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NASA TECHNICAL
I -- -jlow fields
Held at
Ames Research Ceater
Moffett Field, Califoroia
15-16, 1971
HATJOiAl AIROHAUTICS AHD SPACE ADMINISTRATION • WASHJH6T0N, B. C. - FIBIOA8Y J972
https://ntrs.nasa.gov/search.jsp?R=19720013197 2020-01-13T17:52:20+00:00Z
- I4
1. Report No. 2. Government Accession No.
NASA TM X-2506
4. Title and Subtitle
SPACE SHUTTLE AEROTHERMODYNAMICS TECHNOLOGY CONFERENCEVOLUME I - FLOW FIELDS
7. Author(s)
9. Performing Organization Name and Address
NASA Langley Research CenterHampton, Va. 23365
12. Sponsoring Agency Name and Address
National Aeronautics and Space AdministrationWashington, B.C. 20546
3. Recipient's Catalog No.
5. Report DateFebruary 1972
6. Performing Organization Code
8. Performing Organization Report No.L-8156-.
10. Work Unit No.
11. Contract or Grant No.
13. Type of Report and Period Covered
Technical Memorandum
14. Sponsoring Agency Code
15. Supplementary Notes
Held at NASA Ames Research Center, December 15-16, 1971.
16. Abstract
The conference encompasses four technology efforts, each published as a separate volume.
Volume I - Flow Fields (NASA TM X-2506)
Volume II - Heating (NASA TM X-2507)
Volume III - Aerodynamics (NASA TM X-2508)
Volume IV - Operational Flight Mechanics (NASA TM X-2509)
17. Key Words (Suggested by Author(s)) 18. Distribution StatementFlow fieldsHealingAerodynamics Unclassified - UnlimitedOperational flight mechanicsSpace shuttleAerothermodynamics
19. Security dassif. (of this report) 20. Security Classif. (of this page)
Unclassified Unclassified
21. No. of Pages 22. Price*
270 $3.00
For sale by the National Technical Information Service, Springfield, Virginia 22151
PREFACE
A Space Shuttle Technology Conference on Flow Fields, Heat Transfer, Aero-
dynamics, and Operational Flight Mechanics was held at the NASA Ames Research
Center on December 15 and 16, 1971- The objective of this conference was to
review the broad base of aerothermodynamics technology developed for the space
shuttle during the period of the Phase B studies and, thereby, help focus
attention on the technology required for further space shuttle development.
This publication is a compilation of the conference papers. It has been divided
into four volumes, one for each of the sessions. Five papers which were omitted
from the oral presentation at the conference are included in this publication.
Contributing organizations include U.S. Aerospace Contractors, Universities,
Canadian and European Space Agencies, in addition to NASA Research Centers/
iii
CONTENTS
GLOSSARY IX
OPENING REMARKS
1. SHUTTLE PROGRAM STATUS 1Edward P. Andrews, NASA Headquarters
2. SHUTTLE TECHNOLOGY - INTRODUCTORY REMARKS laA. 0. Tischler, NASA Headquarters
VOLUME I.- FLOW FIELDS
3- INTRODUCTION 1^5Joseph G. Marvin, ARC
k. DETERMINATION OF SPACE SHUTTLE FLOW FIELD BY THETHREE-DIMENSIONAL METHOD OF CHARACTERISTICS If7Chong-Wei Chu and S. A. Powers, Northrop
5- APPLICATION OF SHOCK CAPTURING AND CHARACTERISTICS METHODSTO SHUTTLE FLOW FIELDS 65P. Kutler, J. V. Rakich, and G. G. Mateer, ARC
6. FLOW FIELD PREDICTIONS FOR A SLAB DELTA WING AT INCIDENCE 93R. J. Conti, P. D. Thomas, and Y. S. Chou, Lockheed
7. SPACE SHUTTLE ORBITER REENTRY FLOW FIELD AND HEATING ANALYSIS 115W. C. Rochelle, TRACOR; B. B. Roberts, MSCj F. W. Vogenitz,and L. d'Attorre, TRW Systems
8. A VISCOUS STARTER SOLUTION FOR SHUTTLE FLOW FIELD COMPUTATIONS .... 157C. P. Li, Lockheed Electronics Co.; and W. D. Goodrich, MSC
9. CHEMICAL NONEQUILIBRIUM EFFECTS ON THE FLOW IN THE WINDWARD PLANEOF SYMMETRY OF A BLUNTED DELTA ORBITER 185J. A. Lordi, R. J. Vidal, Cornell Aeronautical Laboratory;and C. B. Johnson, LRC
10. INVISCID-SURFACE-STREAMLINE PROGRAM FOR USE IN PREDICTINGSHUTTLE HEATING RATES . ..._.. . 23_9_H. Harris Hamilton, LRC; and Fred R. DeJarnette, North CarolinaState University
11. SUMMARY 255Joseph G. Marvin, ARC
VOLUME II.- HEATING
12. INTRODUCTION ............................. 257James C. Dunavant, LRC
13. EXPERIMENTAL AND THEORETICAL AERODYNAMIC HEATING AND FLOW FIELDANALYSIS OF A SPACE SHUTTLE ORBITER ................ 26lR. K. Matthews, T. D. Buchanan, W. R. Martindale, ARO, Inc.;and J. D. Warmbrod, MSFC
Ik. A REVIEW OF THE GRUMMAN ORBITER WIND TUNNEL HEAT TRANSFER TESTS . . . 297A: R. Mendelsohn, M. Bourbin, M. Jew, and C. W. Osonitsch, Grumman
15. HIGH REYNOLDS NUMBER TURBULENT HEATING TO TWO SIMPLIFIEDSHUTTLE CONFIGURATIONS ......... ........... . .Charles B. Johnson, LRC
16. EFFECTS OF ROUGHNESS ON HEATING AND BOUNDARY -LAYER TRANSITIONI. EFFECTS OF SIMULATED PANEL JOINTS ON BOUNDARY-LAYER
TRANSITION .................. ': ....... 375H. Lee Seegmlller, ARC
II. EFFECTS OF DISCRETE ROUGHNESS ON HEATING ............ 395George G. Mateer, ARC
17. LEE -SIDE FLOW PHENOMENA ON SPACE SHUTTLE CONFIGURATIONS ATHYPERSONIC SPEEDSI. FLOW SEPARATION AND FLOW FIELD VISCOUS PHENOMENA OF A
DELTA-WING SHUTTLE ORBITER CONFIGURATION ...........J. W. Cleary, ARC
II. STUDIES OF LEE -SURFACE HEATING AT HYPERSONIC MACH NUMBERS . . .Jerry N. Hefner and Allen H. Whitehead, Jr., LRC
18. AEROTHERMODYNAMIC MEASUREMENTS FOR SPACE SHUTTLE CONFIGURATIONSIN HYPERSONIC WIND TUNNELS .....................John J. Bertin, Frank E. Williams, Robert C. Baker, Universityof Texas; Winston D. Goodrich, MSC; and William C. Kessler,McDonnell Douglas
19. DETERMINATION OF AEROTHERMODYNAMIC ENVIRONMENT UNCERTAINTIESWITH APPLICATION TO SPACE SHUTTLE VEHICLES ............. 503C."f A. Scottoline, North American Rockwell
20. SPACE SHUTTLE BOOSTER MULTI-ENGINE BASE FLOW ANALYSIS ........ 519Homer H. Tang, Charles P. Gardiner, William A. Anderson, andJohn Navickas, McDonnell Douglas
21. AN ANALYSIS OF THE BOOSTER PLUME IMPINGEMENT ENVIRONMENT DURINGTHE SPACE SHUTTLE NOMINAL STAGING MANEUVER ............. . 607C. J. Wojciechowski, M. M. Penny, Lockheed - Huntsville;T. F. Greenwood, MSFC; and I. H. Fossler, MSC
VI
22. CONNECTIVE HEATING MEASUREMENT BY MEANS OF AN INFRARED CAMERA . . . .Dale L. Compton, ARC
23- HEAT-TRANSFER TESTING PROCEDURES IN PHASE B SHUTTLE STUDIESWITH EMPHASIS ON PHASE-CHANGE-DATA IMPROVEMENT 66lDavid A. Throckmorton, LRC
2k. EVALUATION OF BOUNDARY-LAYER-TRANSITION CRITERIA FOR SPACESHUTTLE ORBITER ENTRY . . . 683Vernon T. Helms III, LRC
VOLUME III.- AERODYNAMICS
25. INTRODUCTORY REMARKS OF SESSION CHAIRMAN .............. 705Beverly Z. Henry, LRC-
26. STATUS OF LANGLEY STUDIES OF AERODYNAMICS AND INTERFERENCE EFFECTSOF TANDEM LAUNCH VEHICLES ..................... 707William I. Scallion and Kermit G. Pratt, LRC
27. IMPACT OF SUBSONIC AERODYNAMIC CONSIDERATIONS ON A SPACE SHUTTLEBOOSTER CONFIGURATION ....................... 737R. L. Roensch, Douglas Aircraft Co.; and R. L. Odenbaugh,McDonnell Douglas Astronautics Co. - West
28. AERODYNAMIC STUDIES OF DELTA-WING SHUTTLE ORBITERSI. LOW SPEED ........................... 785
Delma C. Freeman, Jr., and James C. Ellison, LRCII. HYPERSONICS .......................... 803
Howard W. Stone and James P. Arrington, LRC
29- WING OPTIMIZATION FOR SPACE SHUTTLE ORBITER VEHICLES . . ...... 831T. E. Surber, W. E. Bornemann, and W. D. Miller, NorthAmerican Rockwell
30. REVIEW OF DELTA WING SPACE SHUTTLE VEHICLE DYNAMICS ......... 861J. Peter Reding and Lars E. Ericsson, Lockheed
31. EXPERIMENTS ON THE DYNAMIC STABILITY OF THE SPACE SHUTTLE ..... . .933K. J. Orlik-Ruckemann, J. G. LaBerge, and E. S. Hanff, NationalResearch Council of Canada
AePOTENTIAL PARTICIPATION IN THE DEVELOPMENT OF THE SPACE SHUTTLEORBITER 969M. Fuchs, J. Haseloff, and G. Peters, ERNO
33- SUMMARY REMARKS OF SESSION CHAIRMAN 993Beverly Z. Henry, LRC
vii
VOLUME IV.- OPERATIONAL FLIGHT MECHANICS
3U. INTRODUCTION ............................. 997Victor L. Peterson, ARC
35 . VEHICLE PERFORMANCE IMPACT ON SPACE SHUTTLE DESIGN ANDCONCEPT EVALUATION ........... ............. 999Mark K. Craig, MSC
36. SPACE SHUTTLE ATMOSPHERIC ASCENT FLIGHT DYNAMICS ........... 1041J.. T. Patha, K. A. Noess, and M. V. Lines, Boeing
,7
37. OPTIMAL LIFTING ASCENT TRAJECTORIES FOR THE SPACE SHUTTLE ...... 1063T. R. Rau and J. R. Elliott, LRC
38. OPTIMAL ASCENT TRAJECTORIES OF A TWO STAGE SPACE SHUTTLE VEHICLE . . . 1089R. A. Wilson, North American Rockwell
39. ABORT SEPARATION OF THE SHUTTLE ................... 1105John P. Decker, LRC; Kenneth L. Blackwell, Joseph L. Sims, MSFC;R. H. Burt, W. T. Strike, Jr., AROj C. Donald Andrews, L. RayBaker, Jr., LMSC - Huntsville; and John M. Rampy, Northrop -Huntsville
hO. BOOSTER RECOVERY FOLLOWING PREMATURE SPACE SHUTTLE STAGESEPARATION ............................. 1165M. J. Hurley, General Dynamics /Convair
111. EFFECT OF COMMERCIAL AND MILITARY PERFORMANCE REQUIREMENTS FORTRANSPORT CATEGORY AIRCRAFT ON SPACE SHUTTLE BOOSTER DESIGNAND OPERATION ........................... 1191R. A. Bithell and W. A. Pence, Jr., General Dynamics /Convair
42. SPACE SHUTTLE ORBITER HANDLING QUALITY CRITERIA APPLICABLE TOTERMINAL AREA, APPROACH, AND LANDING ................ 1239Gordon H. Hardy, ARC
43- ORBITER ENTRY TRAJECTORY CONSIDERATIONS . . . . ........... 1265John J. Rehder and Paul F. Holloway, LRC
44. STAGE SEPARATION OF PARALLEL -STAGED SHUTTLE VEHICLES,A CAPABILITY ASSESSMENT ...................... 1301M. " J. Hurley and G. W. Carrie, General Dynamics /Convair
45. SPACE SHUTTLE BOOSTER FLYBACK SYSTEM SYNTHESIS ............ 1397D. W. Jones, W. J. Moran, and V. A. Lee, General Dynamics /Convair
. OPTIMIZED SPACE SHUTTLE TRAJECTORY SIMULATIONLouis Tramonti and Richard G. Brusch, General Dynamics /Convair
van
GLOSSARY
ABES
i AC PS
AEDC
AFB
AFFDL
ALT
APS
AR
ARC
ARDC
BECO
BLOW
BV
BW
BWV
CAL
CALCS
CAL HST
CFHT
CG; C.G.; e.g.
CONFIG
~CRT
Cyl
2-D
3-D
air breathing engines
attitude control propulsion system
Arnold Engineering Development Center
air force basei
Air Force Flight Dynamics Laboratory
altitude
auxiliary propulsion system
aspect ratio
Ames Research Center
Air Research and Development Command
booster engine cutoff
booster lift-off weight
body-vertical tail
body-wing
body-wing-vertical tail
Cornell Aeronautical Laboratory
calculations
Cornell Aeronautical Laboratory hypersonic shock tunnel
continuous-flow hypersonic tunnel
center of gravity . •
configuration7
"cathode ray tube
cylinder
two-dimensional
thr e e-dimens i onal
IX
DAC
DCM
DEX .
DIA
DIAT -
DIF. KEFL.
JDMoC
DOD
DOF
DWO
EHT
EOHT
EPL
EST
ETR
F&M
FAR; F.A.R.
FBS
F.D.
F/0
FO/FS
FPR
FPRE
FR
FREQ
GAG
Douglas Aircraft Company
data control management
exit diameter
diameter
diatomic
differential deflection
three-dimensional method of characteristics
Department of Defense
degrees of freedom
delta-wing orbiter
external hydrogen tank
external oxygen-hydrogen tank
emergency power level
estimated
eastern test range
force and moment
Federal Aircraft Regulation
flyback system
finite difference
fuel-oxygen ratio
fail operational/fail safe
flight performance reserve
flat-plate reference enthalpy
fully reusable
frequency
Grumman Aerospace Corporation
x
GD
GDC
GD/C
G.-E.
GLOW
GTOP
GW
H
HCF
HCR
HeT
HO
H.W.T.
IAC
IBFF
ICD
IFR .
ILRV
ILS
USD
IR
IRAD
KSC
General Dynamics
General Dynamics Corporation
General Dynamics/Convair
General Electric Company
vehicle gross lift-off weight
general trajectory optimization program
gross weight
hydrogen
highly compacted fibers
high cross range
Mach 20 helium tunnel
hydrogen-oxygen system
hypersonic wind tunnel
industrial air center
impulse base flow facility
interface control drawing
instrument flight rules
integral launch and reentry vehicle
instrument landing system
industrial
infrared
Independent Research and Development
Kennedy Space Center
L.E.
LEE
leading edge
leeward
liquid hydrogen
XI
LMSC
L02; LOX
LRC; LaRC
LRU
MAC
MAC Exp
MARK I, MARK II
MAX
MC
MCAIR
MCAS
MDAC
MDC
MIL SPEC
MIN
MM HWT
MOC
MPL
MSC
MSFC
MT.
NA
NAE; N.A.E.
NAR; NARC; NR
WAS
NASA
Lockheed Missiles & Space Company
liquid oxygen
Langley Research Center
link retraction unit
mean aerodynamic chord
exposed mean aerodynamic chord
shuttle configurations
maximum
Monte Carlo
a low-speed wind tunnel
Marine Corps Air Station
McDonnell Douglas Astronautics Company
McDonnell Douglas Corporation
military specification
minimum
Martin Marietta Corporation hotshot wind tunnel
method of characteristics
minimum power level
Manned Spacecraft Center
Marshall Space Flight Center
mountain
North American
National Aeronautical Establishment
North American Rockwell Corporation
Naval Air Station
National Aeronautics and Space Administration
xn
NO.; No.
WOZ
NPL
0/F
GLOW
OMS
P/L
PM
RCC
RCS
Eef
REQD
RFP
RGAS
R.H.
RSI
RTV
S&C
SCT
SF
S.L.; SL
SM
_SEEC
SRM
SS
SSV
ST
number
nozzle
normal power level
oxygen-fuel ratio
orbiter lift-off weight
orbiting maneuvering system
payload
pitching moment
reinforced carbon carbon
reaction control system
reference
required
request for porposals
real gas
right hand engine
reusable surface insulation
room-temperature vulcanizing rubber
stability and control
shock capturing technique
stick force
sea level
service module
specification
solid rocket motors
stainless steel
space shuttle vehicle
straight
Xlll
STAR
STD
STI
STOL
SW
SYM
T/C
T.E.
T.E.D.
TEMP
T.E.U.
THEO
TPS
TEAJ
TVC
Typ
UPWT
USAF
VAC HVWT
VAFB
VDT
VFR
V/STOL
w/o
WT
WWD -
YM
strings and array computer; self-testing and repair computer
standard
Systems Technology, Incorporated
short take-off and landing
southwest
symbol
thermocouple
trailing edge
trailing edge down
temperature
trailing edge up
theoretical
thermal protection system
trajectory
thrust vector control
typical
Unitary Plan wind tunnel
U.S. Air Force
Vought Aeronautics Company hypervelocity wind tunnel
Vandenburg Air Force Base
variable density tunnel
visual flight rules
vertical and short take-off and landing
without
weight
windward
yawing moment
xiv
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39
SHUTTLE TECHNOLOGY - INTRODUCTORY REMARKS
By A. 0. Tischler
Director of Shuttle Technologies Office, OARTNASA Headquarters, Washington, D.C.
This conference is the third large conference covering the general subject
of aerothermodynamics for the reusable earth-to-orbit transportation system, '
commonly called the "shuttle," and the first to be devoted exclusively to the
aerothermodynamic problems and issues. The first of these conferences, held at
the Lewis Research Center in the summer of 1970, told everyone what.the approach
to shuttle technology work would be. The second, held at the Langley Research •
Center in the late winter of 1971, made the overall plan more substantive and :
provided some results. This conference, hopefully, will disclose much data and
correlations on the shuttle-related aerothermodynamic technology..
Aerodynamics has played an important role in shaping the shuttle concept.
Even before the formation of NASA in 1958, serious thought was being given to
the idea of an aerodynamically controllable entry and return space vehicle. It
was only a matter of technological state of the art that led to the use of blunt
conical semiballistic reentry bodies for Mercury, Gemini, and Apollo. The' work
that sprang out of these early deliberations, which led NASA to the lifting-body
programs, and more importantly, led the U.S. Air Force to sponsor the DynaSoar
project, on which some $i+OOM were spent, along with continuing technology work by
the Flight Dynamics Laboratory at the Wright Patterson Air Force Base, gave a con-
siderable background for flyable reentry vehicles. This work, the improved high-
performance propulsion systems being developed by both NASA and Air Force, and
the improvements in refractory materials resulting from a broad frontal research
attack, laid alongside the high present cost of injecting payloads into space,
paved the way for accepting the idea that the time to start developing a reusable
space vehicle was at hand.
The shuttle vehicle has, however, encountered severe constraints in its
fiscal diet for the early development years. Consequently, a series of vehicle
design and configuration studies have been made to determine a vehicle design
approach which, for a prescribed mission model, will have least cost in terms
of the present value of money. The systems that are the front runners at this
moment have been described by Edward Andrews (paper no. 1.)
It is probably unnecessary to remind anyone here that the changing config-
urational picture has kept the aerodynamics and aerothermodynamics personnel
busy. The importance of understanding the aerodynamic and aerothermal effects
on the flight mechanics and structural integrity of this three-piece vehicle
during a flight spectrum which ranges from Mach 0 to Mach 25 and back to Mach 0
under continually varying pressure and density cannot be minimized. In spite of
the obvious difficulties one advantage is the fact that the shuttle does not
have to be a superior airplane. As long as it can be adequately controlled
through the flight regime without scorching its skin it would appear to meet the
mandatory requirement s.
Back in the summer of 1969 OMSF and OART began a precedent-setting joint
effort to examine and prepare a technological base to support the shuttle. As
most of you know this program has pulled together the talents of the research
and space flight centers of NASA, has vastly improved communications at the
problem-solving level, and tied in not qmly the contractors, but also the
European technologists who are interested in participating in the post-Apollo
endeavors.
The management approach to this program is to solicit and to use the advice
of seven Working Groups. These Working Groups, of which the Group on
Aerothermodynamics chaired by Arthur Henderson of Langley Research Center is
one, comprise representatives of all NASA Centers engaged in the work activity.
They recommend the program content; they are also actively engaged in monitoring
it. This conference represents one of the Working Group information dissemination
functions. I would like here to express my appreciation to Dr. Hans Mark and his
entire team for organizing and hosting this symposium.
Funding for the technology effort, which will total $1JOM by the end of
FY 1972, is derived from both OART and OMSF fund sources. The Aerothermodynamics
total effort during this period will be $l6M, a sum which does not include the
salary expenses of NASA personnel engaged in the work, nor any contractors'
efforts paid under vehicle configuration studies, nor any of the independent
research and development funds which various companies have been persuaded to
invest in the shuttle prospect. 925 NASA personnel are directly involved in this
technology work; the aerothermodynamics effort accounts for nearly one-fourth of
these personnel.
Some of the results of this work have been noteworthy. New test methods
for studying heat-transfer rates and shock flow and impingement have been invented
out of necessity to handle the large volume of work. The program has now used
about 20 000 wind-tunnel hours. This technical progress will be covered here in
much detail in the next 2 days.
With the coming fiscal.year, NASA anticipates moving the shuttle program into
the design and development phase. This change will require a transition of many
of our technology investigations into development support. Because of the
intrinsic need to support closely the shuttle configurational design selections,
it seems likely that this aerodynamic work effort will continue at a high level.
In fact, it is expected that test facilities located in Europe will be used to
relieve the load of work imposed on the U.S. facilities if satisfactory working
relationships can be worked out and it is believed that they will be.
I look forward, along with you, to the development and operation of this
system so vital to a healthy and aggressive space program. I expect that this
conference will be seen in retrospect as a significant contribution to the
development of economical access to the space arena.
FLOW FIELDS SESSION
INTRODUCTION
by
Joseph G. Marvin
NASA Ames Research Center
Vehicle aerodynamics, heating, thermal protection system response,
chemical effects on surface materials, and chemical effects within the
shock layer are a few of the many variables that depend on the flow
field around the Space Shuttle vehicle during its flight through the
atmosphere. A need for flow field calculations arises mainly from the
inability to completely simulate the flight environment in ground-based
facilities. For example, tests performed to simulate the high enthalpies
associated with entry often have the incorrect flow chemistry because of
model scale effects. Therefore, the designer must extrapolate test data by
using the best information about the real flow field. Exact three-
dimensional flow field calculations are now at the threshold of providing
the necessary rationale upon which to base this important extrapolation.
At the last Space Shuttle Technology Conference held at Langley
Field in March 1971, there was only one paper devoted to exact flow
field calculations. In this session there are seven papers, five of
which contain exact methods for computing three-dimensional flow fields.
The remaining two papers treat in an approximate way chemical nonequili-
.brium effects and streamline calculations used as input for heating
estimates. The emphasis on flow fields at this conference developed
mainly from recent technology advances made in exact calculation methods
and in computer storage and speed that is necessary in the practical
application of these methods. The papers were selected in order that
the progress made on shuttle flow field calculations can be judged and
so that future needs can be determined.
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S FOR SIMULATED NARC SHUTTLE ORBITER
(Figure 1)
flow field for the NARC space shuttle orbiter included a pointed
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initial conditions. For this case, the SCT code generated its
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quent calculations, which utilized blunted noses, relied on the0) <CO433CO*t
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RC orbiter was approximated by two ellipses whose semi-major
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this configuration by the SCT code is shown in Figure 1 for both
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in the radial direction and 19 points in the meridional direction-4
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RFACE PRESSURES FOR NARC SHUTTLE ORBITER
(Figure 6)
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HA.PE AND SURFACE STREAMLINE PATTERN
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ENTHALPY PROFILE
(Figure 5)
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ing" the normal coordinate. Moreover, we have found that a preset stretching
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e need to change the stretching factor in the meridional direction is not as
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112
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INTRODUCTION
s of a study performed by TRW Systems for NASA/MSC
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INFLUENCE OF CHEMICALON
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preceding papers provide material from which to form a judgement regarding the status andcuH
eds of exact flow field calculations, as summarized in figure 1.cuc01S-l34-13
t methods are available to provide the starting data for the three-dimensional inviscid
ons used when the flow field is predominately supersonic. At the high altitudes where
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ffects in the shock layer are important a two-dimensional method for generating startingCUCO3OCJCO•rl
vailable which has the promise of extension to three dimensions. Methods for calculatingCOCO•HCfl
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flows for realistic shuttle geometries at angles of attack where the flow is predominately
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imate way. In each of the aforementioned inviscid flows, thin boundary-layer methods haveorlexexcfl£*ctf
ied with reasonable success, but extension to three dimensions should be undertaken.
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e the present status indicates good progress toward the ultimate objective of calculating
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ch machines should make possible economical calculations of complete flow fields on a3C/3•CUrH0rl
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