Table Of Contentcl NSWC/WOL/TR 77-28
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WHITE OAK LABORATORY
A PROGRAM FOR COMPUTING STEADY INVISCID THREE-DIMENSIONAL SUPERSONIC FLOW
ON REENTRY VEHICLES , VOL 1: ANALYSIS AND PROGRAMMING
11 FEBRUARY 1977
NAVAL SURFACE WEAPONS CENTER
WHITE OAK LABORATORY
SILVER SPRING, MARYLAND 20910
9 Approved for public release; distribution unlimited.
9]
r NAVAL SURFACE WEAPONS CENTER
1 J WHITE OAK, SILVER SPRING, MARYLAND 20910
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REPORT DOCUMENTATION PAGE READ INSTRUCTIONS
BEFORE COMPLETING FORM
PE8PORT NUMBER 2. GOVT ACCJ.S1oWe. .1...T00-.... N~R
NSWC/WOIL TR-77-28._____________
.TITL~.wd~tte 6qt!TUOVE't RED
A Program for Computing Steady Inviscid Three-
-' Dimensional Supersoqic Flow on Reentry
Vehicles, Vol4 I;.*Analysis and Programming. _6_. __P__E__R_F__O_R__M_ING ORG. REPORT NUMBER
7. AUTH~OR() 8. CONTRACT OR GRANT NUMBER(@)
J. M.-/Solomon, M.,/ Ciment, R. E. /Ferguson,
J. B.I Bell, A. B.i /Wardlaw, Sy _____________
9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK
AREA & WORK UNIT NUMBERS
Naval Surface Weapons Center 0;
.0;
White Oak Laboratory 07 0;
White Oak, Silver Spring, Maryland 20910
______________
I1. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE
11 Febm 77
14. MONITORING AGENCY NAME 8 ADDRESS(iI different frotm Controling Office) 15. SECURITY CLAr'Pfthe"pa*.~t---
Unclassified
15s. DECL ASSI FICATION/ DOWNGRADING
SCHEDULE
16. DISTRIBUTION STATEMENT (of this Report)
Approved for public release; distribution unlimited
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16. SUPPLEMENTARY NOTES
19. KEY WORDS (Continue on reverse side if necessary and Identify by block number)
reentry vehicle, flow fields, three dimensional, supersonic/hypersonic,
inviscid flow, control surfaces, pitch/yaw, finite difference methods,
hyperbolic systems, boundary conditions
20.'\A\UISTRACT (Continue an reverse aide If necessaty and Identify by block number)
A comprehensive computational procedure is presented for predicting the
supersonic region of the flow field on advanced reentry vehicle shapes in
steady flight at pitch and yaw. The procedure utilizes explicit second order
accurate finite difference methods applied to the conservation law form of
the steady inviscid flow equations. Improved numerical methods are used at
the body surface and the bow shock wave. Provisions for treating body-i~
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geometries with discontinuous slopes are also included. Either perfect gas or
real gas equilibrium thermodynamic properties can be used.
The computational procedure is implemented as a fortran computer code
which provides a practicable representation of the inviscid flow field and
the resulting aerodynamic force and moment on the vehicle.
In this report (to.5 the analytical and numerical development of the
procedure is presented and the associated computer code is described. A
comparison report Ma-tw-J' 1-containsd etailed instructions for
operating the code and interpreting the output results.
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NSWC/WOL/TR 77-28
NSWC/WOL/TR 77-28 11 February 1977
A Program for Computing Steady Inviscid Three-Dimensional Supersonic Flow
on Reentry Vehicles, Vol. I: Analysis and Programming
This report describes the analytical, and computational aspects of a
computer program for predicting inviscid flow fields and aerodynamics on
realistic reentry configurations. This work was performed by members of
the Mathematical and Engineering Analysis Branch of NSWC/WOL. The initial
code development was supported by the Naval Sea Systems Command under the
Aeroballistic Reentry Technology (ART) program with some of the fundamental
analytical and numerical work supported by NSWC Independent Research Funds.
Most of the final code development and documentation was supported by the
Air Force Space and Missile System Organization under the technical manage-
ment of the Aerospace Corporation.
The authors gratefully acknowledge the efforts of Mr. R. Feldhuhn, NSWC
coordinator for the ART program, who was responsible for initiating the
present work and whose continued interest and support throughout the
investigation was invaluable. The authors are also indebted to Mr. M. Lyons
and Dr. E. Ndefo of the Aerospace Corporation for several stimulating
technical discussions which lead to important improvements in the final code.
C. A. FISHER
By direction
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NSWC/WOL/TR 77-28
CONTENTS
Page
0. INTRODUCTION...................................4
PART I: ANALYSIS
1. NOTATION (PART I)................................8
2. GOVERNING EQUATIONS AND BOUNDARY CONDITIONS. ............. 13
2.1 Steady Flow Equations. ........................ 13
2.2 Boundary Conditions............................15
3. BASIC COMPUTATIONAL ALGORITHM.......................16
3.1 Computational Region and Transformed Equations .......... 16
3.2 Interior Points............................22
3. 3 Bow Shock Points.............................25
3.4 Body Surface Points. ..................... 30
3.5 Symmetry and Periodic Boundary Points .. ........... 37
3.6 Step Size and Stability. ....................... 39
4. SPECIAL FEATURES. ....... .......................................41
4.1 Discontinuities in Body Slope. .................. .. 1
4.2 Wall Entropy Reduction ........................ 53
4.3 Mesh Clustering............................57
5. FORCE AND MOMENT CALCULATIONS ....................... 63
APPENDIX A - DIFFERENTIAL EQUATIONS FOR BOUNDARY POINTS........68
APPENDIX B - SYMMETRY CONDITIONS. ..................... 82
APPENDIX C - CFL CONDITIONS ............................ 85
6. REFERENCES ..................................... 98
PART II: PROGRAMMING
7. GENERAL REMARKS................................100
COMMON......................................101
-*8.
9. MAIN.................................112
9.1 Section 1 ................................ 112
9.2 Section 2.............................114
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NSWC/W.OL/TR 77-28
Page
10. SUBROUTINES USED IN THE FLOW FIELD CALCULATION. ......... 118
10.1 BODYP, ENTRY BODYPP......................118
10.2 DECODE. ........................................ 119
10.3 EVAL, ENTRY EVALSY, ENTRY EVALPR. ............. 120
10.4 JUMP..............................122
10.5 TRANF, ENTRY TRANFW....................123
10.6 TRANG, ENTRY TRANCW......................124
10.7 WALL..............................125
10.8 SHOCK.............................128
11. AUXILIARY SUBROUTINES........................129
11.1 INTE ........................... 129
11.2 INTRPL.............................130
11.3 REZONE...........................130
11.4 RGAS..............................131
11.5 HRCAS, ENTRY ARGAS ....................... 132
11.6 SERCH, LOCATE ...........................133
11.7 SHFAX, SHFAXD ...........................133
12. INPUT-OUTPUT ROUTINES........................135
12.1 BODY, ENTRY BODYN, ENTRY BODYR. ................ 135
12.2 FIELD...............................136
12.3 OUT..............................136
12.4 RECOVR, SAVE. ....................... 136
12.5 TRAMD.................................138
12.6 TRANGD...............................138
APPENDIX D
-LISTINGS.............................139
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NSWC/WOL/TR 77-28
0. INTROiUCTION
An important aspect of the design and evaluation of maneuverable
and advanced ballistic reentry vehicles is the determination of the
inviscid flow field surrounding the body. The inviscid flow field
provides surface pressure distributions required for determining the
aerodynamic loading on the vehicle and other surface information which
is needed as input for determining surface heat transfer rates and other
boundary layer effects. A cost effective method for obtaining this
information is to use high-speed computer codes which numerically solve
the steady, three-dimensional, inviscid flow equations associated with
arbitrary shaped reentry vehicles flying at supersonic/hypersonic speeds.
The numerical calculation of the inviscid flow field over reentry
vehicles is divided into two parts--the blunt body region calculation
and the supersonic region calculation (see Fig. 1). The blunt body
region calculation determines the transonic flow field near the stagnation
point. The supersonic region calculation determines the flow field
downstream of the blunt body region. The differing nature of the flow
in these two regions requires significantly different computer codes
for calculating each region. The blunt body region is computed first
and is continued downstream until supersonic flow is established everywhere
in the shock layer. The computed results from this calculation are used
to establish an "initial" data plane which is used to start the supersonic
region calculation. This latter portion represents the majority of the
total flow field on maneuverable and high performance ballistic reentry
vehicles.
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NSWC/WOL/TR 77-28
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Fig. 1. Computational regions and cylindrical coordinate system for
reentry vehicle inviscid flow calculations.
5
NSWC/WOL/TR 77-28
In this report, a computer code for performing the supersonic region
calculation is described. This code is based on the conservation law
form of the steady, inviscid equations. Codes of this type are sometimes
referred to as shock capturing techniques since internal (embedded)
shock waves in the flow field are computed in an approximate manner without
explicitly locating (or tracking) the shock surface. The present code
incorporates improved numerical methods at the body surface and the bow
shock wave which yield a wider applicability to missile design than
existing codes of this type (e.g. ref. 1).
This report is divided into two parts. In Part I, the partial
differential equations, boundary conditions, and finite difference
equations which are the basis of the computer code are discussed. In
Part Il, the fcztran computer code is described. A companion report*,
the Users' Manual, contains detailed instructions for running the code
on CDC 6000 series and 7600 machines and foi interpreting the output
results.
*Solomon, J. M., Ciment, M., Ferguson, R. E., Bell, J. B., and Wardlaw, A. B.,
A Program for Computing Steady Inviscid Three-Dimensional Supersonic Flow
on Reentry Vehicles - Vol. II: User's Manual, NSWC/WOL TR 77-32
6
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NSWC/WOL/TR 77-28
PART 1: ANALYSIS
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