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CURRENT CAPABILITIES 

AND FUTURE DIRECTIONS 

IN COMPUTATIONAL 

FLUID DYNAMICS 

Committee to Assess Current Capabilities and 

F'uture Directions in Computational Fluid Dynamics 

Aeronautics and Space Engineering Board 

Commission on Engineering and Technical Systems 

National Research Council 

NATIONAL ACADEMY PRESS 

Washington, D.C. 1986 
NOTICE: The project that is the subject of this report was approved by 

the Governing Board of the National Research Council, whose members are 

drawn from the councils of the National Academy of Sciences, the National 

Academy of Engineering, and the Institute of Medicine. The members 

of the committee responsible for the report were chosen for their special 

competences and with regard for appropriate balance. 

This report has been reviewed by a group other than the authors 

according to procedures approved by a Report Review Committee consisting 

of members of the National Academy of Sciences, the National Academy of 

Engineering, and the Institute of Medicine. 

The National Research Council was established by the National 

Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy's purposes of furthering knowledge 

and of advising the federal government. The Council operates in accordance 

with general policies determined by the Academy under the authority of its 

congressional charter of 1863, which establishes the Academy as a private, 

nonprofit, self-governing membership corporation. The Council has become 

the principal operating agency of both the National Academy of Sciences 

and the National Academy of Engineering in the conduct of their services to 

the government, the public, and the scientific and engineering communities. 

It is administered jointly by both Academies and the Institute of Medicine. 

The National Academy of Engineering and the Institute of Medicine were 

established in 1964 and 1970, respectively, under the charter of the National 

Academy of Sciences. 

This study was supported by Contract NASW-4003 between the National Academy of Sciences and the National Aeronautics and Space Administrat ion. 

Copies available from: 

Aeronautics and Space Engineering Board 

National Research Council 

2101 Constitution Avenue, N.W. 

Washington, D.C. 20418 

Printed in the United States of America 

The cover shows the computed pressure field about the space shuttle 

Orbiter at a free stream Mach number of 1.4 and at zero angle-of-attack using 

the thin layer Navier-Stokes equations. The finite difference calculations were 

carried out on the CRAY-XMP using a segmented grid approach. (Numerical 

simulations by Y. Rirk and S. Ben-Schmuel) 

-w-u Y-UX 
COMMITTEE TO ASSESS CURRENT 

CAPABILITIES AND FUTURE DIRECTIONS OF 

COMPUTATIONAL FLUID DYNAMICS 

RICHARD G . BRADLEY, Chairman, Director, Aerospace Technology, 

General Dynamics Corporation 

DEAN R. CHAPMAN, Professor, Departments of Aeronautics/ 

Astronautics and Mechanical Engineering, Stanford University 

WILLIAM H . HEISER, Vice President/Director, Aerojet Propulsion 

Research Institute 

JOHN L. LUMLEY, Professor, Sibley School of Mechanical and 

Aerospace Engineering, Cornel1 University 

ROBERT W . MacCORMACK, Professor, Department of Aeronautics 

and Astronautics, Stanford University 

ROBERT E. MELNIK, Director of Fluid Mechanics, Grumman 

Corporation 

WILLIAM C . REYNOLDS, Professor, Department of Mechanical 

Engineering, Stanford University 

PAUL E. RUBBERT, Aerodynamics Technology Staff, Boeing Military 

Airplane Company 

MICHAEL J . WERLE, Manager of Gas Dynamics and Thermophysics, 

United Technologies Research Center 

DAVID L. WHITFIELD, Professor, Department of Aerospace 

Engineering, Mississippi State University 

LIAISON REPRESENTATIVES 

JAY P. BORIS, Director, Laboratory for Computational Physics, Naval 

JOSEPH SHANG, Technical Manager, Com.putationa1 Aerodynamics, 

Research Laboratory 

Air Force Wright Aeronautical Laboratories, Wright-Patterson Air 

Force Base 

PETER M. SOCKOL, Assistant Chief, Computational Methods Branch, 

NASA Lewis Research Center 

JERRY C. SOUTH, JR., Chief Scientist, NASA Langley Research 

Center 

JOSEPH STEGER, Senior Staff Scientist, NASA Ames Research Center 

... 

111 
NASA REPRESENTATIVES 

RANDOLPH A. GRAVES, JR., Office of Aeronautics and Space 

LEWIS L. PEACH, JR., Office of Aeronautics and Space Technology, 

Technology, NASA Headquarters 

NASA Headquarters 

STAFF 

ROBERT H. KORKEGI, Study Director 

JoANN CLAYTON, Assistant Study Director 

ANNA L. FARRAR, Administrative Assistant 

iv 

L 
AERONAUTICS AND SPACE 

ENGINEERING BOARD 

JOSEPH F . SHEA, Chairman, Senior Vice President, Engineering, 

JAMES J . KRAMER, Vice Chairman, Manager, Advanced Technology 

MAX E. BLECK, Assistant to the President, Beech Aircraft 

BERNARD BUDIANSKY, Professor of Structural Mechanics, Harvard 

W. BOWMAN CUTTER 111, Partner, Coopers & Lybrand 

R. RICHARD HEPPE, President, Lockheed-California Company 

RICHARD W . HESSELBACHER, Manager, Advanced Development and 

KENNETH F. HOLTBY, Senior Vice President, The Boeing Company 

PETER W. LIKINS, President, Lehigh University 

DONALD J. LLOYD- JONES, President and Chief Operating Officer, 

STEPHEN F. LUNDSTROM, Vice President and Program Director, 

ARTUR MAGER, Consultant, Los Angeles, California 

STANLEY MARTIN, JR., Vice President-V-22 Engineering, Bell 

JOHN L. McLUCAS, Consultant, Alexandria, Virginia 

IRWIN MENDELSON, President, Engineering Division, Pratt & 

JAN ROSKAM, Ackers Distinguished Professor of Aerospace 

ROGER D. SCHAUFELE, Vice President, Engineering, Douglas 

RICHARD S . SHEVELL, Professor, Department of Aeronautics and 

ROBERT E. SKELTON, Professor of Aeronautical Engineering, Purdue 

ALTON D. SLAY, Slay Enterprises, McLean, Virginia 

MORRIS A. STEINBERG, Consultant, Los Angeles, California 

LAURENCE R. YOUNG, Professor of Aeronautics and Astronautics, 

Raytheon Company 

Programs, General Electric Company 

Corporation 

University 

Information Systems, General Electric Company 

Western Airlines 

MCC 

Helicopter Textron 

Whitney Aircraft Group 

Engineering, University of Kansas 

Aircraft Company 

Astronautics, Stanford University 

University 

Massachusetts Institute of Technology 

V 
EX OFFICIO MEMBERS 

JOHN W. TOWNSEND, JR., Senior Vice President, Operations and 

THOMAS M. DONAHUE, Department of Atmospheric and Ocean 

Planning, Fairchild Industries, Inc. 

Sciences, University of Michigan 

STAFF 

ROBERT H. KORKEGI, Director 

JoANN C. CLAYTON, Senior Program Officer 

BERNARD MAGGIN, Senior Program Officer 

ANNA L. FARRAR, Administrative Assistant 

LAURA D'SA, Administrative Secretary 

REGINA D. MILLER, Senior Secretary 

vi 
Contents 

1. SUMMARY OF SIGNIFICANT FINDINGS AND 

RECOMMENDATIONS 

Findings, 1 

External Aerodynamics, 1 

Hypersonics, 3 

Propulsion, 3 

Turbulence, 4 

Recommendations, 5 

2. INTRODUCTION 8 

3. APPROACH 11 

Survey of CFD Codes and Their Capabilities, 12 

Survey of the National Level of Effort in CFD, 13 

Overview, 17 

CFD Capabilities in External Aerodynamics, 18 

4. EXTERNAL AERODYNAMICS APPLICATIONS OF CFD 17 

Capabilities for Steady Aerodynamic Flows, 20 

Capabilities for Unsteady Aerodynamic Flows, 28 

Findings, 31 

Recommendations, 34 

Overview, 35 

Departures from Conventional Aircraft CFD, 37 

CFD Capabilities in Hypersonics: Upper and Lower 

Atmosphere, 39 

Current Status of Hypersonic CFD, 40 

Findings, 44 

Recommendations, 45 

5. HYPERSONIC APPLICATIONS OF CFD 

6. PROPULSION APPLICATIONS OF CFD 

1 

35 

47 

vii 
Overview, 47 

Detailed Design of Components, 48 

Development of Insight and Understanding, 49 

Possibility for Revolutionary Change, 50 

Stationary Systems, 52 

Rotating Systems, 53 

Combustors, 55 

Stationary Systems, 59 

Rotating Systems, 59 

Combustors, 60 

Aerodynamic Coupling, 60 

CFD Capabilities in Propulsion, 51 

Findings, 57 

Recommendations , 61 

Overview, 63 

Turbulence-Averaged Navier-Stokes Equations , 65 

Capabilities of Turbulence Models and Simulation, 66 

7. TURBULENCE IN CFD 

Local Algebraic Models, 67 

Scale Evolution Models, 68 

Transport Evolution Models, 70 

Probability Density Function Models, 72 

Spectral Interaction Models, 73 

Turbulence Simulations, 74 

Emerging Ideas, 76 

Current Status of Turbulence Modeling, 77 

Findings, 78 

Recommendations, 79 

APPENDIXES 

Trends in Computer Hardware Affecting CFD, 83 

Level of Effort Questionnaire, 92 

List of Contributors to CFD Capabilities Questionnaire, 95 

A. 

B. CFD Capabilities Questionnaire, 86 

C. 

D. 

... 

Vlll 

63 
TABLES AND FIGURES 

CHAPTER 3 

Figure 1. The CFD Development Cycle 

Figure 2. Breakdown of Resources Applied to,CFD 

CHAPTER 4 

Table 1. Status of CFD for External Aerodynamic Applications 

CHAPTER 5 

Table 2. Contrasts within Hypersonic CFD 

Table 3. Status of CFD Capability-Hypersonic 

Lower Atmosphere 

Table 4. Status of CFD Capability-Hypersonic Upper 

Atmosphere 

CHAPTER 6 

Table 5. Status of CFD for Propulsion Applications 

CHAPTER 7 

Table 6. Status of Turbulence Modeling 

12 

15 

21 

41 

42 

43 

52 

78 
i 

Summary of Significant 

Findings and Recommendations 

A summary of significant findings is given below, followed 

by specific recommendations for future directions of emphasis for 

computational fluid dynamics (CFD) development. The discussion 

is organized into three application areas-external aerodynamics, 

hypersonics, and propulsion-and followed by a turbulence modeling synopsis. 

FINDINGS 

External Aerodynamics 

The aerospace industry has come to realize that CFD offers 

great potential as a design tool. In the commercial transport 

industry, where the aerodynamics encountered over much of the 

flight envelope represents attached flows and is well understood, 

CFD plays an integral part in the design process. In contrast, 

the design of high-performance military aircraft is usually dominated by more complex flow phenomena, not yet fully amenable to 

CFD analysis, with the result that CFD has had a lesser impact. 

However, this is changing rapidly. 

CFD methods today can simulate flows about complex geometries with simple physics, or about simple geometries with more 

complex physics. They cannot do both. The most pressing need 

today is for algorithm technology that will lead to practical methods for solving the nonlinear flow equations-full-potential, Euler , 

1 
2 

and the various forms of Navier-Stokes equations-about arbitrary and often complex geometries with reliable and predictable 

accuracy. 

For steady aerodynamic flows, only the linear methods based 

on solutions to the Prandtl-Glauert equations have been developed to a mature state in that they provide capability for solving 

the flow about arbitrary and general configurations. Solution algorithms for the full-potential and Euler equations are reaching 

maturity for simple flows but remain low in the development cycle 

for flows of increasing complexity. Simulation capability for the 3- 

dimensional (3-D) Navier-Stokes equations remains in a relatively 

primitive state although realization of the potential is providing 

impetus for increasing activity by the aerospace community. 

CFD methods for unsteady aerodynamic flows have received 

far less attention than those for steady flows. Progress has been 

made in developing algorithms for the inviscid equations for relatively simple geometries. Some work has focused on coupling 

unsteady inviscid codes with steady boundary-layer and on unsteady 2-dimensional (2-D) Navier-Stokes codes. However, the 

viscous unsteady CFD technology is in its infancy. 

Although today’s algorithms for the Euler and Naw’er-Stokes 

equations are more accurate and robust than those of yesterday, 

they are still unsatisfactory in many respects. Major improvements 

are needed in spatial accuracy and solution adaptability, convergence reliability, and convergence rates. Worthwhile codes have 

been produced, but further improvements in algorithm technology 

could multiply their usefulness many times over. Turbulence modeling will become a major issue for Navier-Stokes solvers, but with 

today’s algorithms the various errors associated with numerics are 

probably a larger issue in need of resolution. When those sources 

of error are resolved, then turbulence modeling will become the 

limiting factor. 

There are other areas that should not be neglected. Needs 

and opportunities exist throughout the spectrum of CFD; codes 

solving linear flows, the boundary-layer equations, full-potential 

equations, and Euler and Navier-Stokes equations all will have a 

role to play in the aircraft industry for the foreseeable future. 

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3 

Hypersonics 

I-- Hypersonic GI'U spans a wide range in complexity dependent 

mainly on flight altitude. In the lower atmosphere, air chemistry is in thermodynamic equilibrium, the flow is transitional and 

turbulent, and the corresponding CFD codes are only a modest extension of those for conventional aircraft. In the upper atmosphere, 

nonequilibrium air chemistry prevails and the flow is mainly laminar. The corresponding CFD codes are much more complex and in 

a more primitive state of development due to numerous additional 

molecular physics processes that must be considered. 

The simulation of hypersonic flow fields undergoing nonequiZibrium chemistry requires that vehicle scale be simulated as well 

as flight velocity and altitude. Because this is not possible in existing ground-based experimental facilities, the applications and the 

importance of CFD to hypersonic vehicle design is much greater 

than for conventional aircraft design. For flight in the upper atmosphere, CFD is expected to be the principal source of flow 

simulation information for vehicle design, and flight test is necessary for accurate validation of the computational codes. 

Propulsion 

Computational fluid dynamics is used extensively throughout the propulsion community because of a lack of alternatives 

for achieving insight into the basic controlling mechanisms of the 

complicated, highly coupled interacting aspects of propulsion fluid 

dynamics. It has proven a valuable design analysis tool in a wide 

variety of situations, often more than expected. Use of CFD is 

growing rapidly largely because of its ability to provide detailed 

diagnostic data and to address more complex flows. One of the 

principal challenges now being faced is to provide a way for this 

powerful but costly capability to contribute directly to the formal design of complicated, strongly coupled propulsion system 

components. 

In general, propulsion CFD is in a relatively mature state for 

2-D potential flows with capability dropping off systematically for 

increased levels of complexity. This can be better summarized in 

tern:s of the three major elements of propulsion devices: stationary systems, rotating systems, and combustors. For stationary 

systems, CFD technology is in a relatively mature state for 2-D 
4 

configurations, with a rapid drop in capability for 3-D or unsteady 

flows. For rotating systems, capability naturally lags behind the 

stationary counterpart at all levels-most seriously in the area of 

viscous flow modeling. Combustors, inherently more complicated, 

show the lowest level of CFD development. 

The strong aerodynamic coupling of the major components of 

propulsion systems is another important issue. Examples of this 

include the influence of inlet distortion on engine performance, 

stability, noise, and durability of the fan; and the impact of burner 

exit temperature profiles on turbine life and stagnation (nonrecoverable) stall. With the advent of larger capacity parallel processing 

computers, it may soon be possible to model interacting components. 

The area of hypersonic propulsion systems should be highlighted because of interest in advanced engines for hypersonic and 

transatmospheric vehicles. The flow conditions in these machines 

are so demanding that in many cases they cannot be reproduced in 

existing facilities. Even though existing codes have inadequaies in 

turbulence and chemistry modeling, they offer the only available 

capability and will carry an unusually large share of the design 

burden. 

There is a need for benchmark ezperiments to provide detailed 

data bases against which codes can be calibrated to assist and 

guide the development, especially with respect to turbulence modeling and hypersonic propulsion systems. Diagnostic ezpetimental 

studies are needed to provide detailed data to allow identification of the dominant physics, thus providing critically needed 

insight for establishing and validating appropriate levels of analytical modeling. 

Turbulence 

In complex engineering flows where strong viscous effects dominate, turbulence modeling, including modeling of the laminarturbulent transition, is becoming a pacing technology. Present 

turbulence models are adequate only for use in relatively simple 

flows, and do poorly in flows with strong 3-dimensionality, massive separation, large-scale unsteadiness, strong density gradients, 

strong rotation, and chemical reaction. Large eddy simulations 

(LES) have not yet been developed for boundary conditions, geometries, and Mach numbers of practical interest. It is important 
5 

to develop LES for use in critical portions of complex turbulent 

plied to a full aircraft flow. Full turbulence simulations (FTS) (all 

scales) will be limited to simple flows at relatively low Reynolds 

numbers. While useful in fundamental studies of turbulence, the 

FTS limitations are such that they are not likely to find much 

use in engineering applications in the foreseeable future. Hence, 

some form of turbulence modeling, and modeling of transition, is 

expected to remain an essential element for engineering CFD. 

It is in the most complicated flows, where intuition fails and 

basic experiments are missing, that the turbulence models perform 

most poorly. With the advent of effective methods for solving the 

flow equations, the inadequacies of turbulence modeling may become the pacing item in the future application of CFD to practical 

vehicle design. 

The other items pacing the development of engineering CFD 

are more amenable to rapid advance, as has already been shown in 

the case of grid generation, algorithms, and hardware. Solving the 

turbulence problem is a tough, long-standing issue of growing importance that will require sustained attention by many interacting, 

highly competent groups. 

The current level of effort in the development of better turbulence model8 is limited. The advent of FTS as a tool for gathering data about turbulent flows, advances in the methodology of 

rational structuring of models, and new experimental techniques 

offers promise for more rapid advances in turbulence modeling. 

bUt it be time, if befGie LTPS is 

RECOMMENDATIONS 

The ultimate goal for CFD is the development of a fully mature capability that is user-friendly, cost-effective, and fully verified 

by detailed experimental comparison. The committee feels that 

order-of-magnitude improvements are possible and should be aggressively sought. In this context the following recommendations 

are made 89 a guide for future directions in CFD. 

Algorithm Technology 

Stronger emphasis is needed on the development of more advanced algorithm technology, particularly for the Euler equations 

and the various forms of the turbulence-averaged Navier-Stokes 

equations. Four objectives are recommended. 
6 

f; 

1. Advances to enable computation offtows about complex 

geometries in a manner that is practical and accurate. Such technology must include means for resolving phenomena that occur at 

the differing length scales found in nonlinear flows such as thin 

boundary layers, shock waves, free shear layers, exhaust plumes, 

and regions of separated flow. Focus should be given to developing 

smart difference schemes, including adaptive grids, to achieve the 

required balance. 

2. Major improvements in spatial accuracy, convergence reliability, and convergence rates. Reduction of numerical diffusion, 

artificial dissipation, and smoothing procedures is needed. Most 

large codes are saddled with “knobs” that are empirically set to 

obtain the best balance between accuracy and convergence. Major 

advances in these areas are mandatory before CFD can be relied upon widely for design applications throughout the aerospace 

community. 

3. Verification offlow models and algorithms. General accep 

tance of CFD as an established design tool can only be predicated 

on confidence gained from comparison with detailed experimental 

data to validate the numerical model used to simulate the flow 

physics. 

4. Analytical and computational modeling of aeroelastic loadings on aircraft lifting components, blades, and propellers. CFD 

methods should be extended to model structural aeroelastic coupling. 

Turbulence Simulation and Modeling 

For developments in turbulence modeling to keep pace with 

the other item limiting the effectiveness of engineering CFD, the 

level of effort in turbulence modeling and simulation should be 

increased in a coordinated way. New opportunities for study and 

research in turbulence modeling and simulation and coordination 

among experts are needed. Three objectives are recommended. 

1. Turbulence/traneition modeling for use in the turbulenceaveraged Navier-Stokes computations. While significant and rapid 

progress is being made in most other related areas, little work is 

being focused on this item. Work is needed in development of new 

turbulence models both time-averaged and time-resolved, focusing 

on freestream disturbance effects (e.g., unsteadiness, turbulence, 

and vorticity), transition prediction, and compressible flows. 

t L i 

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7 

2. Continued emphaeie on large eddy and full turbulence aimt!~t:'mo". While the si~.c!atians ~-37 ??ever be develnped to a level 

necessary for routine design application, they may be able to provide a critical data base for fundamental understanding and a 

framework for developing practical turbulence models for use in 

solving the turbulence-averaged Navier-Stokes equations. In addition, these simulations have the potential to solve certain very 

difficult portions of practical flows. 

3. Generation of benchmark and diagnostic ezperimental data 

base8 at a time-resolwed level. Benchmark experimentation combined with the LES/FTS numerical experimentation will aid in 

developing and verifying new turbulence and transition models; 

this is especially needed in the propulsion area. 

Hypersonic Directions 

The emerging importance of CFD as a tool for hypersonic 

system design and analysis has opened new areas of uncertainty, 

especially in the upper atmosphere where nonequilibrium chemistry and transition play dominant roles. Specific emphasis is 

recommended in five areas. 

1. Continuum equation8 of motion. Some inaccuracies in the 

conventional Navier-Stokes equations for hypersonic flow conditions need to be mended and new physics added to the continuum 

equations of motion if they are to integrate accurately through 

shock waves in the upper atmosphere. 

2. Molecular phyeice data baee. Extensive physical data required as inputs for hypersonic CFD codes are needed on chemical 

reaction rates, excitation rates, gas-surface reactions, and transport properties at high temperature. 

3. Transition and turbulence. These problem areas can have a 

major impact on aerodynamic heating and payload weight. 

4. Numerical methode. Algorithms with improved computational efficiency for both continuum and particulate flow simulations are needed to reduce the computer time required to simulate 

flows with important chemical nonequilibrium effects. 

5. Flight teete. Appropriately instrumented flight tests are 

necessary to validate computational codes for hypersonic flight in 

the upper atmosphere due to the inability of gound-based experimental facilities to simulate properly chemical nonequilibrium. 
2 

Introduction 

In recent years national attention has become focused on the 

development of a national computational fluid dynamics (CFD) 

capability.* Significant advances in numerical algorithms, processing speed, and storage capacity of new generations of computers 

prompted the present study to assess the current capability and 

future directions for CFD. 

The study was requested and supported by the Office of Aeronautics and Space Technology of the National Aeronautics and 

Space Administration (NASA) and was undertaken by an ad hoc 

committee of the National Research Council's Aeronautics and 

Space Engineering Board. The committee's membership represented a broad base of expertise in the development and application of CFD capabilities in internal flow and external flow across 

the Mach number range from subsonic to hypersonic flow as well 

as expertise in turbulence modeling. 

The specific charge to the committee follows: 

Computational fluid dynamics (CFD) is becoming an 

increasingly powerful tool in the aerodynamic design of 

aerospace systems as a result of improvements in numerical algorithms as well as in the processing speed and 

* CFD provides the numerical solution of partial differential equations or 

integral equations covering fluid flow. For the purpose of this report, the 

nomenclature of computational fluid dynamics (CFD) is used to broadly cover 

the computation of fluid flows about or within bodies regardless of solution 

method and must be understood to encompass a range of related areas 

such as combustion, rarified gas dynamics, computational aerodynamics, and 

computational aerothermodynamics. 

a 
9 

storage capacity of new generations of computers. As 

the next generation of supercomputers becomes available 

much current CFD work may be expanded to address 

more complex configurations, geometries, flight regimes, 

flow fields, and applications, while some of the existing 

work will become components of more complex systems of 

solutions to problems of modeling, code generation, flow 

field solvers, and flow visualization. Thus, adaptations 

and extensions of current work are expected to provide 

part of the foundation upon which the next level of CFD 

development will advance. 

These advances in CFD as an aerospace-system design tool are proceeding at such a rapid pace that their 

full capability is not widely known by the aerospace community. This study will address the current state of the 

art in computational codes and supporting software for 

aerodynamic and aerothermodynamic applications for: 

0 external and internal flows, 

0 all speed regimes, and 

0 basic and applied research and development. 

The committee will identify sources for unclassified 

CFD codes from government research laboratories, industry, and academia and will develop the fundamental assumptions and technical approach necessary to categorize 

codes by: 

0 application (configuration/geometry), 

0 level of approximation, and flow 

0 complexity. 

Limitations or restrictions of specific codes or categories of codes should be identified, and software architecture should be specified as it relates to compatibility 

of various computer architectures. 

The committee will assess the current status of CFD, 

identify any areas requiring a change in emphasis, and 

make recommendations regarding future directions and 

needs. 

The approach used by the committee in addressing its charge 

is discussed in Chapter 3. 
10 

While the committee's charter did not include an evaluation 

of current or future developments in computer hardware, the close 

relationship between CFD capability and hardware is recognized. 

Appendix A contains some comments on expected trends in supercomputer evolution as a supplement to the study. 

Members of the committee wish to express their gratitude 

to the individuals who served aa liaison representatives for their 

organizations and who worked with the committee in developing 

the report, often making important contributions requiring considerable time and expertise. We also would like to thank their 

organizations for making their services available to us. These individuals are identified on page iii, along with the committee membership. We would especially like to acknowledge the valuable 

assistance of I. C. Bhateley of General Dynamics, who provided a 

LOTUS data base and statistical analysis of the CFD Capability 

Survey responses. Last, thanks are due to those who contributed 

to the Level of Effort Survey and to those who responded to the 

CFD Capability Survey with specific code information. A list of 

contributors appears in Appendix D. 

li' ' 

z 

'L' 

L 

-'II 

E 
3 

Approach 

The committee held three 2-day meetings as follows: July 2-3, 

1985, at NASA Ames Research Center, Moffett Field, California; 

August 27-28, 1985, at the University of Texas, Arlington, Texas; 

and February 17-18, 1986, at the Fort Worth Division of General 

Dynamics, Fort Worth, Texas. In addition, a caucus of subgroup 

leaders was held on January 9, 1986, in conjunction with the 

American Institute of Aeronautics and Astronautics Aerospace 

Sciences Meeting in Reno, Nevada. 

To assure equivalent coverage of important CFD application 

areas, the committee was divided into four subgroups in the following areas: external aerodynamics, hypersonics, propulsion, and 

turbulence. Chapters bearing these headings represent the consensus of the committee. 

To provide a quantitative measure of current capabilities in 

CFD, the committee adopted a numerical scale based on position 

in the CFD development cycle. This cycle is depicted graphically 

in Figure 1. This grading system is used within subsequent chap 

ters of this report to arrive at overall approximate evaluations of 

CFD capabilities. Thus, in the chapters on external aerodynamics, hypersonics, propulsion, and turbulence a grade of 1 represents 

Phase I of the development cycle where the basic elements of the 

enabling technology are formulated and a grade of 5 signifies a 

fully mature capability for dependable, cost-effective design applications, i.e., Phase V in the development cycle. Grades 2, 3, and 

4, then, correspond to Phases 11, 111, and IV, respectively. 

Two surveys were conducted during the course of the study. 

One solicited an evaluation of current CFD capability from a 

11 
12 

Ill IV V 

Mature Demonstration, Putting it Learning 

All Together to use Capability Enabling Technology Effectively 

4 

Most Analysis Some 

Sclentific Limited Pioneering Done Wlthout Level 

Papers Appltcat!ons Supporting of 

0 Know-How Subject to Surprise Experimental Payoff 

Potential for 

Applications 

Phase I: Enabling Technology Produced 

Phase II: 

Understood 

Phase 111: 

Phase IV: Changes the Engineering Process 

Value Exceeds Expectations 

User Groups Acquire New Skills 

Capabilities and Limitations of Technology 

Two Approaches: (A) Major Commitment 

(8) Gradual Evolution 

Phase V: Entrenched, Cost Effective 

FIGURE 1 The CFD Development Cycle. 

wide selection of known workers in the field. The other solicited 

assessments of the current level of effort for fundamental work 

in CFD and turbulence from government agencies known to be 

sponsoring such work. The surveys are described below. 

SURVEY OF CFD CODES 

AND THEIR CAPABILITIES 

To provide a grassroots assessment of U.S. capabilities in CFD 

a nationwide survey was conducted. The four-page survey format, 

reproduced in Appendix B, solicited information on the category 

of code application, governing equations solved, usability of the 

code, believability of the resultant solutions, and the code’s place 

on the CFD Development Cycle as described above. While it 

is recognized that significant CFD work is being accomplished 

outside the United States, the survey was restricted to work within 

the nation in order to place some reasonable bounds on the scope 

of the study. 

The purpose of the survey was twofold: (1) to provide the 

sponsoring agency, NASA, with a data base of current capability 

in the CFD field for use in planning activities, and (2) to provide 

the committee with a source of statistical information. F’rom the 

\ 

r 

L 
13 

outset it was acknowledged that responses to many of the surprovided a valuable stimulant to the committee's deliberations. 

Survey forms were mailed to 244 individuals known to be 

active in the development and application of CFD methods, and 

information was received regarding 259 codes from 142 sources. Of 

the responses, 139 represented seven government agencies, 84 rep 

resented 21 industrial or specialty companies, and 19 represented 

14 universities. All responses that were received in the requested 

format were tabulated into a LOTUS spread-sheet format by I. C. 

Bhateley, who then provided the committee with summary data. 

All of the survey data were supplied to each committee member along with the summary in spread-sheet form. The data 

were used by the committee throughout its deliberations and contributed to the development of the quantitative evaluations of the 

Status of CFD and Turbulence Modeling provided in tables in the 

report. It was the opinion of the committee that publication of 

the survey responses in detail was not justified for several reasons. 

1. The data are too massive to permit practical publication. 

2. Many of the inputs were repetitive in that the codes were 

the same or were variations of the same basic code. 

3. In some cases the information furnished was not sufficiently 

well defined to substantiate the claimed capability. 

Nevertheless, the survey results were extremely valuable when 

weighted with the individual committee member's knowledge and 

judgment. In addition, the entire survey has been supplied to 

NASA for possible compilation into a list of codes available within 

the United States. The large number of responses gives evidence 

of the high degree of interest in the field. 

veji qiiestisna ...-.. WUUIU 1A L- UG mu"JGLt*rG. ".I.:-" :.... Nevzrthe!ess, the respcnses 

SURVEY OF THE NATIONAL 

LEVEL OF EFFORT IN CFD 

The survey of the level of effort being devoted to developing 

CFD methods and turbulence modeling was limited to a selected 

list of government agencies that were known to be sponsoring 

research in CFD. The intent of the survey was not to determine 

the total resources directed toward CFD work but, rather, to 

obtain a representative sample of research activity from sponsoring 

government agencies. The committee believed that such data from 
14 

some of the major sponsors of CFD research would provide an 

indication of the principal focus in the field. 

The form developed for this survey is reproduced in Appendix 

C along with the specific instructions that accompanied the form. 

Responses were received from the Air Force Office of Scientific 

Research, Air Force Wright Aeronautical Laboratories, Office of 

Naval Research, Naval Research Laboratory, NASA, and the Army 

Research Office. The survey was not sent to industry or universities although the responses include some work contracted to 

industry and universities. The responses received represent an effort of about 531 equivalent person years, and are considered to 

be a representative sample of effort in the field. 

For the purpose of analysis, the data were generalized into five 

specific areas of activity. These areas consist of applications, fundamental development, experimental verification, physical modeling, and turbulence simulation. 

A summary of the results of the survey appears in Figure 

2. It shows the greatest effort, 34 percent, is directed toward 

applications of existing CFD codes. Fundamental development 

and experimental verification occupy a respectable amount of the 

total resources. It can be seen that a relatively small effort, 11 

percent, is being put forth in the area of physical modeling and 

only 5 percent in the area of turbulence simulation. The physical 

modeling category is further broken down to illustrate that about 

4 percent of the total CFD effort is directed toward turbulence 

model development. 

In interpreting the survey results, it should be noted that all 

categories of effort represent important building blocks and are 

essential for developing a fully verified national CFD capability. 

Current needs are seen in fundamental algorithm development 

to provide solution and grid generation capability. Efficient algorithms are required for both viscous and inviscid flows over 

complex geometries. Detailed experimental verification is key for 

providing the level of confidence necessary for design applications. 

All of these are discussed further in the following chapter. 

AB basic algorithm development continues to mature, it ap 

pears inevitable that greater importance will be placed on accurate 

turbulence modeling and simulation, especially for flows that are 

dominated by viscous phenomena. However, the level of effort in 

these areas, as shown by the survey samples, is low. Turbulence 
15 

40 

30 

20 

10 

0 

- 

- 34 

Demonstrations 

and 

Applications 

Development 

- 

Total Resources Surveyed: 

Responding Agencies' 

531 Equivalent Person Years 

NASA, AFOSR, ARO, AFWAL, ONR 

29 

Fundamental 

Development 

21 

Experimental 

Verification 

Modeling 

Other 7 ------ 

Turbulence ~.~~~~~ne 

4 ti 

ACTIVITY CATEGORY DEFINITIONS 

DEMONSTRATIONS AND 

APPLICATIONS DEVELOPMENT 

- Code execution for evaluation and verification of codes 

and models for specific application to physical flows. 

Includes testing of basic concepti and iimulation 

methodology, providing predictive analysii capability, and 

initial iupport in diiieminating codei to the user 

community. 

FUNDAMENTAL DEVELOPMENT- Development of algorithms, grid generaton, diagnostics or 

display software for potential flow, Euler, and 

Navier-Stokes iolven. Includes numerical analysis, 

atability and convergence analytis and ruearch codes 

applying new techniques. 

EXPERIMENTAL VERIFICATION - Bmeline canonical or complex experiments designed to 

guide, calibrate, and/or evaluate models and codes. 

Include. both laboratory experiments and computer 

experiments for eddy simulation and "benchmark" exeriments 

to gather detailed surface and flow field quantities. 

PHYSICAL MODELING - Physical model development including generalization of 

existing models, new ideu for model formulation, 

distillation of simple models from complex onea, and 

fabrication of ipccial models for iimple cues. Includes 

modeling of turbulence, heat transfer, chemical reactions, 

transition. mixing, name-holding, and flow itability. 

TURBULENT SIMULATION - Development of algorithm, grid generaton, diagnostics or 

display software for Large Eddy Simulation/Full Turbulence 

Simulation for time-dependent three-dimensional eddy 

iimulation. 

FIGURE 2 Breakdown of Resources Applied to CFD. 
16 

simulation work is almost exclusively directed toward incompressible flows. Compressible turbulence modeling and simulation is 

required for most flows of interest. Of perhaps even more concern 

is the small number of workers known to be skilled in turbulence 

simulation. This subject is discussed in greater detail in the chapter on turbulence modeling. 

In summary, the committee found the information gleaned 

from both surveys useful and stimulating in its deliberations and 

greatly appreciates the input it received from the U.S. CFD community. 

I 

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External Aerodynamics 

Applications of CFD 

OVERVIEW 

External aerodynamics encompasses a host of opportunities 

and needs for the application of CFD. Geometrical shapes of interest range from simple 2-D airfoils to complete 3-D airplanes 

involving not only the major components of wing, body, and tail 

but also the presence of propulsion systems, fillets and fairings, 

flap track fairings, vortex generators, slotted leading and trailing 

edge flaps, antennas, cavities, bleed holes and ports, and surface 

excrescences. The dominant fluid physics can range from simple 

incompressible inviscid flow to the most complex, unsteady, turbulent flow. The insights sought from CFD can range from prediction 

of steady-state force coefficients to detailed revelation of complex 

fluid dynamic phenomena. 

Airplanes must perform and be demonstrated throughout a 

flight envelope. Within that envelope the flow about a typical airplane component can change from simple, low-speed attached flow 

to the most complex, separated, and unsteady behavior. Current 

CFD methods have only demonstrated an ability to simulate flows 

about complex geometries with simple physics or about simple 

geometries with more complex physics. In general, they cannot 

simulate flows about complex geometries with complex physics. 

Hence, one finds both CFD and experimental simulation facilities 

being used, in complementary ways, in the airplane design and 

verification process, with each being used for those things that it 

does best. 

17 
18 

In the world of commercial transport aircraft development, 

the aerodynamics encountered over a large portion of the flight 

envelope are smooth, attached, and well understood. Such aerodynamics have become increasingly amenable to CFD in recent 

years with the result that it has come to play an integral role in 

the design process for modern transport aircraft. 

In contrast, the design of high-performance military aircraft is 

usually dominated by more complex flow phenomena over much of 

the flight envelope. These flows have not been amenable to CFD 

in the past, with the result that CFD has had a lesser impact 

on high-performance military aircraft. However, that situation is 

rapidly changing. Computer developments and algorithm technology have reached the point where CFD can begin to contribute 

to the understanding and prediction of more complex flows, and 

those companies engaged in the military airplane business are becoming increasingly aggressive in the development and pioneering 

applications of CFD. 

The high level of interest in hypersonic and transatmospheric 

vehicles within the United States is propelling the development 

of CFD for those applications. Hypersonic vehicle geometries are 

frequently less complex, allowing surface-fitted grid methodology 

to be effective in computational analysis. The flow is usually 

strongly hyperbolic in character, which means that in the case of 

equilibrium chemistry, iterative solution processes may converge 

in relatively few iterations. There is a dearth of experimental 

facilities capable of reproducing certain hypersonic flows because 

of severe physical requirements-full pressure and enthalpy simulation. Thus, CFD methods for hypersonic flows, including the 

effects of finite rate fluid chemistry are being aggressively developed. Chapter 5 of this report addresses in greater depth activities 

within the hypersonic area. 

CFD CAPABILITIES 

IN EXTERNAL AERODYNAMICS 

A CFD capability is comprised of many factors. No single 

code can reproduce all the physical phenomena. It is typical to 

find that a given code, for a given application, can simulate certain 

features well and other features not so well. One cannot in general 

make a categorical statement concerning whether a code can in 
19 

fact simulate a given flow. It depends entirely upon what one seeks 

to learn about a flow. 

Perhaps the easiest feature to compute for many flows and 

codes is the overall lift. Lift is the result of an integration of forces 

exerted on a configuration by the fluid. The affect of viscosity 

for attached flows is usually small and small local errors in the 

computation have only minor effects on computed lift. Moments 

are usually somewhat more difficult to calculate accurately because 

they can be more sensitive to small errors in local pressure. 

Surface pressure distributions are the most common feature 

typically displayed as the output of a CFD code, and it is common 

to make an overall judgment of a code based on the perceived 

accuracy of calculated surface pressures. However, such an assessment may fall short of revealing a code’s true strengths and 

weaknesses. Accurate surface pressures are indicative of a code’s 

ability to predict lift and moment, but usually do not provide 

an insight into a code’s ability to produce accurate drag. Drag 

is an aerodynamic parameter of major importance for all flight 

vehicles and is strongly dependent on viscous effects. Huge sums 

are expended by aerospace companies in the quest for drag reductions of just a few percent. Yet one finds that today’s CFD codes, 

with certain limited exceptions, are unable to predict drag with 

an acceptable degree of reliability. They can generally provide 

qualitative insight concerning whether a given configuration will 

have “good” or “bad” drag characteristics, but current CFD codes 

can rarely be depended on to produce a quantitatively accurate 

prediction of drag, particularly if the drag is based on integration 

of surface pressures and calculated skin friction. This is a major 

shortcoming and limitation. 

One of the simplest geometries in aerodynamics is a 2-D airfoil, 

but the ability of today’s best CFD codes to predict airfoil drag 

accurately remains controversial. No two airfoil codes have been 

shown to predict the same drag over the angle of attack range. 

Thus, experimental testing of 2-D airfoils continues. Part of the 

difficulty stems from the uncertainties of turbulence modeling, but 

a large part of the difficulty stems from the numerical resolution 

of the detailed features of the flow with sufficient accuracy and 

reliability to predict drag. The situation is markedly worse for 

3-D problems where coarser numerical grids must necessarily be 

used. 
20 

It is important to recognize that a CFD technology capable of predicting accurate surface pressure predictions is far from 

complete, and that much additional payoff may yet be gained 

by further improvements in algorithm technology. Possibly the 

only CFD algorithm technology to date that works acceptably 

well (within the limitations of its approximations) in nearly all 

respects for 3-D flow calculations is the higher order panel method 

technology for simple inviscid linear flows. 

Other factors associated with the definition of a CFD capability involve such items as problem setup time, required user 

expertise, and procedure “tuning.” The influence of these factors 

is perhaps most pronounced in attempts to extend the solution 

of nonlinear flows involving surface fitted grids to more complex 

and arbitrary geometries. Such attempts have frequently involved 

inordinately long and labor-intensive setup times and the accuracy 

of the computed results depends considerably upon decisions made 

by the user concerning grid density and perhaps on the “tuning” 

of artificial dissipation terms. This level of algorithm technology 

remains far from what is needed. 

In spite of the many factors involved in identifying a given 

capability, the committee attempted to summarize its findings in 

a simple format in Table 1. The table shows that CFD methods 

today can simulate flows about complex geometries with simple 

physics (e.g., linear flows governed by the Prandtl-Glauert compressibility rule), or flows about simple geometries (e.g., 2-D and 

axisymmetric) with more complex physics. The areas in the table 

which combine complex physics and complex geometry show little 

capability. 

The following two-part discussion sets forth a more detailed 

assessment of capabilities for solving the various flow equations 

of interest for external aerodynamics. The first part describes 

capabilities that are used principally for steady flows, although 

certain of the methods used therein can also be used for the 

prediction of unsteady flows. The second describes capabilities in 

use for unsteady aerodynamics. 

Capabilities for Steady Aerodynamic Flows 

Linear Methods 

There are several mature codes for calculating flows that can 

be represented by linear theory-the Prandtl-Glauert simulation 
21 

- 

I 

P 

x 

m 

!! 

5 

- 

I 

c 

P 

8 

i 

A 

- 
22 

relation. Most of these are limited to subsonic flows, and they 

all use panel methods. A few panel method codes are available 

which handle supersonic flows within the framework of the linear 

equation, and some have been extended to simulate certain limited 

types of free vortex flows at subsonic speeds. 

The panel method codes of today are unique in that they 

provide a capability for solving the flow about completely general 

configurations. This is a major virtue which makes them very 

useful. Once a user gains familiarity with one of these codes, he or 

she can conduct a host of different applications. Such codes are in 

regular use within every major aerospace company. The computing 

cost of carrying out an analysis about a complex configuration is 

acceptable. Their principal limitation is that they are restricted to 

simple physics as modeled by the linear Prandtl-Glauert equation. 

The general purpose panel method codes are the largest and 

most complex codes in CFD. As such they require systematic 

maintenance, and a “home organization” to adapt them to a new 

computer operating system. 

Three-dimensional codes have been coupled with 2-D (strip) 

direct and inverse boundary-layer codes, and with 3-D boundarylayer codes, but the committee’s survey showed little use of coupled 

viscous analysis. The probable reasons for this are: 

1. Most panel method applications are for attached flows in 

the absence of shock waves, for which viscous effects are not very 

pronounced. 

2. Complex geometries, for which panel methods are used 

extensively, are restricted by the limitations of the boundary-layer 

approximation. Boundary-layer methods cannot simulate discontinuous intersections which characterize a geometrically complex 

configuration. Thus, they are highly restricted in their ability to 

provide accurate simulations on complex geometries. 

One remaining need of the military airplane community is to 

extend the limited abilities of today’s panel methods to better 

handle the simulation of free vortex flows. 

Nonlinear Small-Disturbance Codes 

Several small-disturbance codes exist for calculating transonic 

flows over general 2- and 3-D geometries with subsonic streams. 

Most of the codes employ small-disturbance equations which include extra terms to improve the accuracy near highly swept 3-D - 
23 

shock waves and to broaden the range of Mach numbers for which 

the theory can be usefully applied. The codes use standard mixedflow finite difference schemes to solve the approximate potential 

equation. The use of approximate planar-type boundary condition 

-surfaces permits the use of relatively simple grid structures even 

for complex 3-D geometries. Usually, Cartesian or polar coordinate type grids are employed with grid embedding to permit grid 

clustering near important parts of the flow. The grid-embedding 

techniques employed also allow for the modification of the governing differential equation to better model the flow in each embedded 

region. 

The main advantage of the small-disturbance codes resides 

in their ability to treat, albeit in approximate fashion, complex 

3-D configurations. It is practical to use these codes to compute 

transonic flows over complete aircraft configurations with combinations of nacelles, pods, pylons, winglets, canards, and with 

arbitrary fuselage shapes. They can be used to compute component interference effects in the same way as designers using wind 

tunnels. 

Viscous effects are usually treated in a rudimentary way using 

2-D strip integral boundary-layer methods in the 3-D applications. 

This simulates some of the major viscous effects, but is inadequate 

for the prediction of flow separation and stall. 

The accuracy of these codes has not been precisely established. 

Nevertheless, published results have shown reasonable agreement 

with experimental data for the pressure distribution for a wide variety of 3-D applications. The results of the computation must be 

carefully interpreted and combined with other methods to make 

useful engineering estimates of the aerodynamic forces and moments. 

The computer requirements for these codes are modest-less 

than one-half million words of memory and a few minutes of time 

on a Class VI computer are required for simple wing-body combinations. The ability to compute the pressure distribution on 

complex 3-D configurations with reasonable accuracy and modest 

computer resources make these methods very useful for the aerodynamic design of aircraft. These are relatively mature codes and 

in all probability will not be developed much further. 
24 

Full-Potential Codes 

Several full-potential transonic codes exist for calculating the 

flow about isolated components such as airfoils, wings, and bodies. The algorithms commonly used are finite-difference or finitevolume schemes with surface-fitted grids. Most of these codes are 

designed for flows with subsonic freestreams. 

A lesser number of full-potential codes are available for flows 

with supersonic freestream that are capable of handling embedded 

subsonic pockets. These codes use transverse grid planes and are 

capable of handling more complex geometries, but are not suitable 

for flows with a subsonic freestream. 

With the exception of the codes for supersonic flows, virtually all full-potential codes have evolved down a path that led 

to “configuration-component” codes, each capable of handling a 

restricted class of geometrical shapes. This is a different state 

of affairs than for the world of linear flows, and more restrictive. The capability to handle complex and arbitrary geometry in 

transonic flow does not exist today. Considerable effort has been 

and is being spent on extending conventional, surface-fitted grid 

approaches to more complex geometries by means such as “blockstructured grids,” but the practicality, reliability, and usability of 

those developments have yet to be fully demonstrated. 

Other approaches for handling arbitrary and complex geometries should continue to be explored. Among efforts toward that 

objective are those utilizing triangular and tetrahedron grids, and 

those embodying a rectangular, nonsurface-fitted grid. 

Within the geometrical constraints of today’s algorithm technology, the transonic full-potential codes are much used. They 

are used extensively for wing/body and wing/body /simple-nacelle 

simulation, particularly by the commercial transport aircraft community. For those applications they are generally coupled with a 

boundary-layer code. They provide extensive design information 

in the cruise regime where the flow is attached. They cannot 

handle separated flows, which are a prime consideration for transport wing design for acceptable handling characteristics at the 

perimeter of the flight envelope. Their ability to predict drag, a 

major performance parameter, is also somewhat unreliable. The 

supersonic codes are restricted to attached flow simulations, which 

limits their applicability to a small portion of the flight envelope 

of high-performance military aircraft. 
25 

Extension of this class of numerical technology to treat the 

Euler eqi&lons :sing mu!tip!c p~tentia! (e.g., &Zs& or vector 

potential) or stream function methods has been demonstrated in 

2-D. It would appear to be feasible and desirable to extend these 

procedures to 3-D. 

Euler Codes 

There has been a strong focus on Euler code development in 

recent years. Their ability to produce wake position as an output 

rather than an input, and to model rotational flows and flows 

containing regions of different total pressure is a major asset not 

shared by methods based on potential theory. 

There are several methods being pursued in operational, 3-D 

Euler codes that are under continual refinement, and each possesses its own advantages and disadvantages. The most widely 

used methods fall into two broad classes: 

1. Central-difference methods with dissipation terms added 

to enhance stability and to provide smoothing of shock profiles. 

2. Upwind-differenced flux-splitting and total variation diminishing (TVD) methods. 

The first class of methods usually requires some tuning to 

obtain near-optimum values of the coefficients for the added dissipation terms. The optimum values depend on the application, 

a feature which is undesirable. But the methods are relatively 

simple compared to those of the second class, which require less 

tuning. Both classes are extendable to the viscous Navier-Stokes 

equations. 

The existing 3-D Euler codes, which are most widely used in 

government research laboratories and industry, use nonadaptive, 

body-fitted grids and most are configuration-dependent. Numerical solutions containing shocks, wakes, and vortex structures are 

accompanied by excessive diffusion and loss of resolution in the 

numerics. The algorithms can also produce false entropy due to 

truncation errors or badly chosen artificial damping terms in local regions where resolution is inadequate; the false entropy is 

convected downstream and can result in spurious separation and 

erroneous force coefficients. The computing costs and memory 

requirements of Euler solvers are higher than for full-potential 

solvers, but are acceptable provided one has access to a Class VI 

computer with a large memory. 
26 

Also, today's operational Euler codes suffer from the same 

stringent geometry constraints, imposed by the current surfacefitted grid technology, as the full-potential codes. Euler codes exist 

for wing/bodies, nacelles, actuator disks, detailed propfan blade 

analysis and other such components, but each is a different code. 

There is no Euler capability for general configurations, although 

work is under way involving block-structured grids and triangular 

and tetrahedron grids, as well as a limited look at nonsurface-fitted 

grid technology. Here, also, there is a major need for a general 

configuration capability that does not exist. 

Much could be gained from algorithm researcb aimed at overcoming the limitations of today's computational technology. It 

could render Euler technology far more effective for the aerospace 

community, and new developments in Euler technology will probably also contribute directly to Navier-Stokes technology. 

Boundary Layer, Viscous/Inviscid Interactions, and Parabolized 

Navier-Stokes Codes 

Several good 2-D and 3-D boundary-layer codes have been 

refined over the years. Their primary limitations today are (1) 

accuracy of the turbulence models, (2) concern about the accuracy of crossflow profiles in 3-D integral methods, and (3) the fact 

that reliable inviscid-viscous interaction schemes have yet to be 

demonstrated for complex 3-D flows such as corner flows and flows 

with separation. They are used primarily in airfoil codes, nacelle 

codes, and in transonic wing codes where their role in the shockwave/boundary-layer interaction phenomena makes their use almost essential. They are also being used to assess the accuracy of 

emerging Navier-Stokes codes. 

Further improvement is needed in the technology of interacting boundary layers with an outer flow, especially 3-D viscouslinviscid interaction methods for the simulation of some types 

of separated flows. The computational economics of boundarylayer methods are such that there are significant benefits to be 

gained with these enhancements. 

Parabolized Navier-Stokes (PNS) codes are being used extensively to compute steady supersonic and hypersonic flow about 

streamlined bodies. In the parabolizing approximation the streamwise viscous terms are dropped and a modified streamwise presmre gradient is introduced to allow space marching from upstream 
27 

initial data. Because only one pass through the grid is required, 

these procedures are computationally efficient. With the PNS procedure there is no need to couple an inner viscous region with an 

outer inviscid flow as with conventional boundary-layer methods. 

However, the PNS codes tend to be difficult to use because they 

can exhibit numerical instabilities with respect to refinement in 

streamwise step size. This instability may be avoided with the introduction of semi-elliptic iterative methods but at the expense of 

increased computer time and memory requirements. Current developmental activities with PNS are centered about the inclusion 

of real gas effects and finite-rate chemistry. 

Navier-Stokes Codes 

Solutions of the 3-D, turbulence-averaged, Navier-Stokes 

equations for realistic aircraft configurations is the “Holy Grail” of 

CFD. The cost of Navier-Stokes applications has restricted their 

use to specialized applications, primarily 2-D flows and limited 

regions of 3-D flows. Most of the applications so far have used 

simple algebraic turbulence models with the Reynolds-averaged, 

thin-layer Navier-Stokes (TLNS) approximation. The TLNS uses 

body-fitted meshes so that all of the diffusion terms tangential 

to the solid boundaries can be conveniently dropped from the 

equations, retaining only those normal to the boundaries. This 

eliminates the need to treat meshes that are fine enough in all 

directions to resolve properly all the viscous derivatives. A crude 

estimate of the number of mesh points required to obtain a reasonably accurate solution of the TLNS is twice the number of mesh 

points as for a good Euler solution. 

The point has been reached where the industry is beginning 

to experiment with Navier-Stokes codes, and this is leading to a 

realization of the immense capability that is to come. Algorithm 

development for 3-D Navier-Stokes equations is still in a primitive 

state. All of the problems with Euler solvers carry over to the 

Navier-Stokes, but are often masked by the viscous effects or 

inadequate turbulence models; hence, they may not be so clearly 

evident. Geometrical capabilities are even more limited than for 

the Euler solvers, partly because of the need for resolution of vastly 

differing length scales. 

The issues of Navier-Stokes should be attacked on several 

fronts. Merely awaiting the next generation of supercomputers 
28 

is not enough. Computer time required for present TLNS codes 

for even an isolated wing range from 2 to 8 hours on a Cyber 

205 or CRAY X MP. Improvements in speed of convergence must 

be sought to reduce the required number of iterations to reach 

a steady state from thousands down to hundreds. Algorithms 

are needed that do not suffer serious loss in performance and 

robustness to high aspect ratio meshes and artificial viscosity. 

Even more compelling than in the case of Euler solvers is the need 

for efficient, solution-adaptive meshes that can track and resolve 

shocks, vortex structures, boundary layers, wakes, and free shear 

layers. Work to date has been mostly with global, nonadaptive, 

body-fitted grids for single components such as an airfoil, wing, 

or isolated nacelle. However, promising research has shown the 

possibilities afforded by overlapping embedded grids, zonal bodyfitted grids, and finite-element-type tetrahedral grids. 

Turbulence modeling will become a major issue for NavierStokes solvers, but with today’s algorithms the various errors 

associated with numerics are probably a larger issue in need of 

resolution. When those sources of error are resolved, then turbulence modeling will become the limiting factor. 

Capabilities for Unsteady Aerodynamic Flows 

The principal applications of CFD methods for unsteady flows 

within the aerospace industry have been associated with structural 

dynamics, flutter, and active controls. To date there has been less 

emphasis on the development of methods for unsteady aerodynamics than for steady flows. Several of the computational methods 

in common use for steady aerodynamics can be used in a timeaccurate, unsteady mode. However, in practice many of these are 

never used for unsteady applications, the probable reason being 

that the computing costs required to carry out timeaccurate calculations for the wide range of Mach numbers, angles of attack, 

control surface motions, and dynamic pressures that must be examined for a comprehensive flutter analysis remain beyond the 

normal realm of affordability. 

Linear Methods 

There are several programs for calculating unsteady flows 

based on linear theory. Subsonic kernel function methods are 

LL 

u -‘U 
29 

available for thin lifting surfaces, i.e., wings and tails. Kernel 

methods are available to analyze wings with oaci!!&ing ccstrs! 

surfaces. Doublet lattice methods are available for modeling flows 

past somewhat more complex geometries including pylons and 

nacelles. Doublet lattice codes that have been modified using 

transonic static lift curve slope data (obtained from experiment or 

computations which include viscous corrections and separation) 

are used to extend this capability to the nonlinear range. 

Supersonic lifting surface theory has also been implemented 

for thin lifting surfaces. These methods are also based on small 

perturbation theory. 

Surface panel methods have been developed to compute flows 

about bodies of arbitrary shape in subsonic flow. Attempts to 

extend them to the transonic and supersonic speed ranges are 

ongoing. The shuttle orbiter and the shuttle launch stack are 

examples of complex configurations that have been analyzed using 

panel methods. It is possible to do time-domain or frequencydomain (with complex frequencies) analyses. One current thrust 

is to combine panel methods with a hybrid vortex method to treat 

vortex-dominated flows. Also being developed is a scalar and 

vector potential method for treating viscous, compressible flows. 

Transonic Small-Disturbance Codes 

Several codes exist for calculating 2-D transonic small-disturbance flows. They employ finite difference as the form of discretization. Some use Alternating Direction Implicit (ADI) procedures 

to advance the solutions in time. Others are available for solving 

the low frequency and the general frequency harmonic equations. 

Codes of this latter type are inexpensive to run and have been 

used to compute 2-D transonic small-disturbance flows. 

Three-dimensional small-disturbance methods that advance 

the solution in time have been developed. The current capability 

is for thin clean wings. Some work has been done to add body, 

tail and canard, and tip store capability. Currently, the codes are 

computationally inefficient, expensive to run, and require small 

time steps to maintain stability. 

Methods for computing harmonic transonic linear perturbations about nonlinear steady states are available for 2-D and 3-D 

flows. In 3-D, such methods have thin, clean wing capability. 

When iterative techniques are used to invert the matrices, a limit 

'\, '.., 
30 

on the frequency of the unsteady motion is encountered. This 

limit is a function of the freestream Mach number and the size 

of the computational domain. Use of a direct matrix inversion 

approach serves to overcome this limitation, except that the cost 

and storage can become prohibitive in 3-D problems. 

Full-Potential Codes 

Several time-marching full-potential methods are available for 

calculating 2-D and 3-D flows. Some early 2-D codes solved the 

nonconservative flow equation, but later codes almost exclusively 

solve the conservative equation-usually in a body-fitted coordinate system. Two approaches for implementing boundary conditions are used-one in which transpiration conditions are applied 

on the mean surface and one in which a flow tangency condition 

is applied on the body boundary in a grid system that instantaneously conforms to the body. The relative merits of the two 

approaches have not been clearly established. 

Three-dimensional capability depends on the freestream Mach 

number. The capability to compute flows past complete vehicles 

is available for supersonic flows. For subsonic and transonic flows, 

codes that can do wing and body analysis are mature. An effort 

is under way to develop a single code that can compute subsonic, 

transonic, and supersonic flows past full configurations and that 

includes aeroelastic analysis capability. A 3-D method that includes rotational flow effects is also available for wings. 

Since the 3-D potential methods use body-fitted coordinate 

systems, one of the most significant problems that has to be addressed is gridding about complex configurations. 

A drawback of potential methods, which is experienced particularly in 2-D applications, is the occurrence of nonunique solutions 

that can be obtained when shocks are in the flow field. Progress 

has been made in solving this problem by accounting for entropy 

jumps across shocks in potential flow. Such entropy corrections to 

potential flow are available for ZD and 3-D methods. 

Euler Codes 

Euler codes have received increased attention in the past few 

years. Two-dimensional Euler codes are available that use timedependent conformal grids. There is a capability in 3-D for obtaining solutions for complete aircraft in supersonic flows. At 
31 

transonic speeds, state-of-the-art methods are limited to wing and 

development. As with full potential, a major consideration is grid 

generation for complex configurations. 

Generally, for the number of cases that must be run to do a 

typical aeroelastic analysis, Euler codes are not yet practical for 

everyday engineering use. 

bcdy cenfigUraticns. A methcd fcr inc!uding tai! eFects is under 

Boundary-Layer Codes 

Many inviscid codes are coupled with boundary-layer models 

to simulate viscous effects. An unsteady, integral boundary-layer 

code has been coupled with transonic small-disturbance codes (in 

2-D) with reportedly good results, but it is expensive to run. 

A 3-D unsteady finite difference boundary-layer code is under 

development but has not yet been coupled with any inviscid flow 

code; it has been run for a flat plate. 

Other methods involve coupling unsteady inviscid methods 

with steady boundary layers at each instant in time. In 2-D, 

inviscid codes have been coupled with integral boundary-layer 

methods. In 3-D, the inviscid methods have been coupled with a 2- 

D strip boundary layer at each span station and at each time step. 

The overall accuracy of such approaches has not been determined. 

Navier-Stokes Codes 

Two-dimensional Navier-Stokes codes exist for subsonic, transonic, and supersonic calculations. Codes for solving the full 

turbulence-averaged equations and the thin layer approximation to 

the equations exist for wing alone and for a blended wing and body 

(e.g., shuttle orbiter wing and fuselage configuration). One significant problem is the turbulence model-most codes still use the 

simple flux-gradient concept. The number of grid points needed 

to resolve the viscous region also makes storage a major problem 

for other than simple configurations. In practice, Navier-Stokes 

methods are computationally prohibitive except for perhaps very 

specialized applications. 

FINDINGS 

CFD offers great potential in many areas of fluid flow and 

to a large degree this potential is now being realized in aircraft 
32 

f; 

design. All major aerospace companies have acquired, or will 

soon acquire, supercomputers and the CFD research supported 

by these companies is growing. Within the commercial transport 

aircraft community the application of CFD has become an integral 

part of the aerodynamic design process. The more complex flows 

encountered by high-performance military aircraft have proven 

more difficult, but a few of these are now beginning to succumb to 

computational analysis. However, much remains to be done. 

Today, CFD methods can simulate flows about complex geometries with simple physics, or about simple geometries with 

more complex physics, but they cannot do both. The most pressing need is for algorithm development that will lead to practical 

methods for solving the nonlinear flow equations-full-potential, 

Euler, and the various forms of Navier-Stokes equations-about 

arbitrary configurations. The emphasis to date has been on learning how to solve these nonlinear flow equations for simple geometries about which orderly, surface-fitted, quadrilateral grids can be 

fitted, and progress has been made along that path. Today’s algorithms are cheaper, more accurate, and more robust thd those 

of yesterday, but they are still unsatisfactory in many respects for 

Euler equations and in most respects for the Navier-Stokes. Useful 

codes have been produced, but better algorithm technology could 

multiply their usefulness many times over. 

A greater focus is required today on innovative algorithm research to deal with complez geometries in a practical, usable, and 

reliable manner. The panel methods for linear flows are in a class 

by themselves in this regard and should serve as a model for 

the simulation of nonlinear flows. Examination of typical panel 

method applications in industry reveals the immense value of being able to readily simulate flows about very complex geometries 

replete with components of widely varying length scales. The more 

general of those codes are structured as arbitrary boundary value 

problem solvers, and the codes themselves contain no concept of 

specific airplane components such as wing, body, and tail. They 

can truly solve any properly posed boundary value problem of the 

governing differential equation with great flexibility. 

This generality is what should be sought with the nonlinear 

flow solvers. Much effort is currently directed toward adaptations 

of quadrilateral-based, surface-fitted grids involving block structuring as a means to extend nonlinear flow solvers to more geometrically complex applications. However, it is uncertain whether 

t L i 

L L t P i 
33 

will lead to practical, complex geometry capability. Innovation is 

aimed at solving geometrically complex problems involving many 

length scales. 

Codes solving linear flows, the boundary-layer equations, the 

full-potential equations, Euler equations, and the various forms of 

the turbulence-averaged Navier-Stokes equations all have a role to 

play in the aircraft industry and will continue to do so for the 

foreseeable future. They are all important. The advent of more 

capable supercomputers is not reducing the impact of economic 

limitations. Rather, the opposite is happening. We seek to solve 

larger and more complex problems whenever a new generation of 

computer becomes available, and total expenditures on computing continue to increase. The user community will continue to 

need and use codes solving the simpler equations when allowed by 

the physics, and will use codes solving the more complex physics 

(which are usually more expensive to set up and run) only when the 

complexity of the physics requires it. The engineering application 

of CFD is dictated by economics. 

In addition to the inability of today’s nonlinear solution methods to deal effectively with complex geometries, another significant 

weakness involves the various shortcomings in the basic algorithm 

technology for all but panel methods. The drag prediction abilities 

of all nonlinear 3-D codes are unreliable at best, and for some 

they are so unreliable that computed drag is totally ignored. Most 

of that is traceable to the inefficient numerical algorithm or to 

the prohibitive cost associated with use of the high grid densities 

needed for accurate numerical resolution. Turbulence modeling 

will certainly become a limiting factor in the future, but until the 

numerical accuracy issue is solved, the limitations of turbulence 

modeling will be dificult to assess. 

The greatest need for algorithm improvement is in the technology for Euler and Navier-Stokes solvers, and in fact they are 

closely related. Advances in one should lead to advances in the 

other. Major improvements are needed in spatial accuracy and solution adaptability, convergence reliability, and convergence rates. 

The committee observed that an increasing number of issues 

related to computer science are appearing in the development of 

advanced computational capabilities. As nonlinear codes begin to 

treat more complex 3-D configurations, the issues of code vectorization and multitasking, treatment of large data bases, automatic 

~eedd i~ the search fgr bre&thr~~gh i~ ZCEeiid a!g~rithm~ 

I; I L E fl fl P f: E r 

L 6 
34 

analysis of computed generated results, 3-D graphic displays, and 

surface and grid generation become increasingly important. A 

blend of skills in these areas is becoming increasingly necessary for 

the development of efficient and effective computational capabilities. 

A further area of concern for the user of CFD capability is 

the verification of accuracy and applicability of codes for practical 

design applications. The issue here is the ability of the equations 

and the solution algorithms to represent the physics for flows of 

interest. Industry must develop a high level of confidence in the 

validity of CFD solutions for making management decisions before 

CFD is accepted as a valid design tool. Such confidence is gained 

by careful comparison of solutions with detailed experimental data. 

Verification of flow solvers is a vital part of the CFD development process. The effects of grid density, numerical dissipation, 

turbulence modeling, and convergence reliability need to be understood and related to the flow physics by comparison with reliable 

experimental data. 

RECOMMENDATIONS 

Stronger emphasis is recommended on the development of more 

advanced algorithm technology, particularly for the Euler equations 

and the various forms of the turbulence-averaged Navier-Stokes 

equations. Two objectives must be sought. One is technology to 

enable computation of flows about truly arbitrary and often complex 

geometries in a manner that is practical and for which accuracy 

is predictable. Such technology must include means for resolving 

phenomena that occur at the differing length scales found in nonlinear flows such as thin boundary layers, shock waves, free shear 

layers, exhaust plumes, and regions of separated flow. The other 

objective is for major improvements in spatial accuracy, convergence reliability, and convergence rates. The committee believes 

that order-of-magnitude improvements are possible and should be 

aggressively sought. 

It is further recommended that continuing emphasis be placed 

on verification and validation of flow models and solution algorithms by comparison with detailed experimental data. Such comparisons are a vital part of establishing a mature CFD capability. 
5 

W 

Hypersonic Applications of CFD 

OVERWEW 

During the past three decades, the level of research and development in hypersonic flow phenomena has changed drastically. 

Initially, this effort experienced an intense surge from the mid1950s through the 1960s; then a near demise from the 1970s 

through the early 1980s; and, in the past few years, the beginning of a resurgence as a vital technology for potential NASA 

and Department of Defense (DOD) missions in the 1990s and 

beyond. The initial thrust centered around the Intercontinental 

Ballistic Missile (ICBM) and Apollo programs. It was intensified 

by the newness of many hypersonic flow problems encountered 

at that time. To overcome these, a major national research and 

development effort for about 15 years was required. The subsequent comparatively quiescent period of hypersonic research in 

the 1970s centered mainly on the shuttle program and the Jupiter 

atmospheric entry probe. A resurgence of interest in hypersonics 

has emerged, driven by advanced new applications such as: (1) 

aero-assisted orbital transfer vehicles (AOTV) that achieve payload economy by passing through the earth's upper atmosphere 

to change orbit; (2) transatmospheric vehicles (TAV) that take 

off from earth or a conventional aircraft to enter near-earth orbit, then re-enter the atmosphere with cross-range capability to 

land on an airstrip; (3) hypersonic aircraft anticipated to require 

propulsion by supersonic combustion ramjets; and (4) the Strategic Defense Initiative that potentially involves hypersonic flow 

phenomena such as those associated with signal discrimination 

35 
36 

I; 

and sensor design. Together, these new applications encompass a 

very broad range of hypersonic physics, and bring into prominence 

some new aspects of hypersonic CFD which, in past applications, 

have only been partially dealt with, or not dealt with at all. 

Two major technological phenomena rising into prominence in 

these new applications are nonequilibrium chemistry and radiative 

heating. These arise because vehicles such as AOTV and TAV 

must operate at much higher altitudes than the earlier hypersonic 

vehicles. Although peak heating rates and maximum aerodynamic 

forces are developed in the 40-km to 50-km altitude range, these 

’vehicles will spend greater time intervals in the 50-km to 100-km 

region where the flow characteristics are less well understood. 

For such low densities and high velocities, the molecular reaction rates within a fluid element do not keep pace with the rapid 

flow changes. In consequence, internal molecular energy modes, 

chemical dissociation, species ionization, and molecular radiation 

are all out of equilibrium. This essential nonequilibrium character 

complicates extensively the numerical computation of flow fields. 

It also has a significant impact on the relative roles of computation 

and experimentation in the vehicle design process. 

Experimental simulation of a hypersonic flow field in which 

nonequilibrium reaction-rate chemistry is important would require 

the air density, flight velocity, and vehicle scale all to be reproduced 

simultaneously. This is not possible in existing ground-based experimental facilities. The simultaneous simulation of density, velocity, and scale, however, is possible in computer flow simulations. 

As a result, CFD is anticipated to be the primary tool for providing the extensive flow simulation information required in the 

design process of new hypersonic vehicles operating in the upper 

atmosphere; and flight tests may be the primary means of providing the necessary validation of the computational methods. This 

situation is totally different from that of earlier hypersonic vehicles 

designed on the basis of chemical equilibrium flow, and from that 

of hypersonic aircraft operating in the lower atmosphere; for these, 

small-scale laboratory experiments together with corrections for 

“real gas” effects can provide realistic flow simulation information. 

L t L fl P i: z 
37 

Hypersonic CFD for flight in the upper atmosphere is not 

merely a modest extension of conventional aircraft CFD, but is an 

intricate technology involving new complexities that do not exist 

at the Mach numbers of aircraft flight. Some of these complexities 

are not well-understood, and the necessary data base for many 

others does not yet exist. 

To begin with, the useful equation sets for numerical computation differ considerably. For hypersonic applications small 

perturbation approximations, for example, are virtually useless, 

and even the Euler approximation with coupled boundary layer is 

of relatively limited use because of the inaccuracy of the boundary 

layer approximation in hypersonic flows that are strongly dominated by viscous effects. Some of these flows can require governing 

equations sets quite different from the conventional Navier-Stokes 

equations. 

A major complication is that the continuum fluid model is not 

realistic for all hypersonic flight conditions of interest, whereas 

it is not in doubt for the flight conditions of conventional aircraft. Although the peak heating and principal maneuvering of 

advanced hypersonic vehicles may occur at altitudes within the 

continuum regime, other important aspects of their flight occur 

at higher altitudes where the mean free path of the molecules becomes of sufficient magnitude relative to the vehicle dimensions 

that the continuum model breaks down. Here particulate flow 

simulations must be employed wherein the motion of a large number of molecules is computed, such as in the direct simulation 

Monte Carlo method. Thus, both particulate and continuum numerical flow simulation methods are required for hypersonic CFD 

in the upper atmosphere, whereas only continuum simulations are 

needed for conventional aircraft CFD. 

Another complication is that the conventional continuum 

Navier-Stokes equations of motion-which are not seriously in 

doubt for ordinary aircraft flight conditions-can be unrealistic 

for hypersonic flight in the upper atmosphere, and are of uncertain 

accuracy in the lower atmosphere. Two assumptions embodied in 

the Navier-Stokes equations may become either uncertain or unrealistic under hypersonic flight conditions. One is that of a linear 
38 

I 

relationship between viscous stress and strain rate. This assumption is known to be valid for small departures from equilibrium; 

but in hypersonic flows these departures can be very large indeed, 

and thereby place doubt on the accuracy of this assumption of 

linearity. 

The second questionable assumption is the “Stokes hypothesis”-that although viscous stresses exist when fluid layers slide 

relative to each other without density change, no such stress exists 

when the density changes without fluid layers sliding relative to 

each other. For hypersonic flows the density of a flowing particle 

can change with extreme rapidity, and this brings Stokes’ hypothesis into serious question. In particular, this hypothesis precludes 

taking into account in the equations of motion certain physical 

processes that are known to exist, but that are not represented 

by any term in the conventional Navier-Stokes equations (such as 

the processes of irreversible molecular energy exchange between 

internal and translational modes produced by inelastic molecular 

collisions). Modifications to the Navier-Stokes equations which 

would account for such processes, if indeed needed, have not yet 

been established. 

The lack of realism of the conventional Navier-Stokes equations becomes clear for flight conditions in the upper atmosphere 

wherein the shock-wave thickness itself is not small compared to 

the shock stand-off distance. On the nose of the shuttle orbiter, 

for example, this situation exists at altitudes of about 75 km 

and higher. Under such conditions the CFD code must integrate 

through the shock-wave profile. It has long been known, however, 

that the Navier-Stokes equations are incapable of doing this accurately at Mach numbers above about 2. To do so accurately at 

hypersonic Mach numbers will require that continuum equations 

of motion be developed with a higher degree of realism than the 

conventional Navier-S tokes equations. 

Probably the greatest complication and departure from conventional aircraft CFD is the massive amount of molecular physics 

data needed as inputs in hypersonic CFD, whether of the continuum or particulate type simulation. Quantitative input data 

are required, for example, on reaction rates for all the possible atomic, molecular, and ionized species of air (as much as 11 

different species and over 50 different reaction rates). Likewise, 

similar data are required on the vibrational and radiation excitation rates, since radiative heating can dominate convective heating 
39 

in hypersonic high-altitude flight. Moreover, important gas and 

surkce chemicd rex.ti.\?.,s occ??r, am3 data nn these rate!? alnn are 

required. 

Much of this overall molecular physics data base is, unfortunately, not available at present for the extreme temperatures 

encountered in hypersonic shock layers. Almost all the available 

reaction rate constants for air, for example, were measured over 

25 years ago and only at the lower end of the temperature range of 

interest. It will be a sizable undertaking to provide the necessary 

molecular physics data base. 

CFD CAPABILITIES IN HYPERSONICS: 

UPPER AND LOWER ATMOSPHERE 

The degree to which CFD can contribute to hypersonic design 

applications is quite different for the two extremes of flight in the 

lower and upper atmosphere. For flight in the lower atmosphere 

with equilibrium air chemistry, the feasible applications would be 

generally similar to those discussed previously for conventional 

aircraft. The problems of transition and turbulence, ubiquitous to 

conventional aircraft, are also fundamental to hypersonic aircraft 

since they can affect aerodynamic heating and payload weight 

significantly. 

Hypersonic aircraft configurations, however, are geometrically less intricate than conventional aircraft, and are thus more 

amenable to realistic 3-D grid generation. This characteristic, 

together with the ability of CFD to assess real gas effects not generally simulated in experimental facilities, leads to the expectation 

that CFD applications to hypersonic flight in the lower atmosphere 

will be relatively more extensive than the corresponding applications to conventional aircraft flight. In particular, Navier-Stokes 

CFD simulations contribute to insight and understanding by revealing areas of flow separation and intense heating, locations 

where the bow shock wave intersects other portions of the vehicle, 

and potential problems of inlet-airframe interaction. These simulations also contribute to the evaluation of innovative concepts by 

providing such information as the real gas effects on lift-drag ratio, 

stability, and aerodynamic heating. The applications for the lower 

atmosphere also extend to some design details that are affected by 

real gas corrections to hypersonic wind tunnel data. 
40 

f; 

The other hypersonic extreme of flight in the upper atmosphere may not be a major design driver since peak aerodynamic 

forces and heat rates occur at lower altitudes. However, the importance of CFD as a basic flow analysis tool is expected to be 

very much greater. This is because of the inability of existing 

ground-based experimental facilities to duplicate vehicle scale. 

Thus, hypersonic CFD for this very high altitude environment 

is anticipated to be the primary source of flow simulation information for all aspects of application-insight and understanding, 

evaluation of innovative concepts, and design detail. Because no 

way is known, other than CFD and full-scale flight experiments, to 

simulate fully the reaction-rate dependent hypersonic flow in the 

upper atmosphere, CFD is clearly the primary tool for the design 

of such vehicles. 

CURRENT STATUS OF HYPERSONIC CFD 

In assessing the current status of hypersonic CFD a matrix 

structure of fluid-flow model versus flow-field complexity was selected that is different from that used for conventional aircraft 

CFD. Moreover, different matrix structures are appropriate for 

the two different extremes within the overall scope of hypersonic 

flow computation. The essential elements involved in CFD of hypersonic aircraft, for example, are quite different from those of 

AOTV because of the higher velocities and much higher altitudes 

involved with AOTV. A list of some of these contrasting differences 

appears in Table 2. In a sense, flight altitude affects the nature of 

hypersonic CFD to a major degree in an analagous way that Mach 

number affects conventional aircraft CFD. Consequently, the two 

extremes are used to characterize the present overall status of hypersonic CFD. One extreme is for hypersonic aircraft operating 

in the range of a 0- to 40-km altitude, and the other is for upper 

atmosphere vehicles such as AOTV operating at altitudes of about 

80 km and higher. 

An assessment has been made of the current atatus of hypersonic CFD based on inputs received from the committee’s survey 

of representative CFD codes developed by industry, government 

agencies, and the university community. Approximately 47 individual inputs on hypersonic codes were received to form the main 

basis of this survey. In a few cases these inputs were supplemented 

by committee members’ personal knowledge of existing codes for 

t L t‘ t t: i 7 

L d 

r - 
41 

TABLE 2 Contrasts within Hypersonic CFD 

Lower Atmosphere Upper Atmosphere 

Hypersonic Aircraft AOTV 

Altitudes 040 km 80-110 km 

Flow Type Turbulent and Laminar 

Flow Model Continuum Continuum and Particulate 

Air Chemistry Equilibrium Non-Equilibrium 

Principal Heating Turbulent/Laminar Radiation, Convection 

Molecular Physics None Extensive Data Base Needed 

Surface Boundary No Slip Slip with Momentum, Energy, 

Shock Wave Negligible Sizeable Fraction of 

Reynolds Number High Low 

Transitional 

Convection 

input 

Conditions and Chemical Accommodation 

Thickness Detachment Distance 

which individual inputs were not received. Since few existing codes 

compute nonequilibrium radiative heating, this important aspect 

of hypersonic CFD for flight in the upper atmosphere is not reflected in the data presented in Tables 3 and 4. These tables 

also do not reflect the development status of special numerical 

problems that may arise at very high Mach numbers such as with 

temperature overshoots in shock capturing techniques artificially 

influencing chemical reactions. 

This assessment was quantified by identifying the present 

stage within the code development cycle (described earlier) corresponding to each hypersonic flow-field model and each degree 

of flow-field complexity considered. As before, these range from 

grade 1 for codes in an initial research phase of development, to 

grade 5 for codes in a mature engineering design phase. The assessment results are summarized in Table 3 for hypersonic flight 

in the lower atmosphere (e.g., hypersonic aircraft) and in Table 

4 for the upper atmosphere (e.g., AOTV type vehicles). Within 

each box of these matrix tables, further identification is noted as 

to whether a given stage corresponds to a code for a perfect gas 

(PG), or to equilibrium air chemistry (EC), or to nonequilibrium 

air chemistry (NEC). This supplementary notation is indicated 

because a code for a given hypersonic flow model and given degree 

of flow complexity might be, for example, in grade 3 for a perfect 
42 

TABLE 3 Status of CFD Capability-Hypersonic Lower Atmosphere 

Governing 

Equations 

Euler 

Euler Plus Coupled B.L. 

Laminar 

Euler Plus Coupled B.L. 

Turbulent 

Parabolized 

Navier-Stokes 

Thin-Layer or ShockLayer Navier-Stokes 

Navier-Stokes 

KEY: 

2-D or 

Axial 

Symm. 

5 PG 

4 EC 

1 NEC 

3 PG 

3 EC 

3 PG 

3 EC 

4 PG 

3 EC 

2 NEC 

4 PG 

4 EC 

2 NEC 

4 PG 

3 EC 

1 NEC 

1. Evolving enabling technology 

Geometry 

Blunt 

Body 

4 PG 

4 EC 

2 NEC 

3 PG 

3 EC 

3 PG 

3 EC 

N.A. 

3 PG 

3 EC 

1 NEC 

4 PG 

3 EC 

1 NEC 

3-D ~ 

Lifting 

Vehicle 

3 PG 

3 EC 

1 NEC 

3 PG 

3 EC 

1 NEC 

3 PG 

3 EC 

3 PG 

2 EC 

1 NEC 

2 PG 

2 EC 

1 NEC 

2 PG 

1 EC 

1 NEC 

Lifting 

and inlet 

2 PG 

1 PG 

1 PG 

PG = perfect gas 

3-D 

Separate 

Flow 

N.A. 

N.A. 

N.A. 

N.A. 

2 PG 

2 PG 

1 EC 

1 NEC 

2. Understanding capabilities and limitations EC = equilibrium air chemistry 

3. Beginning to apply 

4. Learning to use effectively 

5. Mature capability 

NEC = nonequilibrium air chemistry 

N.A. = not applicable 

gas, yet only in grade 1 for air undergoing nonequilibrium chemical 

reactions. 

Table 3, representative of hypersonic flight in the lower atmosphere, indicates that the present status of CFD is reasonably well 

advanced regarding the degree of flow-field complexity and the 

degree of completeness of the governing equations solved by the 

codes. Such is to be expected since this case is only a modest extension of supersonic aircraft CFD wherein real gas, equilibrium, 

thermodynamic properties of air are used in place of a perfect 

gas. For some of the simpler degrees of flow-field complexity, the 
43 

TABLE 4 Status of CFD Capability-Hypersonic 

LIpper Atmosphere 

Governing 

Equations 

~ ~ ~~~ 

Parabolized Navier -Stokes 

Shock-Layer or Thin-Layer 

Navier-Stokes 

Navier-S tokes 

Particulate Monte Carlo 

KEY: 

2-D 01 

Axial 

Symm. 

4 PG 

3 EC 

1 NEC 

4 PG 

4 EC 

1 NEC 

3 PG 

3 EC 

1 NEC 

3 NEC 

1. Evolving enabling technology 

Geometry 

_c_ 

Blunt 

Body - 

N.A. 

3 PG 

3 EC 

1 NEC 

3 PG 

3 EC 

1 NEC 

1 NEC 

3-D 

Lifting 

Vehicle 

3 PG 

2 EC 

1 NEC 

3 PG 

3 EC 

1 NEC 

2 PG 

2 EC 

1 NEC 

1 NEC 

3-D 

Separate( 

Flow 

N.A. 

1 PG 

1 PG 

1 EC 

1 NEC 

1 NEC 

PG = perfect gas 

2. Understanding capabilities and Limitations 

3. Beginning to apply 

4. Learning to use effectively 

5. Mature capability 

EC = equilibrium air chemistry 

NEC = nonequilibrium air chemistry 

N.A. = not applicable 

current status is judged to be at or approaching maturity; but, for 

complex 3D flows involving separated flow or inlet and airframe 

integration, for example, current codes are far from maturity. 

Table 4, representative of hypersonic AOTV-type flight in the 

upper atmosphere, exhibits a number of blank boxes in the matrix. These signify that work in such areas is judged not yet to be 

in the first stage of research code development. In some of these 

cases codes are known to be under development, but have not yet 

reached grade 1. This table, of course, represents CFD codes that 

are very much more complicated than those of Table 3. They also 

require much more computation time because of the numerous 

chemical reactions that must be solved simultaneously with the 

equations of fluid motion. Thus, the efficiency of numerical algorithms is an important aspect of this type of code development. 

Table 4 indicates clearly that there is much research and development to be done to bring such CFD codes into a stage approaching 
44 

maturity. Notably, the assessment made of the code development 

stage assumes that all necessary input data on reaction rates and 

so forth are available for the codes to use. As stated earlier this is 

not the case, and a separate and extensive level of research effort 

on molecular physics will be required to provide these data. 

A significant point about the status of particulate flow simulation is not reflected in the entries of Table 4. Present Monte 

Carlo codes generally use human interaction to resize computational cells in accordance with the location in the flow field of 

high or low gas density. Consequently, the efficient exploitation 

of this type of flow simulation will require the development of 

some new automatic self-adaptive method for appropriately sizing 

computational cells. 

FINDINGS 

Hypersonic CFD spans a wide range in complezity dependent 

mainly on flight altitude: Air chemistry is in thermodynamic equilibrium un'thin the lower atmosphere but is strongly in nonequilibrium in the upper atmosphere. The CFD codes for the lower 

atmosphere are only a modest extension of those for conventional 

aircraft, but the corresponding codes for the upper atmosphere are 

much more complex and in a more primative state of development 

due to numerous additional molecular physics processes that must 

be considered. Various hypersonic vehicles cover both the equilibrium and nonequilibrium regimes. The principal design problems 

of past vehicles (e.g., ICBM and Apollo) generally involved equilibrium flow. Potential NASA and DOD vehicles for the 19909 and 

beyond involve higher altitudes and nonequilibrium flow. Other 

vehicles, such as the shuttle, involve some aspects of each regime. 

The degree of accuracy of the conventional Navier-Stokes equations of motion becomes a major issue at altitudes well below the 

limiting altitude for continuum flow. These equations are demonstrably inaccurate in the upper atmosphere where the shock-wave 

thickness can be a substantial fraction of the shock detachment 

distance. Moreover, they are of uncertain accuracy at lower altitudes where the shock thickness is negligible and reaction rates 

are dominant. 

The simulation of hypersonic flow fields undergoing nonequilibrium chemistry requires that vehicle scale be simulated as well as 

t 

-U' 

LL 

Y -'U 

F 

i rLlt 
45 

flight velocity and altitude. Because this is not possible in existimportance of CFD to hypersonic vehicle design is much greater 

than for conventional aircraft design. For flight in the upper atmosphere, CFD is expected to be the principal source of flow 

simulation information for vehicle design, and flight test is necessary for accurate validation of the computational codes. 

A large amount of molecular physics data is needed as inputs 

for both continuum and particulate types of flow simulation. Data 

on many chemical reaction rates, excitation rates, gas-surface reactions, and transport properties are needed especially for the 

higher range of temperatures encountered. 

The computational efficiency of numerical algorithms is of 

increased importance because of the long computing times involved 

when a large number of chemical reaction and species digusion 

equations must be solved simultaneously with the equations of fluid 

motion. 

Because of the much lower Reynolds numbers encountered in 

the upper atmosphere, the flows are mainly laminar and turbulence 

modeling is not anticipated to be a major technical problem. In 

the lower atmosphere, however, the location of transition and 

turbulence modeling is vital for hypersonic aircraft configurations. 

ing gioGiid-bztd experimentd facilities, the applications and the 

RECOMMENDATIONS 

The development of mature, fully realistic, and efficient computer flow simulations for the wide range in altitudes covered 

by advanced hypersonic vehicles will require considerable future 

progress in certain areas. Five particularly important areas warranting special attention are: 

1. Molecular physics data base. Extensive physical data required as inputs for hypersonic CFD codes are needed on chemical 

reaction rates, excitation rates, gas-surface reactions, and transport properties at high temperature. 

2. Continuum equations of motion. Some inaccuracies in the 

conventional Navier-Stokes equations for hypersonic flow conditions need to be mended and new physics added to the continuum 

equations of motion if they are to integrate accurately through 

shock waves in the upper atmosphere. 

3. Flight tests. Appropriately instrumented flight tests are 

necessary to validate computational codes for hypersonic flight in 
46 

the upper atmosphere due to the inability of ground-based experimental facilities to simulate properly the chemically nonequilibrium flow. 

4. Transition and turbulence. These problem areas can have a 

major impact on aerodynamic heating and payload weight. 

5. Numerical methods. Algorithms of improved computational 

efficiency for both continuum and particulate flow simulations are 

needed to reduce the computer time required to simulate chemically nonequilibrium flows. 
6 

Propulsion Applications of CFD 

OVERVIEW 

Despite the complexities of the flows associated with propellers, helicopter rotors, aircraft gas turbines, ramjets and scramjets, and rockets, the pressing need for aerodynamic improvements 

has made the aggressive use of CFD inevitable. The history of 

propulsion is marked by pioneering efforts to harness the latest 

available computational capabilities, going back to the days when 

rooms full of engineering aides using mechanical desk calculators 

carried out component matching and compressible nozzle flow solutions. These beginnings set the stage for the fearless attack on 

even the most unyielding problems and for some remarkably successful achievements. Today, CFD is becoming a mainstay of the 

propulsion world. 

The problems associated with propulsion differ from their 

external aerodynamic counterparts in three principal ways: (1) 

they usually involve complicated, even contorted, geometries and 

thus boundary condition constraints; (2) there is close coupling of 

flow elements involving 3-D flow, unsteady effects, and significant 

lengths of transitional boundary-layer flow (laminar to turbulent); 

and (3) there is a significant energy exchange from either chemical 

reactions or mechanical work. 

While this list seems formidable and could have a daunting 

effect on the growth of CFD technology for propulsion systems, it 

has in fact done quite the opposite. Since this environment is so 

difficult to reproduce experimentally, CFD plays the added role 

of a basic data source, helping to identify the dominant physics 

47 
48 

for a given situation so that analysts are better positioned to 

produce reliable design procedures. CFD is being employed as a 

breaching technology-one used to gain insight and control, and 

then penetration of the roadblocks facing advanced propulsion 

systems. 

The propulsion CFD experience does share one important 

characteristic with the rest of the aerospace field, namely that 

there are many different ways in which CFD has made an impact. 

The three following sections illustrate the breadth and depth of 

the influence of CFD. 

Detailed Design of Components 

There are many engine parts with aerodynamic roles whose 

geometrical surfaces are directly determined by CFD. An outstanding example concerns the current method of designing the 

contours of propeller, compressor, and turbine airfoils in which 

each is carefully created for its specific usage by means of compressible flow and boundary-layer calculations. This precision 

approach has replaced the hiband-miss application of standard 

airfoils drawn from extensive families of relatively simple airfoil 

shapes (e.g., multiple circular arc) which did not take advantage 

of modern understanding of aerodynamics. 

Improvements through the use of CFD in airfoil contour design are significant because they reduce and control airfoil drag, 

the root cause of inefficiency, in a fundamental and sound way. 

Moreover, in the propulsion world a small increase in component 

efficiency has a remarkably large influence on fuel used or payload 

delivered over the life of the system. A more subtle but revealing 

indication of the significance of this change has been the appearance of such brand names as ‘controlled-diffusion” and “tailored” 

airfoils. 

There are other engine components that benefit from the ap 

plication of CFD. Some leading examples include: the internal 

passage design of inlets, transition ducts (between components), 

and nozzles; the geometry of combustors; the shaping of afterburner mixers; and the external design of nacelles, including inlets 

and boattails, taking into account the influence of adjacent surfaces. 

The clear trend is toward a greater use of CFD. In particular, 

the extension of 2-D potential flow calculations to 3-D and from 
49 

simple boundary-layer models to complex ones continues with the 

goal being to achieve improved performance on the first try. 

Development of Insight and Understanding 

An abundance of auxiliary tasks are regularly accomplished by 

CFD and provide a sound foundation for progress in aerodynamic 

design. 

With close interaction between CFD and experimentation, 

advanced computer programs are used both to design an experiment and to predict the results so that the test is under control 

at all times. In some extreme cases, experimental data that had 

first been disregarded because it had no logical explanation was 

later reproduced by sophisticated CFD calculations. This not only 

exonerated the suspect facility, but also provided a clearer understanding of the underlying aerodynamic phenomena. In such cases 

CFD helped delineate the dominant physics of the phenomenon of 

interest. 

The complementary interplay of CFD and experimentation 

is especially important in the modern world of tailored designs, 

where the goal is not to generate half-blind global correlations, 

but to prove the accuracy of a total design system by means of 

benchmark demonstrations in reliable facilities. Consider here, for 

example, the large number of combinations of expensive and timeconsuming cooled turbine airfoil configurations that would have 

to be tested in order to find the best for a given situation. Once 

confidence in CFD methods has been established, the search can 

be primarily carried out on paper. Moreover, the designer gains a 

clear understanding of why the choices have been made. 

Even when available CFD tools are not extremely precise, 

they have often been used to aid designers in what might be called 

a semiquantitative fashion. The importance of the concept follows 

the well-known principle that if one can show an engineer where 

the flow goes and why (qualitatively) then he can usually figure out 

how to control it better. Examples that fit into this category are 

not to be taken lightly and include: the calculation of trends and 

trade-offs in cases where the principal need is to find the direction 

of change most likely to improve performance; the visualization 

of flows (e.g., streamlines, vector fields, vorticity distribution, and 

pressure, temperature or velocity profiles) to explain observed 

behavior and to provide a feel for the flow which can lead to 
50 

improvements; and the almost classical use of early CFD codes to 

explain the complex effect of airfoil shape on transonic flow and of 

freestream turbulence on boundary-layer transition. 

Possibility for Revolutionary Change 

The propulsion world is best described as evolutionary because progress is traditionally gradual and based upon the last 

successful design. Radical changes happen only occasionally, and 

are often the result of necessity, such as the need for ultra quiet and 

low fuel consumption commercial engines or the need for highly 

flexible fighter engines. Among the reasons for this apparent conservatism are the enormous costs and times associated with the 

demonstration of a new propulsion aerodynamic technique, especially when the realities of actual operation must be considered. 

The important point is that propulsion systems necessarily have 

closely coupled and complicated aerodynamic elements that are 

hard to understand independently-much less in interactive roles. 

CFD is breaking this pattern with increasing frequency because it makes possible the accurate assessment of entirely new 

aerodynamic ideas. Several samples illustrate this trend. 

In 1968 streamline curvature CFD methods were used to 

demonstrate the concept that controlled vortex (Le., not free vortex) turbine stages can produce more power at high efficiency than 

had previously been thought possible. This idea was soon proven 

conclusively by experiment and adopted by the turbomachinery 

industry. 

In 1971 many of the remaining barriers to the confident design of both cooled and high-power turbine airfoils were broken 

through the development of reliable boundary-layer and potential 

flow calculation techniques. These became the building blocks 

for many other advances including transonic and laminar turbine 

airfoil designs. 

In 1975 advanced streamline curvature CFD methods were 

used to incorporate several simultaneous improvements (e.g., controlled diffusion, swept leading edges, and sloped inner wall) into 

an advanced, high-pressure ratio, transonic compressor stage design. The result, also demonstrated by experiment, was a truly 

remarkable fan that has had a favorable influence on all subsequent 
51 

compressor and fan designs. In this case CFD clearly made possible the most important forward leap of compressor technology of 

the past generation. 

In 1980 the need to squeeze maximum performance from the 

integrated powerplant, i.e., engine plus airframe, led to the harnessing of 3-D, compressible CFD codes for the entire design of 

transport aircraft nacelles. This approach led to substantial drag 

reductions with no adverse impact on the required operational 

characteristics of the nacelle, e.g., angle of attack stability, and 

windmilling and reverse thrust performance. 

Very recently, in 1984, flow separation in the space shuttle 

main engine turnaround channels (which deliver the hydrogen from 

the high-pressure fuel turbine to the injectors) was eliminated by 

means of a CFD analysis requiring the Cray XMP computer. This 

improved performance by reducing pressure drops and increased 

life by making the outlet flow more uniform and steady. Special 

attention to graphic displays enabled maximum advantage to be 

taken of the results. 

CFD CAPABILITIES IN PROPULSION 

To assess CFD capabilities in propulsion an attempt is made 

in the following section to determine the current degree of CFD 

use, identify its strengths and shortfalls, and establish a reasonable 

basis for setting both short- and long-term directions. To this end, 

this vast subject heading is broken down into generic technology 

areas that represent the critical flow aspects of the propulsion system components. As shown in Table 5 the three major headings 

used here to categorize all propulsion system elements are: (1) 

stationary systems-overing all 2-D and 3-D inviscid and viscous 

flows; (2) rotating systems-focusing on all unsteady and cyclical 

flow elements; and (3) combustor systems-including combusting and noncombusting flow elements. These are then assessed 

according to their technical maturity. As listed in the vertical column of Table 5 these are: inviscid models (full-potential and Euler equations), classical boundary-layer approaches (transitional 

and turbulent), inviscid and viscous interaction approaches, using both integral and finite difference (or volume) techniques, and 

composite viscous approaches employing either the parabolized 

(sometimes referred to as reduced) or turbulence-averaged NavierStokes equation set. 
52 

TABLE 5 Status of CFD for Propulsion Applications 

INVISCID 

Full Potential 

Euler 

VISCOUS 

Transitional/ 

Turbulent 

Boundary Layer 

Parabolized 

Navier-Stokes 

Viscous-Inviscid 

Interaction 

Turbulence 

Averaged 

Navier-S tokes 

- 

2-D 

5.0 

4.5 

- 

4.5 

4.5 

3.5 

3.5 

- 

Stationary - 

- 

3-D 

4.0 

3.5 

3.0 

3.5 

1.0 

2.5 

- 

Unsteady 

3.0 

1.5 

1.0 

0.5 

1.5 

- 

- 

2-D 

4.5 

4.0 

4.0 

4.0 

2.5 

2.5 

- 

Rotating - 

3-D - 

4.0 

2.5 

2.5 

2.5 

0.5 

1.0 

- 

Unsteady 

0.5 

1.5 

1.0 

0.5 

0.5 

Combustors 

2-D 

2.5 

4.5 

2.5 

- 

3-D 

_. 

0.5 

3.5 

2.0 

KEY: 

1. Evolving enabling technology 

2. Understanding capabilities and limitations 

3. Beginning to apply 

4. Learning to use effectively 

5. Mature capability 

Stationary Systems 

The stationary elements of a propulsion system include inlets, 

nacelles, diffusers, and nozzles together with the transfer ducts 

connecting the other components of the system. In applying CFD 

to these elements the analyst first needs to understand the structure of the flow including the location and magnitude of secondary 

flows and separated regions. Next the local values of the wall shear 

stress and surface heat transfer are needed. For supersonic flows 

the location and structure of the shock wave-boundary layer and 

bleed interactions are important. Finally, the analyst needs to be 

able to predict the loss of total pressure in the system. All of 

these concerns dictate that some form of 3-D viscous computation 

be employed, the lower two-thirds of the stationary 3-D column 

in Table 5. On the other hand, the trend toward more complex 

geometries with nonuniform upstream flow conditions for these 

systems has meant that large numbers of grid points, well in excess of lo5 in recent applications, are required to resolve the flow 

structure. As a result, even with the advent of the modern supercomputer, the use of the full turbulence-averaged Navier-Stokes 

1I 

I 

I 
53 

equations is generally considered too expensive for practical applications. Instead, extensive use is now made of paraboliied (or reduced) Navier-Stokes equations with spatial marching procedures 

for both subsonic and supersonic flows. The primary exception to 

this occurs in the analysis of an inlet at angle of attack where 3-D 

potential and Euler codes are in use. Since the pressure variations 

are quite large for this problem, inviscid approaches provide much 

useful information. 

There are many aspects of flows in inlets, diffusers, and nozzles 

for which the status of current CFD tools may be considered 

inadequate. Examples of these include 3-D shock and boundarylayer interactions, local separation regions, surface heat transfer, 

injected coolant flows, and cases with large amounts of bleed. 

The status of unsteady viscous analyses for these components is 

particularly weak (see Table 5). In addition, the nature of flows in 

complex geometries with rapidly varying cross sections is not wellunderstood. Finally, the ability to predict the loss in total pressure 

for these systems is not yet adequate. In general, whether the 

fault lies with insufficient numerical resolution or with inadequate 

turbulence models is not known. However, in all the above cases 

it can be stated that the lack of a data base of sufficient detail to 

answer the numerics versus turbulence question is a major factor 

stifling the application of CFD. 

Rotating Systems 

The rotating elements of propulsion systems include fans, compressors, turbines, propellers, and helicopter rotors. As with the 

stationary elements the CFD analyst is interested in flow structure, including secondary flows and separated regions, values of 

wall shear stress and surface heat transfer, the nature of shock and 

boundary-layer interactions, and the prediction of losees in total 

pressure. There are, however, two significant differences from the 

stationary case. First, these flows are inherently unsteady, a fact 

which is just now beginning to attract attention in the CFD community. Second, the pressure variations are even larger than in 

the stationary cases and as a result inviscid treatments again can 

provide much useful information. 
54 

Most analyses treat a hypothetical steady flow obtained by 

assuming axisymmetric conditions upstream of a single turbomachinery passage. There is extensive use of inviscid codes, 2-D POtential and 3-D Euler, in the design and analysis of Fotating components. Two-dimensional boundary-layer codes are commonly used 

to estimate losses and surface heat transfer. Two-dimensional 

Navier-Stokes codes are becoming available but are not yet in 

frequent use. Three-dimensional Navier-Stokes codes are under 

development but most of those in use are proprietary. 

In short, there is extensive development activity in most of the 

boxes in the rotating 2-D and 3-D columns of Table 5. There are 

also a number of efforts aimed at computing the 2-D unsteady viscous rotor and stator interaction problem, and there is one effort 

under way to model the 3-D viscous averaged flow in multistage 

turbomachinery. As shown in Table 5 the level of development 

for unsteady turbomachinery codes is rudimentary. The true multistage problem is unsteady, nonperiodic, and well beyond the 

capacity of even the next generation of supercomputers. Hence, 

some approximate approach must be found for this important class 

of problems. 

As is the case with stationary components, current CFD tools 

are inadequate to analyze many aspects of rotating machinery 

flows, e.g., the structure of secondary flows and separation regions, surface heat transfer with and without injected coolant, 

and the predicton of total pressure loss and aerodynamic loads 

due to flutter or gust response on blades, rotors, and propellers. 

This is complicated by low Reynolds numbers, under 5 x lo5, and 

high freestream unsteadiness, 10 to 20 percent. This results in 

an inability to predict wall shear stress and surface heat transfer 

on turbine blades where boundary-layer transition may occupy 40 

percent or more of the blade chord. The general question of insufficient numerical resolution versus inadequate turbulence models is 

even more difficult to answer in the rotating than stationary case 

because the CFD problem is considerably more difficult. However, 

it can be stated that the lack of a data base of sufficient detail to 

resolve the numerics versus turbulence issue for rotating machinery is an even larger roadblock for CFD development than it is in 

stationary components. In the future it is expected that much of 

the emphasis will switch to timeresolved measurements of these 

flows as the CFD community mounts a significant effort to address 

unsteady turbomachinery computation. 
55 

Combus tors 

The focus here is on CFD as it applies to the aero/thermodynamic elements of the entire combustor, including both combusting and noncombusting elements of such flows. It is useful to think 

in terms of four major aspects of combustors: (1) oxidizer/fuel 

intake and management which can involve significant regions of 

axially reversed flow; (2) oxidizer/fuel mixing and combustion involving multiphase and multispecies tracking, heat addition, and 

surface heating; (3) exhaust flow management with large secondary flows, dilution, and cooling; and (4) massive coupling and 

interaction of the first three. Within these four areas there are five 

generic computational flow problems that can be identified and 

prioritized according to ascending order of difficulty: (1) largescale secondary flow mixing; (2) reverse flow; (3) heat transfer, 

both convective and radiative; (4) combustion, including phase 

and species change and stability; and (5) flow coupling in complicated geometries. With this in mind, one notes that in Table 

5, the only areas of significant activity are those involving viscous 

effects; boundary layers for surface heating; and parabolized and 

full turbulence-averaged Navier-Stokes for the remainder of this 

complicated environment. 

With regard to secondary flow mixing, this type of flow problem is encountered at two possible sites in a combustion process, 

at the head end where rapid mixing of the fuel and oxidizer is 

desired or at the aft end where dilution of the hot exhaust gases 

is required to avoid destroying downstream components, such as 

a turbine. The flow involves 3-D free shear layer turbulent mixing 

and possibly swirl. Additionally, liquid fuel droplet spray must 

be introduced and tracked through its phase-change just prior to 

the combustion process. Current approaches generally focus on 

use of the time-averaged turbulent version of the Navier-Stokes 

equations or a parabolized version of the same if reverse flow 

is not encountered. In either case, as indicated in Table 5, the 

overall problem is fairly well in hand numerically with three principal frontiers remaining, those of reducing difficulties related to 

numerical diffusion errors, improving fuel spray tracking models, 

and establishing a credible basis for modeling of 3-D turbulent 

mixing. Since turbulence modeling is discussed in more detail in 

Chapter 7 it will not be pursued further here except to note its 

critical importance to this flow arena. 
56 

Numerical diffusion difficulties force the use of relatively fine 

meshes to resolve the thin viscous mixing regions embedded in 

otherwise large-scale vorticity-dominated flows. While this aspect 

of the problem is receiving considerable attention, there is still 

a need for a breakthrough in this area to reduce the computer 

intensive aspect of the flow mixing problem. The fuel tracking 

problem involves tedious accounting of large ensembles of spray 

and species elements that again cause considerable drain on computer resources. This is especially critical to the field of scramjet 

combustion where the physics of the fuel droplet tracking in a 

supersonic stream represents the key element of the combustion 

process. Underlying this is the lack of a good analytical model 

representing the dominant physics of liquid spray formation. 

With regard to recirculating flow it is safe to say that nearly 

all aerospace combustion processes encounter some form of flow 

reversal in the principal flow direction. In some instances it is desirable as a flame ignition and stability mechanism (e.g., combustordomes, augmentors, and flame holders) while in others it is a 

necessary evil (e.g., dump diffusors or scramjet side walls). In 

either case, it usually is of relatively large scale and plays a significant role in the device’s effectiveness-thus making its prediction 

of primary importance. 

The general approach used to attack this problem employs 

algorithms to solve the full turbulence-averaged Navier-Stokes 

equations although recent works based on interaction concepts 

have indicated that some simplification of the diffusion process is 

possible. There has been good progress in the solution of such 

flows at the 2-D level with pioneering work being focused on the 

3-D problem. Here the two principal difficulties appear to be elimination of false (numerical) diffusion and modeling of real turbulent 

diffusion. This problem is especially acute and important because 

it competes with the real physics in the process that controls the 

combustor and combustion process. More research focused on the 

numerical representation of 3-D thin viscous shear layers between 

regions of forward and reverse rotational flows is needed to avoid 

the need for massive computer resources in representing the critical 

physics. 

With regard to heat transfer it is obvious that combustor 

durability is critically dependent on the ability to assess heat 

loads due to convection and radiation to the walls. Current CFD 

technology is unable to help much in representing the convection 

tf 

‘v 1I’ ’ 
57 

heat load due to the extremely complicated nature of the surface 

boundary layers (e.g., very thin, 3-D, and film cooled). Accurate 

prediction of the radiative heat load (which can equal or even 

dominate the convective load) is limited due to the inability to 

solve very sophisticated radiation models efficiently and the lack 

of a simpler representation of the processes involved. 

The numerical representation of the combustion process in 

aerospace application is a frontier problem. Although some progress is being made in the use of simplified (equilibrium chemistry) 

approaches, the field is still in the embryonic stage. Although 

very significant and promising efforts are presently ongoing, major 

challenges remain in the modeling of fuel phase change, finite rate 

chemistry, heat addition, turbulence, and large-scale instability 

representation. The problem area is ripe with opportunity because there exists both the need and use for fundamental work at 

all levels: delineating the dominant physics through benchmark experimentation; identifying new analytical models and their partial 

differential equation representation; and developing new solution 

methodologies employing novel computational techniques. 

The final area of concern is that of flow coupling. Nearly all 

combustors encounter very close coupling of multiple flow element 

interactions that are difficult to represent numerically. A vivid 

example is that encountered in a gas turbine where the inlet air 

is split into multiple 3-D passages and introduced into the combustion process through multiple ports possibly with swirl and 

certainly at large angles to the axial direction. The interaction 

of these multiple elements still represents a major challenge to 

numerical grid generation and boundary condition representation 

for the problem, and are only now beginning to be faced at the 

2-D level. 

FINDINGS 

Computational fluid dynamics is used extensively throughout 

the propulsion community principally because of a lack of alternatives for achieving insight into the basic controlling mechanisms 

of the complicated, highly coupled interacting aspects of propulsion 

fluid dynamics. It has proven a valuable design analysis tool in a 

wide variety of situations, often more than expected. Use of CFD is 

rapidly spreading and growing largely due to its ability to provide 

detailed diagnostic data and to address more complex flows. One 
58 

of the principal challenges now being faced is that of providing a 

way for this powerful but costly and time consuming capability to 

contribute directly to the formal design for complicated, strongly 

coupled propulsion system components. 

There has been a rapid increase of interest in advanced engines to propel hypersonic and transatmospheric vehiqles. The flow 

conditions found in these machines are so demanding that they 

cannot be reproduced in existing facilities. Consequently, the design and evaluation of these enormously powerful engines can only 

be done using CFD. Although existing codes have inadequacies in 

turbulence and chemistry modeling, they offer the only available 

capability and will carry an unusually large share of the design 

burden. Reliance upon thinly substantiated data bases and design 

tools places critical hardware programs at undesirable risk. 

In general, propulsion CFD is in a relatively mature state for 2- 

D potential flows with its capability dropping off systematically with 

the level of complezity. This can be better summarized in terms 

of the three major elements of propulsion devices: stationary systems, rotating systems, and combustors. For stationary systems 

CFD technology is in a relatively mature state for 2-D configurations, with a rapid drop-off in capability for 3-D or unsteady 

flows. Rotating systems capability naturally lags its stationary 

counterpart at all levels-most seriously in the area of viscous 

flow modeling. Combustors, themselves inherently complicated, 

show the lowest level of CFD development. 

The strong aerodynamic coupling of the major components of 

propulsion systems is another important issue. Examples of this 

include the influence of inlet distortion on the performance, stability, noise, and durability of the fan, the impact of burner exit 

temperature profiles on turbine life, and stagnation (nonrecoverable) stall. With the advent of larger capacity parallel processing 

computers, the time is rapidly approaching when serious consideration can be given to modeling interacting components using these 

unique computers and yet-to-be-perfected algorithms. 

The final area of overall concern involves experimental data 

bases. There is a definite need for benchmark ezperiments to assist 

and guide the development of codes especially un'th respect to turbulence modeling. Note that benchmark experiments are generally 

those that provide detailed data bases against which codes can be 

calibrated. Additionally, there is a need for diagnostic experimental studies that can provide the sort of detailed data that allow 

--u -u u -'K 
59 

Stationary Systems 

For stationary systems, Table 5 provides a clear picture of 

the situation-for 2-0 flow the computational technologies are well 

in hand. Additionally, as a third dimension is invoked (be it 

space or time), capability drops off dramatically as one encounters the complications of viscous effects to resolve near wall effects 

(e.g., skin friction, heating, shock-wave boundary-layer losses, and 

bleed flows). Complicated 3-D geometries require very large grids 

(> 105) and codes that are still too expensive to be of utility 

to any except a small segment of the potential user community. 

Additionally, turbulence modeling is rapidly becoming a critical 

issue because we are reaching the point where it is the final key 

factor in determining the payoffs in terms of durability and performance. This is one of the chief reasons why we must maintain an 

extensive program of benchmark and diagnostic experimentation 

for calibration of codes or turbulence model improvement. As a 

final but significant issue, there is a growing concern about numerical errors due to artificial viscosity, numerical diffusion, and 

other factors. A large number, perhaps the majority, of codes 

today contain “knobs” that set levels of these artificial effects in 

admittedly ad hoc fashion, thus limiting their credibility. This is 

especially important for hypersonic flows where a very high level 

of uncertainty exists, 

Rotating Systems 

With regard to rotating systems, Table 5 shows trends somewhat similar to that for stationary systems because this technology 

is following closely and building from its stationary counterparts. 

The major areas of concern are accurate modeling of transitional 

flow effects and unsteady gas dynamics. Transition modeling is 

especially important for propulsion systems where relatively low 

Reynolds numbers are encountered and the length of transition is 

a significant fraction of the component’s length (greater than 10 

percent of chord on turbine blades) or there are large freestream 

vortical disturbances feeding the transition process. As in the 
60 

stationary system case, benchmark diagnostic experimentation is 

presently required to relieve this uncertainty. With regard to unsteady gas dynamics there is a persistent need for advances in the 

analytical and computational modeling of flutter type gas dynamics, rotor and stator interactions, and noise. Advanced blade and 

propeller concepts are being paced by the inability to predict accurately the unsteady fluid dynamics encountered in catastrophic 

aeroelastic events. 

Combust ors 

For combustor systems, the story depicted in Table 5 needs 

some explanation. In general, these flows are so complicated that 

today only parabolized or turbulence-averaged Navier-Stokes approaches are fruitful. Some work on boundary layers is meaningful 

but only to the degree it helps resolve convective heating and viscous loss details near the combustor walls. Surprisingly, one finds 

in Table 5 that the capability levels for combustors in a given 

area are quite close and even ahead of the respective elements for 

stationary or rotating systems. This is not considered contradictory but rather reflects the relative nature of the grading system. 

Very rapid and encouraging progress is being made if this area, 

especially with regard to the numerical representation of inherently complicated geometries. The principal issues faced today 

are those of modeling mixing due to either turbulence, large scale 

secondary flows (steady or unsteady), or false diffusion. This, of 

course, is critical for it directly controls fuel distribution, phase 

change, heat addition, chemical kinetics, and other factors. The 

area of surface heat transfer (convection and radiation) is only 

now being addressed and will prove to be a pacing issue for CFD 

in the near future. 

Aerodynamic Coupling 

There is one remaining important issue to be considered-the 

strong aerodynamic coupling of the major components of propulsion systems. Important examples of this have included the influence of inlet distortion on the performance, stability, noise, and 

durability of the fan and the impact of burner exit temperature 

profiles on turbine life. The outstanding case of this type is stagnation (or nonrecoverable) stall, which results from the interaction 

t 

U. 

L 

u - 

I 

L 

'U ' 

E 

'U 

t 
61 

of at least the compressor, burner, and turbine, and causes the 

engine to lose thrust without either warning or a simple method 

to recover. With the advent of larger capacity parallel processing 

computers, the time is rapidly approaching when serious consideration can be given to modeling interacting components using these 

unique computers and yet-to-be-perfected algorithms. 

RECOMMENDATIONS 

As delineated in the above discussions there are several clearly 

defined areas that require further work in propulsion CFD: 

Turbulence and transition modeling for use in the turbulenceaveraged Navier-Stokes equation modeling of free shear and boundary layers is a critical issue for propulsion CFD. While significant 

and rapid progress is being made in most other related areas, little work is being focused on this item. The turbulence model is 

rapidly becoming the technology limit. Work should be focused in 

two areas: (1) generation of benchmark diagnostic experimental 

data bases at a time-resolved level, and (2) development of new 

turbulence models (time-averaged and time-resolved) focusing on 

freestream disturbance effects (e.g., unsteadiness, turbulence, and 

vorticity) and transition prediction. 

Elimination of numerical diflutsion, artificial dissipation, and 

smoothing procedures in CFD codes will be critical to enhancing 

their credibility and utility. Most large codes today are saddled 

with “knobs” that are empirically set to obtain the best fits and 

convergence. The inability to transform properly the integral 

or differential versions of the conservation laws for vortical and 

viscous flows into discrete linear algebraic equations is the issue 

here. Focus should be given to developing “smart” finite difference 

schemes with good fluid dynamics for the chosen algorithm. 

Analytical and computational modeling of aeroelastic loadings 

on blades and propellers continues as a frontier issue. Work should 

be encouraged in this unique, tedious, nonlinear environment with 

the goal of providing a reliable predictive tool to the structural 

analysis community. 

New techniques for predicting viscous wall effects and processes 

(e.g., skin friction, heat transfer, separation, and bleed) with reduced grid would greatly reduce computer power needs. Accurate 

prediction of such parameters is of critical concern to the performance and durability of propulsion systems. Yet the high “grid 
62 

rl 

tax" required to calculate these accurately is limiting propulsion 

CFD's utility. Therefore, attention should be focused on the development of new schemes for resolving the high gradient regions 

of turbulent and high Mach number fluid and thermal boundarylayer regions. 

Large-scale mizing phenomena as induced by azial vorticity 

should be studied further both analytically and experimentally. This 

technology would have a direct and significant payoff to the combustor and observables community. The principal issue here is 

resolution of the dominant physics and development of the analytical and numerical representation of those data. 

Three-dimensional unsteady fluid dynamics is at the heart of 

numerous elements of multistage turbomachinery. Computational 

techniques are needed to capture the multiscale elements of such 

flows, e.g., unsteady loads, heating, skin friction, and noise spectra. Additionally, time-resolved data are needed to sort out the 

important physics and provide a data base for modeling. 

Modeling of the interactive coupling of large aerodynamic components as it occurs in propulsion systems is a future issue for 

CFD. Representative examples are: airframe and engine integration, multistage compressors and turbines, inlet and fan interactions, and counterrotating propfans. For such environments it 

seems reasonable to expect the use of parallel processing computer architectures to be of key importance. There is a need for 

a small number of highly focused pathfinding programs aimed at 

establishing algorithms capable of handling this degree of sophistication. 

1 L i 

L E z L f: . 

L I E 
R 

I 

Turbulence in CFD 

OVERVIEW 

Turbulence greatly enhances the transport of energy, momentum, and mass across a given region and the rate of mixing and 

chemical reaction within the region. This occurs by a complex 

process of time-dependent, 3-D motions in which vortex stretching and distortion produce small scales of motion responsible for 

molecular mixing, and vortex amalgamation produces the large 

scales of turbulence responsible for turbulent transport. This vorticity arises from viscous effecta at solid surfaces and from density 

gradients. 

Turbulence contains a broad spectrum of scales. The largescale features of turbulent flows are strongly dependent on the 

flow geometry and environment, e.g., rotation. Small-scale turbulence, which adjusts more rapidly to changes, tends to be more 

isotropic but also reflects the environment in which it is embedded 

(the larger-scale turbulent motions). The large-scale motions are 

responsible for turbulent transport, and the small-scale motions 

provide intimate molecular mixing. 

These effects are included in CFD predictions in two general 

ways. With a turbulence “model” one tries to represent the average effects of these complex processes on the mean flow; this 

is very difficult to do in general because of the strong sensitivity 

of the turbulence to flow conditions. In turbulence “simulation” 

one includes the large-scale, time-dependent motions in the computation, perhaps using a model for the effects of the smaller scales; 

63 
64 

this is difficult because of the increased resolution required and the 

need for adequate prescriptions of turbulent boundary conditions. 

Whether turbulence is important in a flow computation depends upon the purpose of the computation. Turbulence is becoming increasingly important as CFD is applied to more complex 

flows. For example, in external aerodynamics with attached flow 

the engineer or designer often can get what he needs without consideration of turbulence; however, turbulence must be considered 

in analysis of gas turbine engines and high-performance aircraft. 

In many engineering problems turbulence is confined to thin 

shear layers, either in a boundary layer along a surface or in a free 

shear layer or wake. If the layer is thin, then the steady pressure 

field is affected only slightly by the turbulence, and an accurate 

calculation of the mean surface pressure (e.g., lift and form drag) 

can be made with the simplest of turbulence models. However, 

as one seeks to refine the accuracy of skin friction predictions, or 

to predict heat transfer, then good turbulence modeling becomes 

essential. Or, if one needs to know details of the time-dependent 

pressure field, say for load or sensor analysis or to determine the 

radiated sound, a very detailed consideration of the turbulence is 

essential. 

Transition from laminar to turbulent flow is important in 

external aerodynamics at high altitudes and in gas turbine engines 

under all operating conditions, and results in substantial increases 

in skin friction and heat transfer over the levels for laminar flow. 

The ability to predict the location of transition and its effects is 

essential for good design of such systems. 

Flow separation localized by a leading edge will cause the discharge of vorticity from the boundary layer into the external flow. 

Since the rate of spanwise mean vorticity flux in a boundary layer, 

for a good approximation, is dependent only on the freestream 

velocity and not on the structure of the boundary layer, inviscid 

(Euler) computational methods that put this vorticity into the 

flow and convect it correctly can give surprisingly good predictions for the global motions and pressure fields, both steady and 

unsteady. However, if the separation point is not localized by a 

sharp edge, but rather by the interaction of the boundary layer 

with the external flow, then a good turbulence model is essential 

for an accurate prediction of even the coarsest aspects of the flow, 

such as the pressure field. This includes cases where the boundary layer separation is induced by a shock wave, the shedding 
65 

of wing-tip vortices, separation on fuselages, and separations in 

turbomachinery that affect blade heat transfer and nyntem perfnrmance. 

Separated flows often possess large-scale unsteadiness. If the 

computation is to represent the average flow, the turbulence model 

must include the effects of this unsteadiness. Or, if the computation will be time-dependent, and will attempt to resolve the 

large-scale unsteadiness, then the turbulence model must include 

the effects of the unresolved turbulence scales. If the unsteadiness 

is largely 2-D, a 2-D time-dependent computation might be used, 

but a model for the effects of 3-D turbulence structures must be 

included. These structures and the transport that they produce 

are strongly influenced by such effects as flow curvature and unsteadiness and these effects must be included in the turbulence 

model if an accurate description of the unsteady 2-D flow is to 

be obtained. Even if the computation is 3-D and timedependent, 

with the goal of resolving all of the large-scale turbulence, a model 

for small-scale turbulence will still be required. 

In turbulent flows with chemistry, detailed turbulence modeling is essential for accurate predictions of all parameters affected 

by the flow composition. In this case the thinness of the turbulent 

layer offers no escape from the need for detailed consideration of 

the turbulence and the need for a turbulence model. Since molecular mixing takes place on the smallest scales, accurate modeling 

of the small-scale turbulence is essential for accurate combustion 

predictions, even if the large-scale turbulence is resolved in the 

computation. 

TURBULENCE-AVERAGED 

NAVIER-STOKES EQUATIONS 

The Navier-Stokes equations @e., the exact equations of me 

mentum, energy, mass, and species conservation in general timedependent, 3-D form) are assumed to describe the flow in full 

detail, including viscous flow phenomena and diffusive energy and 

species transport. Extensions of these equations may be necessary 

for nonequilibrium low-density hypersonic flows as discussed in 

Chapter 5. 

Direct numerical solutions of these equations, accurate to all 

temporal and spatial scales of motion, are now practical only for 

the simplest of turbulent flows at relatively low Reynolds numbers. 
66 

Such simulations are of great potential for use in evaluating and 

developing tuihlence models, and this exploitation of CFD is 

in its infancy. Direct simulation of practical engineering flows at 

moderate and high Reynolds numbers is impossible now or in the 

foreseeable future. Large eddy simulations (LES) will also be of 

limited design utility for the remainder of this century. 

Engineering calculations must instead be based on what we 

shall term the turbulence-averaged Navier-Stokes (TANS) equations. Practically all CFD calculations of the type reported to be 

Navier-Stokes are in fact based on one of two forms of turbulence 

averaging; most computations are based on the averaging procedure developed in the last century by Osborne Reynolds and are 

more properly termed "Reynolds-averaged Navier-Stokes," and 

most compressible computations employ Favre (mass-weighted) 

averaging, and would be more properly termed "Favre-averaged 

Navier-Stokes." LES are based on a different type of turbulence 

averaging, in which the averages are over the unresolved scales of 

motion. Other averaging methods, perhaps based on the orderedlarge-scale structures known to dominate turbulent flows, are expected to be used in the near future. This section refers to the 

Navier-Stokes equations, averaged by some appropriate method, 

as the TANS equations. 

CAPABILITIES OF TURBULENCE 

MODELS AND SIMULATION 

In many engineering problems the dependent variables of the 

TANS equations are all that is of interest. These include the 

mean velocity field, mean pressure field, and other mean prop 

erties. The TANS equations contain turbulent transport terms 

(e.g., Reynolds stresses and turbulent heat fluxes) for which models must be provided. En the usual formulations these involve 

statistical correlations between fluctuating components of quantities measured at the same point in space-time. In some cases 

other turbulence parameters are desired as computational output 

(for example fluctuation amplitudes or correlation lengths). 

The job of the turbulence model is to provide an accurate rep 

resentation of the connections between the turbulence quantities 

needed in the TANS equations and other turbulence parameters 
67 

of interest. This prescription usually includes a combination of algebraic and evolution equations connecting the turbulence parameters with the TANS dependent variables. Since only one-point 

statistical quantities are required in the usual TANS equations, 

most turbulence models deal only with one-point turbulence par ame ters . Ideally one would develop models in a hierarchical manner, 

with simpler models being derived from more complex models by 

simplifying approximations and the more complex models themselves being consistent with (and perhaps calibrated by) numerical 

simulations of turbulence. This is not the case, but it is the line of 

development that should be followed in the future. 

For purposes of this discussion, turbulence models and simulations are divided into seven basic categories: 

1. Local algebraic models 

2. Scale-evolution models 

3. Transport-evolution models 

4. Probability density functions (pdf) models 

5. Spectral interaction models 

6. Turbulence simulations 

7. Emerging ideas 

The review of the status of each of these activities is based 

on a combination of the knowledge of the committee members in 

this area, the results from the surveys described in Appendixes 

B and C, and discussions with leading researchers and CFD code 

developers. 

Local Algebraic Models 

These models relate the turbulent stresses and transports to 

local features of the mean flow, usually through a recipe for a mixing length. The survey revealed that there are many CFD codes 

incorporating models of this type. The Baldwin-Lomax model is 

the most common, primarily because of its ease of implementation, though other models in this class can be more accurate. This 

model was developed by experts in CFD, who for the most part 

did not have deep knowledge of turbulence. As a consequence its 

main virtues are computational utility. 

Models of this type work reasonably well in the simple flows 

for which they have been tuned. They are more than adequate for 
68 

problems in which turbulent transport is not important. Because 

they, in essence, assume that the turbulence has relaxed to equilibrium with the local mean conditions, they do not make any explicit 

consideration of the history of the turbulence. Consequently, they 

do not work well where the mean conditions change abruptly or 

whenever a significant region of the flow is affected by turbulent 

transport. 

There is little new development in models of this type because 

physically motivated models with more structure are proving to 

be better tools for extending turbulence modeling to more difficult 

situations. 

Scale Evolution Models 

These models relate the turbulent transport to a combination 

of local mean field features and a few (1-3) scalar parameters of the 

turbulence. Partial differential equations for the evolution of scalar 

turbulence parameters are solved along with the mean momentum, 

energy, and mass conservation equations, which are coupled to the 

turbulence parameters through local algebraic stress tensor models. Thus, these models take explicit account of the history of the 

turbulence scales but assume that the nondimensional turbulence 

structure is in equilibrium with the local mean field and turbulence 

parameters. 

The evolution equations are based on exact equations derived 

from the Navier-Stokes equations, with models for the unresolved 

statistical quantities. Usually one parameter is a velocity scale 

and the other carries the information on length scales; this avoids 

the need to prescribe the mixing length by an algebraic recipe. 

The k-epsilon 2-equation turbulence models are of this type. The 

committee's survey showed that a surprising number of CFD codes 

are capable of including such models. 

These models generally offer a good first-order estimate of the 

characteristics and physics of simple separated flows or flows with 

gradual changes in boundary conditions, but can be less accurate 

than finely tuned algebraic models in some cases. Current models 

fail in flows with strong rotation, density gradients, energy release, 

and so forth. 

The algebraic tensorial structure model is a critical element of 

such models. Many of these models use an eddy viscosity, which 

assumes that the principal axes of the turbulent stress tensor are 

I 

I 
69 

aligned with those of the mean strain-rate tensor. This is not 

true in shear flows, but the model coefficients are adjusted to 

give the right shear stress, which then makes the normal stresses 

incorrect. In thin shear layers where the normal stresses are not 

very important, good results can be obtained. But in rapidly 

strained flows, including flows at separation and reattachment, 

this model breaks down. The models do very poorly in 3-D (in 

the mean) flow, for example in the boundary layer at a wing-body 

junction or in the boundary layer on a swept wing. 

The usual algebraic structure model is such that most predict 

an unrealizable turbulence state (e.g., impossible stresses and negative energy) during a sudden increase in the mean strain rate, 

for example, as a boundary layer approaches a 3-D obstacle. This 

contributes to the poor performance of these models under rapidly 

changing conditions. 

Similar problems arise in heat transfer modeling, where it is 

usually assumed that the turbulent heat transport vector aligns 

with the mean temperature gradient. This is not true in shear 

flows, which exhibit anisotropic diffusion in which mean temperature gradients in one direction produce turbulent heat transports 

in other directions. Current models do not incorporate this important effect. 

Scale evolution models that make use of more appropriate 

algebraic equations for the stress tensor have also been developed 

(the k-epsilon “algebraic” models). These can be constructed 

in a way that removes the unrealizablity described above, with 

the turbulent heat transport in the proper relationship to the 

mean temperature gradient. Models of this type are at a level of 

complexity near the maximum commensurate with use in large 

CFD codes for design calculations, and thus these methods would 

appear to deserve much more attention. 

Practically all modeling of this type is limited to incompressible flows, and there is very little activity in extending these models 

to supersonic and hypersonic flows. Most of the original work and 

current development of these new models is taking place in Europe. There is some activity in extending these methods in the 

NASA laboratories, notably the NASA Ames Research Center, 

but very little other effort in the United States along these lines. 

It is apparent that significant improvements in the capabilities 

of these models can be achieved through use of data from direct 

, 
70 

turbulence simulations and insight from experiments. The engineering importance of these models is such that the U.S. would 

benefit from a much more vigorous program in this direction. 

Transport Evolution Models 

These models are based on exact equations for the evolution 

of the transport terms in the TANS equations. The equations 

for the transport terms are derived from the parent Navier-Stokes 

equations, and are added to the TANS equation set. In addition, 

one must include at least one equation for a parameter carrying the turbulence length scale information; the dissipation-rate 

(epsilon) equation is commonly used. Local algebraic models are 

made for the higher (still one-point) statistical quantities in these 

equations. The "Reynolds stress transport" models, in which the 

Reynolds stresses become dependent variables of the partial differential equation system, are of this type. The survey revealed 

that only a few codes can incorporate such models, which add 

considerably to the cost of computation. 

Most modelers regard the epsilon equation as providing length 

scale information, and some have criticized this modeling because 

it does not take different length scales in different directions into 

account. But in fact the epsilon equation provides Lagrangian 

timescale information, which can be thought of as information 

on the lifetime of coherent structures; the resulting length scales 

acting in transport terms can be shown to be different in different 

directions. This connection of the epsilon equation with coherent 

structure lifetime may explain why models based on the epsilon 

equation do surprisingly well. 

'llansport evolution models take explicit account of the history of both the scales and structure of the turbulence. These 

models allow the principal axes of the turbulent stress tensor to 

align differently from those of the strain-rate tensor. However, 

they require models for many other turbulence quantities, and the 

evolution is often determined by a delicate balance of these modeled terms, few of which have ever been measured. The net effect 

is that, while transport evolution models are fundamentally on 

stronger ground than lower-level models, they can perform poorly 

if they have not been finely tuned for flows very much like the 

one being studied. They are especially vulnerable if they have not 

1 

i 
71 

been developed on sound mathematical grounds, which has often 

been the case. 

The problems of realizability that plague scale transport models also arise in transport evolution models, but in much more 

sophisticated ways. If the algebraic models for the higher-order 

terms are not properly configured, the model will respond incorrectly to rapid changes in the mean strain-rate and will predict 

unrealizable turbulence states. It is possible to construct these 

models properly so that this does not happen, but fully realizable 

models of this type are extremely complicated, involving a great 

number of tensor combinations of the dependent variables with 

many coefficients. Nevertheless, this complexity has been shown 

to be useful in providing much better models for mixing, buoyancy, 

and combustion. Hence, this type of modeling is beginning to find 

its niche. It is important to develop proper models of this type in 

order to assess their limits, to aid in the hierarchical development 

of simpler models, and for use in complex flow regions where their 

special capabilities are required. 

Among the important effects for which this type of proper 

transport evolution modeling is likely to be useful are density 

gradients, rotation, high freestream turbulence, energy release, 

and other situations where the turbulence is strongly altered by 

some imposed effect. Engine flows form a prime example of such 

conditions. For example, turbulent reattachment, turbulent heat 

transfer, and stage losses easily can experience errors on order of 

a factor of two. Turbulent reattachment is controlled by turbulent 

transport of momentum normal to the separation bubble boundary; this transport is often strongly influenced by flow curvature 

in the streamwise direction, as well as by 3-D effects. 

The ability to put these effects in parametric form in existing models is inadequate or nonexistent. Turbulent heat transfer, 

both external and internal to the blades, is strongly influenced 

by rotation and by pseudo-buoyancy associated with temperature 

fluctuations; the ability to develop parameters of these effects is inadequate or lacking for existing models. Stage losses are associated 

with secondary flows, as well as with separation and boundarylayer development. Development of parameters for turbulence in 

all of these cases in rotating systems is inadequate or absent for 

present models. Without doubt, properly developed transport 

evolution models can be made to handle these effects better, and 

such model development needs competent attention. 
72 

Similar needs arise in flows on airframes. Reattachment in 

such flows is nearly always 3-D, and the location of the reattachment line is determined by turbulent momentum exchange between 

the separation zone and the surrounding flow. This can involve 

complicated secondary flows and complex curvature-induced vortices. Existing models show the parameters of these effects poorly, 

if at all. The physics of the situation is relatively clear; what is 

needed is to apply the understanding of the physics to sophisticated model development. 

There is hope that improved turbulence models can be used 

to elucidate these effects. Fundamental experiments needed to 

calibrate models for these effects are needed. The domain of both 

the models and the experiments need to be extended, especially 

to transonic and supersonic conditions. 

Simplified transport evolution models, constructed in an ad 

hoc way so that they behave properly in the limits of strong 

strain-rate and guided by the more rigorous modeling theory, offer 

a possible compromise between the desire for rigor and the need 

for computational simplicity. Such models are probably the most 

complex that are likely to be used extensively in large CFD ap 

plications during the remainder of this century. Only one or two 

groups in the United States are active in this area. 

Probability Density Function Models 

Driven by problems in combustion modeling, there is increasing interest in turbulence models based on probability density 

functions (PDF). Most of the work has dealt with the joint PDF 

for the velocity components, density, and species concentrations 

at a single space-time point. The equation for the PDF is derived 

from the Navier-Stokes equations. 

This restricted PDF is not sufficient to describe all statistics 

of a turbulence field (the infinite multipoint joint PDF would be 

required), but it does appear to offer some advantages. Specifically, 

the transport terms in the TANS equations do not need to be 

modeled because they are one-point statistical quantities that can 

be calculated from the PDF. However, other terms do need to be 

modeled. 

The models cannot be based on data because none exist. 

Attempts to generate data from simulations on such flows are 

just now beginning. Because of the vast data required for model 
73 

calibration, full simulations will very likely be the only way to 

calibrate PDF models. 

The partial differential equation for the PDF needs to be 

solved in a high-dimensional space defined by the local fluctuation 

variables and the flow geometry. Hence, Monte Carlo computational methods are usually employed. Better numerical methods 

for solving partial differential equations in spaces of high dimension could accelerate the pace of PDF model developments. 

In time these models may develop to the point where they are 

useful for studying isolated engineering problems in combustion. 

They are likely to be very useful in developing simpler computational models for such flows. It is not expected that they will be 

needed or used for flows not involving chemical reaction. 

Spectral Interaction Models 

The models described above are all one-point models in that 

the statistical quantities involved are correlations of turbulence 

quantities at a single point. Models that make use of two-point 

statistical quantities, such as the two-point velocity correlation, 

have also been developed. An equivalent representation is provided by the spectrum function, which can be calculated from the 

two-point correlation. Equations for the two-point correlation, or 

alternatively €or the spectrum, can be derived from the NavierStokes equations. The resulting equations contain terms that must 

be modeled. The Direct Interaction Approximation is a model (in 

spectral space) of this type. 

In principle these models would overcome a serious shortcoming of one-point models, namely their inability to deal with 

turbulence in which spectral nonequilibrium is important (large 

eddies out of equilibrium with the small eddies). This phenomenon 

occurs under rapid deformation, for example in the flow near a 

stagnation point or with sudden energy release. In practice this 

is not so easy because the two-point equations must be solved in 

a high-dimensional space defined by the coordinates of the two 

points. As a result of this complexity the development of these 

models has concentrated on homogeneous flows, where only the 

separation coordinates are important, and there have as yet been 

no engineering applications of the models. 

The atmospheric sciences community in the United States, 

centered at the National Center for Atmospheric Research 
74 

(NCAR), has led in the development of spectral methods, which 

have provided insight into turbulence physics but little in the way 

of computational tools for engineering. However, the French are 

actively attempting to bring two-point models to bear on aircraft 

problems, chiefly through a cooperative effort between the university group at Lyon and the aerospace company, Dassault. A 

complete US. program on turbulence modeling certainly should 

include a small effort along these lines. 

Turbulence Simulations 

Direct numerical simulations of all important scales of turbulence (also called full turbulence simulations or FTS) are possible 

only at relatively low Reynolds numbers. Current computers can 

treat only the simplest flows in the vicinity of transition Reynolds 

numbers; by the end of this century the range will be extended up 

ward by something less than an order of magnitude, still far below 

the range of most engineering applications. Nevertheless, these 

simulations provide extremely valuable data for use in developing 

simpler models of turbulence and transition. 

Large eddy simulations (LES) use time-dependent equations 

averaged over the unresolved scales of motion, with models for the 

subgrid stress term introduced by the averaging, to calculate the 

evolution of the largescale field. The idea is that the smaller scales 

of turbulence can be modeled more simply since they adjust more 

rapidly to local conditions. The large, computed scales are responsible for most of the turbulent transport. Moreover, since the 

dominant eddies are resolved directly, a relatively unsophisticated 

turbulence model can be used for the small-scale turbulence. 

It has been established that relatively simple subgrid models 

allow accurate LES of simple turbulent flows (e.g., channel flow) 

where neslip or periodic boundary conditions can be applied. 

To become useful in engineering calculations, better methods for 

modeling the unresolved turbulence, particularly near walls, are 

needed, and methods for creating turbulent inflow conditions with 

the proper structure are needed. Subgrid turbulence models need 

to be extended to variable resolution grids and to be made dynamic 

so that the small scales can be out of equilibrium with the large 

scales. Active research on all of these problems is under way, 

primarily for incompressible flow. These programs need to be 

extended to flows with large separated regions and to supersonic 
75 

flows. This expansion in effort will require considerably more 

manpower than is presently deployed in LES development. 

Perhaps early in the next century LES will begin to become 

a useful tool for design computations. LES will be essential for 

such problems as sound generation by, and transmission through, 

boundary layers. But for the next decade or so the first use of LES 

will be to provide data that cannot be measured experimentally 

on simple flows to guide the development of simpler models of the 

scale evolution and transport evolution type. 

The first engineering problems likely to be tackled by LES are 

those in turbomachinery. Here the freestream turbulence levels 

are very high, the scales are very large, the flows are far from 

equilibrium and often contain embedded vortices, and it may prove 

very difficult to develop a generalized turbulence model to handle 

this complexity. Moreover, the Reynolds numbers in these flows 

are relatively low, and so the flows are closer to what can be 

reached by FTS. Indeed, FTS and LES may prove to be the only 

viable means for computing such flows. With a strong, ordered 

program of development, it should be possible to begin LES and 

FTS exploration of these flows in the next decade. 

The United States is clearly the world leader in developing 

LES and FTS, which are being pursued vigorously in NASA centers and other government laboratories and in a few key universities with supercomputer access. However, the Europeans and 

Japanese are very actively exploring LES for industrial applications, and the French Electricite de France (EDF) is probably the 

world leader in industrial development of LES. The U.S. lead in 

this area is threatened by these developments, especially in Japan 

where Cray performance is available on the national network for 

under $100 per hour. 

With the advent of a set of national supercomputer centers, 

formed by the National Science Foundation (NSF), an expansion of 

effort in LES and FTS is beginning. A typical doctoral dissertation 

project involving a fundamental FTS or LES may involve several 

hundred hours of supercomputer computation. In view of this 

enormous expense, it is important that such computations be 

very well planned, not unknowingly duplicated at another center, 

and that the computed data be saved and archived so that it 

can be used by other investigators. At present there is no national 

coordination of these efforts and few serious attempts at archiving, 

thus many of these very heavy computations will be of dubious and 
76 

temporary value. Some method for coordination of these activities 

is needed. 

Emerging Ideas 

There are a number of emerging ideas that may have an impact on turbulence modeling and simulation. The concept of fractal geometry, in which structures are seen as containing smaller 

structures of similar shape, which in turn contain smaller structures of similar shape, and so on, is an appealing model for the 

smaller scales of turbulence. It is possible that this concept, and 

the related quantifications of renormalization theory, will lead to 

formulation of better subgrid scale models for LES, and perhaps 

to improved algorithms for LES. These ideas deserve attention, 

but are at present far from implementation in practical problems. 

Dynamical systems theory, which deals with discrete coupled 

systems, shows that systems which appear to be deterministic can 

exhibit chaos, which is reflected in a broad spectral response that 

appears to be random. Such a system is said to possess a “strange 

attractor.” In essence, the nonlinear coupling reduces the number 

of parameters (dimensions) required to describe states of the system. The statistics of a low-dimensional system could presumably 

be described by the coupled dynamics of a very few modes, and so 

the hope is that very complex systems might thereby be described 

more simply. There is some indication that certain turbulent flows 

may be of this type. However, if the dimension is very high, as 

appears to be the case in shear flows, statistical approaches and 

LES would probably remain the preferred alternatives. 

These ideas may find their way into LES in a more immediate 

way. Ideas for using the dynamical system equations to generate 

chaos, either for the subgrid model or for turbulent inflow conditions, have been suggested. Initial explorations of these ideas are 

under way. 

An old type of stochastic model, the Cellular Automata (CA) 

model, is being reexplored and was recently publicized by Los 

Alamos as revolutionizing CFD. In this approach a very simple 

bit switching algorithm is executed; the statistics of the resulting bit states have been shown, in the limit of many elements 

and switches, to approach the solution of partial differential equations resembling the Navier-Stokes equations. The advance at Los 

Alamos was in the algorithm used for the bit switching, which 

\ 

l 
77 

makes the process run faster. However, it has only been shown for 

2-D cases, and really has yet to produce anything resembling true 

turbulence. Examinations of this work have shown that the advances in the CA algorithm are certainly significant for CA theory, 

but -that the prospect for a serious impact on modeling practical 

turbulent flows, at high Reynolds numbers and especially at high 

Mach numbers, is remote. For equivalent precision, the cost of CA 

models is prohibitive. 

The existence of large-scale structures in turbulent shear flows 

has been recognized for two decades. But this obviously important physical information has as yet to find its way into turbulence 

models, except through the interpretation of the time-scale information carried by the epsilon equation as a large-eddy coherence 

time. A viable turbulence model based on the concept of coherent 

structures would seem a logical target for a concentrated effort 

in turbulence modeling, but no such model has been put forth 

as yet. This would seem to be an avenue worthy of exploration. 

Although this has occurred to many capable researchers, the right 

combination of ideas has yet to emerge. 

A method for turbulence simulation that does recognize cherent structures is vortex dynamics, in which one follows the 

motion of concentrated vortices in an inviscid flow. These methods are reasonably well-developed for incompressible, ZD, inviscidly dominated turbulent flows. Some special 3-D incompressible 

flows dominated by concentrated vortex structures have also been 

treated. Extensions to compressible flow and to vorticity diffusion 

may not be possible, and so this method of turbulence simulation 

may be quite limited in practical problems. Nevertheless, it has 

provided and will continue to provide valuable insight into the 

physics of large-scale turbulent motions that undoubtedly will be 

helpful in structuring simpler turbulence models. Further development of this technology should be an important component of 

future turbulence research. 

CURRENT STATUS OF 

TURBULENCE MODELING 

The discussion in the previous section highlighted the problems and potentials of turbulence modeling. Table 6 presents an 

evaluation of the state of turbulence modeling as it applies to 
78 

TABLE 6 Status of Turbulence Modeling 

Local 

Algebraic 

Flow Scale Transport 

Evolution Evolution 

Simple Shear Flow 2.0 

1 .o 

1.0 

1.0 

1 .o 

1.0 

1 .o 

Flow Complexity: 

Scalar Transport 

Separation/Reattachment 

Rotation/Curvature 

High Strain Rate 

3-D Mean Flow 

Suuersonic Flow 

2.0 3.0 

2.0 3.0 

1.0 2.5 

1.5 2.5 

1.5 0.0 

1.5 0.0 

1.0 0.0 

Scale: 

0 Not tried yet 

1 Tried with generally poor results 

2 Demonstrated with fair success 

3 Case has been made that it is useful 

4 Being used productively in research 

5 Operationally effective in codes requiring its capabilities 

Large Eddy 

Simulation 

3.0 

3.0 

0.0 

3.0 

3.0 

0.0 

0.0 

simple shear flows and flow features characteristic of complex engineering flows. The four main types of turbulence models and 

simulations viewed as having significant impact on CFD in the 

remainder of this century are rated in terms of'their states of 

development and promise. This subjective evaluation is based on 

performance at the 1981 Stanford Conference on Computation of 

Complex Turbulent Flows, recent evaluations by NASA personnel, 

input gathered from various members of the committee, and the 

working knowledge of those committee members most active in 

turbulence modeling and simulation. 

FINDINGS 

Turbulence modeling is becoming a pacing item in the development of CFD codes for many engineering design applications. The 

modeling problem is acute with regard to aircraft engine design 

codes, and is becoming a key factor in airframe codes in situations where viscous effects dominate. In many of today's codes 

the significance of turbulence modeling is masked by excessive numerical diffusion in the algorithms. Once this numerical diffusion 

is eliminated the significance of the turbulence model will become 
79 

clearly evident, It is anticipated that turbulence modeling will be 

There is no substitute for modeling of some sort. LES or FTS 

-may help develop models and even be used in some critical design 

situations, but they will not serve most of the needs in design 

codes in the foreseeable future. Furthermore, better turbulence 

modeling is also needed for LES. 

The committee's level of effort survey (see Chapter 3 and Appendix C) indicated that only about 4 percent of the effort in CFD 

development is being devoted to the improvement of turbulence 

models, and only about 5 percent to turbulence simulations. Thus, 

less than IO percent of the CFD eflort is being applied to developing 

better methods for treating what is possibly the greatest challenge 

for applied CFD. It is believed that this effort is low in view of the 

importance of the problem. 

ennentid elem-ent. in CPD cedes fcr 'he re=.=inder =f the century. 

RECOMMENDATIONS 

Turbulence model improvements are possible and will be made 

most rapidly by careful interaction among direct simulation, large 

eddy simulation, theory, model development, and experimentation. 

' It is essential that this development be carried out in cooperation 

with the user community and tailored to the needs of CFD code 

developers. The effort should be conceived initially in those few 

places where a critical mass of talent can be achieved, but also 

must extend as broadly as possible so that a wide diversity of 

competent ideas are brought to bear. 

The importance of turbulence and transition in engineering 

systems needs to be reemphasized. Perhaps the exciting new developments in the ability to control turbulence, through understanding of its physics, can be used to spark the needed reawakening. Special programs of the type that have given CFD and 

supercomputers such a big push in the last decade should be considered as a means for accelerating the pace of developments in 

turbulence modeling and simulation. A renewed interest in fundamental graduate education in turbulence will be necessary to 

produce the proper training required for this task. 

Supercomputer- based research employing full turbulence simuhtiOfl8 and large eddy simulations needs to be continued and coordinated to eliminate unnecessary duplication of effort and to ensure 

that data are archived in a way that maintains them for future 
analysis. These simulations form a critical basis for fundamental understanding and a framework for development of practical 

turbulence models. 
APPENDIXES 
A __ __ J!-- A ~ppellulK LL 

Trends in Computer Hardware 

Affecting CFD 

Computational fluid dynamics (CFD) will evolve in response 

to changing computational, graphical, and diagnostic capabilities as well as new models, algorithms, and eventual applications. 

The anticipated future environment in which CFD will be pursued will influence significantly the algorithms that are used and 

the methodology by which computational research is pursued. 

Detailed projections concerning these emerging capabilities and 

approaches are bound to be highly uncertain, as with most emerging new technologies. Detailed consideration of future hardware 

trends is beyond the charge of the committee, nevertheless, certain 

future trends are evident. 

As the cost of fast computer memory decreases, the appearance of memory-intensive models using many millions of words of 

primary data is already beginning to influence algorithm selection 

in favor of faster, more efficient algorithms that make less use 

of each computational degree of freedom. This means that much 

more data will have to be analyzed and stored in the future. This 

trend is likely to accelerate because a gradual shift to highly parallel computing seems inevitable, and laser disk storage is becoming 

a reality. Fine-grained parallelism, through pipelining and vector 

processing, has taken over the supercomputing scene in the last 15 

years. It seems likely, given the intrinsic limitations imposed by 

the speed of light and component technology, that this trend toward increasingly extensive parallelism will continue in the future. 

Already systems with tens of thousands of small processors are being produced and sold commercially, and the U.S.-manufactured 

supercomputers are multiprocessors. 

83 
Using this brand of multitasking, i.e., coarse-grained parallelism, is very different from scalar or vector processing. Different 

algorithms will appear to be most favorable for this kind of supercomputing, and new programming methodologies will have to be 

adopted. In some cases, simpler, less-accurate solution algorithms 

and grids will be adopted because they lend themselves better 

to computation on highly parallel processors. In other cases the 

mathematical models themselves will evolve to reflect the computer systems on which they are being implemented. Multilevel 

parallelism, for example a vector of loosely coupled array processors or a large closely coupled matrix of small scalar processors, will 

force additional changes in modus operandi. A number of fairly 

high-performance systems are available commercially at modest 

price so the CFD community should have a reasonable corporate 

understanding of these capabilities when the time comes to replace 

Crays and Cyber 205s. 

Continually improving supercomputer performance has already brought another evolutionary change that may force the 

CFD community to exhibit a broader mix of skills than has been 

necessary to date. The feasibility of large 3-D calculations on a 

daily (and even hourly) basis deluges the researcher in data which 

he may be ill-equipped to handle. The numbers are formidable 

in analyzing multidimensional evolving simulations. Special diagnostic and data base management software are needed. Simply 

storing restart dumps from a three-dimensional (3-D) calculation 

(e.g., 40 megabytes per dump) at frequent enough intervals to 

reconstruct some of the important temporal variations (e.g., every 

250 cycles for 25,000 steps) fills several large disks. 

Interactive graphics methods and the associated hardware and 

software will become absolutely crucial to monitoring, interpreting, understanding, and presenting the computational results. Although these are not new issues, they are becoming dominant 

considerations for the future. High-performance graphics workstations will not be sufficient to solve the problems. It is also 

necessary to move data from the computational and bulk storage 

facilities directly onto the graphics screen at multimegabyte/sec 

speeds. Reasonably continuous variation (2 12 frames/sec) and 

reasonably high resolution (1,024 x 1,024 pixels, for example) require average data transmission at the 12 Mbyte/sec level. For 

comparison, MC 68000-based graphics workstations can accept 

new data at only 150-200 Kbytes/sec today and thus treat only 
85 

one image at a time. Electronic storage of 1000-frame ‘movie” 

sequences for analysis, about 1-2 minutes when projected, will 

require about 1 gigabyte of storage. The CFD community will 

have to pursue this technology base steadily in using the emerging 

parallel processing systems effectively. A 256 x 256 interactive 

graphics system is required simply to monitor the instantaneous 

performance of a 64K processor system with only 1 pixel of color 

per processor. 
Appendix B 

NATIONAL RESEARCH COUNCIL 

COMMISSION ON ENGINEERING AND TECHSICAL 5'1 STELIS 

1101 Conintunon AWIIYO Hashmglon D C 20418 

July 24, 1985 

Dear Colleague: 

The National Aeronautics and Space Administration has requested the 

Aeronautics and Space Engineering Board of the National Research Council to 

assess the current status of computational fluid dynamics (CPD) in the design 

of aerospace systems and to make recommendations regarding future needs. We 

would appreciate your assistance in helping to determine the state of the art 

in ComputatlOMl codes for aerodynamic and aerothermodynamic applications. 

Enclosed is a questionnaire designed to obtain information about CPD codes 

currently in use. We are seeking a broad, representative sampling of codes 

and have tried to design the questionnaire to require a minimum of your time 

to respond And yet to provide useful information for the purposes of the 

survey. If you, or those on your staff who are developing or using CFD codes, 

would return completed forms for individual codes by the middle of August, it 

wuld help us proceed to the next phase of our study. I believe you will find 

the questionnaire self-explanatory, but I would like to say that any other 

comments in addition to the informtion sought will be welcome. If you have 

any questions, please telephone me at 817/763-1609 or the Study Director, Dr. 

Robert H. Korkegi, at 202/334-2855. 

For your information a list of study participants is enclosed with the 

questionnaire. We will, of course, provide you with copies of the report when 

we have completed our talk. 

Sincerely, 

Assessment of Current nd Future Capabilities 

in Computational P1 id Dynamics 

-- J 

Enclosures: 2 copies of questionnaire, I 

Study membership list 

Stamped return envelope 

-u -u Y "U 
87 

CFD CAPABILITY ASSESSMENT 

I. Category of Application (circle approprlate items) 

A. Flow Type 

1. External Air Vehicle 2. Propulsion Systen 

3. Hypersonic Flow 1. Other 

8. Geometry Applicability 

1. External Air Vehicle 

a. Airfoil, airfoil flap 

b. Wing, wrng-body, wing body-nacelle/stores, 

c. 

d. Lr 

Complex configurations - multi surface flaps, 

ropulsron rnteractrons, etc. 

2. Propulsion Systam 

a. Inlet, nozzle, nacelle, duct, mixer 

b. FUI, compressor, turbine c. Combustor, afterburner, plume 

d. Propeller, rotor e. Rocket components 

f. Other 

3. Hypersonic Flow 

A. Body, wing 

b. Wing body, wing body fin c. Intagrated propulsion system, plume, etc. 

d. Other 

C. Range of Applicability (shade applicable range) 

Mach: I I I I I I 

I I I I 1 I 

0.0 0.1 1.0 2.0 10.0 

Angle of Attack 

(degrees) 0 5 10 15 20 25 

YES UQn 

SeparAted Flow 

mrgy Addition (propulsion) 

u 

'Ih ' 
88 

CID CAPABILITY ASSESSMENT 

Page 2 

11. Equations Solved (Check Appropriate Element) 

A. Equations 

CONTINUUM 

Inviscid 

Linear 

Small Disturbance 

Full Potential 

Euler 

Other 

Laminar Boundary 

Turbulent Boundary 

Full Llloinar Flow 

Parabollzed N.S. 

Thin Layer N.S. 

Full Navier Stokes 

Other 

Monte Carlo 

Other 

Vi8COUS 

Layer 

Layer 

PARTICULATE 

B. Turbulence 

For ViScOUI 8OlutiOn8 give nam of turbulence model U8.d lf 

poaslble 

OtherVire indicate turbulence model wed IS f0llWS: 

Eddy trmrport coefficients (mixing langth aodel) 

k-c with eddy viscority model 

k-r wzth other algebraic rtress model. 

Uyaolds etress transport equation 

Other 

C. Additional ?matures 

Electromagnetic 

Combustion 

Other 

f 

u 
89 

CtD CAPABILITY ASSESSMENT Paqe 3 

A. code identifier/n.nc 

8. poaition in developmnt CYClC (See Attachment A) 

I I1 I I11 I IV V oemonstrat%on/ Evolving into Learning how to MAture capability Confidence usable code use it effectively (Oosign tool) 

C. 

D. 

E. 

F. 

G. 

a. 

I. 

~ype of user required 

1 I I Code Developer CPO Professional Engineer/Designer 

computer typdresources rmuired 

What additional work is neded? 
CFD CAPABILITY ASSESSMENT 

Page I 

fv. Believability 

A. What is the confidence level of the solution's validity: 

Matches expected Agrees with other Agrees with precise 

physical trends accepted solutions experimental data 

8. Has the sensitivity to grid size/aeometry been established? 

YES NO n 

C. What flow quantities are output? 

I3 pressure 0 density 0 gas composition 

temperature 0 velocity II 

What integrated quantities? 

lift 0 

streamline tracing 0 heat transfer 

drag: 

moments a loads 0 

0 wave 0 profile n induced 0 friction u 

I3 propulaion : component efficiency n preraure drop 

(_I cyclo efficiency 

D. For what caser ha. the code been validated? 

- Case Publiahed? 

1. 

2. 

3. 

Nma & affiliation: 

U U Y -'K 

2: P i 

fr 

k 

~ 

Li 
91 

e. 

.. ?> 

I 

m I m 

c z L n 
Appendix C 

NATIONAL RESEARCH COUNCIL 

COMMISSION ON ENGINEERING ANDTECHNICAL SYSTEMS 

1101 Conraluhon Avenue Wihin@on D C 20(18 

October 2, 1985 

Dear Colleague: 

As part of an assessment of current capabilities and future 

directions in computational fluid dynamics, we are making an assessment of the level of effort being devoted to fundamental developments 

in numerical methods--algorithms, grids, turbulence model development, 

code development, experiments, and code evaluation. We would very 

much appreciate your assistance in obtaining this information on the 

programs that you sponsor that involve these areas. 

attached form you will find a glossary describing the information that 

we request on the form. In a few days a member of our committee will 

call you to answer any questions that you may have. We realize that 

the completion of this form will require subjective judgement on your 

part, and we very much appreciate the time you will take in making 

these judgements. 

On the back of the 

We would appreciate receiving the information. together with any 

comments you may care to provide on the trends of the research in your 

program, by November 1, 1985. Please return the forms directly to this 

office. 

Yours truly, 

Robert H. Korkegi 

Study Director, Assessment of 

Current Capabilities and Future 

Directions in Computational 

Fluid Dynamics 

Enclosures: 1. Survey with glossary 

2. committee membership list 
93 
94 

Glossary 

1. 

2. 

Project Descriptors: essence of project in a few key words 6.1 

= basic research, 6.2 = applied RtD. 

Approximate total annual man-years: estimated effort for the 

project; for university, research, you may wish to use 0.2 manyears per faculty member and 0.5 man-years per graduate 

student as a standard. 

Estimated percentages used for CFD/Turbulence Modeling: 

% of listed total effort used in each category, based on your 

understanding of the project. 

CFD Development: development of algorithms, grid generators, diagnostics or display software; 

a) General capability for potential flow, Euler, and 

Navier-Stokes solvers 

b) LES/FTS for timadependent, three-dimensional eddy 

simulation 

Turbulence Model Development: rigorization and significant 

generahation of existing models; new ideas for model formulation; distillation of simple models from complex ones; 

fabrication of special models for simple cases. 

6. Baseline Experiments: canonical experiments designed to 

guide/ calibrate/evaluate models; complex experiments used 

to evaluate models and codes. 

3. 

4. 

5. 

a) 

b) 

lab. laboratory experiments for above 

comp. eddy simulation for above 

7. Code/Model Testing: code execution for evaluation of codes 

and models. 

c t L I 

L E z P L I i i rl 
I; 

1.- n Appenalx u 

List of Contributors to 

CFD Questionnaire 

Persons from the following organizations responded to the 

questionnaire in Appendix B with data regarding specific CFD 

codes. 

ACUREX CORPORATION 

Mountain View, California 

AEROSPACE CORPORATION 

Los Angeles, California 

AIR FORCE WEAPONS LABORATORY 

Kirtland Air Force Base, New Mexico 

AMTEC ENGINEERING, INC. 

Bellevue, Washington 

ARNOLD ENGINEERING DEVELOPMENT CENTER 

Arnold Air Force Station, Tennessee 

BOEING AEROSPACE COMPANY 

Seattle, Washington 

BOEING COMMERCIAL AIRPLANE COMPANY 

Seattle, Washington 

BOEING MILITARY AIRPLANE COMPANY 

Seattle, Washington 

CALSPAN FIELD SERVICES/AEDC 

Arnold Air Force Station, Tennessee 

COLORADO STATE UNIVERSITY 

Fort Collins, Colorado 

CORNELL UNIVERSITY 

Ithaca, New York 

95 
COLUMBIA UNIVERSITY 

New York, New York 

DOUGLAS AIRCRAFT COMPANY 

Long Beach, California 

DCW INDUSTRIES, INC. 

La Canada, California ERA, INC. 

Albuquerque, New Mexico 

Kent , Washington 

Fort Worth, Texas 

Cincinnati, Ohio 

Operations) Indianapolis, Indiana 

Bethpage, New York 

Bethpage, New York 

Windsor Locks, Connecticut 

Fort Collins, Colorado 

Ames, Iowa 

Houston, Texas 

Los Alamos, New Mexico 

Huntsville, Alabama 

Cambridge, Massachusetts 

St. Louis, Missouri 

St. Louis, Missouri 

Moffett Field, California 

FLOW RESEARCH COMPANY 

GENERAL DYNAMICS CORPORATION 

GENERAL ELECTRIC COMPANY 

GENERAL MOTORS CORPORATION (Allison Gas Turbine 

GRUMMAN AEROSPACE CORPORATION 

GRUMMAN CORPORATION 

HAMILTON STANDARD/UNITED TECHNOLOGIES 

INSTITUTE FOR COMPUTATIONAL STUDIES 

IOWA STATE UNIVERSITY 

LYNDON B. JOHNSON SPACE CENTER 

LOS ALAMOS NATIONAL LABORATORY 

GEORGE C. MARSHALL SPACE FLIGHT CENTER 

MASSACHUSETTS INSTITUTE OF TECHNOLOGY 

McDONNELL AIRCRAFT COMPANY 

McDONNELL DOUGLAS RESEARCH LABORATORY 

NASA AMES RESEARCH CENTER 
97 

NASA JOHNSON SPACE CENTER 

Houston, Texas 

NASA LANGLEY RESEARCH CENTER 

Hampton, Virginia 

NASA LEWIS RESEARCH CENTER 

Cleveland, Ohio 

NAVAL SURFACE WEAPONS CENTER 

Silver Spring, Maryland 

NIELSEN ENGINEERING RESEARCH, INC. 

Mountain View, California 

NORTHROP CORPORATION 

Palos Verdes Peninsula, California 

OHIO STATE UNIVERSITY 

Columbus, Ohio 

PEDA CORPORATION 

Palo Alto, California 

PENNSYLVANIA STATE UNIVERSITY 

University Park, Pennsylvania 

PRATT dc WHITNEY (UNITED TECHNOLOGIES) 

East Hartford, Connecticut 

PRINCETON UNIVERSITY 

Princeton, New Jersey 

ROCKWELL INTERNATIONAL 

Canoga Park, California 

RUTGERS UNIVERSITY 

Piscataway, New Jersey 

SANDIA LABORATORIES 

Albuquerque, New Mexico 

SANDIA LABORATORIES 

Livermore, Caliiornia 

SCIENCE APPLICATIONS INTERNATIONAL CORPORATION 

Princeton, New Jersey 

SCIENCE APPLICATIONS INTERNATIONAL CORPORATION 

Wayne, Pennsylvania 

SYSTEMS, SCIENCE AND SOFTWARE 

San Diego, California 

UNITED TECHNOLOGIES RESEARCH CENTER 

East Hartford, Connecticut 

UNIVERSITY OF ARIZONA 

Tucson, Arizona 

Ii If li 1' u li- . x If 'II- 
98 

UNIVERSITY OF CALIFORNIA AT DAVIS 

UNIVERSITY OF TENNESSEE 

UNIVERSITY OF TEXAS AT AUSTIN 

VRA, INC. 

Davis, California 

Kerrsville, Tennessee 

Austin, Texas 

Blacksburg, Virginia