cloudiness ......................................................................................................... 140

NASA Johnson Space Center

Fred W. Martin, Jr. Space Shuttle Flow Field ................................................................................................................101

(with NASAAmes Research Center)

Phil C. Stuart Mars Rover/Sample Return Aerocapture Vehicle........................................................................... 162

197
Luen T. Tam Thermochemical and Radiative Nonequilibrium FlowSimulation for theAeroassist

Flight Experiment........................................................................................................................ 170

(with Lockheed Engineering and Sciences Company)

Thomas C. Wey Application of Unstructured Grids toShuttle Computational Fluid Dynamics............................... 184

(with Lockheed Engineering and Sciences Company)

NASA Langley Research Center

John T. Batina Validation of a Three-Dimensional Flux-SplitEuler Algorithm for Unstructured Grids....................... 7

William B. Compton II1 Transonic Navier-Stokes Solutions of Three-DimensionalAfterbody Flows ....................................24"

(with Analytical Services and Materials, Inc.)

Pramote Dechaumphai Integrated Fluid-Thermal-Structural Analyzer Demonstrates Heat- -.

Transfer/Deformation Coupling ....................................................................................................29

J. Philip Drummond Simulation of Supersonic Chemically Reacting Flow Fields ............................................................34

N. M. EI-Hady Control of the Flow Field about an Airfoil Section by Localized Surface Heating ........................... 42

(with Analytical Services and Materials, Inc.)

G. Erlebacher Compressible Turbulence................................................................................................................ 44

(with ICASE)

Javier A. Garriz Validation of 3-D Wind Tunnel WallInterference Assessment/Correction Codes ........................... 49

Peter A. Gnoffo Hypersonic Flows in Chemical and ThermalNonequilibrium ..........................................................51

Robert A. Golub Flow-Field Simulation Around Different Rotor Planforms ................................................................. 52

(with Lockheed Engineering and Sciences Company)

W. L. Grose Three-DimensionalAtmospheric Simulation Model ......................................................................... 55

Julius E. Harris Supersonic Laminar-Flow-Control Computational Fluid Dynamics ................................................. 61

Peter M. Hartwich General, Fast, Accurate Floating Shock Fitting Procedure for Unadapted Meshes ....................... 62

(with ViGYAN, Inc.)

Peter M. Hartwich Navier-Stokes Solutions for Vortical Flows over a Forebody ........................................................... 63

(with ViGYAN, Inc.)

C.-H. Hsu Prediction of Vortical Flows Using Incompressible Navier-StokesEquations ................................. 72

(with ViGYAN, Inc.)

Ajay Kumar Three-Dimensional Shock/Shock Interactions on the Inlet Side Wall .............................................. 81

Geojoe Kuruvila Numerical Study of Fundamental Fluid Dynamics using Navier-StokesEquations ........................ 82

C. H. Liu Computational Prediction and Control ofSteady and Unsteady Asymmetric VortexFlows

around Cones .............................................................................................................................. 89

(with Old Dominion University)

James M. Luckring Transonic Navier-Stokes Solutions about a Complex High-Speed Accelerator Configuration ....... 90

M. G. Macaraeg Nonlinear Evolution ofSupersonic Disturbances in Mixing Layers ................................................. 93

L. Maestrello Radiation and Control of theAcoustic Field Caused by a WavePacket Evolving along

a Concave-Convex Surface ......................................................................................................... 97

(with Analytical Services and Materials, Inc.)

Mujeeb R. Malik Transition in Hypersonic and Three-DimensionalBoundary Layers ............................................... 98

(with High Technology Corporation)

198
Dimitri J . Mavriplis Solution of the Steady State Navier-Stokes Equations on Unstructured and 

Adaptive Meshes ....................................................................................................................... 102 

(with ICASE) 

Charles R . McClinton National Aero-Space Plane Propulsion Flow-Path Analysis and Code Certification ...................... 104 

S . Naorni McMillin Incipient Leading-Edge Separation ...................... ..................................................................... 1 08 

N . Duane Melson Multiblock. Multigrid Method for the Solution of the Three-Dimensional 

Euler Equations ............... .................................................................................................... 109 

Joseph H . Morrison Multi-Tasked Numerical Simulation of Complex Configurations in Hypersonic Flow ................... 118 

9 . A . Naik Transonic Potential Flow about Transport Aircraft .................... (with ViGYAN Inc., The Boeing Company) 

Ajay K . Pandey Flux-Based Finite-Element Formulation Reduces CPU Time for Thermal-Structural 

Analysis ...................................................................................................................................... 127 

(with Lockheed Engineering and Sciences Co.) 

James L . Pittman Generic National Aero-Space Plane Afterbody ............. ......................................................... 29 

James L . Pittman NASP-TMP Forebody/lnlet Integration ........... .......................................................................... -130 

Ramadas K . Prabhu Finite-Element Analysis of Equilibrium and Nonequilibrium Flows .............................................. 133 

(with Lockheed Engineering & Sciences Co.) 

R . Ramakrishnan An Adaptation Procedure Combining Mesh Refinement with Mesh Movement 

for Compressible Flows .............................................................................................................. 139 

R . Clayton Rogers Hydrogen-Air Combustion Simulation in a Pulse Facility ................. .......................................... 145 

Balu Sekar Direct Simulation of High-speed Mixing Layers With and Without Chemical Heat Release .......... 151 

John V . Shebalin Ionized Flow Around a Reentry Vehicle ....................................................................................... 152 

Craig L . Streett Numerical Simulation of Wave Interactions Related to Transition .................................................. 160 

Craig L . Streett Transition Simulations in Nonhomogeneous Geometries ........................................................... 161 

R . C . Swanson Development of Algorithms for Solving the Three-Dimensional Navier-Stokes Equations ............ 1 66 

Rajiv Thareja computation of Three-Dimensional Flows Using Unstructured Grids ............................................ 172 

Rajiv Thareja Viscous Hypersonic Flow over a 24-Degree Compression Corner ................................. ...... 1 73 

Veer N . Vatsa High Reynolds Number. Transonic. Viscous Flow over Aircraft Components .............................. 177 

Kenneth J . Weilmuenster Winged Entry Vehicle Computations ............................................................................................ 182 

Richard G . Wilmoth Shock Interactions in Rarefied Hypersonic Flows .......................................................................... 185 

(with California Institute of Technology) 

T . A . Zang 

Development of an Euler-Based Method for Turboprop Integration .............................................. 191 

(with The Boeing Company. ViGYAN. Inc.) 

Incompressible Transition to Turbulence ......................... ....................................................... 192 

NASA Lewis Research Center 

William J . Coirier Three-Dimensional ShocWBoundary-Layer Interactions in Hypersonic Inlets ................................. 23 

James D . Heidmann An Analysis of the Viscous Flow through a Compact Radial Turbine by the AveragePassage Approach .................................................................................................................. 68 

Danny Hwang Computational Advanced Propulsion Technology Research .......................... ........................... 77 

199 
John L. Klann Solar Dynamic Space Power-System Design and Performance Analysis ........ ....................... . 80 

(with Analex Corporation) 

S. J. Leib Nonlinear Instability of Shear Layers ..... . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 

(with Sverdrup Technology, Inc.) 

Christopher J. Miller Numerical Simulation of Advanced Propellers . ....... ................... ...................................... 1 16 

(with Sverdrup Technology, Inc.) 

Wolfgang Mueller Electronic Structure of Superconductors . . . . . . . . . . . . . . .. . . . . , , . , , , , , . , . , . , .. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 

(with Analatom, Inc.) 

R. M. Nallasamy Unsteady Flow Field on an Advanced Propeller ................. .... .......... ... ..................... 122 

(with Sverdrup Technology, Inc.) - 

M. S. Raju Analysis of Rotary Engine Processes and Computer Codes ......... .. ........ ................................. ... 138 

(with Sverdrup Technology, Inc.) 

William C. Rose National Aero-Space Plane Inlet Boundary Layer Control, Phase 11 ........................................ 146 

(with Rose Engineering & Research, Inc.) 

Jian-Shun Shuen Advanced Numerical Algorithms for Chemically Reacting Flows.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. .. . . . . . . . . 154 

(with Sverdrup Technology, Inc.) 

B. M. Steinetz National Aero-Space Plane Engine Corner-Flow. .. . . . . . . . . . . . . . . . . . . .. . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 

(with Sverdrup Technology, Inc.) 

NASA Marshall Space Flight Center 

Edwin B. Brewer Direct Simulation of Aerothermal Loads for the Aeroassist Flight Experiment ............................... . 10 

Naval Oceanographic and Atmospheric Research Laboratory 

Harley E. Hurlburt Eddy-Resolving Model of the Pacific Ocean ... .. .. ... .. ....... ....... . .............................. 76 

(with JAYCOR) 

Naval Research Laboratory 

Russell B. Dahlburg Dynamical Modeling of the Solar Atmosphere .............................................................. 26 

Fernando F. Grinstein Simulation of Compressible, Spatially Evolving, Reactive Planar Shear Flows ......... ...................... 54 

Elaine S. Oran Unsteady Diffusion Flames.. . . . .. . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 

(with Berkeley Research Associates) 

Nielsen Engineering & Research, Inc. 

William W. Bower Calculations of Unsteady, Supersonic-Jet Flow Fields and Acoustics.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 

(with McDonnell Douglas Research Laboratories) 

Steven C. Caruso An Unstructured Triangular-Mesh/Navier-Stokes Method for Computing 

the Aerodynamics of Aircraft with Ice Accretion.. .......................... ....................... ............... 16 

Michael R. Mendenhall Vortex-Induced Nonlinearities on Submarines ....... .... .......................................................... 11 1 

David Nixon PegasusTM Aerodynamic Analyses.. . . . . . . . . . .. .. . . . . . .. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 

North Carolina State University 

H. A. Hassan Monte Carlo Simulation of Hypersonic Flows ................................................................... 64

H. A. Hassan Turbulence Modeling of Separated Flows ....................................................................... .... 65 

H. A. Hassan Turbulent Supersonic Mixing Layers .................................................................................. 66 

Scott D. Holland A Computational and Experimental Parametric Study of Three-Dimensional Side- Wall 

Compression Scramjet Inlets at Mach 10 .................................................................................... 70 
Northrop Aircraft Division 

Rung T. Ling Application of Computational Fluid Dynamics Methods to Radar Cross 

Section Computations.. ................................................................................................................ .88 

John Mangus Navier-Stokes Analysis of the Air Force Vortex Flap Model and the F/A-18 .................................... 99 

(with McDonnell Aircraft Company) 

Northwestern University 

Arthur J. Freeman Electronic-Structure Study of High Superconductors ................................................................... 47 C 

Old Dominion University 

C. H. Liu Computational Prediction and Control of Steady and Unsteady Asymmetric Vortex Flows e around Cones ............................................................................................................................. ..89 

(with NASA Langley Research Center) 

The Pennsylvania State University 

George S. Dulikravich Acceleration of Iterative Algorithms for Euler and Navier-Stokes Equations ................................ 35 

Charles L. Merkle Absorption of Microwave Energy in a Flowing Gas .................................................................... 1 15 

QUEST Integrated, Inc. 

Suresh Menon Large-Eddy Simulations of Ramjet Combustion Instability ........................................................ 113 

Suresh Menon Mixing Enhancement for Scramjet Flameholders ........................................................................... 1 14 

Rockwell International, North American Aircraft Division 

Jong H. Wang Navier-Stokes Predictions of Hypersonic Chemically Reacting Flows ........................ ............. 180 

Chung-Jin Woan Computational Fluid Dynamics Design of a Laminar-Flow Control Glove.. ................................ .I86 

Rockwell International, Rocketdyne Division 

S. J. Lin Computational Fluid Dynamics Analysis of Space Shuttle Main Engine Turbopump 

Rotor/Stator Flows in Two and Three Dimensions ....................................................................... .87 

Ruey-Jen Yang Multistage Rotor/Stator Interaction in the Space Shuttle Main Engine Turbopump Turbine. ......... 188 

Rockwell International Science Center 

Sukumar R. Chakravarthy FueYAir Turbulent Combustion in a Three-Dimerisional Combustor Geometry 

in Supersonic Flow.. ...................................................................................................................... 1 7 

Dan F. Dominik Advanced Solid Rocket Motor Study ................................................................................................ 33 

(with Rockwell International, Space Transportation Systems Division) 

Rockwell International, Space Transportation Systems Division 

Dan F. Dominik Advanced Solid Rocket Motor Study ........................ .................................................................. 33 

(Rockwell International. Science Center) 

Rose Engineering & Research, Inc. 

William C. Rose National Aero-Space Plane Inlet Boundary Layer Control, Phase I1 ........................................... 146 

(with NASA Lewis Research Center) 

William C. Rose National Aero-Space Plane Inlet Flow Fields. ............................ .... ................................................. 147 

(with NASA Ames Research Center) P 

William C. Rose Three-Dimensional Viscous Flow in High-speed Inlets.. ............................................................. .I48 

(with NASA Ames Research Center) 

Spectrex Inc. 

R. Balasubramanian Direct Simulation of Large-Eddy Breakup Devices ............................................................................ 6 

Stanford University 

Donald Baganoff Discrete Particle Simulation of Compressible Flow ...................... ................................................. 5 

(with NASA Ames Research Center) 
Dean R. Chapman Continuum Computational Fluid Dynamics for Hypersonic High-Altitude Flight ....... ......... ........ 19 

Professor John K. Eaton The Interaction of Particles with Homogeneous Turbulence ................... ...... .... ............. 36 

Robert W. MacCormack Simulation of Highly Ionized Flows .................... ................................................................. 94 

(with Analatom, Inc.) 

Stanford University School of Medicine 

Dennis Sullivan Microwave Hyperthermia Computer Modeling.. . . . .. . . . .. . . . . . . . .. . . . . , . . . . . . . . . . . . , , . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 

Sverdrup Technology, Inc. 

H. T. Lai Computation of Single-Expansion-Ramp and Scramjet Nozzles ..... ..... ............. .. ......................... 84 . 

S. J. Leib Nonlinear Instability of Shear Layers ..... ....... ............. .............................. ., ,,......... ............... ......... (with NASA Lewis Research Center) 

Christopher J. Miller Numerical Simulation of Advanced Propellers .... . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . .... . . , . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 16 

(with NASA Lewis Research Center) 

R. M. Nallasamy Unsteady Flow Field on an Advanced Propeller ...................................................................... 122 

(with NASA Lewis Research Center) 

M. S. Raju Analysis of Rotary Engine Processes and Computer Codes . .................. . .... ... .... .... .. ................. (with NASA Lewis Research Center) 

Jian-Shun Shuen Advanced Numerical Algorithms for Chemically Reacting Flows ... ................. .. ..... .. ............. 154 

(with NASA Lewis Research Center) 

6. M. Steinetz National Aero-Space Plane Engine Corner-Flow ............................................................... 158 

(with NASA Lewis Research Center) 

United Technologies, Pratt & Whitney 

John J. Erhart CFD Analysis of the Flow Paths of Spherical Convergent Flap Nozzles ...... ... ... .. ........ ... ......... . 43 

Ronald K. Takahashi Unsteady Euler Analysis of the Redistribution of an Inlet Temperature Distortion 

in a Turbine ........................ .......... ..... ....... ..................... . ... . . ....... ... . 169 

United Technologies Research Center 

Roger L. Davis The Impact of Hot-Streak Migration on Turbine Heat Transfer ............................ ... .................... 27 

T. Alan Egolf Advanced CFD Codes for Rotary-Wing Airloads and Performance Prediction ... .... .. ...... ... ......... ... 39 

University of Arizona 

K.-Y. Fung Computational Studies of Compressibility Effects on Dynamic Stall ... .. .. .. .. . . . .. . . . . . .. .. . . . . . .... . . . . . . . . . . . 48 

University of California, Berkeley 

William H. Miller Quantum Mechanical Reactive Scattering ......................................... .... ........ . . . . 1 17 

Andrew Pohorille Vapor-Phase Growth of Crystals in Microgravity ................... ...... .. . . . ... .... .. . . . . 132 

University of California, lrvine - 

S. E. Elghobashi Direct Simulation of Turbulent Reacting Flows ........................ .............................................. 40 

S. E. Elghobashi Dispersion of Solid and Fluid Particles in Turbulent Homogeneous Flows With and 

Without Turbulence Modulation .................................... .... ................................................ 41 

William A. Sirignano Ignition and Flame Spread above Liquid Fuel Pools: Gravity Effects .. ...... ................... .. ............. 155 

University of California, Santa Barbara 

Frank J. Spera Magma Chamber Convection ................................................................................................... 157 

University of Colorado, Boulder 

Karl E. Gustafson Vortex Dynamics in Aerodynamic Flows ................................... ..... ............................. 57 
Kadosa Halasi Parameter Study in the Driven Cavity...............................................................................................58

(with Kansas State University)

University of Evansville

Ben R. Riley Kinetic TheoryModel for the Flow of a Simple Gas from a Three-Dimensional

Axisymmetric Nozzle.................................................................................................................. 142

University of Illinois, Urbana-Champaign

M. B. Salamon Advanced Computational Materials ............................................................................................. 149

Pratap Vanka Hot Gas Ingestion by STOVLAircraft ............................................................................................. 175

.University of Iowa

V. C. Patel Hydrodynamics ofSelf-Propelled Bodies ...................................................................................... 128

(with Iowa Instituteof HydraulicResearch)

University of Michigan

Bram van Leer Calculation of Hypersonic Flows with Strong Surface Blowing ......................................................176

University of Minnesota

Donald G. Truhlar Scattering Theoryand Calculations for Chemical Reactions and Molecular

Energy Transfer.......................................................................................................................... 174

U.S. Army Aeroflightdynamics Directorate---AVSCOM

W. J. McCroskey Aerodynamic Flows about High-Performance Rotor Blade Tips....................................................105

(with NASAAmes Research Center)

W. J. McCroskey Airloads and Acoustics of Rotorcraft ..............................................................................................106

(with NASAAmes Research Center)

Roger C. Strawn Computational Fluid Dynamics Prediction of Advanced Rotor Performance ................................159

(with NASAAmes Research Center)

U.S. Army Missile Command--Redstone Arsenal

Bill J. Walker Tactical Missile Aero-Propulsion Interaction ..................................................................................178

ViGYAN, Inc.

Peter M. Hartwich General, Fast, Accurate Floating Shock Fitting Procedure for Unadapted Meshes ........................62

(with NASALangley Research Center)

Peter M. Hartwich Navier-Stokes Solutions for Vortical Flows over a Forebody ............................................................63

(with NASALangley Research Center)

C.-H. Hsu Prediction of Vortical Flows Using Incompressible Navier-Stokes Equations................................. 72

(with NASALangley Research Center)

D. A. Naik TransonicPotential Flow about TransportAircraft ..........................................................................121

(with NASALangley Research Center, The Boeing Company)

N. J. Yu Development of an Euler-Based Method for Turboprop Integration ..............................................191

(with The Boeing Company, NASA Langley Research Center)

Virginia Polytechnic Institute and State University

,.Robert W. Waiters Development of Unstructured and Nonequilibrium Chemistry Upwind Algorithms

for Hypersonic Flows ..................................................................................................................179.

Vista Research, Inc.

Charles L. Rino Scattering from Ocean Surfaces and Near-Surface Objects ......................................................... 143

Wright Research and Development Center

Gary W. Huband Numerical Simulation of an F-16Aat Angle of Attack ......................................................................74

203

"# U.S. GOVERNMENT PRINTING OFFICE: 1991--588-266
The Navier-Stokes Mach contours 

at transonic speeds about a 

generic high-speed shape 

NASA 

National Aeronautics and 

Space Administration 

Ames Research Center 

Moff ett Field, California 94035-1 000