NASA Contractor Report 181817 

FEASIBILITY AND BENEFITS 

OF LAMINAR FLOW CONTROL 

ON SUPERSONIC CRUISE 

AIRPLANES 

A.G. Powell 

McDonnell Douglas Corporation 

Douglas Aircraft Company 

Long Beach, California 90846 

i 

S. Agrawal 

T.R. Lacey 

McDonnell Douglas Corporation 

McDonnell Aircraft Company 

St. Louis, Missouri 63166 

CONTRACT NAS1-18037 TASK #3 

JULY 1989 

National Aeronautlcs and 

Space Admrnistratlon 

Lanulay Resoarch Center 

Hampton. Virginia 23665-5225 
FOREWORD 

This document covers the contract work performed by the Douglas Aircraft 

Company and the McDonnell Aircraft Company of the McDonnell Douglas 

Corporation, on Laminar Flow Control (LFC) under NASA Contract NAS1-18037 

entitled "Study of Supersonic Laminar Flow Aerodynamics". 

part of an overall effort to improve the energy efficiency of a wide range of 

airplane types, supported by NASA through its Langley Research Center. 

This contract is 

Acknowledgement for their support and guidance is given to Mr. R.D. 

Wagner, NASA LFC Project Manager, to Mr. D.V. Maddalon, the NASA Contract 

Manager, and also to Drs. W. Pfenninger, F.S. Collier, and C. Vemuru. 

The Douglas personnel primarily responsible for this work were: 

Mr. M. Klotzsche Director, CRAD Programs 

Dr. A.G. Powell Principal Investigator, Aerodynamics 

Mr. A.A. Killeen Aerodynamics 

Mr. W.E. Herr Aerodynamics 

The McDonnell personnel primarily responsible for this work were: 

Mr. T.R. Lacey Branch Chief, Aerodynamics Technology 

Dr. S. Agrawal Lead Engineer, Aerodynamics 

Mr. T.A. Kinard Aerodynamics 

The McDonnell Douglas Research Laboratories personnel involved in a 

consultory capacity were: 

Dr. A.B. Cain Scientist, Aerodynamics Research 

PRECEDING PAGE BLANK NOT FILMED 

iii 
. 

CONTENTS 

1 . SUMMARY ......................................................... 1 

2 . INTRODUCTION .................................................... 3 

3 . SYMBOLS AND ABBREVIATIONS ....................................... 7 

4 . LAMINARIZATION CONSIDERATIONS ................................... 13 

5 . DAC AST WING - LFC FEASIBILITY .................................. 19 

6 . MODIFIED AST WING - LFC BENEFIT ................................. 39 

7 . MACH 4 TRANSPORT - FEASIBILITY .................................. 53 

8 . LFC ON SUPERSONIC FIGHTERS ...................................... 57 

9 . SF-1107 FIGHTER WING ............................................ 59 

10 . SF-1302 FIGHTER WING ............................................ 83 

11 . CRITICAL TECHNICAL ISSUES ....................................... 91 

12 . RECOMMENDED RESEARCH PROGRAM .................................... 95 

13 . TEST FACILITIES ................................................. 99 

14 . CONCLUDING REMARKS .............................................. 103 

REFERENCES ...................................................... 105 

APPENDIX A: LFC DRAG ACCOUNTING AND 

PUMPING SYSTEM THERMODYNAMICS ....................... 109 

APPENDIX B: CALCULATION OF ISENTROPIC EQUIVALENT 

Cp FOR SUPERSONIC LEADING ..................... 117 

RECEDING PAGE BLANK NOT FlLMEO 

V 

I 

. 
FIGURES 

5.10 

5.11 

5.12 

NUMBER TITLE PAGE(S) 

1.1 MDC SUPERSONIC LFC STUDY CONFIGURATIONS.................... 2 

2.1 PROCEDURE FOR PREDICTING TRANSITION AND SUCTION I LAMINARIZATION REQUIREMENTS. ............................... 4 

2.2 COMPUTER CODES............................................. 4 I 

I 

4.1 OBSTACLES TO LAMINARIZATION................................ 16 

4.2 COMPONENT VELOCITY PROFILES................................ 16 

4.3 LEADING EDGES - SUBSONIC VS. SUPERSONIC....,............... 17 

5.1 DAC MACH 2.2 AST POTENTIAL LAMINARIZATION PROBLEMS......... 20 

i 

I 5.2A-F BOD-60 EULER VS. W.T. TEST DATA............................ 21-23 I 

i 5.3A-F FM-67 EULER VS. W.T. TEST DATA............................ 24-26 

5.4 AST WING STATIONS FOR B.L. STABILITY ANALYSIS.............. 27 

, 5.5 ATTACHMENT LINE CONDITIONS - INBOARD AST WING.............. 28 

I 5.6 CONVERSION OF GORTLER VORTICES TO CROSSFLOW WAVES.......,.. 29 , 

5.7 

5.8 

5.9 

POLAR COORDINATE SYSTEM USED IN THE K-C CODE............... 30 

STATIONARY CROSSFLOW WAVES - SUPERSONIC L.E. 

USING ATTACHMENT LINE STARTING SOLUTION.................... 31 

LFC FEASIBILITY ON ORIGINAL AST WING 

UPPER SURFACE SUCTION DISTRIBUTIONS........................ 32 

LFC FWIBILTY ON ORIGINAL AST WING 

LOWER SURFACE SUCTION DISTRIBUTIONS........................ 34 

THEORETICAL MINIMUM SUCTION DUCT AREA AT WING ROOT......... 35 

LFC PLANFORM MODIFICATION.................................. 36 

ATTACHMENT LINE CONDITIONS - 

ORIGINAL, AND MODIFIED AST WINGS............................ 37 

I vii 

1 PRECEDtNG PAGE BUNK NOT FILMED 
5.14 

6.1 

6.2 

6.3 

6.4 

6.5A 

6.5B 

6.6A 

6.6B 

6.7A 

6.7B 

6.7C 

6.8 

6.9 

ZERO-SUCTION ATTACHMENT LINE MOMENTUM THICKNESS 

REYNOLDS NUMBER AS A FUNCTION OF ANGLE OF ATTACK......... .. 38 

TYPICAL COMPONENT VELOCITY PROFILES 

IN A REGION OF WEAK CROSSFLOW.............................. 40 

CHORDWISE PRESSURE DISTRIBUTIONS - 

MODIFIED AST WING. ......................................... 41 

UPPER SURFACE FINAL SUCTIONS - 

MODIFIED AST WING.......................................... 42 

LOWER SURFACE FINAL SUCTIONS - 

MODIFIED AST WING.......................................... 43 

BOUNDARY LAYER STABILITY 

MODIFIED AST WING - FINAL SUCTION 

UPPER SURFACE @ ETA = 0.18................................. 44 

BOUNDARY LAYER STABILITY 

MODIFIED AST WING - INCREASED L.E. SUCTION 

UPPER SURFACE @ ETA = 0.18................................. 45 

BOUNDARY LAYER STABILITY 

MODIFIED AST WING - FINAL SUCTION 

LOWER SURFACE @ ETA = 0.74................................. 46 

COMPONENT VELOCITY PROFILES 

MODIFIED AST WING - FINAL SUCTION 

LOWER SURFACE @ ETA = 0.74, X/C - 0.03..................... 46 

BOUNDARY LAYER STABILITY 

MODIFIED AST WING - FINAL SUCTION 

UPPER SURFACE @ ETA = 0.74................................. 47 

COMPONENT VELOCITY PROFILES 

MODIFIED AST WING - FINAL SUCTION 

UPPER SURFACE @ ETA = 0.74, X/C = 0.022.................... 48 

COMPONENT VELOCITY PROFILES 

MODIFIED AST WING - FINAL SUCTION 

UPPER SURFACE @ ETA = 0.74, X/C = 0.31..................... 48 

LFC BENEFIT ESTIMATE 

ORIGINAL AST WING, 

BASED ON FLAT PLATE 

SKIN FRICTION CALCULATIONS................................. 50 

LFC BENEFIT SUMHARY 

MODIFIED AST WING, 

INCLUDING SUCTION AND 

PUMPING SYSTEM EFFECTS..................................... 52 

Viii 
7.1 

7.2A 

7.2B 

7.2C 

8.1 

8.2 

8.3 

9.1 

9.2 

9.3 

9.4 

9.5 

9.6 

9.7 

9.8 

9.9 

9.10 

9.11 

DAC HSCT CONFIGURATION..................................... 53 

SCRAM EULER SOLUTION FOR HSCT CONFIGURATION 

16 PERCENT LENGTH AXIAL STATION............................ 54 

SCRAM EULER SOLUTION FOR HSCT CONFIGURATION 

48 PERCENT LENGTH AXIAL STATION............................ 55 

SCRAM EULER SOLUTION FOR HSCT CONFIGURATION 

80 PERCENT LENGTH AXIAL STATION............................ 55 

SF-1107 SUPERSONIC CRUISE FIGHTER CONFIGURATION............ 57 

SF-1302 SUPERSONIC CRUISE FIGHTER CONFIGURATION............ 57 

A CHARACTERISTICS COMPARISON OF THE SF-1107 

AND SF-1302 AIRCRAFT....................................... 58 

SURFACE PRESSURE DISTRIBUTION AT 50% SEMISPAN 

SF-1107 WING WITH BICONVEX SECTION......................... 59 

UPPER SURFACE PRESSURE CONTOURS, SF-1107 WING.............. 60 

DISTRIBUTION OF VELOCITY Ue ON THE UPPER SURFACE 

AT 50% SEMISPAN, SF-1107 WING.............................. 60 

DISTRIBUTION OF VELOCITY We ON THE UPPER SURFACE 

AT 50% SEMISPAN, SF-1107 WING.............................. 61 

SECOND DERIVATIVE Cp" VS. X/C ON THE UPPER SURFACE 

AT 50% SEMISPAN, SF-1107 WING.............................. 61 

BOUNDARY LAYER VELOCITY PROFILES ALONG THE RADIAL 

DIRECTION ON THE UPPER SURFACE AT 50% SEMISPAN, 

SF-1107 WING, NO SUCTION................................... 62 

CONSECUTIVE VELOCITY PROFILES IN SCALED COORDINATES 

AT 50% SEMISPAN, SF-1107 WING, NO SUCTION.................. 62 

SECOND DERIVATIVE OF VELOCITY VS. SCALED NORMAL 

COORDINATES AT FOUR CONSECUTIVE CHORD STATIONS, 

SF-1107 WING, NO SUCTION................................... 63 

WALL SHEAR STRESS VS. X/C AT 50% SEMISPAN, 

SF-1107 WING............................................... 63 

EFFECT OF SUCTION ON VELOCITY PROFILES AT 25% CHORD 

AND 50% SEMISPAN LOCATION, SF-1107 WING.................... 64 

EFFECT OF SUCTION CROSSFLOW PARAMETER, DELTCF, AT 

50% SEMISPAN LOCATION, SF-1107 WING........................ 65 

ix 
9.12 STATIONARY CROSSFLOW INSTABILITY WITHOUT SUCTION, 

SF-1107 WING.................. ............................. 66 

9.13 FREQUENCY VS. CORRESPONDING TO N = 9, NO SUCTION, 

50% SEMISPAN, SF-1107 WING................................. 67 

9.14 AMPLIFICATION FACTOR FOR DIFFERENT FREQUENCIES 

NO SUCTION, 50X SEMISPAN, SF-1107 WING........... .......... 68 

9.15 BOUNDARY LAYER VELOCITY PROFILES AT PSI = 70 DEGREES, 

50% SEMISPAN, NO SUCTION, SF-1107 WING..................... 69 

9.16 BOUNDARY LAYER VELOCITY PROFILES AT PSI = 80 DEGREES, 

50% SEMISPAN, NO SUCTION, SF-1107 WING..................... 69 

9.17 BOUNDARY LAYER VELOCITY PROFILES AT PSI = 85 DEGREES, 

50% SEMISPAN, NO SUCTION, SF-1107 WING..................... 70 

9.18 BOUNDARY LAYER VELOCITY PROFILES AT PSI = 90 DEGREES, 

50% SEMISPAN, NO SUCTION, SF-1107 WING..................... 70 

9.19 EFFECT OF SUCTION ON AMPLIFICATION FACTOR AT PSI = 80 

DEGREES AND F = 5000 He, 50% SEMISPAN, SF-1107 WING........ 71 

9.20 AMPLIFICATION FACTOR FOR DIFFERENT WAVE ANGLES WITH 

SUCTION, 50% SEMISPAN, M = 2.0, (Y = 4 DEG., 

SF-1107 WING........ ....................................... 72 

9.21 EFFECT OF SUCTION ON THE GROWTH OF STATIONARY WAVES 

50% SEMISPAN, SF-1107 WING................................. 73 

9.22 EFFECT OF SUCTION ON THE GROWTH OF NONSTATIONARY 

CROSSFLOW WAVES, 50% SEMISPAN, M = 2.0,0= 4 DEG., 

SF-1107 WING............................................... 73 

9.23 EFFECT OF SUCTION ON THE GROWTH OF NONSTATIONARY 

CROSSFLOW WAVES, 50% SEMISPAN, SF-1107 WING................ 74 

9.24 BOUNDARY LAYER VELOCITY PROFILES AT PSI - 70 DEG., 

50% SEMISPAN, WITB SUCTION, SF-1107 WING................... 75 

9.25 BOUNDARY LAYER VELOCITY PROFILES AT PSI = 80 DEG., 

50% SEMISPAN, WITH SUCTION, SF-1107 WING................... 75 

9.26 BOUNDARY LAYER VELOCITY PROFILES AT PSI = 85 DE., 

50% SEMISPAN, WITH SUCTION, SF-1107 WING................... 76 

9.27 BOUNDMY LAYER VELOCITY PROFILES AT PSI = 90 DEG., 

50% SEMISPAN, WITH SUCTION, SF-1107 WING................... 76 

9.28 BREAKDOWN OF WETTED AREAS LAHINARIZED, 

SF-1107 CONFIGURATION...... ................................ 78 

X 
9.29 EFFECT OF LAMINARIZATION ON SKIN FRICTION DRAG 

COEFFICIENT, SF-1107 CONFIGURATION......................... 78 

9.30 EFFECT OF LAMINARIZATION ON MINIMUM DRAG COEFFICIENT 

AGAINST MACH NUMBER, SF-1107 CONFIGURATION................. 79 

9.31 EFFECTS OF LFC ON PERFORMANCE/AIRCRAFT SIZE 

SF-1107 CONFIGURATION...................................... 79 

9.32 FIGHTER SWEEP MISSION FOR THE SF-1107 CONFIGURATION........ 80 

9.33 COMBAT AIR PATROL MISSION FOR THE SF-1107 

CONFIGURATION. ............................................. 81 

10.1 UPPER SURFACE PRESSURE CONTOURS, SF-1302 WING.............. 83 

10.2 PRESSURE COEFFICIENT VS. X/C, 18.75% SEMISPAN 

SF-1302 WING............................................... 84 

10.3 PRESSURE COEFFICIENT VS. X/C, 50X SEMISPAN 

SF-1302 WING............................................... 84 

10.4 PRESSURE COEFFICIENT VS. X/C, 81.25% SEMISPAN 

SF-1302 WING............................................... 85 

10.5 CRITICAL STATIONARY CROSSFLOW WAVE, 

LEADING-EDGE REGION, SUCTION ON. 

50% SEMISPAN, SF-1302 WING................................. 86 

10.6 CRITICAL STATIONARY CROSSFLOW AMPLIFICATION 

IN THE ADVERSE PRESSURE GRADIENT REGION, WITH SUCTION 

50% SEMISPAN, SF-1302 WING................................. 87 

10.7 CRITICAL STATIONARY CROSSFLOW AMPLIFICATION 

IN THE ADVERSE PRESSURE GRADIENT REGION, INCREASED 

SUCTION, 50% SEMISPAN, SF-1302 WING........................ 87 

10.8 BREAKDOWN OF WETTED AREAS LAMINARIZED, 

SF-1302 CONFIGURATION...................................... 88 

10.9 EFFECT OF LAMINARIZATION ON MINIMUM DRAG COEFFICIENT, 

SF-1302 CONFIGURATION...................................... 89 

10.10 EFFECTS OF LFC ON BASELINE PERFORMANCE, 

SF-1302 CONFIGURATION...................................... 89 

10.11 FIGHTER SWEEP MISSION FOR THE SF-1302 CONFIGURATION........ 90 

13.1 COMPARISON OF STUDY AND POSSIBLE TESTBED AIRCRAFT.......... 100 

13.2 COMPARISON OF POTENTIALS OF F-15A AND F-16XL 

AIRCRAFT AS TESTBEDS....................................... 100 

xi 
13.3 

13.4 

A1 

A2 

A3 

A4 

A5 

A6 

A7 

AS 

B1 

PLANFORMS OF STUDY AND POSSIBLE TESTBED AIRCRAFT ........... 101 

F-16XL WITH LFC GLOVE ...................................... 102 

LFC WING DRAG ACCOUNTING ................................... 110 

FLAT PLATE DRAGS VS . SUCTION ............................... 110 

SUPERSONIC SYMMETRIC AIRFOIL ............................... 111 

LPC PUMPING SYSTEM MODEL . IDEALIZED ....................... 112 

THERMODYNAMIC PERFORMANCE OF LFC SYSTEM .................... 113 

INCORPORATION OF SUCTION POWER INTO DRAG ACCOUNTING ........ 114 

FUEL-EQUIVALENT DRAG INCREMENT DUE TO LFC PUMPING .......... 115 

ALGORITHM FOR SUCTION SYSTEM DRAG ACCOUNTING ............... 116 

ALGORITHM TO COMPUTE EQUIVALENT ISENTROPIC 

Cp FOR STABILITY ANALYSES. SUPERSONIC 

LEADING EDGE CASE .......................................... 118 

xii 
1- SUMMARY 

This report details the results of a preliminary investigation into the 

application of Laminar Flow Control (LFC) technology to Supersonic cruise 

airplanes. The objectives of this study were: (1) to determine the 

applicability and realistic benefit potential of LFC technology on a 

representative supersonic transport, (2) to determine the applicabilty of LFC 

to other supersonic airplane types, (3) to identify the technical issues 

critical to supersonic LFC application, (4) to determine how those issues can 

be addressed through flight and wind-tunnel testing, and (5) to make 

recommendations for a future development program. 

Vehicle types studied include an advanced supersonic transport 

configuration designed for transpacific range at 2.2 Mach, a Mach 4.0 

transport, and two generic supersonic-cruise fighter concepts. These are 

shown in figure 1.1. 

subsonic and transonic wing laminarization have been applied and in some 

cases modified; the results are presented in this report. 

Laminar flow control methodologies developed for 

I 

For the wing of the Mach 2.2 supersonic transport, it was found that 

attachment line conditions could be made acceptable with moderate suction. 

Upper and lower surface suction to the control surface hingeline has been 

found to be the preferred LFC approach due to the large wing chorda, the 

absence of midchord shocks, and the relatively even benefit split between 

upper and lower surfaces. Suction requirements were found to strongly depend 

on the wing pressure distribution. Accelerating chordwise pressure 

distributions were found to be detrimental to laminarization due to 

associated cross-stream pressure gradients and the resulting boundary layer 

crossflow. The lowest required suction levels were found for distributions 

characterized by spatially rapid flow acceleration in the leading edge region 

followed by a nearly constant-velocity rooftop. Realistic LID improvements 

in the range of 12 to 17 percent were found for the DAC Advanced Supersonic 

Transport. 

For the Mach 4 High-speed Connnercial Transport (HSCT) design considered, 

attachment line conditions were found to prohibit laminar flow. 

management and boundary layer stability considerations make this vehicle an 

impractical candidate for laminarization. 

Thermal 

The McAir SF-1107 and SF-1302 generic supersonic cruise fighter 

configurations were found to be relatively easy to laminarize, but showed 

small sizing benefits, due to their short mission ranges. 

It is concluded that LFC technology is applicable to supersonic cruise 

airplanes of the Mach 2 class, even ones of large size. 

aerodynamic problems have been identified as a result of this study. Several 

key technical issues, such as contamination avoidance and excresence criteria 

have been identified, and should be persued further through analysis and 

research testing in wind tunnels and flight. 

No intractable 

1 i 
DAC D3233-2.2-1C AST 

A 

McAIR SF-1302 FIGHTER 

McAIR SF-1107 FIGHTER 

Figure 1.1 MM: SUPERSONIC LFC STUDY CONFIGURATIONS 

2 
2, INTRODUCTION 

The high fuel fractions typical of long range airplanes give increased 

leverage to cruise drag minimization technologies, such as Laminar Flow 

Control (LFC), in terms of size, weight, and perhaps even vehicle cost. 

Current projections show increa e 

times are sufficiently long to warrant interest in supersonic flight. 

traffic for certain distant city pairs, 

particularly on the Pacific Rim tlf . For many of these, subsonic travel 

Subsonic LFC technology development has been ongoing for many years, and 

many excel ent papers have been written describing progress made in this 

area (29394f. Improvements in the computation of inviscid and viscous flows 

and in predicting transition have allowed an expansion of the knowledge base 

from that of the X-21 program in the early and mid 60s. 

NASA Leading Edge Flight Test program established the practicality of systems 

designed to protect the critical wing leading edge region from contamination 

in day-to-day service, and demonstrated the efficacy of electron-be 

perforated wing skins for boundary layer stabilization using suction 

For example, the 

arp4 1 . 

The application of LFC technology to supersonic airplanes has received 

far less attention. Supersonic wind tunnel investigations have established 

the fea ibili y of achieving substantial runs of laminar flow using wall 

suction 95*6975. The effectiveness of the linear theory transition 

prediction methods ha 

variety of geometries fa? . However, the feasibilty and performance benefits 

of laminarizing supersonic cruise airplanes have not been established. 

een demonstrated over a wide Mach number range for a 

This report describes a first attempt at addressing the aerodynamic 

problems associated with applying LFC technology to the wings of supersonic 

cruise airplanes. 

leading-edge wing designs. 

the aerodynamic benefits of doing so are addressed. 

The study considered both supersonic and subsonic 

The feasibility of laminarizing such wings and 

The process of determining the laminarization potential and benefit for a 

specific configuration at a particular flight condition requires the accurate 

computation of both the outer inviscid flowfield and the boundary layer. 

Specific criteria are applied to determine if the boundary layer can be 

stabilized and transition delayed to the extent desired. Of the various 

methods proposed for laminar boundary layer stabilization, low-level wall 

suction has proven to be the most versatile and practical in most instances. 

The minimum level of suction required for laminar boundary layer 

stabilization must be determined, and is a strong function of the pressure 

distribution imposed by the external flowfield. 

involved in the determination of the required suction distribution is shown 

in figure 2.1. 

The iterative procedure 

Current capabilities in laminar flow control have been largely built upon 

the NASA Lang e progr t develop lam na boundary layer stability codes 

such as SALLYtg7, MARI~lo~ , and COSAL t1l5. These and other 

analytical tools available at the time of this study are swIlmarized in figure 

2.2. 

3 
I 

4 

N-Factor 

1 

Adjust Sudin 

Requirements 

toprovide t 

CODE TYPE DESCRIPTION 

OUTER INVISCID W 

FLO-67 EULBR uMc/BODY. suBsow1c/suPERsoN1c 

BOD-60 EuLKIl wrNc/BODY. sv8scmIc/suPERsONIc 

SCRAn EuLKR WINC/BODY. MCHING SupEIIsoNIC 

BOUNDARY Urn 

KAUPS-CEBECI CMPRE3SIBL.E. LAHINAB WLY. SUCTION 

ALLOVED, COWICAL APPBOXMATION TO 3-D 

BLP -SIBIS. LAHIWAR AND TURBm 

2-D STRIP WITH SUCPION 

WINAIL BOUNDARY Uyllll STABILITY 

SALLY INCOCIPRESSIBLB, T-S AND CI 

MIA 1-1BLE. APPROXMATK. 

COSAL Co)(p11IIsSIBU. T-S AND CF 

STATIONARY CF OWLY 

PRESSURE DISTRIBUTIONS 

PRESSURE DISTRIBUTIONS 

INTEGRATED FORCES 

VELOCITY PROFILES 

FOR STABILITY ANALYSIS 

SKIN FRICTION DRAG, 

B.L. DISPUC- EFFECTS 

NOT US=. COSAL PREDECESSOR 

eimmINAgY SUCTION 

ESTIMATES 

SUCTION MINMIUTION 

Figure 2.2 COMPUTER CODES 

4 
I 

Of th 

layer ?13'S , and the COS& boundary layer stability code were used the most 

extensively. The HARIA crossflow stability code, although incompressible and 

approximate, was used to identify critical stationary crossflow waves, and to 

get an initial idea of the suction levels required in the leading-edge 

region. With the exception of the COSAL code, the application of these codes 

to the supersonic case required a certain amount of caution and some 

development, as they were written principally for the transonic case. 

the supersonic case, potential codes, such as FLO-22, were excluded, due to 

their inherent inability to properly account for shock waves. 

c des listed, the PLO-67 Euler(12), the Kaups-Cebeci boundary 

For 

5 
3. SYMBOLS AND ABBREVIATIONS 

A/C Aircraft, aerodynamic center 

Angle of attack 

Advanced, Medium Range Air-To-Air Missile 

Aspect ratio 

Advanced Supersonic Transport 

Referring to the boundary layer 

Chord, local wing chord 

Average chord, mean geometric chord 

Combat Air Patrol mission 

0, ALPW 

AMRAAM 

AR 

AST 

B.L. 

C 

- 

I C 

CAP 

CP Referring to boundary-layer crossflow or crossflow waves 

CP 

CFX 

Skin-friction coefficient 

Skin-friction coefficient component in radial coordinate 

direction, positive away from virtual tip of tapered wing 

as used in the Kaups-Cebeci (K-C) code 

CFZ Skin-friction coefficient component in circumferential 

direction, positive aft from leading edge of tapered wing 

as used in the K-C code 

Pressure coefficient 

Cp" Second derivative of pressure coefficient with respect to 

x/c. 

CPR 

cq 

Referring to compressor 

Suction coefficient: ratio of wall suction massflux to 

f reestream massf lux 

DAC 

D 

DP 

Douglas Aircraft Company, Long Beach, Ca. 

Drag force 

Drag due to pressures acting on body 

7 

1 

I 

PRECEDlNG PAGE BLANK NOT FILMED 
Dram 

Dtotal 

DV 

DW 

DELSTX 

w 

?, ETA 

PS 

F 

FF 

hO1 

hp, ALT 

HSCT 

K-C 

L.E. 

LFC 

L/D 

L.S. 

11 

12 

M 

H 

McAir 

Drag due to destruction of freestream momentum of captured 

suction air 

Total drag force 

Drag due to net effect of viscous shears acting on body 

Drag computed from wake momentum deficit 

Boundary layer displacement thickness associated with 

radial component velocity profile, as used in the K-C code 

Energy maneuverability 

Semispan fraction ,dimensionless normal coordinate in 

boundary layer, or efficiency 

Pumping system efficiency: ratio of nozzle thrust power to 

compressor input shaft power 

Physical frequency 

Fuel fraction: fraction of airplane takeoff gross weight 

due to fuel 

Height in boundary layer at which the crossflow velocity 

is one-hundredth of its maximum value 

Pressure altitude 

High-speed Conmercial Transport 

Referring to the Kaups-Cebeci conical laminar boundary 

layer code 

Leading edge of wing 

Laminar Flow Control 

Lift-to-drag ratio 

Referring to the wing lower surface 

Leading-edge sweep angle 

Trailing-edge sweep angle 

Mach number, million 

Mass flowrate 

McDonnell Aircraft Company, St. Louis, Mo. 

8 
N, N-factor 

NL sust 

NOZ 

Pin Ppump 

PSFC 

Reef 

Re, Rtheta 

% N=9 

s, sw 

TIC, t/c 

e 

TOGW 

T-S 

Natural log of the ratio of local amplitude to that at the 

neutral stability point, for a hypothetical boundary layer 

wave 

Maximum sustained load factor for given altitude and Mach 

conditions 

Referring to exhaust nozzle 

LFC compressor input shaft power 

Power specific fuel consumption; fuel flowrate per unit of 

output shaft power 

Specific excess power; maximum available steady-state 

climb rate at a given Mach number and altitude 

local orientation angle in a plane parallel to the surface 

bounding the flow, measured from the direction of the 

local boundary layer external velocity vector 

Total pressure; isentropic stagnation pressure 

Dynamic pressure 

Reynolds number 

Reynolds number based on freestream conditions and local 

chord 

Crossflow Reynolds number; Reynolds number based on 

maximum crossflow velocity, h01 as defined above, and 

local external fluid properties 

Momentum-thickness Reynolds number; Reynolds number based 

on freestream velocity, local external fluid properties, 

and local boundary layer momentum thickness 

Momentum-thickness Reynolds number at a point where a 

particular hypothetical boundary layer wave has reached an 

amplification factor of 9 

Wing gross planform area 

Wing section thickness/chord ratio 

Local boundary layer momentum thickness, angular 

coordinate in the K-C code 

Airplane takeoff gross weight 

Referring to Tollmien-Schlichting waves 

9 
TSFC 

T/W 

U 

U" 

UE, Ue 

U.S. 

W 

V 

VE 

Ve 

vi 

Vfs Ufs 

vlMX 

WEUFS 

w/s 

W.T. 

XIC 

XLENC 

Y 

y. 95 

Engine thrust-specific fuel consumption; fuel flowrate per 

unit of net thrust 

Airplane thrustlweight ratio 

Boundary-layer velocity component in the radial direction 

on a linearly tapered wing; positive away from the virtual 

wingtip 

Second derivative of u with respect to distance measured 

normal to the local wing surface 

Radial velocity component at the boundary layer edge 

Referring to the wing upper surface 

Boundary-layer velocity component in the circumferential 

direction on a linearly tapered wing; positive away from 

the attachment line along an arc at fixed distance from 

the virtual wingtip 

Boundary layer local total velocity, generalized velocity, 

or freestream velocity 

Local crossflow velocity; boundary layer velocity 

component in a direction perpendicular to the total edge 

velocity 

Total boundary layer edge velocity 

LFC pumping system exit velocity 

LFC pumping system inlet velocity 

Freestream velocity 

Maximum crossflow velocity 

Velocity ratio 

Airplane wing loading 

wE/ufs# as used in the K-C code 

Referring to wind tunnel 

Local chord fraction 

Wavelength/chord ratio, as used in the COSAL code 

Distance in a direction normal to the wing surface 

distance y above the wing surface at which the boundary 

layer total velocity is .95 of its edge value 

10 
I 

SLIMAX 

ZOIMAX 

301MAX 

Referring to maximum thrust conditions at sea level 

Referring to maximum thrust conditions at 20 kft 

Referring to maximum thrust conditions at 30 kft 

11 
i 

4. LAMINARIZATION CONSIDERATIONS 

The external and boundary layer flows over a swept wing are highly 

three-dimensional. 

early transition of the boundary layer. 

The first category is what Morkovin calls "bypass mechanisms 11(14). 

includes freestream turbulence, surface excresences, noise, vibration, and 

pre-existing turbulence created at points upstream. 

mechanisms is a prerequisite for laminar flow to exist, so they are listed 

first. 

insect remains and bird droppings pose a potentally great threat to 

laminarization. The penalties increase inversely with aspect ratio, since 

turbulent wedges caused by accreted excrescences occupy larger areas on low 

aspect wings. 

On a swept wing there are many mechanisms which can cause 

These are summarized in figure 4.1. 

mis 

The absence of these 

From a practical standpoint, wing surface contamination from accreted 

Along the attachment line of a swept wing, where the normal flow 

stagnates, there exists a boundary layer caused by the spanwise flow. 

leading-edge radius and sweep are constant, this boundary layer will have 

congruent mean flow profiles at all span stations. 

be stable as a laminar layer, can be laminar but unstable to disturbances, or 

can be turbulent. If the laminar boundary layer is unstable to disturbances, 

turbulence from some point inboard can propagate outward along the leading 

edge, making laminar flow over the affected part of the wing impossible. 

Boundary layer waves can also cause transition in the flow along the 

attachment line. This is the Tollmien-Schlichting mechanism, and is 

discussed el w. 

Pfenninger 

momentum-thickness Reynolds number, Re. 

the transonic regime are 100, as the upper limit for a stable laminar 

attachment line, and 240 as the upper limit for a laminar attachment line in 

the absence of disturbances. 

If the 

This boundary layer can 

A useful stability criterion given by Bacon and 

for an attachment line boundary layer is the value of the 

Typical critical values used in 

Boundary layer crossflow - i.e. twisted velocity profiles caused by 

cross-stream pressure gradients, is a comn condition in regions of 

acceleration on a swept wing and is a potential cause of early transition. 

Consider the projection of such a twisted velocity profile onto a plane at 

some arbitrary azimuthal direction, but parallel to the surface, as shown in 

figure 4.2. 

approaching 90 degrees, these projected profiles can be highly inflectional. 

Such profiles are known to be unstable, amplifying boundary layer waves in 

the direction of the inflected profile. 

co-rotating vortices within the boundary layer. 

sufficient strength to influence, and interact with their neighbors, causing 

transition. 

For large angles relative to the external flow direction, 

These "crossflow waves" are actually 

They can rapidly grow to 

PRECEDIING PAGE BUNK NOT FILMED 

13 
The Tollmien-Schlichting waves observed in 2-D and axisymmetric flows 

The instability mechanism has been described by Morkovin as a 

result from a type of instability which can exist in the absence of pressure 

gradients. 

resonance between local and instantaneous pressure and vorticity fields 

within the boundary layer. This "viscous-tuned" mechanism does not require 

inflectional velocity profiles, but is very sensitive to profile shape, 

particularly in the near-wall region, with more convex profiles being more 

stable than weak ones. 

requires generally lower wall suction than for the inflectional crossflow 

mechanism. 

in high-speed flows weaken the mechanism substantially, lowering suction 

re uirements still further. 

in full profiles, so are stabilizing unless they are associated with 

significant cross-stream gradients, as is typically the case with swept 

wings. Presumably, in a three-dimensional flow this mechanism applies to 

component profiles as well as streamwise ones, muddling the traditional 

distinction between T-S and crossflow waves. Like crossflow waves, when T-S 

waves grow to the point of interacting with their neighbors, transition is 

iminent . 

Stabilizing the boundary layer against this mechanism 

The temperature and viscosity profiles created by viscous heating 

Favorable streamwise pressure gradients result 9 

The distinction between crossflow and Tollmien-Schlichting waves is of 

much less practical importance, in the author's view, than the distinction 

between "inflectional" and. "viscous-tuned" instability mechanisms as 

described by Morbovin, owing to the potentially large differences in wall 

suction required for boundary layer stabilization, and the effects of Mach 

number. Inflectional instability, such as found in 3-D flows in regions of 

strong boundary layer crossflow and in 2-D flows in regions of adverse 

pressure gradient, is known to require higher suction levels to suppress than 

does viscous-tuned instability on a 2-D flat plate at the same Reynolds and 

Mach number. As noted above, the temperature and viscosity profiles in 

high-speed boundary layers have a significant stabilizing effect on the 

viscous-tuned instabil t mechanism, but have much less effect on the 

depends exclusively on conditions in the near-wall region, whereas the 

inflectional mechanism depends on conditions which can exist much higher up 

in the boundary layer. 

profile shape is largest, and the effect of Mach number on local temperature 

(and viscosity) is highest. 

inflectional mechanism tl& . This is because the viscous-tuned mechanism 

In the near-wall region the effect of suction on 

Gortler vortices are counter-rotating, streamwise vortices which are 

caused by a centrifugal instability mechanism due to concave streamwise wall 

curvature. 

are not a problem if the wall curvature is convex or flat. 

These too can intensify to the point of causing transition. They 

The wings of supersonic cruise airplanes can be divided into two types, 

in terms of the value of the leading edge normal component of Mach number: 

those whose leading-edge-normal Mach numbers are less than one are said to 

have subsonic leading edges, while those whose leading edges are exposed to 

supersonic normai flow are said to have supersonic leading edges. 

14 
The sigificance of this distinction is that for the subsonic leading edge, 

pressure information of a wing section's imminent approach is signalled from 

stations inboard and upstream, allowing the air to change direction gradually 

and pass around the leading edge isentropically. 

upwash caused by stations inboard and upstream of a wing section can be 

capitalized upon. Essentially this allows low pressures to act on forward 

facing su faces, giving potentially much lower drag due-to-lift at supersonic 

speeds( 16f. For wings having supersonic leading edges, this so-called 

"leading-edge thrust" is absent, giving the drag coefficient a tangent 

dependence on angle of attack, similar to a separated flat plate in subsonic 

flow. 

supersonic cruise wing designs to be a combination of these two types. 

For a lifting wing, the 

Compromises to low-speed performance and handling cause most 

Subsonic and supersonic leading-edged wings are compared in figure 4.3, 

in terms of laminarization issues. Of the two, the supersonic leading-edged 

wing has much more favorable conditions at the leading edge, due to the very 

small radius. 

due-to-lift of this type of wing means that the leading-edge sweep does not 

have to be large. 

small, so it is very easy to satisfy the attachment line momentum thickness 

Reynolds number criterion of Bacon & Pfenninger over a wide angle of attack 

range. 

physical length, so stationary crossflow would not be expected to present 

problems. 

leading-edged wing is largely driven by the streamwise contour: slab-sided 

sections, such as the modified double wedge, give stepped pressure 

distributions with narrow regions of acceleration between the steps, and 

convex surfaces give smoothly accelerating pressure distributions. In the 

absence of sweep, an accelerating chordwise pressure distribution acts to 

stabilize boundary layer velocity profiles and extend laminar run. For the 

swept wing case, any chordwise pressure gradient has an associated 

cross-stream component, so boundary layer destabilization by crossflow is a 

potential problem. 

The fact that sweep plays only a small role in the drag 

The attachment line travel with angle of attack is very 

Any leading-edge acceleration region would be extremely short in 

The chordwise pressure distribution for a section in a supersonic 

For the subsonic leading-edged wing, the attachment line has high sweep 

omentum-thickness Reynolds 

(inside the Mach cone) and nonzero leading-edge radius. 

to unacceptably large values of attachment-li e 

number, requiring locally high suction levels ?15'P . The acceleration 

imediately downstream of the attachment line takes place in the most highly 

swept region of the wing, resulting in potentially powerful boundary-layer 

crossflow. 

result. 

bluntness is small. 

designing the wing pressure distribution to minimize total suction flow while 

providing for structurally desirable local section thickness, and additional 

room for suction ducting. 

This could give rise 

High levels of suction may be required in this region as a 

For a Subsonic leading edge, the drag penalty for leading-edge 

The use of a blunt leading-edge gives freedom in 

15 
OBSTACLES TO LAMINARIZATION 

1. "BYPASS" MECHANISMS : SEPARATION 

NOISE 

ROUGHNESS (BUGS. ICE, .to) 

WAVl N ESS 

0te 

2. AlTACHMENT LINE : TURBULENCE PROPAGATION 

LAMINAR STABILITY 

3. CROSSFLOW WAVES (INFLECTIONAL INSTABILITY) 

4. 1-S WAVES (VISCOUS INSTABILITY) 

5. GORTLER VORTICES (CONCAVE FLOW REGIONS) 

Figure 4.1 OBSTACLES TO LAMINARIZATION 

Figure 4.2 COMPONENT VELOCITY PROFILES 

16 
SUBSONIC SUPERSONIC 

CONSIDERATION LEADING EDGE LEADING EDGE 

LEADING-EDGE THRUST YES NO 

HI-SPEED A/C SHIFT NO YES 

LOW-SPEED AERO CHAR. POOR BETPER 

SWEEP HIGH LOWER 

LEADING EDGE BLUNT SHARP 

Figure 4.3 LEADING EDGES - SUBSONIC VS. SUPERSONIC 

For a subsonic leading edge, the sweep must increase with design Mach 

number. This reduces low-speed wing lift-curve slope and maximum lift, and 

increases yaw-roll coupling, all of which is undesirable. There exists, 

therefore, an upper Mach number limit for which an all-subsonic-leading-edged 

wing is acceptable. Compromise with low speed characteristics have caused 

most of the recent study wings, including the Mach 2.2 DAC AST, to have a 

subsonic inner panel and supersonic outer panel. The span fraction of the 

leading edge sweep break typically decreases as design Mach number is 

increased. 

If laminarization were found to be feasible for supersonic leading edges 

For this 

only, the drag due-to-lift disadvantage would have to be counted against LFC, 

and the resulting net gain would probably be small or nonexistent. 

reason, the laminarization of wings with subsonic leading edges has been 

given high priority in this study. 

17 
5.DAC AST WING - LFC FEASIBILITY 

The Douglas Advanced Supersonic Transport (AST) configuration, shown in 

the upper left-hand corner of figure 1. 's one of several developed under 

NASA contract in the mid- to late 1970sti7f. It was designed as a 

transpacific (5750 nm), high capacity (308 passengers) airplane intended to 

cruise at Mach 2.2. It featured four underwing variable cycle engines with 

mixed-compression conical inlets and an efficient cranked arrow wing with 

leading- and trailing-edge flaps for low speed operation. 

made of superplastic formed and diffusion bonded (SPF/DB) titanium in the 

wing structure. 

semispan, with a subsonic (71 deg.) leading edge inboard of the break, and 

supersonic (61.5 deg.) leading edge outboard. The entire wing is cambered 

and twisted for minimum pressure irag due-to-lift under cruise conditions. 

The lower sweep of the outer panel gives improved low-speed performance and 

handling at minimal compromise to supersonic cruise efficiency, while 

avoiding the large structural span of an all-subsonic leading-edged wing. 

The wing trailing edge also has a sweep break. 

was found to offer a performance advantage over an unswept or negatively 

swept trailing edge due to a favorable interaction with the closing fuselage 

afterbody. Laminar flow control was not considered in the original design. 

The specific configuration used in this study, designated the D3233-2.2-1C, 

was chosen as a base in , since its geometry and performance characteristics 

were well documented t18e . 

Extensive use was 

The wing leading edge has a sweep break station at 70X 

The aft-swept trailing edge 

Some of the potential laminarization problems presented by the AST wing 

as a candidate for LFC are shown in figure 5.1. 

leading-edge radius, the high leading-edge sweep of the inboard wing could 

make attachment line laminarization difficult. Concave curvatures exist on 

the wing lower surface near the leading edge, so there was a potential for 

Gortler instability. The leading-edge sweep outboard of the sweep break is 

such that the normal component of Mach number at cruise is only 1.03, giving 

rise to a detached or lambda-type shock on the lower surface at the leading 

edge. It seemed doubtful that a laminar boundary layer could survive this 

abrupt deceleration. The low absolute pressure of the air, especially over 

the wing upper surface, coupled with the high freestream massflux at cruise, 

could cause the ducting for the suction air to be unduly large. 

Despite the relatively small 

The first step in determining the prospects for laminarizing a wing is to 

get a solution for the inviscid flowfield. Although linear small-disturbance 

methods were used in the design of the wing, these methods were found to lack 

the necessary accuracy and resolution, particularly in the leading-edge 

region. Inboard of the leading-edge sweep break, where the leading edge is 

subsonic, the small-disturbance methods could not allow or properly account 

for spatially rapid pressure variations. 

supersonic leading edge, it is necessary to correctly account for the 

leading-edge shock. 

effects. Two advanced-grid Euler codes, BOD-60r19) and FLO-67(12), were 

used in this analysis. 

FLO-58 Euler. 

supersonic flows, an important feature in the low supersonic regime.' 

For the outboard panel, which had a 

Compressible Euler codes h ve the ability to model these 

The BOD-60 code is an improved version of Jameson's 

Both codes have the capability of computing mixed subsonic and 

19 

PRECEDlNG PAGE BLANK NOT FlLMEQ 
PLOWS 

Figure 5.1 DAC MACH 2.2 AST POTENTIAL LAMINARIZATION PROBLEMS 

Direct comparisons were made with supersonic wind-tunnel data for an earlier 

AST configuration, and are shown in figures 5.2A through 5.2P for the BOD-60 

code, and figures 5.3A through 5.3F for the FLO-67. 

the wind-tunnel model (2 ft. span), the agreement for both codes was judged 

to be acceptable. 

reasonably well resolved and smooth in the leading-edge region and 

elsewhere. 

pressure distributions at the span stations used in the boundary layer 

analyses is shown in figure 5.4. 

Considering the scale of 

The computed pressure distributions were found to be 

A schematic representation of the AST wing planform, with BOD-60 

Conditions along the leading-edge attachment line are critical to the 

attachment line were established at low speed by Bacon and 

achievement of laminar flow on a wing. 

flow along th 

Pfenninger(l57, and use a Reynolds number based on the laminar momentum 

thickness: if Re is less than 100, the laminar attachment line boundary 

layer is stable; if Re is greater than 240, T-S waves can grow and 

spontaneously transition the boundary layer. 

established turbulence will propagate, but the attachment line will remain 

laminar in the absence of disturbances. The value of is increased by 

sweep, leading edge radius, and unit Reynolds number, but can be reduced with 

suction. In this study it was assumed that these criteria apply to the 

supersonic case. 

known effect of viscous heating in stabilizing the boundary layer. The 

development of attachment line criteria valid throughout the Mach number 

range is an important objective for the research program recomended- in 

section 12. 

Criteria for the existence of laminar 

For Re between 100 and 240, 

This assumption is felt to be conservative in view of the 

ORlGINA\L PAGE 

BLACK AND WHITE PHOTOGRAPH 

20 
*+ ** ' *t+ 

# *+v**+ 

r* i ** 

*' #,*+ t + 

+* t 

hi*+ 

+ BOO60 

0 MPERlMENTAL US. 

0 EXPJflMEhTALLS. 

M = 2.16, ALPHA = 1.95 DEG., ETA = .125 

0.2 

1 I I I I I 

0.0 0.2 0.4 0.6 0.8 1.0 

x/c 

M = 2.16, ALPHA = 1.95 DEG., ETA = .227 - 

I I I I 

Figure 5.2A BOD-60 EULER vs. W.T. TEST DATA 

-0.1 

CP 

0.0 

0.1 

Y ARC 

t 

+i +' 

Figure 5.2B BOD-60 EULER VS. W.T. TEST DATA 

21 
-0.2 r 

-0.2 

CP -0.1 

OBO 

0.1 

0.2 

-0.1 

- 

fh 

- t t /----- + ++ +t 

T b :+ * *+ - .t 

I Born 

3 MP3rrEhTN U.S. ++ 'W 

A aPakrimL LS. 

M = 2.16, ALPHA = 1.95 DEG., ETA = .535 

- 

I I 1 I I 

CP 

0.0 

0.1 

A ME2IM3TALLS 

M = 2.16, ALPHA = 1.95 DEG., ETA = .433 

0.2 

0.0 0.2 0.4 0.6 0.8 1.0 

Xl c 

Figure 5.2C BOD-60 EWER vs. W.T. TEST DATA 

Figure 5.2D BOD-60 EULER vs. W.T. TEST DATA 

22 
-0.2 r 

0.1 

0.2 

CP 

r: p--+*t ....--- tt+ 0 D(P3lMMkL C.S. 

**I,,, 4 O(73Mih7ALLS --------.----_.--_____ I 

M = 2.16, ALPHA = 1.95 DEG., ETA = .741 - 

CP 

-0.2- 

-0.1 

0.0 

-0.1 

0.0 

- 

t 

t - 

b 

b 

- 

-4- - - - 

0. 

F' 

+ 

Figure 5.2F BOD-60 EULER vs. W.T. TEST DATA 

23 
-0.15 

0 Fu)61us. 

W.T. MTA US. 

W.T. MTA LS. 

-0.05 

0 

0 0 OO 

0 00 

CP 

0.00 0 

-0.15- 

-0.10 

-0.05 

CP 

o.oo= 

0.05 

I 

0.10 

0.15r 

0.05 

0 FLO67LS. 

0 Flo67u.s. 

A W.T. MTA LS. 

- W.T. MTA US 

A 

0 

- 0 

0 

7 

- 

0 

M = 2.16, ALPHA * 1.95 DE., ETA = .227 

M = 2.16, ALPHA = 1.95 DEG., ETA = .125 

0.15 

I 

f 

0.201 I I 1 I I 

0.0 0.2 0.4 0.6 0.8 1.0 

x/c 

Figure 5.3B FLO-67 EULER vs. W.T. TEST DATA 

24 
i A W.T. MTA U.S. i + WT MTA I C 

-0.20c 

n 0 FLDQLS. 0 FLo67us. 

..... -..-. -. 

- h 

ODO0~O 

C 

0 

00 

0 

0 

0 

0 

0.10- 

M = 2.16, ALPHA = 1.95 DEG., ETA = .433 2 

0.151 I 1 I 1 1 

0.0 0.2 0.4 0.6 0.8 1 .o 

x/c 

Figure 5.3C , FLO-67 EULER vs. W.T. TEST DATA 

-0.20~ 

-0.15 

-0.05 

CP 

0. 

0. 05 oo 

OOl 

A W.T. MTA US 

0 

0 

oooo~o 

0 0 

0 0 

M = 2-16, ALPHA = 1.95 DEG., ETA = -535 0.10 

0.15 I I 1 1 1 

0.0 0.2 0.4 0.6 0.8 1.0 x/c 

Figure 5.3D FLO-67 EULER vs. W.T. TEST DATA 

25 
0 FLO67L.s. 

0 m67us. 

a W.T. DATA US. 

+ W.T. DATA LS. 

-0.20- 

-0.15- 

00 

-0.10 0 0 

0 

0 

-0.15 

-0.10- 

-0.05' 

CP 

0.00: 

0.05 

0.10- 

0.15- 

0.20 

CP 

M = 2.16, ALPHA = 1.95 DEG., ETA = .741 

- 

A W.T. DATA US. 

W.T. DATA IS 

Do 

Q 0 0 

0 0 

0 

3 09 

- 0 

00 

O0 O O O 

3 

0 M = 2.16, ALPHA = 1.95 DEG., ETA = -944 / 

I I 1 1 1 

0.0 0.2 0.4 0.6 

x/ c 

0.8 110 

26 
Figure 5.4 AST WING STATIONS FOR B.L. STABILITY ANALYSIS 

Both the BOD-60 and FLO-67 Euler solutions were used in the computation 

of 

suction level in figure 5.5. At each station, the differences in are 

due to the computed attachment line locations, which are near the relatively 

sharp leading edge in the FLO-67 solution, but below and behind it in the 

BOD-60 solution. 

the proper attachment line location at the design point. 

solution, attachment line values allowing laminar flow can be achieved 

with moderate suction. was computed using a newly developed algorithm 

that allows the attachment line Cp values to differ from their simple-sweep 

attachment line values. 

attachment line Cp, and the fact that the leading-edge-normal velocity 

component at the attachment line is zero, to compute the local effective 

sweep angle at which the flow approaches the leading edge. 

sweep is then used in the calculation of leading-edge normal velocity for 

each of the two points straddling the attachment line. 

velocity gradient is then used in the formula for 

Pfenninger. 

for the two inboard span stations. These are shown as a function of 

Of the two, the FLO-67 solution is more representative of 

According to either 

The new approach uses the computed or measured 

This effective 

The resulting normal 

given by Bacon and 

The wing lower surface inboard of the leading edge break featured an 

extensive region of streamwise concavity, and there was concern that Gortler 

instability could cause early transition in this region. 

counter-rotating Gortler vortices are due to centrifugal instability, and can 

form in a laminar boundary layer in regions of concave flow curva ure. 

indicated that the presence of boundary layer crossflow can destroy Gortler 

vortices. 

Stationary, 

However, recent theoretical and experimental investigations (20,215 have 

27 
0 

3 

(Y 

L 

3 

a 

M - 22. ALPHA - 2.0 deg 

REF# BACON (L PFENNINGER. AFFDL-TR-87-33 

hp - 58 kft. 

\.2 -\ '\' 

\ h. 3m 

04 + 

0 -.Q103 -.mt -.OD15 1002 -.5 -.om -.m -.a 

attachment line Cq 

Figure 5.5 ATTAC"T LINE CONDITIONS - INBOARD AST WING 

Figure 5.6 shows the definition of the crossflow Reynolds number, the value 

of which serves as a rough criterion for Gortler vortex destruction, per 

reference 20. If this Reynolds number exceeds 45, Gortler vortices of one 

rotational sense have been raised up out of the boundary layer, where they 

decay rapidly, while those of opposite sense are converted to crossflow 

waves. Calculations were done on the lower surface of the AST wing in the 

concave region. The average crossflow Reynolds number was found to be 84, 

over twice that required to destroy Gortler vortices. 

that Gortler instability does not pose a threat to laminarization on this 

wing. 

Collier et a1(22) have pointed out that the concave curvature does 

It is thus concluded 

provide an additional mechanism for crossflow wave amplifica io 

accounted for in the current production version of the COSAL 

layer stability code. 

that is not f boundary 

This effect was not considered. 

determined by boundary layer 

stability analysis, employing the NASA MARIA 7?67 and COSAL codes. The 

large chordlengths of the AST wing precluded serious consideration of a 

hybrid laminarization scheme. A full-chord suction scheme was adopted, with 

transition targeted for the control-surface hingeline. The low cruise lift 

coefficient of approximately 0.10, coupled with the low ambient pressure at 

the initial cruise altitude of 58 kft mans that the density differences 

between upper and lower wing surfaces might be expected to compensate 

somewhat for the differences in velocity, so that the upper/lower 

laminarization benefit split would be more even than for the subsonic. case. 

Calculations have since borne this out; the computed benefit split is 

approximately 317 upper, 417 lower. 

Suction requirements for laminarization 

28 
B.L. CROSSFLOW: VELOCITIES WITHIN THE BOUNDARY LAYER 

ARE NOT PARALLEL TO THE EXTERNAL FLOW. 

Ro 5 45 => COMPLETE CONVERtlON OF 

GORTLER VORTICES ro 

CROSSFLOW WAVES. 

REF. COLLIER & MALIK 

AIM-87-1412 

FOR DAC AST. AVERAGE Rocb. = 84 

IN L.3. CONCAVE REGION. 

Figure 5.6 CONVERSION OF GORTLER VORTICES TO CROSSFLOW WAVES 

It is therefore important to laminarize both wing surfaces if possible. The 

major concern here was the suction volume flow, and the required size of 

internal ducting. 

Both boundary layer stabil't codes use the conical laminar boundary 

layer code of Kaups and Cebeci tlr) to generate velocity profiles. Since 

this code was written for the subsonic and transonic cases, it is not 

surprising that some modifications, both to the code and the way it is used, 

were found to be necessary for supersonic application. Fortunately, the 

modifications were small, and were confined to three areas: velocity 

overshoots, supersonic leading edges, and near-wall symmetric oscillations. 

The Kaups-Cebeci code uses a conical wing approximation to solve the 

three-dimensional flow on straight tapered wings, in which profiles are 

assumed to be similar on rays from a virtual wingtip. 

used in the program is shown in figure 5.7. The modified versions of the 

code used with the MARIA and COS& codes contained statements prohibiting 

velocity overshoots in which w/WE or u/uE exceed unity below the boundary 

layer edge. 

near a wing leading edge?23y. The overshoot prohibition was, in certain 

cases, creating velocity profiles that were not smooth, resulting in 

artificial eigenvalues in the stability analysis. These statements were 

removed. 

The coordinate system 

Such oversh ot are known to occur in supersonic boundary layers 

29 
X 

0 

(1c.+ou7-PD 

Figure 5.7 POLAR COORDINATE SYSTEM USED IN THE K-C CODE 

The supersonic leading edge case presented problems in that the boundary 

layer code was not designed to deal with the total pressure losses caused by 

leading-edge shocks, nor did it have the option of a wedge flow or flat plate 

starting solution. 

swept-wing case is the infinite swept cylinder attachment line. 

leading-edge shock problem was dealt with outside of the boundary layer 

program by assuming that the shock is detached slightly from the leading 

edge, and that all streamlines entering the boundary layer pass through the 

leading-edge-normal part of the shock. Since the leading edge is swept, 

oblique shock relations are used to calculate the correct total external 

velocities at each station, based on the computed (nonisentropic) pressure 

coefficients. The boundary layer code expects the flow to be isentropic, so 

equivalent isentropic pressure coefficients are then computed from the total 

external velocities. A simple program, written in IBM BASIC-A, was used to 

make these calculations. The problem of 

curved shock waves and the resulting velocity and total pressure gradients 

found downstream is much more complicated. 

for. 

The only starting solution needed for the subsonic 

The 

A listing is given in appendix B. 

This effect was not accounted 

Although low supersonic pressure drag demands a sharp leading edge 

outboard of the break, the only existing starting solution in the 

Kaups-Cebeci boundary layer code is that of a swept cylinder attachment 

line. 

blunt, was still found to be usable. 

the leading edge region in order to provide for a spatially rapid but smooth 

acceleration from the attachment line Cp. 

This solution, which assumes that the leading edge is to some degree 

Computational points were bunched in 

30 
This gives rise to leading edge crossflow which is not fundamental to the 

stability of the boundary layer if the leading edge is reasonably sharp. 

However, the stability consequences of this short acceleration region were 

found to be addressable by using the MARIA stability code to separate the 

very short wavelength stationary crossflow waves amplified in the leading 

edge region from the longer waves amplified by the basic pressure 

distribution. The wavelengths and amplifications of those waves generated in 

the rapid acceleration region varied directly with the physical length of the 

region, so the length was simply adjusted downward until the resulting waves 

were so short and little amplified as to die off in the first 102 chord or 

so. 

airfoil's basic pressure distribution, as shown in figure 5.8. 

thin boundary layers in the attachment line region, not many computational 

points were available for stability calculations. 

acceptable, since the profiles giving rise to the longer wavelengths 

generally were adequately resolved. 

amplified crossflow waves were found using MARIA, the COSAL stability code 

was used to compute their amplifications. Even at Mach 2.2 the MARIA code 

was found to do a good job of identifying the most amplified stationary 

crossflow waves. 

This made them readily distinguishable from those arising from the 

With the very 

This was considered 

Once the wavelengths of the most 

1tO LONGER CF WAVES 

FUNDAMENTAL TO BASIC 

PRESSURE DISTRIBUTION 

SHORT CF WAVES 

WC PCRCOIT oyy(D 

LONGER CF WAVES 

FUNDAMENTAL TO BASIC 

PRESSURE DISTRIBUTION 

SHORT CF WAVES 

WC PCRCOIT oyy(D 

Figure 5.8 STATIONARY CROSSFLOW WAVES - SUPERSONIC 

USING ATTACHMENT LINE STARTING SOLUTION 

L.E. 

31 
-Oo20 I 

o*lol 0.20 

-0.201 

0.20' 

-0.20, 

-0.10, . . - ... ... -0. . 

0.00 

0.10 

0.20 

-0.20 

-0.10. .. .. .. 

0.10, 

0.20. 

0.0 0.2 0.4 0.6 0.8 1 

XlC 

:L 4 2 

0' - 

::I 

0.0 0.2 0.4 0.6 0.8 1.0 

XIC 

Figure 5.9 LFC FEASIBILITY ON ORIGINAL AST WING 

UPPER SURFACE SUCTION DISTRIBUTIONS 

(M = 2.16, ALPHA = 1.95 deg, hp = 58 kft) 

32 
Small near-wall oscillations were observed in the computed velocity 

profiles in the vicinity of Mach 2 and above. These oscillations were found 

to be symmetric station-to-station, and are a result of the manner in which 

the equations of motion are solved. In the iteration scheme, the momentum 

and continuity equations are solved, then the energy equation is solved 

externally and used to update the fluid properties prior to the next 

continuity-momentum loop. This procedure is efficient and works well in the 

transonic regime, but the larger variation of temperature with total velocity 

at the higher Mach numbers causes the inherently lagging fluid properties to 

affect the solution. The problem was visible as a sawtooth variation in wall 

skin friction station-to-station. Modifications were made to the code to 

correct this problem, but comparisons of stability characteristics computed 

with and without the code modification showed no differences. 

For the feasibility analysis, the required suction levels were determined 

conservatively. 

stationary crossflow waves in the leading edge region was determined using 

the MARIA code, then the adequacy of the levels was checked using COSAL. An 

N-factor of 9 was taken as critical. 

MARIA code always erred on the conservative side of COSAL, indicating larger 

stationary crossflow amplifications for a given suction level. The adequacy 

of an assumed suction level of C 

verified using COSAL. Both stationary and nonstationary crossflow waves, as 

well as T-S waves were computed. 

due the conservatively high suction levels. 

demonstrate feasibility, not minimize suction, these results are not 

presented. 

laminar regions, pressure coefficients and suctions. The hatched regions 

indicate turbulent flow. 

wedge was assumed, based on extrapolated ub onic data. This value is in 

agreement with the correlation of Fischer f!247 at Mach 2.2. 

The suction required to prevent excessive growth of 

For the conditions of this study, the 

= -.0002 over the rooftop was also 

All boundary layer wave growth was small 

q 

Since the object here was to 

Figures 5.9 and 5.10 show the upper and lower wing surface 

On both surfaces a 6 degree bodyside turbulent 

The leading-edge sweep angle on the outboard panel was such that the 

normal Mach number is only 1.03. On the lower surface, at the cruise angle 

of attack, the local flow-deflection angle was too high for an attached shock 

to exist. The result was a strong adverse pressure gradient in the 

leading-edge region which prevented laminarizing the lower surface outboard 

of the leading-edge break. Therefore, no suction was used on the lower 

surface in the tip region. The station immediately inboard of the break is 

laminar, but the required suction is considerably larger than at the inboard 

station. This is due to the stronger favorable gradient, and underscores the 

strong dependence of required suction on pressure distribution. 

33 
I -0.20 

0.20 t - I 

0.0 0.2 0.4 0.6 0.8 1.0 

XlC 

0-.0 0.2 0.6 0.6 0.8 1.0 

XlC 

Figure 5.10 LFC FEASIBILITY ON ORIGINAL AST WING 

LOWER SURFACE SUCTION DISTRIBUTIONS 

(M = 2.16, ALPHA = 1.95 deg, hp = 58 kft) 

34 
In order to establish the feasibility of fitting the suction ducting into 

the wing, the suction distribution was integrated over the wing area to 

determine the total suction flow. 

the wing upper surface, makes the penalty for large skin pressure drops 

rather large in term of duct volume. 

assumed for the skin, and no loss was assumed in the ducting. 

the skin pressure drop is set by design. Strictly for the purpose of 

establishing the feasibility of providing the required suction capacity 

within the available wing volume, the suction air was assumed to pass 

internally through the wing root at maximum massflux, i.e. a ducting Mach 

number of 1.0,. 

is shown in figure 5.11. 

In a practical system, ducting Mach numbers would probably not be allowed to 

exceed 0.2 to 0.3, so the actual ducting size would be accordingly larger. 

This amounts to a factor of 2 to 3 on duct area. 

The low average pressure, particularly on 

A total pressure loss of 102 was 

In practice, 

The resulting duct area as a fraction of wing footprint area 

The small (3%) area fraction is very encouraging. 

Although the analysis described above identified no intractable 

aerodynamic problems that would preclude the successful application of LFC to 

the DAC AST wing, the original wing is far from an optimum design from a 

laminarization standpoint. 

deemed appropriate to analyze this wing, since it was felt that large 

improvements in required suction flow and laminar area fraction could be made 

if the wing were redesigned. 

In the benefit analysis to follow, it was not 

WING FOOTPRINT AREA = 366 sqft 

MINIMUM DUCT AREA = 10 sqft 

(ONLY 3% OF FOOTPRINT) 

Figure 5.11 THEORETICAL MINIMUM SUCTION DUCT AREA AT WING ROOT 

35 
The original AST wing had two problems: The lower surface wingtip could 

not be laminarized, and the acceleration of flow to the rooftop level in the 

leading edge region typically took place over too great a surface distance. 

This aggravates the crossflow instability problem, and requires large amounts 

of suction to overcome. 

problems. 

Bluntness was added to the inboard wing leading edge, and the wingtip was 

unswept to 50 degrees. 

the lower surface at cruise angle of attack. These modifications did not 

degrade the wing's drag due-to-lift characteristics over the baseline, nor 

did they significantly worsen conditions along the attachment line. 

assumed that any changes in volume wave drag could be compensated for by rearea ruling the fuselage. 

A modified wing was developed to solve these 

The original and modified planforms are shown in figure 5.12. 

The lower sweep allowed an attached shock to exist on 

It was 

One major concern with the blunted leading edge was that the 

attachment-line momentum-thickness Reynolds number would be increased to such 

an extent as to make laminarization of the new wing impossible. 

calculations were made based on FLO-67 solutions for the original and 

modified wings. 

in figure 5.13 over a range of attachment line suction coefficients. 

Laminarization is still possible, but increased suction on the attachment 

line would be necessary to achieve the same 

wing. In either case it is necessary to keep the leading edge and wing 

clean, since turbulent wedges pose a very serious threat to the realization 

of LFC benefit on low-aspect, highly swept wings. According to this 

analysis, the blunted leading edge of the modified wing does not present an 

A comparison at the 20 and 60 percent span stations is showvalues as the original 

intrktable attachment line probiem for 

ORIGINAL 

laminar izat ion. 

MODIFIED 

Figure 5.12 LFC PLANFORM MODIFICATION 

36 
0 

M = 2,2. hp = 58 kft. ALPHA = 2.0 deg 

REF: FLO-67. BACON 8 PFENNINGER AFFDL-TR-67-33 

ORIGINAL AST 

-- mOIFIED WING 

f 

0 -.am -.mi -.mi5 -.a12 -.- -.om -.0035 -.m 

Attachment Line Cq 

Figure 5.13 ATTACHMENT LINE CONDITIONS - 

ORIGINAL AND MODIFIED AST WINGS 

One concern with the highly swept leading edges is that of the variation 

varies rapidly with surface distance in the region of cruise attachment line 

travel. This variation of attachment line location with angle of attack is 

typically largest in the vicinity of the sweep break. 

zero-suction Q were made for angles of attack from 0 to 3 degrees for both 

original and modified wings, based on the FLO-67 solutions. 

in figure 5.14. 

the above, and because it is on the inboard, highly swept region of both 

original and modified wings. 

computed Q are greater for the original wing, due to numerical problems 

near the sharp leading edge in the FLO-67 solution. 

minimal Q variation over this angle of attack range is clear. 

with angle of attack, particularly if the local radius of curvature 

Calculations of 

These are shown 

The 63% span station was chosen for comparison because of 

It should be noted that the uncertainties in 

However, the trend of 

37 
I4 - 2.2 Alt. - 58 kft. Eta - 0.8284 LE. Sweep - 71.0 dog 

300 ,1 

r 

0 1 2 3 

Angle Of Attack (deg.) 

Figure 5.14 ZERO-SUCTION ATTACHMENT LINE MOMENTUM THICKNESS 

REYNOLDS NUMBER AS A FUNCTION OF ANGLE OF ATTACK 
6. MODIFIED AST WING - LFC BENEFIT 

In order to maximize LFC benefit, it is important to minimize the suction 

Suction minimization is done through an iterative procedure in 

flow, since this relates directly to suction system size, weight, and power 

requirements. 

which complete boundary layer stability calculations are performed using 

COSAL for various trial suction levels. COSAL has three commonly-used 

options for computing boundary layer stability, all of which compute the 

amplification of waves of constant frequency. 

maximum amplification method, conducts a search in waveangle and wavelength 

for the most amplified wave, at each chordwise station. 

wavelength constant, and searches through waveangle for the most amplified 

wave. Option 6 holds waveangle constant, searching through wavelength for 

the most amplified wave. 

were the most physically realistic, so these options were used exclusively. 

In order to be conservative, the option giving the higher amplification was 

used. 

less than about 85 degrees, and option 5 was used at higher average 

waveangles. 

amplification factor, N, which is the natural logarithm of the ratio of the 

local integrated amplification rate to a reference amplitude of the wave 

taken at the point of neutral stability. A growing body of experimental 

Option 1, commonly called the 

Option 5 holds 

For this study it was felt that options 5 and 6 

Typically this meant that option 6 was used for average waveangles 

Boundary-layer transition is correlated to the so-called 

supports values in the range of 8-12 for a wide variety of evide?Se flows . A value of 9 has been taken as indicating transition. This 

value was chosen to allow reasonable estimates of suction requirements to be 

made; more conservative values of 5 to 7 are typically used in the design 

process. 

The procedure used in determining the minimum suction distribution starts 

with the attachment line. The criterion is satisfied by the application 

of an appropriate suction level over the region of expected cruise attachment 

line travel. In the attachment-line region and imediately downstream, the 

boundary layer is most unstable to stationary, or very nearly stationary 

crossflow waves. The MARIA code is useful in identifying the most amplified 

wavelengths of the stationary waves, and for a first estimate of the required 

suction levels. The COSAL code is then used to better determine the 

crossflow amplifications, and to iterate the suction to the minimum required 

level. In the leading-edge region, increased suction causes a decrease in 

the wavelength/chord ratio of the most amplified or critical waves, due to 

thinning of the boundary layer and changes in the profile shapes. This must 

be recognized in finding the minimum suction level. Fortunately, MARIA does 

an excellent job of identifying the critical waves, even under the conditions 

of this study. 

travelling waves are favored, the determination of minimum suction is much 

more complicated, since the waveangle and frequency of the most amplified 

wave vary with the suction level, and no inexpensive guidance is available. 

In the region downstream of the leading edge, where 

39 
The reason for the variation of critical wave frequency and angle with 

suction is best explained with reference to figure 6.1. This figure shows 

component velocity profiles with and without suction in a region of weak 

crossflow. Profiles are shown for various angles, PSI, relative to the 

external flow direction. In the figure, the crossflow is a result of using 

an airfoil having a constant favorable chordwise pressure gradient in a swept 

wing. 

profiles show inflection. Inflectional profiles are unstable, and the rate 

of amplification of boundary layer waves in a particular direction depends on 

the stability characteristics of the component profile in that direction. 

Note that the elevation of the inflection point above the surface increases 

with angle. With suction applied (dashed lines), all of the profiles are 

changed, but the inflection persists only for the higher angle profiles (85 

and 90 degrees). 

wave to higher waveangles as suction is increased, and explains why the 

stationary (nearly 90 degree) crossf low waves require the highest suction 

levels to subdue. 

With no suction (solid lines) the 70, 85, and 90 degree component 

This is consistent with the observed shift of the critical 

0.40 

as 

Qso 

0s 

E os0 

0.6 

0.w) 

0.a 

0.00 

-0.4 -0.3 -03 4.1 

i’ e * 

, . I 

I 

Figure 6.1 TYPICAL COMPONENT VELOCITY PROFILES 

IN A REGION OF WEAK CROSSFLOW 

40 
Chordwise pressure distributions computed using FLO-67 are given is 

figure 6.2 for three span stations. Comparison of these pressure 

distributions with those of the original wing (figures 5.3A-5.3F) illustrates 

the success of the redesign. These pressure distributions were used in the 

stability analyses with the intent of minimizing the required suction. Final 

suction distributions for the LFC-modified AST wing are given in figures 6.3 

and 6.4 for upper and lower surfaces, respectively, for the three span 

stations investigated. 

I 

I 

I 

I 

I 

I 

I 

I i 

I 

ETA = 0.18 0.101 I 

-0.10 I 

0.0ot I 

f 0.20' - - - - - . - . . - ' 

-0. 

20 

0.0 0.2 0.4 0.6 0.8 1.0 

x/c 

Figure 6.2 CHORDWISE PRESSURE DISTRIBUTIONS - 

MODIFIED AST WING 

41 
I -0.10 

0.0 0.2 0.6 0.6 0.0 1.0 

xic 

Figure 6.3 UPPER SURFACE FINAL SUCTIONS - 

MODIFIED AST WING 

42 
-0.10 

*L 0 

0.0 0.2 0.4 0.6 0.8 1.0 

XIC 

Figure 6.4 LOWER SURFACE FINAL SUCTIONS - 

MODIFIED AST WING 

43 

I 
Figures 6.5A through 6.7 highlight typical boundary layer stability 

results taken, after extensive iterative analysis, at the final suction 

levels. 

station. 

rapid acceleration from the attachment line Cp of roughly 0.12 to a rooftop 

level around -0.02, followed by a short adverse-gradient region, then an 

extended region of gradual acceleration. As expected, the most highly 

amplified waves found in the initial acceleration region are the stationary 

crossflow waves. Only the "critical" waves, i.e. those threatening to pass 

through N = 9, are shown. 

just sufficient to prevent any of these waves from exceeding N = 9. The 

leading-edge suction level in figure 6.5B is slightly higher. 

illustrate the sensitivity of the critical wave amplification to applied 

suction. 

due to discretization. 

wave is halted by the peak in the Cp distribution. 

Figures 6.5A and 6.5B show the upper surface of the inboard 

The chordwise pressure distribution is characterized by a spatially 

In figure 6.5A, the leading-edge suction level is 

These figures 

An uncertainty on the order of 0.5 in amplification factor exists 

In both cases, the growth of the stationary crossflow 

16-r14 

12 

* 2 IO 

"= 8 - M 

6, 

4 

2 

0.0 0.2 0.4 0.6 0.8 1.0 

XlC 

Figure 6.5A BOUNDARY LAYER STABILITY 

MODIFIED AST WING - FINAL SUCTION 

UPPER SURFACE @ ETA = 0.18 

M = 2.2, hp = 58 kft, ALPHA = 2.0 deg 

44 
I 

I4 

12 

5 10 

Id 

9 * 

6 

4 

2 

0.12 

0.088 0.0 0.2 0.4 0.6 0.8 1.0 

16.3 -- 

- 

XIC 

I--------- 

0.0 0.2 0.4 0.6 0.8 I 

XlC 0.0 0.2 0.4 0.6 0.8 1.0 

XlC 

Figure 6.5B BOLJNDARY LAYER STABILITY 

MODIFIED AST WING - INCREASED L.E. SUCTION 

UPPER SURFACE @ ETA = 0.18 

The secondary, or sustaining suction level was set by the amplification 

of travelling crossflow waves in the mild gradient region, so no waves were 

found in the flat region ahead of X/C = 20%. 

theoretically, be reduced in this region. 

gradient region at this suction level are relatively low frequency (f = 125 

Hz) highly oblique travelling crossflow waves. 

levels the frequency of the most amplified waves was higher, and the 

waveangles lower (not shown). 

The suction could, 

The favored waves in the mild 

At lower secondary suction 

Figure 6.6A give stability results for the span station just inboard of 

the break on the lower surface. 

more rapid, and the difference between the attachment line Cp (0.12) and the 

rooftop value (0.03) is less. 

amplification to below the critical level, even without suction. However, 

the low-gradient region in the first 8 or 10 percent chord gives rise to 

travelling crossflow waves. The critical wave is found, at this suction 

level, around 4970 Hz at 75 degrees waveangle. 

profiles in this region, shown in figure 6.6B, display inflection for 

waveangles of 65 degrees and above, confirming the identification of these 

waves as travelling crossflow. 

higher and lower waveangle are shown in figure 6.6A. The suction required to 

subdue these waves was retained over the chord, and was sufficient to prevent 

growth of all waves in the lower gradient region aft of 10% chord. 

small suction reduction could have been realized. 

The acceleration to the rooftop is spatially 

This reduces stationary crossflow 

Suction-on velocity component 

The most highly amplified competing waves at 

Again, a 

45 
-0.04 

0.00 

0.04 

0.08 

0.12 

CP 

0.0 0.2 0.4 0.6 0.8 1.0 

XlC 

wm -0.08- 

' 

2 lo' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -- 

A 

Figure 6.6A BOUNDARY LAYER STABILITY 

MODIFIED AST WING - FINAL SUCTION 

LOWER SURFACE @ ETA = 0.74 

WL- 

-ai 0.0 01 01 OJ OA 01 M a? QI an LO 

Vyv MT 

Figure 6.6B COMPONENT VELOCITY PROFILES 

MODIFIED AST WING - FINAL SUCTION 

LOWER SURFACE @ ETA = 0.74, X/C = 0.03 

46 
Figure 6.7A represents perhaps the most interesting case. This station, 

located on the upper surface just inboard of the sweep break, exhibits all 

three types of instability. The rooftop velocity level is higher than for 

the inboard station shown in figure 6.5A, Cp= -0.07 as opposed to -0.02. 

Stationary crossflow waves are amplified in the initially steep gradient, but 

so are travelling crossflow waves in the less steep region from about 1% to 

5% chord. A stepped suction distribution was used here, resulting in the 

critical waves shown. Figure 6.7B shows the velocity component profiles at 

X/C = 0.022 with the suction shown in 6.7A. 

of the 85 and 88 degree component profiles identifies the 600 Hz, 87.5 degree 

wave as travelling crossflow. The very mild adverse region downstream of the 

velocity peak at 5% chord apparently has a beneficial effect, since the 

suction level required to stabilize the boundary layer downstream is very 

small, about Cq = -.00002. 

at 1000 Hz and 70 degrees. A look at the velocity profiles in figure 6.7C, 

taken at X/C 5 0.31 with nominal suction, shows the virtual absence of 

boundary layer crossflow at this station, and confirms the identif ca ion of 

this wave as T-S. This is in agreement with Pfenninger and Vem~rut~~j, and 

shows the potential that careful design of the wing pressure distribution can 

have on suction requirements, and hence suction system size, weight, and 

cost. 

The clearly inflectional nature 

The most amplified wave in this region is found 

-0.08 

-0.04 

0.00 

0.04 

CP 

XlC 

I~~M-J ~ .................................................. _._.... 

14 

12 wa(0ota r' -1-s 

. 'L ..rc I' Wac 

--mota 

4 10 

3 8 

- 6 

4 

2 2 

0 

i -. . . . . . . . 0.0 0.2 0.b 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 

XlC XIC 

Figure 6.7A BOUNDARY LAYW STABILITY 

MODIFIED AST WING - FINAL SUCTION 

UPPER SURFACE @ ETA = 0.74 

47 
Figure 6.7B COMPONENT VELOCITY PROFILES 

MODIFIED AST WING - FINAL SUCTION 

UPPER SURFACE @ ETA = 0.74, X/C = 0.022 

ai ol 0.3 0.8 OA am 

Figure 6.7C COMPONENT VELOCITY PROFILES 

MODIFIED AST WING - FINAL SUCTION 

UPPER SURFACE @ ETA = 0.74, X/C = 0.31 

48 
The required suction levels from the stability analysis were interpolated 

and integrated over the wing to determine a suction massflow for laminar flow 

on both surfaces aft to the control surface hingeline. The total suction 

massflow was 22.3 lbm/sec at initial cruise conditions of Mach 2.2 and 58 

kft. 

AST wing used in the feasibility analysis is 23.8 lbm/sec. Although that 

an. iysis used conservatively high suction levels, the lower surface wingtip 

could not be laminarized, and had no suction. Although the feasibility of 

fitting suction ducting into the wing has been established, the design of a 

ducting system was not seen as appropriate to this study, and was not 

undertaken. 

For comparison, the total suction massflow computed for the original 

The skin friction drag was computed on the wing using the Douglas 

strip-theory boundary layer code, BLP. This program computes both laminar 

and turbulent boundary layers, with user-specified transition location, and 

correctly accounts for the effects of wall suction. 

friction with suction was computed. 

viscous drag calculation is important, since it contains what subsonically is 

accounted for as ram drag. 

made for purposes of comparison. 

The laminar skin 

The inclusion of suction into the 

A turbulent calculation with no suction was also 

Wing-body drag due-to-lift, configuration volume wave drag, and trim drag 

were assumed not to differ from those computed for the original AST. 

was deemed appropriate to the scope and intent of the study. 

of proper wing drag accounting and optimum discharge of suction air have been 

addressed, and have been found to be significant issues at supersonic 

speeds. 

through internal ducting to a compressor driven by shaft power extracted from 

the thrust engines, then pass through ducting to an optimally expanded, aft 

facing nozzle, where it is ejected. 

formulated and used to quantify pumping and nozzle thrust effects for the 

suction air. This is described in appendix A. 

This 

The questions 

Suction air is assumed to enter through the porous skin, pass 

A thermodynamic model has been 

A simple skin-friction estimate of the performance improvement of the 

laminarized original AST wing is shown in figure 6.8. This was done using 

flat-plate skin-friction charts. 

comparison with the results of more detailed calculations, shown in figure 

6.9. 

and properly account for the effects of pressure distribution, wall suction, 

and the thermodynamics of the LFC pumping system. 

trailing edge there is no adverse pressure gradient associated with pressure 

recovery, there is no pressure drag benefit for laminarization, as in 

subsonic flow. 

estimate would be reasonably accurate for the supersonic case. Note the 

estimated 12% improvement in L/D for full wing laminarization. 

It is given in this section for purposes of 

The more detailed calculations utilize a strip-theory boundary layer, 

Since with a supersonic 

For this reason it was expected that a simple skin friction 

49 
Baseline TOGW = 750 000 lbf 

5750 run Mission 

LFC weight penalty on suction area: 

both surfaces - 2.82 psf 

one surface - 1.98 psf 

----- RESIZE -------- LAMINAR EXTENT LID TOGW FUEL BURN 

L'D INCREASE CHANGE CHANGE 

TURBULENT 

BASELINE 

BOTH WING SURFACES 

TO CNTL HINGES, EXCEPT 

LOWER SURFACE OUTBD & 11.35 10.7% -6.5% -12.4% 

6 DEG TURBULENT WEDGES. 

TURBULENT V & H TAIL. 

BOTH WING SURFACES 

TO CNTL HINGES, EXCEPT 11.49 12.1% -7.5% -14.02 

6 DEG TURBULENT WEDGES. 

TURBULENT V & H TAIL. 

WING AND V & H TAIL, 

TO CNTL HINGES, EXCEPT 11.79 15.02 -9.3% -17.0X 

6 DEG TURBULENT WEDGES. 

WING AND V & H TAIL, 

TO CNTL HINGES. 11.99 17.0% -9.5% 

NO TURBULENT WEDGES. 

-18.12 

Figure 6.8 LFC BENEFIT ESTIMATE - 

ORIGINAL AST WING, 

BASED ON FIAT PLATE 

SKIN FRICTION CALCULATIONS 

50 
The performance benefits for LFC, including the increased skin friction 

due to suction and the thermodynamics of the suction system compressor and 

exhaust nozzle, were computed and are presented in figure 6.9 for the AST 

with the LFC-modified wing. 

total pressure loss for suction air from the wing surface to the compressor. 

A 5% duct loss is assumed between the compressor and nozzle. 

efficiencies of 80Z for the compressor and 98% for the nozzle were assumed. 

Despite the additional detail, the results of figure 6.9 compare very well 

with the simple skin-friction estimates of figure 6.8. The details of the 

suction system drag accounting are given in appendix A. 

The aerodynamic benefits are based on a 10% 

Realistic 

The gross weight and mission fuel burn reductions for the LFC 

configurations are the results of sizing calculations. Since the baseline 

AST engine sizing was based on a takeoff noise constraint, engine size was 

assumed to be proportional to take-off gross weight (TOGW). 

the wing, suction system, and landing gear were proportional to gross weight 

as well. The LFC system weight, based on reference 26, was assumed to be 

2.82 psf for both-surface suction and 1.98 psf for single-surface suction, 

based on suction area. 

other weights were considered fixed. 

figures is principally due to the fuel reduction. The wing planform areas 

are reduced by the same percentages as the TOGW, but the resulting operating 

empty weights are found to be in the neighborhood of 0.5% less than that of 

the turbulent baseline airplane for all of the cases shown. 

The weights of 

Takeoff wing loading was held constant. Fuselage and 

The decrease in TOGW seen in the 

51 
Baseline TOGW = 750 000 lbf 

5750 run Mission 

LFC weight penalty 2.82 psf 

over suction area only. 

e---- RESIZE --__---- 

LAMINAR EXTENT LID LID TOGW FUEL BURN 

INCREASE CHANGE CHANGE 

TURBULENT 

BASELINE 

BOTH WING SURFACES 

TO CNTL HINGES, EXCEPT 

6 DEG TURBULENT WEDGES, 

TURBULENT V & H TAIL. 

DISCHARGE AT Vfs. 

BOTH WING SURFACES 

TO CNTL HINGES, EXCEPT 

6 DEG TURBULENT WEDGES, 

TURBULENT V & H TAIL. 

SONIC DISCHARGE. 

WING AND V & H TAIL, 

TO CNTL HINGES, EXCEPT 

6 DEG TURBULENT WEDGES, 

SONIC DISCHARGE. 

WING AND V & H TAIL, 

TO CNTL HINGES 

NO TURBULENT WEDGES, 

SONIC DISCHARGE. 

10.25 ----- ---e- ----- 

11.52 12.4% -7.82 -14.4X 

11.50 12.2% -7.6% -14.1% 

11.80 15.1% -9.4% -17.2% 

12.00 17.1% -9.6% -18.2% 

Figure 6.9 LFC BENEFIT SUMHARY - 

MODIFIED AST WING, 

INCLUDING SUCTION AND 

PUMPING SYSTEM EFFECTS 

52 
7. MACH 4 TRANSPORT - FEASIBILITY 

As part of an overall attempt to identify the applicability limits of 

Laminar Flow Control, and to identify useful trends, the feasibility of 

laminarizing a configuration with a higher design Mach number was 

undertaken. 

High-speed Commercial Transport (HSCT) studies, being done under NASA 

contract. 

designed for a cruise Mach number of 5.0, and was fully blended, with an 

inboard wing leading-edge sweep of 80 deg. 

surface was a section of a cone at zero degrees angle of attack, so that 

spatial pressure variations would be minimized. 

dictated by practical constraints regarding volume distribution and 

packaging. 

The configuration chosen was developed as part of ongoing 

The configuration is shown in figure 7.1. This configuration was 

At the cruise attitude, the lower 

The upper surface shape was 

I 

, 

YLgure 7.1 DAC HSCT CONFIGURATION 

53 
The analysis was conducted at a Mach number of 4.0, which was the highest 

Mach number for which a solution could be obtained from the Kaups-Cebeci 

boundary layer code. The angle of attack was 4.75 degrees, corresponding to 

best configuration LID. 

appr xi ately 85 kft. The configuration was run through the MDC SCRAM Euler 

code ?271f at Mach 4.0 and the design angle of attack. At this Mach number 

the sonic sweep angle is 75.52 degrees so the 80 degree inboard leading edge 

is subsonic. 

three selected planes taken at different axial stations on the 

configuration. 

leading-edge region, an essentially flat design pressure distribution was 

achieved on the lower surface. The theoretical attachment line pressure 

coefficient for Mach 4.0 and 80 degrees sweep is .0340. 

maximum pressure coefficient is substantially above the theoretical value, 

and is found on the lower surface inboard of the leading edge at all axial 

stations shown. These pressure coefficients are, in fact closer to the 

wedge-flow values corresponding to the local surface incide ce 

the freestream. Comparisons with the calculations of Jones P287 for 

elliptical cones in supersonic flow indicate that attachment is indeed 

occurring at the point of maximum pressure coefficient. 

The corresponding initial cruise altitude was 

Figures 7.2A through 7.2C show the pressure distributions in 

Only one side of the configuration is shown. Except in the 

Note that the 

relative to 

The surface velocity field computed by the SCRAM code was used to 

directly calculate the momentum-thickness Reynolds number along the indicated 

attachment line in the midspan region. 

felt that this high 

surface, so further analysis of this configuration was terminated. 

The computed value was 1827. It was 

value would preclude laminarization of the lower 

-o'lol UPPER SURFACE CONTOUR 

0.10- 

0.20- 

LOWER SURFACE CONTOUR 

I 

0.0 0.2 0.4 0.6 0.8 1.0 

Y/ (b/2 1 local 

I I 1 I 1 

Figure 7.2A SCRAM EULER SOLUTION FOR HSCT CONFIGURATION 

16 PERCENT LENGTH AXIAL STATION 

MACH = 4.0, ALPHA = 4.75 deg 

54 
0.00 

0.05- a 

V 

0.10 - 

0.15- 

UPPER SURFACE CONTOUR 

LOWER SURFACE CONTOUR 

r 

0.0 

1 I 1 

0.2 0.4 0.6 0.8 1 .o 

Y/(b/2)local 

Figure 7.2B SCRAM EULER SOLUTION FOR HSCT CONFIGURATION 

48 PERCENT LENGTH AXIAL STATION 

MACH = 4.0, ALPHA = 4.75 deg 

0.051 -\ 

0.0 0.2 

Figure 7.2C 

7 

LOWER SURFACE CONTOUR 

0.10 1, 1 I f 1 I 

0.4 0.6 0.8 1.0 

Y/(b/2)local 

SCRAM EULER SOLUTION FOR HSCT CONFIGURATION 

80 PERCENT LENCTH AXIAL STATION 

MACH = 4.0, ALPHA = 4.75 deg 

55 
I 

8. LFC ON SUPERSONIC FIGHTERS 

I 

One emerging application of supersonic cruise technology is to fighter 

aircraft, where efficient supersonic cruise capability can greatly enhance 

operational utility and survivability. 

of determining the applicability of LFC to various types of supersonic cruise 

airplanes, a study of the application of LFC to supersonic cruise fighter 

airplanes was conducted. 

determine the feasibility of applying LFC technology to this type of aircraft 

and to evaluate LFC benefits for typical missions involving significant 

supersonic cruise segments. 

shown in figures 8.1 and 8.2. 

In keeping with the study objective 

The objectives for this part of the study were to 

The two configurations chosen for study are 

Figure 8.1 SF-1107 SUPERSONIC CRUISE FIGHTER CONFIGURATION 

PRECEDING PAGE BLANK NOT FILMED 

57 
The two configurations, designated SF-1107 and SF-1302, are generic 

examples of fighter aircraft designed to cruise at or near Mach 2.0. 

SF-1107 aircraft uses the supersonic wing leading edge approach, while the 

SF-1302 employs a highly swept subsonic wing leading edge design. A 

comparison of the physical characteristics of the two configurations is shown 

in figure 8.3. 

a prescribed distance from the target, accelerate and climb to Mach 2.0 

cruise conditions, dash to and from the target at Mach 2.0 over the 

prescribed hostile territory, then return to base subsonically. 

configurations evolved during a rather detailed advanced design study to 

investigate the respective sizes of aircraft to meet certain supersonic 

cruise mission requirements for both low sweep and highly swept wing 

configurations. They should, therefore, be fairly representative of fighter 

configurations one might expect to see in the future. 

however, that the SF-1302 aircraft is significantly larger than the SF-1107 

not because it is inherently less efficient, but because it it was designed 

to a longer mission. 

The 

Their basic missions are to cruise out at subsonic speeds to 

These 

It should be noted, 

A major part of this study effort was concentrated on the stability of 

the boundary layer on the two aircraft wings. 

boundary layer and its stability with and without suction on the two fighter 

wing configurations was conducted for a cruise Mach number of 2.0 and angle 

of attack of 4.0 degrees. 

(FLO-67) are used to generate the boundary layer solutions using a modified 

version of the Kaups-Cebeci code. 

with compressible linear stability methods, using the NASA COSAL code. 

Performance and sizing analyses were conducted to determine the effects of 

laminarization on the gross weight required to make certain specified 

missions. 

A detailed analysis of the 

The inviscid pressures obtained from an Euler code 

The boundary layer stability was analyzed 

Itom 

Conf burrtion 

SF-1 107 SF-1 302 

1. WingArea (112) 530 74 1 

2. LESweep (deg) 31 71161.5 

3. Wingspan (ft) 38.15 37.51 

4. Aspect Ratio 2.75 1 .a9 

5. TakeoffGW 

6. internal Fuel 

(Ib) 33,200 37,869 

10,702 13,681 

7. Combat Radius on 

SuDenonic Cruise Mission (NMI 400 500 

Figure 8.3 A CHARACTERISTICS COMPARISON OF THE SF-1107 

AND SF-1302 AIRCRAFT 

58 
9. SF-1107 FIGHTER WING 

I 

I 

I 

1 

I I

I 

I 

I 

I 

I 

'I 

I 

I 

I 

I 

, 

The SF-1107 fighter configuration is shown in figure 8.1. The wing is 

simple geometrically, consisting of 52 thick symmetric parabolic biconvex 

sections with no twist. Wing chord varies linearly from 22.50 ft. at the 

centerline to 5.45 ft. at the tip. Leading edge sweep is 32 degrees. The 

inviscid flow solutions on the isolated SF-1107 wing were obtained using the 

FLO-67 Euler code. The pressure distributions were found to be very smooth, 

which is essential for an accurate stability analysis. The surface pressure 

distribution at the 50% semispan station is shown in figure 9.1. 

corresponding upper surface isobar plot, which is very conical, is shown in 

figure 9.2. 

almost linearly with X/C, giving a nearly constant favorable gradient over 

the chord. 

Tollmien-Schlichting waves, the presence of boundary-layer crossflow caused 

by isobar sweep causes amplification of high-waveangle crossflow waves. 

The 

For the parabolic biconvex airfoil in supersonic flow, Cp varies 

Although this stabilizes the boundary layer against low waveangle 

4.2 

__---- __---- _--- _---- 

--- 50% Semispan 

_---- -- 

c, 0.2 - _-I-- 

\ ,* 

.- 

0.4 1 

0.6 

0 0.2 0.4 0.6 0.8 1 

XEL: 

D 

Figure 9.1 SURFACE PRESSURE DISTRIBUTION AT 502 SEMISPAN 

SF-1107 WING WITH BICONVEX SECTION 

M,=2.0, a-4. 

The boundary layer solutions for this case, obtained using the modified 

All boundary layer analyses 

version of the Kaups-Cebeci code, were examined in detail to allow confidence 

in their subsequent stability characteristics. 

were conducted for a freestream Mach number of 2.0 and 4 degrees angle of 

attack, at a standard day altitude of 40 kft. Some sample results of the 

analyses are shown in figures 9.3 through 9.11. 

figures are for 50% semispan on the upper surface with no boundary layer 

suction. Figures 9.3 and 9.4 show very smooth distributions of external 

velocities, UE and WE, obtained from the FLO-67 Euler code, in the polar 

coordinate system (figure 5.7) used in the Kaups-Cebeci code. For emphasis, 

the second derivative of Cp with X/C is also shown in figure 9.5. These 

distributions are plotted against chord fraction, X/C. 

distribution of Cp" is necessary for accurate stability calculations. 

The results shown in these 

The smooth 

59 
-1 7 

Figure 9.2 UPPER SURFACE PRESSURE CONTOURS, SF-1107 WING 

50% Semispan 

Uppor Sutfaa 

M, - 2.0 

a I 4' 

50% Semispan 

Uppor Sutfaa 

M, - 2.0 

a I 4' 0.4 - 

0.2 

0.1 - 

- o-2L 

O L, o!l 0: ob 

\ 

o.! 6.5 d.6 7 

Figure 9.3 DISTRIBUTION OF VELOCITY Ue ON THE UPPER SURFACE 

AT 50% SEMISPAN, SF-1107 WING 

60 
! 

WEUFS 0.60 

0.30 

SOK Semispan 

upper SudM, = 2.0 

a =4* 

Olllllll 

0 0.1 02 0.3 0.4 0.5 0.6 0.7 

XK: 

-7- 

Figure 9.4 DISTRIBUTION OF VELOCITY We ON THE UPPER SURFACE 

AT 50% SEMISPAN, SF-1107 WING 

t 1 

OT I 

12 I I I I I 

i 0.1 0.2 0.3 0.4 0.5 0.6 .7 

Figure 9.5 SECOND DERIVATIVE Cp" VS. X/C ON THE UPPER SURFACE 

AT 50% SEMISPAN, SF-1107 WING 

The boundary layer velocity profiles along the radial direction are shown 

in figure 9.6 at four different chord fractions ranging from 1% to 51%. 

Figure 9.7 shows the high degree of self-similarity of typical consecutive 

velocity profiles in scaled coordinates, Y/DELSTX. However a closer 

examination indicates that they do not exactly fall on a single curve as 

anticipated for zero radial pressure gradient. Figure 9.8 shows that the 

second derivative of the radial velocity, u", is well behaved for the middle 

and outer regions, but not near the wall. This problem was alluded to in 

section 8. The near-wall numerical oscillation is also reflected in the wall 

shear stress (Figure 9.9). 

61 
0.014 

0.012 

0.010 

Y 0.008 - 

('1 0.006 - 

0.004 - 

i 

I 

t 

l 

8 

I 

I 

.---- 1% c 50% Semispan 

10% c M, = 20 

3oxC a -4' 

51% c 

- 

..... - 

- --- 0 

- l 

- L 

0 02s 0.50 0.75 1.00 

w aR+ou7.40 

Figure 9.6 BOUNDARY LAYER VELOCITY PROFILES ALONG THE RADIAL 

DIRECTION ON THE UPPER SURFACE AT 50% SEMISPAN, 

SF-1107 WING, NO SUCTION 

4.0 

0 0.25 0.50 0.75 1 .00 

w acl+oUlJ).o 

Figure 9.7 CONSECUTTVE VELOCITY PROFILES IN SCALED COORDINATES 

AT 50% SEMISPAN, SF-1107 WING, NO SUCTION 

62 
Figure 9.8 SECOND DERIVATIVE OF VELOCITY VS. SCALED NORMAL 

COORDINATES AT FOUR CONSECUTIVE CHORD STATIONS, 

SF-1107 WING, NO SUCTION 

1.4 

4.2 o*o* 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 

xx: oIoou7.w) 

Figure 9.9 WALL SHEAR STRESS VS. X/C AT 50% SEMISPAN, 

SF-1107 WING 

63 
- 44 

- om 0.00 0.2s 0.60 

---- 1.00 200 

x IC 

mS.mb9.n 

25% Chord 

These oscillations caused great concern in the early phase of this study, 

and motivated the addition of a simple averaging scheme to the Kaups-Cebeci 

code. 

the oscillation dissappear, as shown by the solid line in figure 9.9. 

Comparison stability analyses conducted wit.h and without the modification 

have shown no differences in computed N-factors. It should be noted, 

however, that the oscillations have been observed to increase with Mach 

number, so the improved code incorporating the averaging scheme would likely 

have to be used under these conditions. 

By averaging each consecutive pair of velocity profiles, all signs of 

Prior to conducting stability analyses, the effects of suction on 

boundary layer velocity profiles were also studied. 

effects of suction. 

effective Reynolds number. This thinning effect is demonstrated in figure 

9.10, where the velocity profiles at 25% chord station are plotted against 

the normal coordinate (Y) for different suction values. With increased 

suction, the thickness of the boundary layer is reduced considerably. 

Another effect of suction is to change the boundary layer shape factor. 

There are several 

Suction thins the boundary layer and thereby lowers the 

This 

is quite evident from figure 9.10, which shows that 

changes appreciably. 

the profile shape also 

3.5 - 

3.0 - 

2.5 - 

2.0 - 

1.0 - 

0.5 - 

M, - 20 

Figure 9.10 EFFECT OF SUCTION ON VELOCITY PROFILES AT 25% CHORD 

AND 50% SEMISPAN LOCATION, SF-1107 WING 

64 
The suction also causes the inflection point of the crossflow profile to 

move closer to the wall, where the increased viscosity acts to help damp out 

crossflow waves. This is demonstrated in figure 9.11, where a crossflow 

parameter, (DELTCF) is plotted against chord fraction for two different 

suction levels. This crossflow parameter is an integrated value of the 

crossflow boundary layer thickness. It is quite clear that this thickness is 

reduced substantially with suction. All of these effects o s ction are 

known to have a stabilizing influence on the boundary layer f29Y . 

A stability analysis of the boundary layer profiles obtained from the 

Kaups-Cebeci code was performed using COSAL. 

suction was conducted to determine the most amplified wave. 

both the constant waveangle and constant wavelength options were used, for 

the reasons outlined in the beginning of section 6. 

stationary and nonstationary crossflow waves was calculated. 

and lower surfaces of the wing were examined in detail. 

stations (inboard, midspan, and outboard) were analyzed. 

Analysis with and without 

In this study, 

The growth of both 

Three spanwise 

Both the upper 

1.4 I 3 

Cmr Flow 

Parameter 

(DELTCF) 

x (104) 

b, ba - 0.0 0.0 

12 - ----- 1.0 2.0 

0.8 - 

\ 

\ 

soKS.misp8n 

a -40 

\ 

M,- 20 

0 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 

xx= QcI+Ou1310 

Figure 9.11 EFFECT OF SUCTION CROSSFLOW PARAMETER, DELTCF, AT 

50% SEMISPAN LOCATION, SF-1107 WING 

65 
For the zero suction case, initially a broad range of frequencies, 

waveangles, and wavelengths were analyzed to identify the most amplified 

waves. 

stability analysis on the upper surface at the midspan station. 

N-factors are plotted against X/C for different values of the 

wavelength-to-chord ratio, (XLENC). 

XLENC for which the growth of these waves could be important, and it appears 

that the band lies between 0.001 and 0.003. 

occurs near XLENC = 0.0015. 

Figure 9.12 shows the results of a stationary (f = 0.5 Hz) crossflow 

The 

An attempt was made to find a band of 

The maximum amplification factor 

14 

12 

10 

8 

N 

6 

4 

2 

0 

~ 

Fnqrrmc~ = 0.5 HZ XLENC 

- 0.00100 - - o.oOp0 

0.00125 - O.Ow50 

0.00150 -*- O.Oa300 

e -. 

-... 

..... -. 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 

m 

waso447- 

Figure 9.12 STATIONARY CROSSFLOW INSTABILITY WITHOUT SUCTION, 

SF-1107 WING 

66 
Figure 9.13 shows a stability chart constructed from the results of many 

runs for the zero suction case. Frequency is plotted against the local 

momentum-thickness Reynolds number, Re, where N = 9 was first found, 

indicating transition. Several wave orientation angles are shown. Since the 

computed N-factor varies with wavelength, waveangle, and frequency, Re N=9 

as defined here is the dependent variable. It is observed that the minimum 

Re ~~9 is approximately 1935 (found at approximately the 8% chord station), 

and the frequency and orientation angle of the corresponding wave are 10-12 

kHz and 80 degrees, respectively. The largest N-factors computed are found 

for frequencies around 5 kHz and PSI = 80 degrees. The corresponding XLENC 

was around 0.004 (not shown here). 

80 degrees and several different frequencies. 

value of nine at approximately the 8% chord location for f = 10 kHz. This 

indicates that natural laminar flow could exist only up to the 8% station. 

For a frequency of 5 kHz, the N-factor reaches a value as high as 23, whereas 

for higher frequencies the maximum values are considerably smaller. 

higher frequency waves have more rapid initial growth, but become stable in a 

shorter distance from the leading edge, due to the thickening boundary layer. 

Figure 9.14 shows the N-factors for PSI = 

The N-factors first reaches a 

The 

14 

12 

10 

F 

8- 

(KHZ) 

6- 

4- 

2- 

It is perhaps worth noting here that the results of the linear stability 

theory may not be too meaningful when computed N-factors are very large, 

since presumably the boundary layer would have undergone transition, or at 

least departed the linear region (reference 30). 

significance should be attached to the question of which wave reaches the 

critical range of, say, 7 to 12 first. For practical purposes a critical 

N-factor of 9 is being used in this study. 

Therefore, more 

16 

i 

- 

- 

- 

m --- 850 .... *-. : a. 1 I . e. 

-- --- 

01 I I I I I I I 

1,500 2.000 2,500 3.000 3,500 4.000 4,500 5,000 5,500 

-1- 

Figure 9.13 FREQUENCY VS. CORRESPONDING TO N = 9, NO SUCTION, 

50Z SEMISPAN, SF-1107 WING 

67 
N 

4 I-:: 

0 

/ 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 

XK: wssoawm 

Figure 9.14 AMPLIFICATION FACTOR FOR DIFFERENT FREQUENCIES 

NO SUCTION, SOX SEMISPAN, SF-1107 WING 

The boundary layer velocity profiles on the wing were analyzed in order 

to gain insights into the type of instabilities present at high waveangles as 

observed here. 

orientation angles were examined at several chord stations at the SOX 

semispan location. The analysis offered some valuable information aaout the 

development of inflections in the velocity profiles from the leading edge to 

the 60% chord station for different wave orientation angles. Figures 9.15 

through 9.18 show component velocity profiles at different chord stations, 

but no suction, for orientation angles of 70, 80, 85, and 90 degrees 

respectively. It is observed that for angles, PSI, of 80 degrees and up, 

there is a visible inflection, which becomes deeper and farther above the 

surface as waveangle is increased. 

mechanism of instability for the critical waves found in the stability 

analysis is inflectional, so the waves should be classified as travelling 

crossflow waves. 

The velocity profiles resolved along different wave 

This analysis indicates that the 

68 
Figure 9.15 BOUNDARY LAYER VELOCITY PROFILES AT PSI = 70 DEGREES, 

50% SEMISPAN, NO SUCTION, SF-1107 WING 

Figure 9.16 BOUNDARY LAYER VELOCITY PROFILES AT PSI = 80 DEGREES, 

50% SEMISPAN, NO SUCTION, SF-1107 WING 

69 
0.014 

0.012 

0.01 a 

0.008 

(n) 0.006 

0.004 

0.002 

0 

0.014 

0.012 

0.010 

0.008 

0.006 

0.004 

.#- / 

- 1% c 5(ms.mispsn 

- I.... I M, - 20 aoWC 

4QKC 

51% c 

.-- 

.._..". a- 4O 

- 

.. , .. * .. 

.. .. . - . 

I 

2 e - *.*' ; 

/'- *.. . . .. ..... . . ; ,,.' -. ':*. :: 

- ;a . 

i' 

j~ I -mispan 

I a- 4" 

M, - 2.0 I 

I 

I I I 

50 100 150 200 250 300 3 0 

Figure 9.17 BOUNDARY LAYER VELOCITY PROFILES AT PSI = 85 DEGREES, 

50% SEMISPAN, NO SUCTION, SF-1107 WING 

v - wsec 

Figure 9.18 BOUNDARY LAYER VELOCITY PROFILES AT PSI = 90 DEGREES, 

50% SEMISPAN, NO SUCTION, SF-1107 WING 

70 
The boundary layer with suction has also been analyzed in detail. In the 

next several figures are shown the results of the stability analysis with 

suction. Figure 9.19 shows the effect of suction on the amplification of the 

5 kHz, 80 degree wave. 

factor with suction off. Note the extent to which growth of this wave can be 

controlled with relatively low suction levels. 

This wave had the highest maximum amplification 

Due to the various adverse aspects of boundary layer suction, such as 

system weight, increased skin friction drag, etc., the aim is to apply just 

emough suction so that the N-factors do not grow beyond a value of 9. From 

this figure it would appear that the suction level corresponding to the label 

(1.00,0.50), which is one half of that shown in the same figure in the lower 

right-hand corner, is perhaps sufficient. However, further stability 

calculations indicated that a higher level of suction was needed (labeled as 

2.00,l.OO and shown in the lower right-hand corner of the figure). 

distribution was used in several calculations to make sure that the growth of 

neither stationary nor nonstationary crossflow waves ever reached a value of 

9. 

This 

Some of these results are shown in figures 9.20 through 9.23. 

24 

20 

16 

N 12 

8 

4 

0 

0.1 02 0.3 0.4 0.5 0.6 ( 7 

Figure 9.19 EFFECT OF SUCTION ON AMPLIFICATION FACTOR AT PSI = 80 

DEGREES AND F = 5000 Hz, 50% SEMISPAN, SF-1107 WING 

71 
One effect of applying suction was a much greater damping of the high 

frequency waves. For example, compare the effect of applying suction, 

labeled as (2.00,1.00), on waves of frequency 5 kHz (figure 9.19) with the 

same at 2 kHz (figure 9.22). 

shift of the most amplified wave to a lower frequency (from 5 kHz to 2 kHz) 

when suction, labeled as (2.00,l.OO) was applied. 

In fact, this level of suction results in a 

Figure 9.20 shows the amplification factors computed for several 

different values of PSI, but fixed at a constant frequency of 2 kHz. 

Calculations are shown here for 2 kHz only, as it corresponds to the most 

amplified disturbance. The distribution of suction level is also shown in 

the figure. Once again it is noticed that the largest amplification is found 

to be for highly oblique waves (87.5 degrees in this case). In fact, the 

orientation angle of the most amplified wave has increased as a result of 

suction application. 

9.21, whereas nonstationary crossflow calculations for 2 and 3 kHz (also done 

holding wavelength constant) are shown in figure 9.22 and 9.23, 

respectively. The value of XLENC corresponding to the most amplified wave is 

found to be about 0.0020 (figure 9.22). 

suction on the nonstationary crossflow waves is much greater than that on the 

stationary crossflow waves. 

Stationary crossflow calculations are shown in figure 

It is noted that the effect of 

24 

20 

16 

N 12 

8 

4 

0 

x IC 

I I 

I I I 

0.1 0.2 0.3 0.4 0.5 0.6 0 r 

Figure 9.20 AMPLIFICATION FACTOR FOR DIFFERENT WAVE ANGLES WITH 

SUCTION, 50% SEMISPAN, M = 2.0, a= 4 DEG., 

SF-1107 WING 

72 
24 

20 

16 

N 12 

8 

4 

0 

F- I 0.5 HI 

0 0.2 0.4 0.0 0.0 1 .O XLENC 

-. 0.0010 

- - 0.00 

- 

0.1 0.2 0.3 0.4 0.5 0.6 ( 7 

Figure 9.21 EFFECT OF SUCTION ON THE GROWTH OF STATIONARY WAVES 

50% SEMISPAN, SF-1107 WING 

24 

XLENC h.qunoy.2P00w 

- 

-0.001 5 

o.oO20 

N 

WC -1LD 

Figure 9.22 EFFECT OF SUCTION ON THE GROWTH OF NONSTATIONARY 

CROSSFLOW WAVES, 5OZ SEMISPAN, M = 2.0,cr= 4 DEG., 

SF-1107 WING 

73 
N 

F- = 3.000 HZ 

- 0.001 07 

20 - -_... 

--- 

m-a 

16 - 

12 - 

8- 

x IC 

4- 

0 0.1 O! 63 014 d.5 0.16 C 7 

-1M WC 

Figure 9.23 EFFECT OF SUCTION ON THE GROWTH OF NONSTATIONARY 

CROSSFLOW WAVES, 502 SEMISPAN, SF-1107 WING 

An analysis, similar to that shown in figures 9.15 through 9.18, was also 

conducted to examine the development of inflections in the boundary layer 

velocity profiles with suction. 

same as in figures 9.15 through 9.18. The results from this analysis are 

shown in figures 9.24 through 9.27. 

The semispan and chord locations were the 

74 
M, - 20 

a- 4. 

aDKC 

- - - 51%~ 

---_- 

:: I 

:: I 

:I I 

0.012 YIKC 

ai -1 *I 

#I 0.010 - *I -1 

:: 

:: 

0.008 :: - 

f 

0.006 - 

0.004 - 

0.002 - 

V-lchw: 

0 

Figure 9.24 BOUNDARY LAYER VELOCITY PROFILES AT PSI = 70 DEG., 

50% SEMISPAN, WITH SUCTION, SF-1107 WING 

Figure 9.25 BOUNDARY LAYER VELOCITY PROFILES AT PSI = 80 DEG., 

50% SWISPAN, WITH SUCTION, SF-1107 WING . 

75 
0.014 I I, 

0 

v-wsec QPs5QOD6D 

Figure 9.26 BOUNDARY LAYER VELOCITY PROFILES AT PSI = 85 DEG., 

50% SEMISPAN, WITH SUCTION, SF-1107 WING 

0.014 I I 

0.010 

0.008 

v-fv!mc aPm3aQa-1*0 

Figure 9.27 BOUNDARY LAYER VELOCITY PROFILES AT PSI = 90 DEG., 

50Z SEMISPAN, WITH SUCTION, SF-1107 WING 

76 
Not surprisingly, the profiles change considerably when suction is applied. 

The boundary layer is thinner as expected. 

almost absent at PSI = 80 degrees. They do, however, show their presence at 

85 degrees and beyond. Once again, this analysis indicates that the highly 

oblique waves (PSI = 87.5 degrees) corresponding to the largest amplification 

factor as determined from the stability results, are indeed travelling 

crossflow waves. One effect of suction, therefore, is to move the visible 

inflection to higher waveangle. 

Moreover, the inflections are 

Similar results have also been obtained at 18.75X and 81.252 semispan 

locations on the SF-1107 wing. Since the pressure distributions at these 

locations are very similar to that at the 50X location, calculations were 

reduced considerably. 

50% semispan, the ranges of frequencies, wavelengths and waveangles were 

bracketed very well. 

they were very similar to those at 50% semispan. 

Knowing the trends of the different wave growths at 

Results for those calculations are not shown here as 

Calculations were also performed on the lower surface at the same three 

span stations. 

close to the leading edge. 

gradient exists near the leading edge of the wing for the conditions examined 

(figure 9.1). 

predicted location of transition was delayed to 60% chord. 

favorable pressure gradient had been used, less suction would have been 

required. 

Without suction the transition is predicted to occur very 

This can be expected since adverse pressure 

With the suction distribution shown in figure 9.19 the 

If a less 

Since the SF-1107 wing has a relatively sharp supersonic leading edge, it 

was thought that attachment line conditions would not be critical. 

Calculations have verified this, with computed attachment line momentum 

thickness Reynolds numbers below 50 for all three span stations. 

A performance and aircraft sizing analysis was conducted on the SF-1107 

configuration. 

surfaces of the wing outboard of the strake, and on both surfaces of the 

horizontal and vertical tails. On the wing, suction was applied back to the 

flap hingeline and inboard of the wing tip cap. 

surface inboard of its tip cap was laminarized, and the vertical surfaces 

were laminarized back to the rudder hingeline below the tip cap. Fully 

turbulent flow was assumed on the other surfaces of the aircraft. A 

breakdown of the wetted areas which were laminarized is given in figure 

9.28. 

are shown in figures 9.29 and 9.30. 

performance were calculated for the baseline configuration and for a 

laminarized version with and without a system weight penalty. 

weight penalty was 2.82 lbflsqft of planform area affected by the 

laminarization system, taken from reference 26. The effect of LFC 

performance on system performance is sunrmarized in figure 9.31. 

Distributed suction was applied to both upper and lower 

The entire horizontal tail 

The effects of the laminarization on skin friction drag and CD min 

Energy maneuverability (EM) and mission 

The assumed 

77 
Wetad x Aru - H"2 

Actual hminrrized Laminarized Component 

A. Wing 664 424 64 

6. Horizontal Tail 206 192 93 

C. Venical Tail 182.5 120 5 93 

0. Total 2.232 736 5 33 

QCIIOU741 

Figure 9.28 BREAKDOWN OF WETTED AREAS LAMINARIZED, 

SF-1107 CONFIGURATION 

0.006 

0 

11111111111 

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.6 2.0 2.2 

M 

amsenI-1.0 

Figure 9.29 EFFECT OF LAMINARIZATION ON SKIN FRICTION DRAG 

COEFFICIENT, SF-1107 CONFIGURATION 

78 
- wine 

0.030 

0.025 - 

0.020 - 

I 

0.005 - 

0- I I I I I 

0 0.4 0.8 1.2 1.6 2.0 2.4 

(Jpc+ou7-17D Mach Number 

Figure 9.30 EFFECT OF LAMINARIZATION ON MINIMUM DRAG COEFFICIENT 

AGAINST MACH NUMBER, SF-1107 CONFIGURATION 

~ ~~ 

IlrSOllM 30.743 1.8 58 0.34 400 2W 6.0 9.2 1.248 13 7 25.3 ~ ~~~ 

IlrSohM &re. 

LFC Drag 

- WiO Wt RMQ 30.743 1.8 58 0.34 484 278 6 1 9.3 1.273 13.3 24.8 

- Wi WPrrurb 31.862 115 60 033 449 243 5.8 89 1.218 13 9 260 

Lzsd to Basma 

hri LFC Drag 

- WlOWlRtWQ 2%.%79 18 57 5 032 400 211 60 9 1 1,257 13 6 25 3 - 

- W/ Wt Rdty 31.131 18 57.5 0 31 400 201 60 9 1 1.253 13 6 25 3 

P -.ST 

Figure 9.31 EFFECTS OF LPC ON PWFOR"CE/AIRCRAPT SIZE 

SF-1107 CONFIGURATION 

In figure 9.31 mission performance is presented for a fighter sweep mission 

(figure 9.321, and for a combat air patrol mission (figure 9.33). 

in figure 9.31 is the effect of LFC on aircraft size if the fighter sweep 

mission radius is held constant. If Laminarization can somehow be affected 

at no weight penalty, the takeoff gross weight is reduced from 30 743 lbf to 

28 879 lbf, a size reduction of 6.1 percent. Using the aforementioned 

weight penalty, however, the takeoff weight actually increases to 31 131 lbf, 

a size increase of 1.3 percent. 

Also shown 

79 
Mission Dotinition 

@ Warmup 30 min Idle 

@ Takeoff Max Power Accel Mach 0 - 0 6 

Credit Distance 

@ Minimum Fuel Climb to Optimum Cruise 

@ Optimum Cruise 

0 Climb Accel to Mach 2 o and Optimum Altitude 

@ Dash at Mach 2 0 

@ Combat 25% Fuel. Fire Missiles 

@ Dash At Mach 2 0 and Optimum Altitude 

@ Decel, Descend To Optimum Subsonc Mach 

and Altitude 

@ Optimum Cruise 

0 20 min Loiter at Optimum Mach, Sea Level 

-7-1 I 

Figure 9.32 FIGHTER SWEEP MISSION FOR THE SF-1107 CONFIGURATION 

80 
(4) AYIMMS 

Mission Dofinition 

@ Warmup: 30 min Idle 

@ Takeoff: Max Power Accel Mach 0- 0.6 

@ Minimum Fuel Climb to Optimum Cruise 

@ Optimum Cruise 

@ 2 hr Loiter at Subsonic Corner Speed 

@ Combat: 25% Fuel, Fire Missiles 

@ Optimum Cruise 

@ 20 min Loiter at Optimum Mach, 

Sea Level 

(pI+ou7-10 

Figure 9.33 COMBAT AIR PATROL MISSION FOR THE SF-1107 

CONFIGURATION 

i 

81 
10. SF-1302 FIGHTER WING 

The SF-1302 configuration, shown in figure 8.2, features an arrow wing 

with a subsonic leading edge inboard of the leading edge sweep break at 70% 

semispan. The leading edge is swept 71.0 degrees inboard of the break, and 

61.5 degrees outboard. 

inboard of the break, and 5% thick parabolic biconvex airfoils outboard. 

gross planform area is 741 sqft. 

constraint. 

The wing consists of uncambered NACA 64A005 airfoils 

The 

The wing camber suface was not optimized as was that of the AST. 

The wing twist was set by a moment 

FLO-67 Euler solutions were obtained on the wing at supersonic cruise 

conditions of 2.0 Mach at 4 degrees angle of attack. 

on the upper surface are shown in Figure 10.1 while the chordwise pressure 

distributions at 18.75%, SO%, and 81.25% semispan are shown in Figure 10.2 

through 10.4. 

The pressure contours 

Figure 10.1 UPPER 

-74 

SURFACE PRESSURE CONTOURS, SF83 

PRECEDING PAGE BLANK NOT FILMED 

1302 WING 
4.4 I 

0.4 

0 02 0.4 0.6 0.8 1 .o 

Figure 10.2 PRESSURE COEFFICIENT VS. X/C, 18.75% SEMISPAN 

SF-1302 WING 

0.4 

0 02 0.4 0.6 0.8 .O 

Figure 10.3 PRESSURE COEFFICIENT VS. X/C, 50% SEMISPAN 

SF-1302 WING 

84 
Figure 10.4 PRESSURE COEFFICIENT VS. X/C, 81.25% SEMISPAN 

SF-1302 WING 

At a Mach number of 2.0, the leading edge of the outboard panel is still 

operating in the subsonic regime, since the planform was designed for 

reasonable dash performance at 2.2 Mach and above. 

upper surface chordwise pressure distribution is decelerating past 3% chord 

length. It is noted here that no effort was made to modify the geometry of 

the wing in order to tailor the pressure distribution for improved laminar 

flow. One point must be kept in mind regarding the conical flow assumption 

used in the boundary layer code. 

wing did not exhibit a high degree of conicality. The extent to which this 

affected the stability results can only be determined from comparisons with 

COSAL results calculated using a fully 3-D boundary layer code. 

stability package was unavailable at the time this study was done. 

For the SF-1302 wing, the 

The inviscid flow solutions on the SF-1302 

Such a 

Attempts were made to run the Kaups-Cebeci boundary layer code on the 

upper surface at the 50% semispan station using the pressure distribution 

shown in figure 10.3. Without suction, the laminar boundary layer could not 

negotiate the the adverse pressure gradient region downstream of roughly the 

15% chord station. However, the code was successfully executed with a 

suction level of Cq = -.0003 

Because of the shape of the upper-surface pressure distribution, and the 

high suction levels required to even get a laminar boundary layer solution, 

only a cursory stability analysis was carried out. 

identify how much additional suction would be required for laminar flow with 

such a pressure distribution. 

The intent was to roughly 

Figure 10.5 shows the most amplified stationary crossflow wave found in 

This is really the 

The maximum 

the leading edge region at the suction level indicated. 

end result of an iterative process in which various suction levels were tried 

and the most amplified waves were found for each level. 

amplification of the critical crossflow wave at this suction level is below 

9. This process was explained in detail in section 6. 

85 
XLENC = 0.0002 10 

- F - 0.5 HZ 

8k 

N , , 2 s.0 4 

Ob 02 0.4 0.0 0.0 1 .O 

x IC 

0.00 0.01 0.02 0.03 0.04 0.05 

acc+oUls+D XIC 

Figure 10.5 CRITICAL STATIONARY CROSSFLOW WAVE, 

LEADING-EDGE REGION, SUCTION ON. 

50% SEMISPAN, SF-1302 WING 

Figure 10.6 shows the critical stationary crossflow wave amplification in 

the adverse region without additional suction. 

gradient region was then progressively increased until the critical 

stationary crossflow wave was not amplified beyond N = 9. 

the amplification of the critical stationary crossflow wave after the suction 

was increased. 

investigated, so are not shown, although none were found which were more 

highly amplified than the stationary wave. 

waves would be more attenuated by suction than the stationary waves, since 

their inflection points have been shown to lie closer to the surface. The 

amount of suction required to stabilize the boundary layer against stationary 

crossflow waves, as shown in figure 10.7, is large. This underscores the 

importance of carefully tailoring the pressure distribution for LFC 

application. 

The suction in the adverse 

Figure 10.7 shows 

Travelling crossflow waves were not comprehensively 

Also it is likely that travelling 

Difficulty was also encountered in obtaining a boundary layer solution on 

the lower suface at 50% semispan when the attachment line was assumed to be 

at the leading edge. 

had if a high level of suction was applied in the leading-edge region. 

case is similar to the HSCT case discussed in section 7, in which the 

attachment line is actually located aft of the leading edge on the lower 

surface, and the attachment line Cp is higher than the simple-sweep value of 

.1177. It is anticipated, however, that by suitably modifying the wing 

geometry, as shown in section 6, the attachment location and pressure 

distribution could be changed so that both upper and lower surfaces are 

amenable to laminar flow. 

It was found that a boundary layer solution could be 

This 

The attachment-line momentum-thickness Reynolds number was computed at 

the 50% span station, and was found to be 152.5. This value could easily be 

reduced by slightly increasing the suction level. Therefore, the attachment 

line instability is again not expected to present any difficulty for an 

airplane of this size. 
N 

OO 

G 

0.2 0.4 0.8 0.8 1 

- Fm I 0.5 HZ 28 

.o 

50% Semispan 

M, 12.0 

a=c 

12t . I XLENC = 0.00124 

4 '1 J 8' "'D L 010*0.00.01.0 

x IC 

Figure 10.6 CRITICAL STATIONARY CROSSFLOW AMPLIFICATION 

IN THE ADVERSE PRESSURE GRADIENT REGION, WITH SUCTION 

50% SEMISPAN, SF-1302 WING 

N 

- XLENC - o.Ooo5 

sow *mispan 

M, = 20 

a -4' 

Fnqrrmc~ = 0.5 Hz 

1 8 '0 01 0.4 0.00.0 1.0 - x IC 

0.4 0.6 0.8 1 

XIC 

CRITICAL STATIONARY CROSSFLOW AMPLIFICATION 

IN THE ADVERSE PRESSURE GRADIENT REGION, INCREASED 

SUCTION, SOX SEMISPAN, SF-1302 WING 

Qcl+OuFigure 10.7 

87 
A performance and sizing analysis, based on simple skin friction 

estimates, was conducted for the SF-1302 configuration. Laminar flow was 

assumed on both upper and lower surfaces of the wing outboard of the engine 

nacelle - wing intersection and inboard of the tip cap, aft to the 

trailing-edge flap and aileron hingelines. Laminar flow was also assumed on 

the vertical tail forward of the rudder hingeline. Fully turbulent flow was 

assumed on all other surfaces of the aircraft. A breakdown of the wetted 

areas which were laminarized is provided in figure 10.8. 

WOlt~d ha % - ft"2 

Componrnl Actual laminarued LaminarkEd 

A. Wing 1,384 920 66 

6. Vertical Tail 274 189 69 

C. Total 1.658 1.109 67 

a~u.0~4747 

Figure 10.8 BREAKDOWN OF WETTED AREAS LAMINARIZED, 

SF-1302 CONFIGURATION 

The effects of the laminarization on CD min are shown in figure 10.9. 

The effect of LFC on baseline performance is sununarized in figure 10.10. 

Mission performance was calculated for a fighter sweep mission (figure 

10.11). 

when the fighter sweep mission radius is held constant. Under the assumption 

of no LFC system weight penalty the takeoff gross weight is reduced from 43 

622 lbf to 38 292 lbf, a size reduction of 12.2 percent. Using the assumed 

system weight penalty of 2.82 lbf/sqft (reference 26) the aircraft gross 

weight reduces to 41 951 lbf, a size reduction of 3.8 percent. It is noted 

that these sizing effects are significantly greater than similar results on 

the SF-1107 configuration, which were a 6.1% reduction without the weight 

penalty and a 1.3% increase in size with it. 

attributed primarily to the larger baseline radius requirement of the SF-1302 

aircraft (890 nm), as compared to 400 rim for the SF-1107. 

essentially a cruise technology, the benefit should be expected to improve as 

the length of the cruise segment increases. 

Also shown in figure 10.10 is the effect of LFC on aircraft size 

These differences are 

Since LFC is 

88 
Mach Nu-r 

8 

(IpI+os(I-lCO 

Figure 10.9 EFFECT OF LAMINARIZATION ON MINIMUM DRAG COEFFICIENT, 

SF-1302 CONFIGURATION 

WM 43.622 142 42 2 045 890 W.5 58 103 1.013 18 2 32 1 

&SOkM -8. 

LFC Orag 

- WlOWt Rnrw 43622 142 42 2 045 1.070 810 59 104 1,040 17 1 31 0 

- WI WRN@ 45.337 137 438 043 1.010 745 56 99 990 11 9 32 6 

DZUI m ewnu 

Pod LFC hg 

- WIOWhUHY 38.292 146 422 041 W 645 58 103 1,051 17 1 31 0 

-WlWPrnrl~ 41.951 147 422 040 890 625 58 104 1.M 16 1 306 

-.sv 

Figure 10.10 EFFECTS OF LFC ON BASELINE PERFORMANCE, 

SF-1302 CONFIGURATION 

89 
Mission Definilin 

Warmup: 30 min Idle 

Takeoff: Max Power Accel Mach 0-0.6 

Minimum Fuel Climb to Optimum Cruise 

Optimum Cruise 

Climb Accel to Mach 2.0 and Optimum Altitude 

Dash at Mach 2.0 

Combat: 25% Fuel, Fire Missiles 

Dash: At Mach 2.0 and Optimum Altitude 

Decel. Descend: To Optimum Subsonic Mach 

and Altitude 

Optimum Cruise 

20 min Loiter at Optimum Mach, Sea level 

Credit Distance 

acI+ou7~12 

Figure 10.11 FIGHTER SWEEP MISSION FOR THE SF-1302 CONFIGURATION 

90 
11. CRITICAL TECHNICAL ISSUES 

One of the objectives of this investigation was to identify technical 

issues which would be critical to the successful application of laminar flow 

control to supersonic airplanes. Accordingly, a list of technical issues was 

kept and updated as the study progressed. Each of the issues is listed and 

discussed below. The items are given in prioritized order; those issues 

whose satisfactory resolution would have the greatest impact on the success 

of supersonic LFC are listed first. 

1. ATTACHMENT LINE CONTAMINATION PROTECTION - One of the important 

discoveries of this study is that supersonically the payoff for 

lower-surface laminarization is as large or larger than that for the 

upper surface. 

the high sweeps make for attachment line Q values greater than 100, 

even with moderate to high suction levels. 

than 100 were feasible, a turbulent wedge emanating from an excrescence 

on or near the leading edge could eliminate laminar flow on a large 

fraction of the wing area, due to the high sweep and low aspect ratio. 

It is therefore essential to provide protection against accumulated 

supercritical excrescences due to insect strikes and other sources of 

environmental contamination. The leading-edge Kreuger-shield which 

proved so 

experimentfbf is inappropriate, since it is important supersonically to 

laminarize the lower surface as well the upper surface. 

shield leaves the accreted insect remains on the lower surface leading 

edge. 

leading edge collects debris is not well understood. Fortunately, 

methods now exist to allow this to be studied on a parametric basis. 

This could be supplemented by parametric testing in environmental tunnels 

to develop a database for sweep effects at the high sweep end of the 

spectrum. 

of leading-edge contamination on various existing supersonic aircraft. 

high sweep angles, systems can be designed to provide protection. 

Oozing anti-icing or other fluids out of the wing surface is one method 

that could be employed. Others include spray application of sublimating 

material prior to takeoff, or using an onboard or ground-based 

refrigeration system or recirculating cold fuel to cause the appropriate 

regions of the wing to ice up, using ambient moisture. Although this 

last idea would be out of the question for a subsonic airpAane, there are 

two good reasons this approach could be acceptable for a highly-swept 

supersonic configuration: 

separated flow phenomena in low-speed flight, so icing does not present a 

safety concern, and (2) cruise skin temperatures are sufficiently high to 

preclude ice'retention. A related question is whether there exists a 

Mach number above which insect remains would simply char off, as in a 

self-cleaning oven. 

Furthermore, for airplanes similar to the AST in size, 

Even if values of Q less 

u cessful in the (subsonic) Leading-Edge Flight Test 

Stowing the 

The role leading-edge sweep plays in how well or poorly a wing 

Applicable data could also be obtained by field observations 

Once the physics of contaminant accretion are well understood at 

(1) highly-swept wings of necessity exploit 

91 
2. STEP, GAP, AND ROUGHNESS CRITERIA AT HIGH MACH NUMBER - The viscous 

dissipation occurring in the laminar boundary layer gives rise to 

elevated temperatures near the wall. The resulting increased viscosity 

in the near-wall region should result in improved damping of disturbances 

relative to the incompressible case. From a practical standpoint this 

should mean a relaxation of step, gap and roughness criteria as Mach 

number is increased. The roughness issue is particularly important as it 

relates to how large an excrescence can be and still be subcritical. The 

step and gap issue relates to thermal expansion joints and possible 

leading-edge high lift systems. 

steps and gaps, the mechanism involves the amplification of waves in a 

locally separated boundary layer, as well as pressure jumps associated 

with any shock waves created. 

therefore be expected to be of first-order importance. 

data would therefore come from flight test, where the spurious effects of 

freestream turbulence and tunnel noise would be absent. 

For the case of transition caused by 

The disturbance environment would 

The most useful 

3. DEVELOPMENT OF ATTACHMENT LINE T ULENCE DIVERTERS - In the NASA 

successfully diverted boundary layer turbulence emanating from the 

fuselage boundary layer, allowing extensive laminarization along the 

leading edge of the test article. This same problem will need to be 

faced for supersonic laminarization to be successful where subsonic 

leading edges are used, but the notch/bump may not be the best solution 

at supersonic speeds. Alternate solutions include a region of reduced 

sweep and sharpened leading edge in the root region, where the induced 

upwash caused by the highly swept wing leading edge is a minimum. Testing 

on a lifting wing will be necessary in order to arrive at the best 

solution. 

Leading-Edge Flight Test program E7 , a leading-edge notch/bump 

4. ATTACHMENT LINE MOMENTUM-THICKNESS REYNOLDS NUMBER CRITERIA AT HIGH MACH 

NUMBER - The increased viscosity in the wall region of high-speed 

boundary layers can have a beneficial effect on the upper critical level 

of attachment line momentum-thickness Reynolds number. 

critical Reynolds number, Tollmien-Schlichting waves do not grow in the 

attachment line boundary layer, but existing turbulence can propagate. 

Above this level attachment line boundary layer transition can occur due 

to amplifying T-S waves. The upper critical a1 e of 4, according to 

various sources, including Bacon SI Pfenninger Yl4y is about 240. This 

value is for an incompressible attachment line boundary layer, and has 

not been extended to higher Mach numbers. For correlation purposes, the 

external Mach number component along the attachment line seems a logical 

choice. 

attachment line Mach number. 

wing design make this an important issue. 

Below this 

The upper critical 4 value is expected to increase with 

The high sweeps of interest in supersonic 

92 
5. LEADING-EDGE RADIUS EFFECTS FOR SUPERSONIC LEADING EDGES - The detached, 

curved leading-edge shock waves associated with blunt leading edges 

create rotational wakes, which can impose an external velocity profile on 

the boundary layer. 

to the boundary layer thickness over the airfoil should have a 

first-order effect on boundary layer stability characteristics. This 

problem is amenable to both theoretical analyses and wind tunnel 

research, and should be pursued. 

The scale of the leading edge bluntness in relation 

6. DEVELOPMENT OF SCHEMES FOR LIMITING TURBULENCE SPREAD - For highly swept, 

low aspect wings, the bodyside turbulent wedge can occupy a large 

fraction of the wing planform area. 

the area lost to laminar flow, the laminarization benefit could be 

improved. Simple-skin-friction estimates for the DAC AST indicate a 

potential of about .5 in L/D or 28X of the total wing laminarization 

benefit. A highly swept, aft- and inward-facing step of height 

comparable to the local turbulent boundary-layer thickness is one 

possible device for controlling the spread of bodyside turbulence. 

Whether this or other ideas could be developed into a practical device 

could be determined by parametric supersonic wind tunnel testing. 

If means could be found to reduce 

7. DEVELOPMENT OF LAMINAR SWEEP-BREAK GEOMETRIES - The geometric transition 

from highly swept but blunt subsonic leading edge to less swept but sharp 

supersonic leading edge provides an opportunity for a turbulent wedge to 

be created, due to abrupt spanwise variation in flow properties. 

exactly this can be designed around is not clear at the present. 

Sharpening up the leading edge as the break is approached from inboard 

might be expected to work over a narrow angle-of-attack range, but could 

have other unforseen consequences. Wind-tunnel or flight testing of 

alternative concepts needs to proceed so this issue can be resolved. 

How 

8. FUSELAGE RADIATED NOISE - If the fuselage, and in particular the 

forebody, is not laminarized, sound waves created by turbulent eddies in 

the fuselage boundary layer can propagate outward and disturb the wing 

boundary layer flow, resulting in earlier transition or an increase in 

suction requirements. 

can only be resolved by flight testing, since too many spurious effects 

are present even in a "quiet" supersonic tunnel. 

Whether or not this in fact proves to be a problem 

9. CROSSFLOW IN C NCAVE REGIONS, EFFECTS ON GORTLER INSTABILITY - Low-speed investigation^?^^*^^) have identified beneficial effects of boundary 

layer crossflow in destroying existing Gortler vortices. 

mechanism responsible for this is affected by compressibility effects is 

not well understood. Conversely, the effect of streamwise surface 

concavity on crossflow stability characteristics is not widely 

understood. 

number need to be undertaken in order to understand these effects. 

How the 

Critical analyses and experimental studies at high Mach 

93 
10. SENSITIVITY OF ATTACHMENT LINE LOCATION AND TO ANGLE OF ATTACK - 

According to simple-sweep theory, for small angles of attack the rate of 

change of leading-edge-normal angle of attack with streamwise angle of 

attack is proportional to the secant of the sweep angle. 

thickness ratios required for low drag in supersonic flight cause the 

local surface curvature to typically fall off rapidly with surface 

distance going away from the leading edge on either the upper or lower 

surface. 

swept leading edges to depart from attached flow at relatively low angles 

of attack, and can cause the attachment line momentum thickness Reynolds 

number to vary rapidly with angle of attack. An assessment, made on the 

modified Mach 2.2 AST wing in the vicinity of the cruise angle of attack, 

showed this not to be a problem at the 71 degree leading-edge sweep angle 

of this wing. 

sweeps, and should be considered in any LFC design. 

for wings having supersonic leading edges, as long as the leading-edge 

shock remains attached, since for this case the attachment line travel is 

nil. 

The low section 

The combination of these two effects causes wings with highly 

The problem could be significantly worse for higher 

It is not a problem 

94 
12. RECOMMENDED RESEARCH PROGFtAM 

In order for supersonic laminar flow to be rendered a practical 

technology, each of the technical issues discussed in section 11 must be 

addressed. Since technology development paths and timelines may vary with 

available funding levels, the individual tasks comprising the research 

program recommended here will only be given in a temporal sequence. 

program is divided into four categories of endeavor: code development, 

analysis, wind-tunnel test, and flight test. 

program elements address a comon technical issue, the above sequence also 

defines a sensible temporal,sequence, i.e. analysis precedes wind-tunnel 

test, which precedes flight test, etc. Economy of effort results when 

several issues can be addressed by one experiment, so this is made use of 

where applicable. 

sufficient funding is not made available for the entire program, but it is 

highly recomended that issues 1 through 7 be addressed, as a minimum. 

The 

Where two or more suggested 

The priorities indicated in section 13 can be applied if 

CODE DEVELOPMENT: 

1. Continue the development of a fully 3-D, all-speed boundary layer 

stability package, including the effects of suction, nonadiabatic 

wall conditions, and allowing attachment line and wedge flow 

starting solutions. 

experimental results and for LFC design. The correct accounting for 

curv tu e effects as recently incorporated into the COSCUR stability 

code T22f should be included. 

This will be needed for the interpretation of 

2 Develop a wing-body inverse wing design procedure, in which the wing 

geometry is determined from input pressure distributions, for the 

supersonic case which does not make use of small-perturbation 

assumptions. 

leading edges, where modeling of flow through shock waves is 

important. 

subsonic leading edges is not clear, due to the conical shock from 

the fuselage forebody. 

An inverse Euler would be necessary for supersonic 

Whether or not a potential method is sufficient for 

ANALYSIS : 

1. Investigate the effect of leading edge sweep on particle catch 

efficiency in the high sweep angle regime, using particle tracing 

techniques. 

deposition. 

highly swept supersonic aircraft in operational service. 

predictive capability for insect accretion. 

Formulate an improved criterion for insect remains 

Accumulate a database for insect remains accretion on 

Develop a 

95 
2. 

3. 

4. 

5. 

6. 

Determine the effect of Mach number on separation bubble length 

Reynolds number to transition in zero pressure gradient. Combine 

this information with the existing database to produce an estimated 

permissible gap criterion as a function of Mach number. Attempt to 

formulate generalized roughness and step criteria as well. 

Determine the effect of attachment-line tangential Mach number on 

the growth of Tollmien-Schlichting waves in the attachment line 

boundary layer on a swept cylinder with subsonic normal Mach 

number. 

line 

dimensionless parameters. 

Formulate a relationship for the upper critical attachment 

as a function of this Mach number or other significant 

Perform a parametric 2-0 study on the effects of supersonic 

leading-edge radius on boundary layer velocity profiles and 

stability, using a full Navier-Stokes code. Downstream of the 

leading edge, a flat pressure distribution is of the most interest. 

Perhaps vary Re/l for a fixed geometry, and look around Mach 2 to 

3.5. 

leading-edge radius/chord. 

Identify favorable or unfavorable combinations of Re/l and 

Perform a study similar to 4. above with swept infinite wings to 

identify any sweep effects. 

to 60" sweep range, from Mach 2 to 3.5. 

The most desirable data is in the 40" 

Perform a study of crossflow effects in 3-D concave regions at 

supers ni speeds. 

Kohama P2lT but at supersonic Mach number. This would establish 

any new physics brought about by compressibility effects. 

This study would be similar to the one done by 

WIND-TUNNEL TESTS: 

1. 

2. 

3. 

Test a swept cylinder in an environmental tunnel with insects 

introduced into the flow upstream. 

determine the catch efficiency as a function of leading-edge sweep 

angle and other parameters. The test insects (real or simulated) 

should cover the range of ballistic coefficients of real insects. 

The data would be used to corroborate theoretical results, and 

possibly to improve the theoretical model. 

Vary the sweep angle and 

If necessary, conduct simple impact tests to determine a 

normal-velocity criterion for insect remains deposition. 

Plan and conduct a half-span supersonic test on an appropriate wing 

planform for the empirical development of the following items: 

1. supersonic turbulence diverters, 

2. laminar sweep-break geometries, and 

3. devices for turbulent wedge minimization. 

96 
1 

4. 

5. 

6. 

7. 

Conduct a series of tests to measure supersonic leading-edge 

bluntness effects on boundary layer stability and transition. 

data would be used to substantiate theoretical analyses (item 5, 

These 

ANALYSIS 1. 

Conduct a supersonic research test to substantiate the results of 

analysis (item 6) regarding the effects of boundary layer crossflow 

in concave regions. 

Use a low-speed tunnel test to develop concepts for 

contamination-avoidance on the modified wing of whatever airplane is 

to be used for supersonic LFC flight tests. The 2-D approaches used 

in the past for subsonic airplanes may not work well enough on a 

highly swept supersonic wing. 

Low-speed, subsonic, and supersonic testing may be necessary in 

order to establish the acceptability of the aerodynamic 

characteristics of the modified airplane to be used for LFC flight 

tests. 

FLIGHT TESTS: 

It is assumed that all flight tests will be conducted using a single 

modified airplane. 

establish that supersonic LFC is in fact achievable and can be made 

practical. 

The overall objective of the flight testing is to 

1. 

2. 

3. 

4. 

5. 

6. 

Verify the effectiveness of turbulence diverters, laminar 

leading-edge sweep break geometry, and turbulent wedge control 

devices. Establish any limitations in their operation. 

Conduct a series of tests to establish data for supersonic step, 

gap, and roughness criteria at different Mach numbers. Determine 

the validity of theoretical estimates. 

Verify contamination system effectiveness, and continue development 

of these technologies. 

Confirm the correctness of leading-edge radius criteria for the 

supersonic outer wing panel. 

Using high-response acoustic sensors, determine the amplitude and 

frequency spectrum of noise in the laminar wing boundary layer at 

several key locations. With a loudspeaker mounted at an appropriate 

axial station on the fuselage, attempt to change measured transition 

locations by acoustic means. 

radiated from the fuselage is a concern. 

Determine whether or not noise 

Through comparisons with Euler code predictions, verify the extent 

of attachment line travel with angle of attack on the highly swept 

subsonic leading-edge part of the wing. 

97 
13. TEST FACILITIES 

13.1 SUPERSONIC WIND TUNNELS: 

With the exception of the NASA LaRC 3.0 ft x 7.5 ft subsonic low 

turbulence wind tunnel, the 8 ft transonic facility at LaRC, the 10 in x 6 in 

M = 3.5 Beckwith quiet tunnel at LaRC, and the recently activated 1.0 ft 

quiet trisonic facility at NASA Ames, most wind tunnels in the U.S. are 

ill-suited for most laminar flow investigations because of test section noise 

and unsatisfactory turbulence levels. 

even more noisy and turbulent; however, certain types of laminar flow testing 

have been successfully completed at supersonic Mach numbers. 

19609, scale model tests were run at Mach numbers from 2.0 to 4.0 in the AEDC 

tunnel A facility on flat plates, a parabolic nose body of revolution and two 

swept wing planforms with and without suction to determine whether laminar 

flow s attainable via suction applied through a series of spanwise 

when suction was applied in this manner. 

Supersonic wind tunnels tend to be 

In the early 

slots f7) . Full chord laminar flow was apparently achieved in these tests 

13.2 FLIGHT TEST VEHICLES: 

Several supersonic aircraft could be made available as a supersonic test 

bed. These would include the F-106, F-15, F-16XL. and F/A-18. 

and other aircraft hardware and support equipment may become progressively 

more scarce on the F-106 aircraft, our study was limited to the three more 

recent aircraft. 

characteristics and performance capabilities of the supercruise study 

aircraft, the AST, the SF-1302 and SF-1107, with those of the F-16XLD F-15 

and F/A-18. 

F-15 or F-16XL due to its hx of 1.7 and its low wing sweep which would 

limit the supersonic flight testing to the supersonic leading edge condition. 

Since engines 

Figure 13.1 compares some of the more relevant physical 

The F/A-18 would appear to be less desirable than either the 

Both the F-15 and F-16XL would appear to be reasonable testbeds for 

supersonic LPC testing. A comparison of the flight test potential of these 

two aircraft is shown in figure 13.2. The F-15 has a bx = 2.2 capability 

whereas the F-16XL has bx of approximately 2.0. 

offers much improved time at supersonic speeds, and has a planform which is 

more representative of long range supercruiser concepts. 

comparison of the candidate testbed aircraft and study fighter aircraft is 

shown in figure 13.3. 

the SF-1302, so is not shown. As was noted earlier, the highly swept 

subsonic leading edge is the approach of choice for long range supercruisers 

due to better drag due-to-lift characteristics, and since any LFC benefit 

would otherwise have to overcome the inferior performance of the supersonic 

leading edge in order to show a net improvement. 

edge sweep of the F-16XL is therefore an essential feature. 

feature of the F-16XL is its relatively simple geometry, and location of the 

inlet below the fuselage. 

the wing flowfield. 

However the F-16XL 

A planform 

The AST planform is geometrically similar to that of 

The high inboard leading 

Another valuable 

This allows for reduced uncertainty in computing 

99 __ PRECEDING PAGE BLANK NOT FILMED 
- 

AIRCRAFT SW CAR L.E. --TIME AT M (M1N)-- bx 

(sqft) (ft) (den.) Mach 1.5 Mach 1.8 

2.20 

2.20 

2.20 

DAC AST 10 000 64.8 1.84 71/61.5 ---- ---- 

SF-1107 530 15.4 2.75 32 ---- ---- 

SP- 1302 630 24.1 1.89 71/61.5 ---- ---- 

F/A- 18 400 11.5 3.52 27 11.3 ---- 1.71 

F-15A 608 16.0 3.01 45 9.5 5.6 2.4 

F-16XL 663 24.7 1.58 70/50 42 21 2.0 

Figure 13.1 COMPARISON OF STUDY AND POSSIBLE TESTBED AIRCRAFT 

MU8H FugM Tost ~lttbl WlbS 

F-15 Supersonic Flight Testing Fran Leading Edge Root Extensions 

Mach 1 .O Through Mach 2.2 Provide Excellent Location for 

With Limbd Testing at Mach 2.4 Suction Pumps and Plumbing 

Both Subsonic and Supersonic 

Leading Edge Testing Possible Provides Good Depth in Which 

to House the Suction Flutes 

and Pknums Reqlnred to Route 

Elaed Air to Suction Pumps 

Relatively Thick Airfoil 

Wing Planform Fairly 

Representative oi SF-1 107 

Supercruise Configuration 

F-16x1 0 

0 

0 

0 

Supersonic Flight Testing From Will Probably Be More 

Mach 1 .O Through Mach 2.2 Available for LFC Testing 

Subsonic Leading Edge Testing Than Other Aircraft 

Wing Planform Fairly 

Representative of SF-1302 

Supercruise Configuration and 

the DAC Supercruise Transport 

Testing of Leading Edge Break 

Is Possible 

Figure 13.2 COMPARISON OF POTENTIALS OF F-15A AND F-16XL 

AIRCRAFT AS TESTBEDS 

100 
Configuration sF-1107 AR n 

Figure 13.3 PLANFORMS OF STUDY AND POSSIBLE TESTBED AIRCRAFT 

Dynamic similarity to transport scale aircraft is partially served by the 

high dynamic pressure capability of fighter aircraft, which allows high unit 

Reynolds numbers. 

readily be resolved by design of the glove test article. 

concept is shown in figure 13.4. 

bodyside allows experimentation with various supersonic turbulence diverter 

concepts. 

leading-edged wingtip provide an opportunity to probe laminarization issues 

related to this type of geometry, an added plus. 

resolved, the F-16% is the clear choice for a supersonic LFC testbed. 

Specific similarity issues like the attachment line can 

A possible glove 

The local leading edge unsweep near the 

The presence of a leading-edge sweep break and supersonic 

If hardware problems can be 

101 
Figure 13.4 F-16XL WITH LFC GLOVE 

102 
14. CONCLUDING REMARKS 

This study represents a first attempt to apply Laminar flow control 

methodologies developed for subsonic and transonic swept wings to the problem 

of achieving extensive regions of laminar flow on airplanes designed to 

cruise efficiently in the supersonic regime. As such, it tested and extended 

the capabilities of the current methods, pointed to needed improvements, and 

indicated technical areas ripe for theoretical and experimental 

investigation. 

The results of this study indicate that supersonic LFC is technically 

feasible, and is a viable way of providing substantial fuel burn and sizing 

improvements. Significant technical issues remain, however, which need to be 

pursued vigorously. If commercial supersonic transports remain the 

technological hostages of arbitrary regulations on such things as jet noise 

and sonic boom, this study will at least have added to our general LFC 

knowledge base. 

the attachment line momentum-thickness Reynolds number, a complete 

understanding of proper LFC drag accounting and pumping system 

thermodynamics, and some important insights into the nature of T-S and 

crossflow waves in 3-D boundary layers. 

Significant spinof'fs include an improved way of calculating 

The weight, cost, and maintenance requirements of the LFC suction system 

comprise the bulk of the economic risk as seen by airframe manufacturers and 

operators. 

both subsonic and supersonic cases this requires careful and precise control 

of the wing pressure distribution. 

control of low levels of boundary layer crossflow is the key to minimizing 

suction. 

design capability beyond what is currently available. 

These are all minimized when suction massflow is minimized. In 

Particularly at higher Mach numbers, 

To accomplish this for the supersonic case requires aerodynamic 

Although for subsonic and transonic wing design, inverse methods, in 

which the designer specifies the desired pressure field, and the 

corresponding wing geometry is computed, have achieved a high degree of 

sophistication and accuracy, the same cannot be said for supersonic wing 

design methods. 

forward or analysis mode; no 3-D inverses exist. 

due to the elegance with which velocities are represented, the creation of 

inverse design codes has proven to be relatively straightforward, yet no such 

simplifications appear to apply to the Euler formulations. The Euler is a 

necessity if shock waves or vorticity exist in the region of interest. 

However, it is not clear that vorticity behind curving shockwaves is a 

significant effect in the supersonic flow over a wing-body configuration, if 

the body is sufficiently sharp and slender, and the wing leading edge is 

either subsonic or sharp. 

capability without going to a full Euler inverse. Since the influence of the 

fuselage on the wing pressure field is substantial in supersonic flow, it is 

necessary to design the wing in the presence of the fuselage. While 

developing this design capability is a difficult task, it is within the realm 

of possibility, and would move us closer to the goal of designing optimum 

configurations, allowing the minimization of economic risk associated with 

the application of LFC technology. 

State-of-the-art Euler codes currently operate only in the 

For the potential methods, 

It may therefore be possible to get the desired 

103 
1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

Graf, D.A.: 

Rim Focus", 

the Pacific 

REFERENCES 

"High-Speed Commercial Transportation and the Pacific 

Douglas Paper 7960, presented to Comercial Aviation in 

Rim Conference, Hong Kong, September 14-16, 1987. 

Wagner, R.D., Maddalon, D.V., Bartlett, D.W., and Collier, F.S.: 

"Fifty Years of Laminar Flow Flight Testing", presented to SAE 

Aerotech '88 Aerospace Technology Conference and Exposition, 

Anaheim, California October 3-6, 1988. 

Harvey, W.D. and Bobbitt, P.J.: "Toward Lower Drag With Laminar Flow 

Technology", ICAS-88-4.1.2, Presented to 16th Congress of the 

International Council of the Aeronautical Sciences, Jerusalem, 

Israel, August 28 - September 2, 1988. 

Anon.: "Research in Natural Laminar Flow and Laminar-Flow Control", 

NASA CP-2487, 

Center, Hampton, Virginia., March 16-19, 1987. 

Proceedings of Symposium held at Langley Research 

Groth, E.E.: "Low Drag Boundary Layer Suction Experiments on a 5% 

Thick Biconvex Airfoil Section at M = 2.23 and 2.77", Northrop 

Report NAI-58-195 or BLC-105, March 1958. 

Pate, S.R. and Brillhart, R.E.: "Investigation of Boundary-Layer 

Transition on Swept Wings at Mach Numbers 2.5 to 5", 

AEDC-TDR-63-109, July 1963. 

Groth, E.E., Pate, S.R., and Nenni, J.P.: "Laminar Flow Control at 

Supersonic Speeds", AGARDograph 97, Part IV, Section B, May 1965. 

Bushnell, D.M., Malik, M.R., and Harvey, W.D.: "Transition 

Prediction in External Flows via Linear Stability Theory", Presented 

to IUTAM Symposium Transonicum 111, Gottingen, West Germany, May 

24-27, 1988. 

Srokowski, A.J., and Orszag, S.A.: "Mass Flow Requirements for LFC 

Wing Design", AIAA Paper 77-1222, August 1977. 

Dagenhart, J.R.: "Amplified Crossflow Disturbances in the Laminar 

Boundary Layer on Swept Wings with Suction", NASA TP-1902, November 

1981. 

Malik, M.R.: "COSAL - A Black Box Compressible Stability Analysis 

Code for Transition Prediction in Three-Dimensional Boundary 

Layers", NASA CR-165925, May 1982. 

Jameson, A.: "A Vertex Based Multigrid Algorithm for 

Three-Dimensional Compressible Flow Calculation", presented at the 

ASME Symposium on Numerical Methods for Compressible Flow, Anaheim, 

California, December, 1986. 

105 

PRECEDlNG PAGE BLANK NOT FlLMED 
13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 

21. 

22. 

23. 

24. 

25. 

26. 

Kaups, K. and Cebeci, T.: "Compressible Boundary Layers with Suction 

on Swept and Tapered Wings", J. Aircraft, Vol. 14, 1977. 

Morkovin, M.V.: "Instability, Transition to Turbulence and 

Predictability", AGARDograph No. 236, 1978. 

Bacon, J.W. and Pfenninger, W.: "Transition Experiments at the Front 

Attachment Line of a 45 degree Swept Wing with a Blunt Leading 

Edge", Technical Report AFFDL-TR-67-33, June 1967. 

Shapiro, A.H.: The Dynamics and Thermod.ynamics of Compressible 

Fluid Flow, Vol 11, pp. 706-709, The Ronald Press Co., New York, 

Copyright 1954. 

Anon.: "Supersonic Cruise Research '79", NASA CP 2108, Proceedings 

of a Conference held at Langley Research Center, Hampton, Virginia, 

November 13-16, 1979. 

Douglas Aircraft Co.: "Technology Study for Advanced Supersonic 

Cruise Vehicles", NASA CR-165723, June 1981. 

Halsey, N.D. and Zaretsky, B.: "Grid Generation for NASP 

Configurations", MDC report in preparation. 

Collier, F.S. Jr. and Malik, M.R.: "Stationary Disturbances in Three 

Dimensional Boundary Layers Over Concave Surfaces", AIM-87-1412, 

Presented to AIM 19th Fluid Dynamics, Plasma Dynamics, and Lasers 

Conference, June 8-10, 1987. 

Kohama, Y.: 'Three-Dimensional Boundary Layer Transition on a Curved 

Wall", Presented at the IUTAM Symposium on Turbulence Management and 

Relaminarization, Bangalore, India, January 19-23, 1987. 

Collier, F.S. Jr., Bartlett, D.W., and Wagner, R.D.: "Curvature 

Effects on Swept Wing Boundary Layer Stability-Theory and 

Experiment", Presented to SAE Aerotech '88, Anaheim, California, 

October 3-6, 1988. 

Reshotko, E. and Beckwith, I.E.: "Compressible Laminar Boundary 

Layer over a Yawed Infinite Cylinder with Heat Transfer and 

Arbitrary Prandtl Number", NASA TR-1379, 1958. 

Fischer, M.C., "Spreading of a Turbulent Disturbance", AIM Journal, 

Vol. 10, NO. 7, pp. 957-959, July 1972. 

Pfenninger, W. and Vemuru, C.S.: "Design aspects of Long Range 

Supersonic LFC Airplanes with Highly Swept Wings", SAE Technical 

Paper 881397, Presented at SAE Aerotech '88, October, 1988. 

Douglas Aircraft Co.: "Evaluation of Laminar Flow Control Systems 

Concepts for Subsonic Conanercial Transport Aircraft", NASA 

CR-159251, June 1983. 

106 
27. Verhoff, A. and O'Neil, P.J.: "Accurate, Efficient Prediction Method 

for Supersonic/Hypersonic Inviscid Flow", McAir Paper 87-006, 

Presented at the AIM 19th Fluid Dynamics, Plasma Dynamics and 

Lasers Conference, Honolulu, Hawaii, June 8-10, 1987. 

28 Jones, D.J.: "Numerical Solutions of the Flow Field for Conical 

Bodies in a Supersonic Stream", National Research Council of Canada 

Aeronautical Report LR-507, July 1968. 

29. Lekoudis, S.G.: "Stability of Three-Dimensional Compressible 

Boundary Layers over Wings with Suction", AIAA paper No. 79-0265, 

January 1979. 

Stability Theory and the e* Method, with Emphasis on Swept-Wing 

Applications", NASA TP-1645, April 1980. 

30. Hefner, J.N., and Bushnell D.M.: "Status of Linear Boundary-Layer 

107 
APPENDIX A 

LFC DRAG ACCOUNTING AND 

PUMPING SYSTEM THERMODYNAMICS 

The intent of this appendix is to explain the logic behind a system of 

drag accounting and a pumping system thermodynamics algorithm for LFC which 

was developed and used in the course of this study on supersonic LFC. The 

entire algorithm is applicable to the subsonic case with essentially no 

modification, and allows optimization of the LFC pumping system for minimum 

total fuel flowrate. This approach, unlike earlier ones, makes no 

idealizations, allowing correct and detailed accounting for all loss 

mechanisms. 

Figure A1 shows the control-volume momentum equation. According to this 

equation, the drag can be computed either using the control volume approach, 

as is commonly done subsonically, or by integrating pressure and skin 

friction over the surface in the appropriate fashion. The important message 

of this figure is that viscous drag t pressure drag = wake drag t suction ram 

drag. 

since pressure drag is relatively easy to calculate, and the control volume 

momentum integration is much more cumbersome due to shocks, expansions, etc. 

For the supersonic case, if the control volume approach is not used one 

should not expect to see a ram drag. As will be shown, the suction ram drag 

is accounted for as part of the viscous drag. 

The control volume approach is abandoned for the supersonic case, 

Figure A2 shows the variation of various drags with suction for a laminar 

flat plate. 

boundary layer program, BLP, which is a well proven and trusted code at DAC. 

Plotted versus suction coefficient are the four drags, each computed 

independently in the correct fashion. Note that the sum of viscous drag and 

pressure drag is identical to the sum of wake drag and suction ram drag, as 

the control-volume momentum equation demands. A subsonic wing section would 

be expected to have similar characteristics, since the pressure drag is 

small. 

The calculations were made using Cebeci & Kaups' strip-theory 

Figure A3 shows the various drag components computed for one side of a 

symmetric biconvex airfoil at Mach 2.2 and zero angle of attack. 

Note that the pressure drag is almost unaffected by the boundary layer, 

either transition location or wall suction, so the suction ram drag component 

is essentially accounted for in the viscous drag component entirely. If the 

wake drag is backed out by subtracting the suction ram drag from the total 

drag, the result is physically reasonable, as comparison with the flat plate 

result (figure A2) shows. 

principally to total pressure losses in the shocks. 

The much higher wake drag is expected, due 

109 

PRECEDLNG PAGE BLANK EBB FILMED 

~~ ~ 
EFFECT OF AIRFLOW ON WIf4C SECTION 7 EFFECT OF WING SECTION ON AIRFLOW 

CF 

= Dy + Or 

EffECTS OF IMCREASCD 

SUCTION ARE SEEN AS 

INCREASED CF . VERY SMALL EmCT OM Dp 

THERE EXISTS MO DRAO 

THAT CAN BE NEATLY CATEOOWZED 

AS SUCTION RAY DMO! 

BETTER lFOR SUCERtOmC CASES 

.mnJ 

.-- 

.5- 

EQUIVALENT 

TO 

RAM 

WAKE 

- 0,- 4 0 

DTu?AL WAKE 

Figure A1 LFC WING DRAG ACCOUNTING 

0 

SUCTION COEFFICIENT. Cq 

Figure A2 FLAT PLATE DRAGS VS. SUCTION 

110 
ONE SURFACE MACH 2.2 Rc 29 million 

t/c - 2.5% 8 65% CHORD 

.mz - 

I 

.ax - 

.am- .mas0- -. 

Figure A3 SUPERSONIC SYMMETRIC AIRFOIL 

/ 

/- 

,--- 

----- SKTICN RAW .. /-/- 

For both subsonic and supersonic cases, the additional drag due to 

suction equals the product of suction massflow with freestream velocity. 

Whether this is accounted for inside the pumping system calculation or 

externally as part of the aerodynamic drag is entirely arbitrary; the end 

result of the calculations is identical. In this analysis, the additional 

drag due to suction is left as part of the aerodynamic drag, SO no momentum 

loss terms appear in the pumping system thermodynamic analysis. Separating 

the ram drag from the thermodynamic analysis is acceptable at any speed since 

the suction airflow is set by laminarization requirements, and does not vary 

with engine thrust. 

look exceptionally good in comparison to the thrust engines. 

accounting system, the pumping system functions as a rocket engine with a 

fixed massflow supply of free propellant. 

this air. 

analysis. 

With the pumping system rid of the ram penalty, it can 

With this 

Of course, work must be done on 

Just how much work is optimal is the subject of the thermodynamic 

I 

111 
In the thermodynamics analysis, the suction air is brought in through the 

porous skin, passes through ducting to a compressor, and then is ejected aft 

through an optimally expanded nozzle. An important indicator of performance 

is what we have termed the pumping system efficiency, defined as the ratio of 

nozzle thrust power to system input shaft power. Inasmuch as this definition 

is identical to that of a propeller efficiency, it is useful to consider 

simple actuator-disk momentum theory as a guide to interpreting the 

correctness of the thermodynamic model. This is summarized in figure A4 

below. The ideal actuator disk differs from a real propeller in that the 

exit flow has no swirl, so only axial velocities are considered. 

input shaft power is equal to the rate of production of kinetic energy of the 

air passing through the disk. 

efficiency is derived for two cases: the typical propeller, in which the 

velocity into the disk is the freestream velocity, and the LFC pumping case, 

in which this velocity is zero. 

is still the freestream velocity. For the propeller case, the ideal 

propulsive efficiency has a theoretical maximum of 2 at zero exit velocity, 

but the disk only produces net thrust for exhaust velocities greater than 

freestream. 

producing thrust. For the LFC pumping case, we are only concerned with gross 

thrust, since the momentum inflow into the disk is zero. The ram drag 

penalty for collecting the suction air has already been paid elsewhere in the 

form of increased drag over the wing surface. 

ideal propulsive efficiency is higher. In the thermodynamic model, the 

pumping system efficiency should reflect this. 

thermodynamic model to recover the dependence shown by the upper curve in the 

figure, if all component efficiencies are set to 1, and there is no pressure 

drop in the ducting or skin. 

Also the 

In the figure, the ideal actuator disk 

The speed used in computing the thrust power 

The efficiency is therefore always less than 1 if the disk is 

For this basic reason, the 

We should expect the 

DEFINE PUMPING SYSTEM EFFICIENCY, 'Ips - 'fs - ?prop 

Pin 

IDEAL ACTUATOR DISK: NO SWIRL => Pin RATE OF INCREASE OF PROPELLANT K.E. 

0 .5 1 1.5 2 2.5 3 

Ve/Vf s 

Figure A4 LFC PUMPING SYSTEM MODEL - IDEALIZED 

112 
Figure A5 shows some sample results from the pumping system thermodynamics 

calculation. The solid curve (labelled "ideal") demonstrates that the 

thermodynamic model does indeed recover the actuator disk result under zero 

loss conditions. The results shown in the figure assume that pump power is 

extracted from the main thrust engines, so the pumping system input power is 

shaft power. The level ot which the pumping system's overall efficiency 

equals that of the thrust engines depends on the product: 

With the values used in this example, the break-even point occurs at an 

ordinate value of 1.0, which is equivalent to saying that the thermal 

efficiency for extracted power is equal to the thrust engine's overall 

efficiency, a conservative assumption. A better assumption is that the 

thermal efficiency for shaft power extraction is equal to the thermal 

efficiency of the installed engine. In any event, if the power comes via an 

engine-mounted alternator and electric motor, the electomechanical conversion 

efficiencies will lower the pumping system efficiency proportionally. 

PSFC f V 1 TSYC. 

The amount of total pressure loss between the wing skin and the 

compressor has a first-order effect on the pumping system performance. 

average collection pressure is also an important driver with high collection 

pressure having a favorable effect. 

for these curves. 

surface should be divided into two or three collection pressure "zones". 

from each zone could be pumped to a different optimum pressure ratio, and 

discharged through a separate nozzle. It is important to realize, however, 

that the optimum pumping system performance as indicated above pertains to 

the system in isolation. 

addressed below. 

The 

The average collection Cp was taken as 0 

Air 

For maximum suction system performance, the wing suction 

The optimum performance for the LFC airplane is 

VC ADV. supERsoNIC TRANSPORT AT 2 2 58 kft 

IwnNLEDlsc1.z)~ MIL =.-~ 

Or~-hrp3/h~ 0 .Q 

d.1- h / c &mm 

- ImMm04 v 

0 .2 .4 .8 .8 I I. 2 1.4 I. 8 1. 8 2 

NOZZLE EXIT VELOCITY / FREESTREAH VELOCITY 

Figure A5 THERMODYNAMIC PERFORMANCE OF LFC SYSTEM 

113 
Optimum performance for the airplane is achieved when the pumping system 

is operated such that airplane overall fuel flow is minimized. This is 

explained in figure A6. The total fuel flowrate is expressed in terms of a 

thrust specific fuel consumption (TSFC) times the total thrust required, plus 

a power specific fuel consumption (PSFC) times the total auxiliary shaft 

power required. 

propulsive fuel flow. With some rearrangement, and the introduction of the 

pumping system efficiency, an expression is obtained which represents the 

drag equivalent of the fuel flow increment due to the suction system. This 

appears in drag coefficient form as the second additive term in the 

denominator of the boxed expression for airplane LID. This equivalent drag 

increment is negative if the pumping system efficiency is greater than the 

quantity: (PSFC * V) / TSFC. 

lie above the solid horizontal line, and means that in terms of fuel flow, 

the nozzle thrust has paid for the pumping power with some excess thrust left 

over. Examination of the ideal (zero loss) case reveals that the magnitude 

of this effective drag reduction is always less than the additional skin 

friction drag due to suction. This is because some power is necessary to 

drive the compressor, and is one reason it is desirable to minimize the 

suction flowrate in LFC design. 

Note that the LFC system nozzle thrust reduces the 

This is satisfied when the curves in figure A5 

The straight breakeven line on the plot of figure AS is somewhat of an 

idealization, since both TSFC and PSFC would be expected to vary with shaft 

power extraction, as well as thrust and flight conditions. 

connection, an accurate model of the thrust engine cycle would be a necessary 

part of any detailed analysis. 

In this 

ASSUMPTION : SUCTION AtR IS COMPRESSED. 

THEN CJCCRD MROUOH A NOZZLE. 

= O,,&+ ( * Ps?c ,+I- -) *- 

V 

A NCf NCI. SAWNO. R-ULTS FROM 

ANY SUCTION SYS'KY NOZZLE THRUST! 

MORS NLL LfflCtSNl WAN THWIT 

CNOlNCS! 

114 
Any fuel flow minimum will occur when the fuel-equivalent drag increment 

is its most negative value. The presence of pumping power in the expression 

for fuel-equivalent drag increment means that the LFC airplane optimum nozzle 

exit velocity, if it exists, is higher than would be indicated by the maximum 

of the appropriate pumping system efficiency curve. 

The fuel-equivalent drag increment is plotted in figure A7 for the same 

conditions as figure AS for each skin-and-ducting total pressure loss. This 

represents, in drag coefficient form, the extent to which the pumping system 

nozzle thrust exceeds the drag equivalent of the LFC pumping power. For an 

ideal case, in which compressor and nozzle efficiencies are unity, and there 

are no total pressure losses in the system, the optimum exists at an exit 

velocity ratio of unity, if (PSFC * V)/TSFC = 1. 

optimum is found at higher exit velocity ratio. 

If (PSFC * V)/TSFC < 1, the 

For the realistic example there is no optimum, although all of the curves 

show a stationary region slightly above an exit velocity ratio of unity. 

This is due to the greater heating of the air in the nonisentropic 

compressor. This effect only becomes pronounced at the higher velocity 

ratios, where nozzle total temperature plays an increased role in determining 

the thrust. 

Lastly, a program, written in IBM BASIC-A has been created and is 

included as figure AS. 

conditions, compressor and nozzle efficiencies, total pressure losses, 

collection pressure coefficient, etc. and parametrically vary the nozzle 

total pressure ratio, Pt3/Ptfs. The nozzle is assumed to be optimally 

expanded, and aimed directly aft. 

The approach taken is to set the freestream 

LFC Mv. supERsoNIC TRANSPORT AT 2.2 MACH L 58 kft 

.s QIlpREssQzEFF. WZ NOnLEEFF. W% AVCCp-0 

tmAUmm1.a,rvMI AIDL -.amOtopr-hm3/Rv - .Q 

0 A\‘\. \. .. . 

0 

-1 

< 

IJ 

w 

0 

\ ’-.\ -\ I / 

--. 

0 .2 .4 .a .a 1 1.2 1.4 1.0 1. a 2 

NOZZLE EXIT VELOCITY / FREESTREAM VELOCITY 

Figure A7 FUEL-EQUIVALENT DRAG INCREMENT DUE TO LFC PUMPING 

115 
!O PRINT PROGRAM LFrEXH 9A5 

20 P!?INT LFC: PUMPING SYSTEfl THERJIODYNAHICS AND DRAG ACC'YNTING 

30 PRINT 

40 PRINT "ASSUflPTIONS: " 

50 PRINT "LFC COMPRESSOR IS DRIVEN ELECTRICALLY 9FF OF MAIN THRVST ENGINES ' 

60 PRINT 'LFC EXHAUST NOZZLE IS OPTIWLLY EXPANDED AND AIMED DIRECTLY AFT 

30 PRINT STATIONS: 1-SKIN. 2-CPR IN. JA-CPR OUT* 3-NO2 IN. E-NO2 EXIT" 

100 PRINT SET KEYBOARD ALL CAPS -- 

70 PRINT 

90 PRINT "' 

110 CP.6007 1:R=1716 3:TF=390 

120 VRAp1=0 .REfl VRAH=VRsVF IF RAM CHARGED TO PUflPING SYS 

130 EA-l:Efl=l 

140 PRINT "" 

150 PRINf "EDIT PCM LN 130 TO CHG ALTERNATOR DR HOTOR EFFICIENCY. DEFAULT=l 0 

160 PRINT "FOR DIRECT SHAFT DRIVE SET ALT EFF=l. USE flOTOR EFF AS GEARBOX EFF 

170 PRINT "" 

180 PRINT "****** INITIAL INPUTS ************" 

190 INPUT "COnPRESSOR EFFICIENCY (DECIMAL FRACTION) = ':EC 

200 INPUT "NOZZLE EFFICIENCY = ":EN 

210 INPUT "FREESTREM MACH NUFIBER = ":fl 

220 INPUT "WINO SURFACE-TO-COHPRESSOR LOSS. (Pl-PtZ)/Pl = ";RlDP 

230 INPUT "CGHPRESSOR-TO-NOZZLE LOSS. fPt3A-Pt31/Pt3A = ":RDP3 

240 INPUT "AVO SURFACE Cp = ':PC 

250 IF PC(I-1/(.7*fl-2)) THEN PRINT "GIVEN Cp IS BELOW VAC LIM1T'":GOTO 240 

260 INPUT "SPECIFY SKIN TEHP. OVERRIDING ADIABATIC WALL? IY/NI ':TI 

270 IF T¶=''Y' THEN INPUT "Tskin IRI z":Tl 

280 INPUT CHARGE RAM DRAQ TO PUMPING SYSTEfl' fY/NI RI 

290 PRINT ****** RECURRINQ INPUTS ************* 

300 INPUT "Ptnor/Ptis = ":R3FP 

310 VF=H*SQR(l.4*R*TF) 

320 IF RI="Y" THEN LET VR=VF 

330 RTF=1+.2*H-2 

340 RPF-RTF-3.5 

350 PlRF:l+PC*.7*H-2 

370 IF T¶="Y" THEN LET TZT-TI 

380 PEPTJ=l/IRSFP*RPF) 

390 P2TF=PlRF*fl-R1DPI 

400 P3TF=l/PEPT3 

410 PA3TF=P3TF/fl-RDP31 

420 PR3AZ=PA3TF/P2TF 

430 T3T-T2T/Il-l/EC*Il-PR3AZ-f-l/3.5 

440 IF PEPT3>1 THEN PRINT "TOO LOW." 

450 YE=S4RfZ*EN*CP*T3T*(l-~PTJ-f1/3 

360 TPT~TF*fIl-SQRI.7ZI~*PlRP^I1/3.5 

:REfl Via 

:REfl TTfs/Tfs 

:REM Ptts/Pis 

:REPI Parf/Pfs 

*SQRf.72I*RTFl :REM TTZ-Tsri-Tau 

:Fan ~is/~t3 

:REP( pt?/Pra 

:REfl Pt3/Pis 

:REM PtSA/Pis 

:REM Pt3A/Pt? II :REM Tt3 

OOTO 300 

5111 :RBI EXH VELOC 

460 EPS~EA*M*EC*VF/ICP*T~T~*~~H-VRI/(PR~A~^~~/~.~I-~):REM NZL THRSTPUR/CPR PUR 

470 WHC=CP*ITJT-TZTI/32.1739 .REM CPR WRI fft-#f/Sml 

480 RVEFrVE/VF :REM NZL VELOC RATIO 

490 TE=T3TrVE'2/(2*CP) 

520 PRINT USIW "CCWRESSOR PRESS RATIO = rra.rrar":~~3~~ 

550 PRINT USINQ -NOZZLE pt / pis = SS*.~~SS-:PSTF 

560 PRINT USINQ "NOZZLE EXIT HACH NUMBER I SS.SSSS*':~ 

570 PRINT USINQ "NOZZLE Vexit / Vis = SS.SSSU":RVEF 

580 PRINT USINO WOZZLE THRUST POWER COMPRESSOR POWER =ssaa.sas-:EPs 

590 IF D¶><"Y" TWN PRINT "****** END OF OUTPUTS *************" 

600 IF D¶="Y" THEN 720 

610 INPUT "COMPUT% FUEL-EQUIV DELTA Cd AND NOZZLE A exlt? IY/NI":D¶ 

620 I? DS="Y" THEN 880 

630 INPUT "NEW Pt noz /Pt is ' IY/NI":N¶ 

640 IF N¶><"N" TWN 290 

650 GOT0 10 

660 INPUT "TSFC OF TtIRUST ENGINES IUm/hr-SfI = :FT 

670 INPUT "PSFC FOR AUX POWER EXTRACTION fSm!hr-hp~ = ":FP 

680 INPUT "WINO REFERENCE AREA. S r*f fsqft) = ";S 

890 INPUT "F!3 PRESSURE IPSFAl = ":PF 

700 9=.7*PF*H^2 

710 INPUT "SUCTION HASSFLOW ( Sm/SECI = ' :flS 

720 DCD=(~/f~*550l-BPS'VFI*~C*HS/S/Q :REM PHP SYS CD INCR 

730 ~=~/32.1739*S~fR+T3Tl*(1+.Z*MEIE^2I^3/(P3TF*PF*SPRf1.4)*~El :REfl EXIT A 

740 PWRC=US*UUC/550 

750 IF Ds="Y" THEN PRINT "I**+** OUTPUTS ************" 

760 PRINT USING "FUEL-BURN EOUIV CD INCREMENT I SS.SSSSSS8":DCD 

770 PRINT WINO "NOZZLE EXIT AREA = StIUS.*SS S9FT":AE 

790 IF DI z "Y" THEN PRINT "**I*** END OF OUTPUTS  a** *******v" 

800 GOT0 630 

810 END 

:REM NZL EXIT STATIC TEMP 

500 HE=VE/SQRf1.4*R*TEI -REM NZL EXIT tlACH 

510 PRINT "*I***+ OUTPUTS t***lt+***88*ZI*+*89*" 

530 PRINT USINQ "CCWIWSSOR Tt OUT = US0SS.S deg R":TST 

540 PRINT USINQ "COMPRESSOR WORK/MASS = SSSSSSS. it-lbi/lbm":UHC 

780 PRINT USING "COWRESSOR SHAFT POWER INPUT I xaaas s hp":mc 

Figure A8 ALGORITHM FOR SUCTION SYSTEM DRAG ACCOUNTING 

116 
APPENDIX B 

CALCULATION OF ISENTROPIC EQUIVALENT Cp 

FOR SUPERSONIC LEADING EDGES 

For the case of the supersonic leading edge, the presence of a leading 

edge shock changes the nature of the external flow, particularly in the 

leading edge region. 

external velocities from the input pressure coefficients, under the 

assumption of isentropic external flow. 

and transonic conditions for which the code was designed. 

line, the total external velocity is known to have no component perpendicular 

to the attachment line, so the direction of the external velocity is known. 

From this point aft, the direction of the external total velocity vector is 

reckoned station-by-station, using the condition of irrotationality of flow 

in planes parallel to the local surface. 

The Kaups-Cebeci conical boundary layer code computes 

This is appropriate to the subsonic 

On the attachment 

If the leading edge is supersonic, pressure coefficients computed using 

an Euler code will be correct for purposes of determining lift and drag, but 

will cause the K-C code to compute incorrect total velocities, since the 

isentropic assumption is violated by the presence of a leading-edge shock 

wave. One way of computing correct external flow velocities is to input to 

the K-C code the equivalent isentropic pressure coefficients corresponding to 

the correct but nonisentropic values computed by the Euler code. 

approach was taken in the current study. 

air entering the boundary layer would have passed through the 

leading-edge-normal part of a detached shock, yawed to the onset supersonic 

stream by the leading edge sweep angle. 

edge is ignored. 

equivalent isentropic Cp values for input to the Kaups-Cebeci code. 

listing of the program is given in figure B1. 

This 

The assumption used was that all 

Shock curvature near the leading 

A simple program was written in IBM BASIC-A to compute the 

A 

117 
10 PRINT "EQVISEN.BAS: EQUIVALENT ISENTROPIC CP FOR K-C B.L. INPUT" 

20 PRINT "FOR SUPERSONIC LEADING EDGE" 

30 REM ASSUMES ALL B.L. AIR TO PASS THRU L.E. NORMAL PART OF 

40 REM DETACHED L.E. SHOCK. SHOCK CURVATURE EFFECTS IGNORED. 

50 PRINT "IDENTIFIERS: FS = FREESTREAM, 1 = JUST DOWNSTREAM OF SHOCK," 

60 PRINT I' L = LOCAL, N = LEADING-EDGE NORMAL, 2 SQUARED" 

70 PRINT '"I 

80 Gr1.4 :REM GAMMA 

90 INPUT "FREESTREAM MACH =";MFS 

100 INPUT "L.E. SWEEP (DEG) =";SWPLED 

110 SWPLER=SWPLED*3.141593/180 :REM CONVERT TO RADIANS 

120 MNFS2=(MFS*COS(SWPLER) 1-2 :REM FS NORMAL MACH SQD 

130 PlOPFS=l+2*G/(G+l)*(MNFS2-1) :REM SHOCK PRESS RATIO 

140 TlOTFS=1+2*(G-l)/ (G+1)-2*(G*MNPS2+1)/MNFS2*(MNFS2-1) :REM SHOCK TEMP RATIO 

150 MlN2=( l+(G-1)/2*MNFS2)/(G*MNFS2-(G-1)/2) :REM DOWNSTREAM NORMAL MACH SQD 

160 MlP2=(MFS*SIN(SWPLER))-2/TlOTFS :REM DOWNSTREAM MACH PARALLEL TO L.E. SQD 

170 MlTL2=MlN2+MlP2 :REM DOWNSTREAM TOTAL MACH SQD 

180 INPUT "PHYSICAL CP =";CP 

190 IF MNFS2<=1 THEN CPS=CP:PRINT "SUBSONIC NORMAL FL0W":GOTO 250 

200 ML2=2/ (G- 1 )*( (l+(G- 1)/2*MlTL2)/( ( l+G/2*MFS-2*CP)/PlOPPS)-( (G-1 )/G) -1 ) 

210 REM ABOVE IS LOCAL TOTAL MACH CORRESPONDING TO THE GIVEN CP. 

220 TLOTl=(l+(G-1)/2*MlTL2)/(1+(G-l)/2*ML2) :REM T LOCAL / T1 

230 VLVFS2sML2 /MFS 2*TLOT 1 *TlOTFS :REM VELOC RATIO (LOCAL TO FS) SQD 

240 CPSm2/( G*MFS-2)*( ( l-(G-1)/2*MFS-2*(VLVFS2- 1) )-(G/(G-l) ) -1 ) :REM ISEN CP 

250 PRINT USING "ISENTROPIC EQUIV CP =111111.~11111lllM";CPS 

260 PRINT I"' 

270 INPUT "GIVE NEW CP (Y/N)?";CP$ 

280 IF CP$<>"N" THEN 180 

290 GOT0 90 

300 END 

Figure B1 ALGORITHN TO COMPUTE EQUIVALENT ISENTROPIC 

LEADING EDGE CASE 

Cp FOR STABILITY ANALYSES, SUPERSONIC 

118 
Report Documentation Page 

1. Raport No. 2. Government Accession No. 

NASA c~-iai817 

4 Title and Subtitle 

3. Recipient's Catalog No. 

5. Report Date 

Feasibility and Benefits of Laminar Flow Control 

on Supersonic Cruise Airplanes 

7. Author(s) 

A.G. Powell, S. Agrawal, and T.R. Lacey 

9. Performing Organization Name and Address 

McDonnell Douglas Corporation 

3855 Lakewood Blvd. 

July 1989 

6. Performing Organizatton Code 

8. Performing Organization Repon No 

10. Work Unit No. 

505-60-41-01 

11. Contract or Grant No. 

17. KOV w~dr (suggllt.d bv AUWSH 

Laminar Flow Control 

Supersonic Cruise Airplanes 

Feasibility 

Benefit 

Long Beach, California 90846 

18. Diwibuton statomom 

Unclassified - Unlimited 

Subject Category 05 

NAS1-18037 

13. Tv# of Rmon and Pwiod Covered 

19. Socurny Chd. 20. Socurtty Clamif. (of thm p.0.I 21. No. Of pl0.r (Of tht8 fopon) 

12. Sponsoring Agency Nun and Address 

National Aeronautics and Space Administration 

Langley Research Center 

Hampton, VA. 23665-5225 

22. PfK. 

I 

15. Suppkmontary Notos 

Unclassified 

Langley Technical Monitor: Dal V. Maddalon 

Final Report 

Unclassified 119 

16. Abstract 

An evaluation was made of the applicability and benefits of Laminar Flow 

Control (LFC) technology to supersonic cruise airplanes. Ancillary 

objectives were to identify the technical issues critical to supersonic 

LFC application, and to determine how those issues can be addressed through 

flight and wind-tunnel testing. 

a Mach 4.0 transport, and two Mach 2 - class fighter concepts. 

control methodologies developed for subsonic and transonic wing laminarization 

were extended and applied. 

airplanes of the Mach 2 class, even ones of large size. 

17 percent in lift-drag ratio were found. 

as contamination avoidance and excresence criteria were identified, and 

recommendations are made for their resolution. 

wing design methodology is indicated. 

Vehicle types studied include a Mach 2.2 supersonic transport configuration, 

Laminar flow 

No intractible aerodynamic problems were found in applying LFC to 

Improvements of 12 to 

Several key technical issues, such 

A need for an inverse supersonic