NASA-TM-111599

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AIAA 96-1803

Review of Blunt Body Wake Flows at

Hypersonic Low Density Conditions

J. N. Moss and J. M. Price

NASA Langley Research Center

Hampton, VA 23681-0001

31st AIAA Thermophysics Conference

June 17-20, 1996/New Orleans, LA

For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics

370 L'Enfant Promenade, S.W., Washington, D.C. 20024

https://ntrs.nasa.gov/search.jsp?R=19960029344 2018-05-11T16:25:42+00:00Z

REVIEW OF BLUNT BODY WAKE FLOWS AT HYPERSONIC LOW DENSITY CONDITIONS

James N. Moss* and Joseph M. Price**

Mail Stop 408A

NASA Langley Research Center

Hampton, VA 23681-0001

Abstract

Recent results of experimental and

computational studies concerning hypersonic

flows about blunted cones including their near

wake are reviewed. Attention is focused on

conditions where rarefaction effects are present,

particularly in the wake. The experiments have

been performed for a common model

configuration (70 ° spherically-blunted cone) in

five hypersonic facilities that encompass a

significant range of rarefaction and

nonequilibrium effects. Computational studies

using direct simulation Monte Carlo (DSMC)

and Navier-Stokes solvers have been applied to

selected experiments performed in each of the

facilities. In addition, computations have been

made for typical flight conditions in both Earth

and Mars atmospheres, hence more energetic

flows than produced in the ground-based tests.

Also, comparisons of DSMC calculations and

forebody measurements made for the Japanese

Orbital Reentry Experiment (OREX) vehicle (a

50 ° spherically-blunted cone) are presented to

bridge the spectrum of ground to flight

conditions.

Nomenclature

A

CD

CH

base area of cone, A = _d2/4

drag coefficient, C D = 2D /p_A

heat transfer coefficient, CH = 2q/pocV 3

CH

%

db

D

Kn

M

n

P

q

Q

Rb

Rc

Rn

Reo¢

S

Ww

u

V

X

Y

_t

P

overall heat transfers coefficient,

CH = 2Q/p®V3_ A

modified pressure coefficient,

Cp =2pw/po¢

base diameter

drag

Knudsen number, Kn = k/d

Mach number

number density

pressure

heat transfer rate

overall (integrated) heat transfer

cone base radius

corner radius

nose radius

Reynolds number, Reoo = pooVood/_to:

distance along the body surface

measured from the stagnation point

surface temperature

axial velocity

freestream velocity

axial distance from stagnation point

measured along symmetry axis

radial distance from symmetry axis

mean free path

viscosity

density

Subscripts

w surface values

o: freestream values

Introduction

* Research Engineer, Gas Dynamics

Division, Fellow AIAA.

** Research Engineer, Gas

Dynamics Division.

Copyright, 1996 by the American

Institute of Aeronautics and Astronautics,

Inc. No copyright is asserted in the United

States under Title 17, U.S. Code. The U.S.

Government has a royalty-free license to

exercise all rights under the copyright

claimed herein for Governmental purposes.

All other rights are reserved by the

copyright owner.

Since December 1991, the AGARD Fluid

Dynamics Panel (FDP) has promoted 1 the

activities of Working Group 18 (WG 18) to focus

on a wide range of problems associated with

hypersonic flows. One of the problems selected

for investigation was the effect of rarefaction

and real gas on blunt body wake flows. Interest

in this particular problem arises from the

complex flow features that evolve as the

compressed forebody flow expands into the near

wake. Flow features of importance for flight

application include high-temperature effects

(thermochemical nonequilibrium), rarefaction,

separation, free shear layers, flow
reattachment, and transition and turbulence at

high Reynolds number conditions. Also, of issue

are the conditions under which the near wake

flow can become unsteady. Not only are these

processes of fundamental importance, but also

of practical importance for the design of

planetary probes and aerobrake vehicles.

An objective of the WG 18 activity was to

promote both experimental and computational

studies such that the synergy would produce an

enhanced understanding of the physical

phenomena and a test of the computational

capability to predict/model such phenomena.

The blunt body wake problem was organized

(see Ref. 1) as two subproblems: (1) high

Reynolds number flows where the major

emphasis would be on test conditions conducted

in moderate to high enthalpy impulse facilities

complemented with perfect gas wind tunnel

data, and (2) low Reynolds number test

conditions conducted in low-density wind

tunnels, free jets, and high enthalpy impulse

facilities by testing at either low pressure

conditions or by using small models. The latter

subproblem is the focus of the present review

complemented with high altitude generic flight

conditions for making code-to-code comparisons.

The forebody configuration for all

experimental and flight conditions was a

spherically blunted 70 ° half angle cone with an

outer corner radius as shown in Fig. 1. The

forebody configuration is the same as that for

the Mars Pathfinder Probe scheduled for launch

in December 1996 onboard a Delta II rocket;

Mars arrival is planned for July 1997. The test

models were supported with either an afterbody

sting or small wires. Figure 2 displays the test

conditions in terms of rarefaction as indicated

by lines of constant M_/_/Reoo where the

characteristic dimension is the base diameter.

The larger this parameter, the more rarefied the

flow. As indicated, experiments have been

performed in five different hypersonic facilities:

(1) SR3 is a low density wind tunnel of the

CNRS, Meudon, (2) V2G is a low density wind

tunnel of the DLR, GSttingen, (3) V3G is a free

jet facility at the DLR, GSttingen, (4) HEG is

the world's largest free piston shock tunnel

located at the DLR, GSttingen, and (5) LENS is

the Large Energy National Shock tunnel located

at Calspan, Buffalo. Results obtained with

these five test facilities for the common model

(70 ° blunted cone) configuration are given in

Refs. 2 through 11.

An extensive number of calculations have

been performed for the experimental test

conditions using direct simulation Monte Carlo

(DSMC) and Navier Stokes (NS) solvers

(Refs. 12-23). In addition, calculations have

been reported for generic flight conditions for

both Earth (Refs. 24-26) and Mars (Ref. 27)

entry environments for the same forebody

configuration with a base diameter of 2 meters.

The purpose of this review is to identify and

summarize the extent of the experimental and

computational data base currently available,

identify significant findings, and identify gaps

or possible deficiencies in the current data.

The final item discussed concerns

comparisons between aerothermodynamic data

extracted from the Japanese Reentry

Experiment (OREX)28, 29 and computational

findings 29-33 under rarefied conditions. The

DSMC comparisons with both the WG 18 test

cases and the OREX data provide a broad

spectrum of flow conditions for establishing a

level of credibility for both the computational

and experimental results.

Blunt Body/Wake Closure Experiments and

Computations

A number of fundamental issues exist

concerning such flows: how does the wake

structure change as a function of rarefaction;

what role does thermochemical nonequilibrium

play in the near wake structure; and to what

limits are continuum models realistic as

rarefaction in the wake is progressively

increased. In an effort to address these issues,

as part of the AGARD WG 18 activity, both

experiments and computations have been

performed for the same forebody configuration:

a 70 ° blunted cone with a nose radius equal to

one-half the base radius and the corner or

shoulder radius equal to 5 percent of the base

radius (Fig. 1). Computations have been made

for both wind tunnel and flight conditions for

the same forebody configuration. Results of

experiments performed in each of five

hypersonic test facilities are briefly summarized

along with some of the findings of the

computational studies that have been made for

specific test conditions.
Thenominaltestconditionsforthelow

densitywindtunnelsparticipatingin the

AGARDWG18investigationarelistedin

Table1. Alsoincludedarethetestconditions

fortwoimpulsefacilities. Onetestwasrunin

theLargeEnergyNationalShockTunnel

(LENS)facility10,11at a lowpressure

conditiontoproduceMach15.6nitrogenflow.

Also,tests7wereconductedin theworld's

largestfreepistonshock-tunnelcalledtheHEG

(HighEnthalpyGSttingen)usingsmallmodels

(db= 5 mm) and two of the test conditions in air

are included in Table 1.

These test conditions provide a range of flow

environments that include both nonreacting and

reacting flows. Also, thermal nonequilibrium

issues exist for even the lowest enthalpy tests

(translational-rotational) with more internal

nodes participating for the higher enthalpy

flows. Hence, the conditions include a variety of

flow environments that serve as excellent test

cases to measure the ability of numerical

schemes to calculate such flows where

compression, expansion, and separation are key

features.

SR3 Results

Reference 2 provides the most recent

summary of the experiments conducted by the

CNRS at Meudon, France using the SR3 wind

tunnel. Three test conditions (Table 1) were

considered where the freestream was nitrogen

at a nominal Mach number of 20 and Reynolds

numbers, based on model based diameter,

ranging from 1,420 to 36,265. Three sets of data

were obtained: density flowfields, heating rate

distributions, and aerodynamic forces. Density

flowfield measurements were made with the

electron beam fluorescence technique for the

two more rarefied conditions and for two angles

of incidence: 0 ° and 10 °. Heating rate

distributions along forebody, base, and sting as

well as aerodynamic forces are presented for

angle of incidence between 0° and 30 °.

The test models utilized had the same

external dimensions and were sting supported.

The model base diameter was 5 cm while the

sting had a diameter of 1.25 cm and extended

7.5 cm downstream of the base plane before the

sting cross sectional area began to increase (see

Ref. 1, Chapter 4, Fig. 9). Details concerning

the models, instrumentation, test procedures,

and tabulated and graphical presentations of

results are given in Ref. 2.

A unique aspect of the SR3 tests was the

density measurements which included flowfield

values both with and without the model. The

use of the nonintrusive electron beam

fluorescence technique to provide measurements

of the near wake and forebody density field

provided the first such data for a generic

aeroassist orbital transfer vehicle (AOTV)

configuration.

An extensive number of computations have

been made for the SR3 test conditions since the

test parameters were defined well in advance of

the actual experiments. Test condition 2 (Table

1) was a test case of the 4th European HighVelocity Database Workshop, ESTEC,

Noordwijik, The Netherlands, Nov. 1994. Eight

DSMC solutions were presented at this

workshop and a summary of those results are

given in Ref. 22.

Calculations using both DSMC and NavierStokes solvers were made either prior to the

experiments (Refs. 12, 13, and 21 through 23,

for example) or prior to release of the

experimental data at the ESTEC Workshop 22.

Reference 14 provides an extensive presentation

of information concerning flowfield features and

surface quantities (including tabulated surface

results) resulting from DSMC calculations. Also

reported in Ref. 14 are the results of parametric

studies concerning numerics (cell size and time

step) and physical modeling (rotational collision

number and surface reflection model).

Examples of the calculated and measured

results for the SR3 tests are shown in Figs. 3-5.

Examples of the surface heating distributions at

zero incidence are presented in Fig. 3 for each of

the three test conditions. As evident by the

comparisons, the DSMC solutions 17 show a

better agreement with the measured values

than do the Navier-Stokes 34, 35 solutions (with

surface slip and temperature jump boundary

conditions) along the base plane and sting,

regions where rarefaction effects are most

significant. The agreement is outstanding along

the sting and base plane since the measured

signal along the base for Cases 1 and 2 were so

small that the heating magnitude could only be

characterized as being less than 0.002 and

0.004 W/cm 2 for Cases 1 and 2, respectively

(indicated by symbol with downward pointing

arrows in Fig. 3).

3
Alongtheforebodytheagreementbetween

calculated and measured results are not as good

as expected 17. Along the blunted cone forebody,

the quality of the agreement between

calculation and measurement decreases with

decreasing rarefaction. This is most evident for

Case 3 where the experimental value at

s/R n = 1.56 is 55 percent of the DSMC value.

When the DSMC results along the forebody are

compared with the Navier-Stokes solutions 17,

the agreement is 10 percent or better.

Currently, the discrepancy observed in

measured and computed heat transfer

distributions along the forebody remain

unresolved. Further experiments should be

conducted to resolve this issue.

Figure 4 presents the measured and

calculated heat transfer distributions were the

calculated values are the 3-D solutions of

Pallegoix 23 for incident angles of 0 °, 10 °, and

20 °. Heat transfer measurements were made

only along the windward ray. The agreement

achieved is very good.

A number of computational studies have

presented graphical results of the forebody and

wake flow features demonstrating the influence

of rarefaction on the flow structure. The DSMC

calculations of Refs. 12 and 14 yield a wake

vortex for each of the three test conditions with

the size of the vortex increasing with decreasing

rarefaction. Also, the location of maximum

heating along the sting is downstream of the

location of the free shear layer reattachment as

indicated by the sting shear stress distribution.

As mentioned earlier, non-intrusive electron

beam fluorescence measurements of the

flowfield density were made 2 and Fig. 5

presents as an example a comparison of a

DSMC calculation 17 with measured values.

(See Ref. 20 for even better agreement of

computed and calculated results and Ref. 23 for

comparisons at 10 ° incidence.) The measured

results are presented as the ratio of local

density with model to freestream values without

model since density gradients exist in the

undisturbed flow. The calculated results are

local values ratioed to the freestream value

(Table 1). The overall quantitative features of

the two data sets are similar with the exception

of the expansion of the flow about the outer

corner of the model and the sudden up-turn of

the 0.5 density contour adjacent to the sting.

The calculated density contours in the near

wake show a concentrated expansion from the

rewarded facing portion of the outer corner.

This behavior is consistent with other DSMC

calculations that have been made for Case 2 as

summarized in Ref. 22, both at 0 ° and 10 °

incidence. The measurements show a more

diffuse expansion extending down the base of

the model. Part of this discrepancy may be due

in part to a measurement resolution issue, since

the gradients in density are substantial near the

surface and occur in a rather small volume. As

suggested in Ref. 22, the up-turn of the

measured density contours along the sting are

most likely due to an increase in the cross

sectional area of the sting starting 80.4 mm

downstream of the forebody stagnation point of

the model. The change in the sting

configuration was not included in the numerical

simulations; however, a numerical simulation

accounting for the change in sting configuration,

even if approximate, would be instructive.

The aerodynamic forces, moments, and

center of pressure were also measured for each

flow condition at six angles of incidence

spanning0 ° and 30 ° Tabulated results of these

measurements are presented in Ref. 2. As

reported in Ref. 17, the maximum difference in

the measured and DSMC calculated drag

coefficients for zero incidence was 6 percent.

Reference 23 presents DSMC results for axial,

normal, pitching moment, and center of

pressure results for Case 2 flow conditions at 0 °,

10 °, and 20 ° incidence. The discrepancies with

measured values are 11 percent or less.

V3G Results

An experimental test program 7 has also

been conducted for the 70 ° blunted cone with

the V3G free-jet facility of the DLR GSttingen.

Drag, lift, global heat transfer, and recovery

temperature were measured in a Mach 9

nitrogen free-jet flow. These measurements

were made for various degrees of rarefaction by

including most of the transitional regime

(0.03 < Kn o < 6) for stagnation temperatures of

300 K and 500 K. The wall-to-stagnation

temperature ratio was varied between 0.8 and

1.5. The copper model with a base diameter of

5 mm was suspended with a thermocouple at

angles of attack of a =0 °, 20 °, and 40 °. Details

concerning the experiments, data reduction, data

accuracy, and results are included in Ref. 3.
Resultsfor TO = 300 K, Tw/T o = 1.0 and zero

incidence are presented in Figs. 6(a) and 6(b) for

the drag and overall heat transfer coefficient

( C. = 2Q/p®V 3 A ), respectively. The overall

accuracy of the experiments was estimated 3 to

be ± 8 percent for these conditions. The DSMC

solutions of Refs. 18 and 19 are in very good

agreement with the experimental results.

V2G Results

The vacuum wind tunnel V2G at DLR,

GSttingen has been used extensively to support

the blunt body/wake research. Both qualitative

and quantitative data have been reported in

Refs. 5 through 7 for models with and without

sting. The experiments were conducted in

rarefied nitrogen flow at a nominal Mach

number of 16 (see Table 1). Calibration results

for the 15 ° half angle conical nozzle used to

produce the flow is reported in Ref. 4.

Reference 6 details much of the qualitative

results obtained for 50 and 25 mm base

diameter models with and without (wire

suspension) stings. The data includes high

frequency glow discharge flow visualization

showing the shock shape, oil flow pictures giving

surface streamlines, liquid crystal surface

temperature visualization providing lines of

constant temperature (lines of constant heat

transfer under certain restrictions), and pitot

pressure measurements in the wake. Data

obtained with 5 mm base diameter model is

included in Ref. 7.

Reference 6 and 8 describe the experiments

conducted in V2G utilizing the Patterson probe

to extract molecular flux information within the

wake as a function of location and view

direction. The 5 cm base diameter models

suspended at zero incidence by three tungsten

wires of 0.1 mm diameter were used in this

study. The measurements show that a vortex is

established for the most rarefied case (Case 1)

and increases in length with decreasing

Knudsen number. This is consistent with the

DSMC calculated vortices included in Appendix

A of Ref. 5. Figure 7 presents calculated and

measured results for test Case 2 (Po = 5 bars)

indicating good agreement for the wake

centerline number flux, nu, ratioed to the

freestream flux, (nV)oo. The agreement is good

in terms of both the extent of separation and the

magnitude of the molecular fluxes. A more

extensive presentation of the features of the

wake flow including the non-Maxwellian

behavior of the distribution function for these

test conditions are given in Ref. 8 where DSMC

calculations are compared with the

measurements.

HEG Results

A series of experiments has been conducted

at the DLR GSttingen with a 70 ° blunted cone

having a base diameter of 15.24 cm. These tests

have contributed to the high enthalpy, high

Reynolds number portion of the WG 18 activity.

Reference 7 describes several tests that have

been conducted in air with enthalpies of 10 to

23 MJ/kg at freestream Mach numbers of

approximately 10. For some of these tests, an

array of four small models, 5 mm in diameter,

were tested simultaneously with the larger

model. The small models were located off

centerline of the nozzle axis as was the large

model. Objectives of the small model tests were

to assess different heating rate measurement

techniques as well as to obtain heating rate data

along the forebody. Details concerning the

experiments, models, and data reduction are

given in Refs. 7 and 9. Reference 7 presents the

freestream conditions including the freestream

gas composition as calculated with a onedimensional nonequilibrium nozzle code for nine

tests conditions. Table 1 lists the freestream

conditions for two of these tests [shots 132 (Case

1), and 131 (Case 2)] for which DSMC

calculations have been made. The calculations

were made using a 5-species reacting air gas

model. For the lower enthalpy condition (Case

1), the maximum mole fraction of atomic

nitrogen behind the bow shock was of the order

of 0.01 while the value for Case 2 was of the

order of 0.2. The calculated heating rate

distributions for both cases are presented in

Fig. 8 where the surface is assumed to be

non-catalytic at a cold wall temperature of

300 K. Also shown are the measured results 7 at

the stagnation point and an s/RN location of 0.6.

Good agreement is obtained for both shots

concerning the distributions and absolute

values.

The estimated 7 error of the heat transfer

measurements for the small cone tests is

± 25 percent. The scatter as shown in Ref. 7 is

within ± 20 percent.
LENS Results

As with the HEG experiments, several

series of experiments have been conducted at

Calspan with the large (db = 15.24 cm) blunted

cone models. Tests have been made with the

LENS facility using both nitrogen and air as

test gases. Tests at both 5 and 10 MJ]kg

conditions have been completed. Measurements

consist of surface pressure and heating rates

along the forebody, base, and sting. The focus of

these tests are at continuum conditions;

however, one test has been made at low

pressure conditions where rarefaction effects

should be evident in the wake. The specifics of

this test condition are listed in Table 1. Results

of the experimental measurements for the low

pressure test were presented in Ref. 10 and

DSMC results for this test condition have been

reported in Refs. 10, 11, 15, and 17. Figures 9

and 10 present comparisons of calculated

surface quantities for heating rate and pressure.

The current DSMC results are compared with

predictions obtained by Hash using an implicit,

3-temperature Navier-Stokes solver36-37. The

slip boundary conditions used are those

discussed in Ref. 38. The overall agreement is

shown to be good, particularly along the sting.

Largest differences occur along the base plane.

The implication of the present comparison is

that a Navier-Stokes solver can provide an

adequate prediction of surface quantities for the

current test problem.

Also shown in Figs. 9 and 10 are

comparisons of measured and calculated values.

As evident, there is good agreement between the

calculations and experiments, both in the

separated region and toward the end of the

recompression process, indicating 10 that the

size of the base flow region is well predicted.

The agreement between the experiment and

calculations along the forebody are not as good.

The experimental pressure values are

anomously high (yielding a stagnation pressure

coefficient of Cp = 3.0), and should be

disregarded 39 since the range of the pressure

sensors were not appropriate along the forebody

for this test. With only two heat transfer

measurements along the forebody, it is not

possible to establish the experimental trend for

the heat transfer distribution.

Results for Generic Flight Condition_

The flight test cases consist of four

individual cases to provide code-to-code

comparisons for a 70 ° blunted cone with a 2 m

base diameter. No experimental results are

available for these test cases. The test cases are

for both Earth and Mars entry using both

reacting and nonreacting gas models. The

freestream and surface boundary conditions are

specified in Ref. 1 and listed in Table 2. These

conditions correspond to altitudes of

approximately 85 and 68 km in the Earth and

Mars atmospheres, respectively. Only results

for Earth entry conditions have been reported

(Refs. 24-26); however, Ref. 27 has presented

results for conditions similar to the Mars test

case, the only difference being that the

freestream number density is 0.727 percent of

the test case value and the wake is not included.

Findings from these computational studies

follow.

Reference 24 presented results for both the

reacting and nonreacting air test cases

calculated with the DSMC method and also

reacting air solutions using an axisymmetric

3-temperature, 5-species implicit Navier Stokes

solver 36. The DSMC and Navier-Stokes results

(Ref. 24) were in close agreement for the wake

flow field quantities. Also, the size of the vortex

as measured from the base of the blunted cone

to the wake stagnation point is identical for the

two solutions (Ref. 24). However, there are

some noticeable differences in the chemical

composition within the wake. The most

significant difference between the two solutions

is in the surface heating calculations along the

base plane (Fig. 11). The Navier-Stokes results

are 25 to 200 percent greater than the DSMC

results, while good agreement exists along the

forebody. When the calculation is made for nonreacting air as was done in Ref. 24, the results

compared with the reacting air solution shows:

much higher surface heating rates, particularly

along the base plane (240 percent higher); a

smaller vortex; similar values for the wake

density contours and essentially the same value

for drag.

DSMC solutions along the forebody are also

included in Ref. 26 for this test case, where a

different chemical reaction model is used

compared to that of Ref. 24. Reacting and

nonreacting results are presented showing the

effect of the chemistry on stagnation
temperatureanddensityprofiles,but noton

heatingrates. Thereactingheatingrateresults

aresomewhathigher,particularlyin the

stagnationregion,whencomparedtothat of

Ref.24. Comparisonofthenonreactingheating

resultsforthesetwodifferentsolutionswould

beuseful.

ForMarsentryconditions,Ref.27presents

forebodysolutionswith andwithoutchemical

reactionsfortheCO2andN2freestreamgas

mixture(Table2). Comparisonbetweenthetwo

casesprovideanindicationoftheeffectof

non-equilibriumchemicalreactiononflowfield

quantitiesandsurfaceheating.Thecalculated

effectonsurfaceheatingisverysignificantasis

shownin Fig. 12.Theheatingratesforthe

nonreactinggasareoftheorderofthreetofour

timesthereactinggasresults,showingthat the

chemistryhasa muchlargerimpactonforebody

heatingthanfortheair testcase.

Additionalcalculationsareneededforthe

genericflight test cases,particularlytheMars

testcase,to assessthedifferencesamong

solutionmethodsaswellasthemodelingissues

associatedwith nonequilibriumchemistry.

Solutionswith andwithoutchemicalreactions

helpstoisolatedifferencesthat mightexist

amongsolutions.Acriticaldiscriminatoris the

surfaceheating.

Comvarison with Fliuht

A major benefit of combined

experimental/computational studies is often the

sanity check one provides the other. A goal of

the computational effort is to demonstrate

capability for various test cases to enhance the

reliability of calculations for actual flight

conditions. This section will comment on recent

applications of one of the DSMC codes 40 that

has been applied to several of the previously

discussed test cases to a flight experiment. This

was the Japanese Orbital Reentry Experiment

(OREX) vehicle which was a 50 ° half angle,

spherically blunted cone with a base diameter of

3.4 m, a nose radius of 1.35 m, and a shoulder

corner radius of 0.1 m.

OREX was flown in February of 1994 and

initial results from this experiment are

discussed in Refs. 28 through 31. The authors

are not aware of any base heating or wake flow

measurements made for the OREX.

Results of DSMC calculations that span the

transitional flow regime (200 to 80 km) are

presented in Refs. 32 and 33 where comparisons

are made with flight inferred data and

continuum calculations. Comparisons of DSMC

results with OREX results were made for

acceleration, surface pressure, and stagnationpoint heating rates. In general, the

comparisons show good agreement. For

acceleration, the agreement is good (Fig. 13).

The surface pressure data are in qualitative

agreement (see Ref. 33). Calculated and

measured surface pressure values are in good

quantitative agreement for the lower altitudes

but depart with increasing altitudes as they

should due to the high degree of nonequilibrium

that exists at and within the inlet system used

for the "measured pressures". This is a

situation where the inlet measured pressure can

be substantially less than the surface pressure.

Agreement for calculated and measured

stagnation-point heating rates is fair. Figure 14

presents the flight inferred stagnation-point

heating rate results as a function of time from

launch of OREX. Continuum results obtained

with viscous shock layer (VSL)39 and NavierStokes 31 solutions are shown for altitudes of

105 km to 48.4 km. The VSL results were for a

no-slip and a non-catalytic surface. The DSMC

results shown for 105 to 79.9 km included the

finite catalytic wall boundary conditions used in

the VSL calculations; however, the finite

catalytic and non-catalytic boundary conditions

yield essentially the same results over this

altitude range (see Ref. 32). Inclusion of slip

boundary conditions at the higher altitudes

yield substantially lower heating rates for a

continuum solution as is discussed in Ref. 32.

The heating rates are inferred from the

temperature measurements made on the back

surface of a carbon-carbon material. As

additional data are reported, opportunities will

exist for comparing calculated and measured

results at various locations along the forebody.

The overall good correspondence of flight and

calculated results is encouraging.

Concluding Remarks

A review of recent experimental and

computational studies focused on blunt body

forebody and wake flows is presented where the

emphasis is on rarefied flows. An objective of

this AGARD Fluid Dynamics Working Group 18

problem was to determine how the near wake
structureis influencedbyrarefactionand real

gas effects. The approach to achieve this

objective was to select a generic blunt body

configuration (70 ° spherically blunted cone) and

encourage experimental contributions from the

AGARD community. Once the experimental

conditions were defined or conducted,

computational contributions were solicited for

the various experiments along with two generic

flight conditions for entry into the atmosphere of

Earth and Mars.

A key aspect of the success of this activity

has been the experimental contributions from

five hypersonic facilities that have fostered a

significant number of computational

contributions. The synergy of the

computational/experimental activities has

produced a significant data base that can serve

as a valuable aid for aerobraking mission

designs. Some of the key contributions or

findings of this activity are: (1) first

experimental measurements of density field and

number flux for a generic Aeroassist Space

Transfer Vehicle configuration; (2) data base

involving both quantitative and qualitative

information that spans a wide range of

conditions (nonreacting to reacting flows) in the

transitional regime; (3) demonstrated capability

of different DSMC codes to simulate selected

test cases (SR3, Condition 2); (4) the

experimental (V2G, Patterson probe) and

computational findings which show that the size

of the wake vortex increases with decreasing

Knudsen number; (5) the maximum heating

along a sting/afterbody for zero incidence was of

the order of five percent of the forebody

stagnation value; (6) the location of wake

reattachment and maximum sting heating rate

are not coincident, but the separation between

the two locations decrease with decreasing

rarefaction; (7) inclusion of slip boundary

conditions in the Navier-Stokes solvers provided

improved agreement with experimental and

DSMC results; (8) results from the NavierStokes solutions suggest that the overall

Knudsen number should be less than about

0.001 before good agreement is achieved

between experiment or DSMC for the near wake

surface and flow features, and that the NavierStokes solutions agree with the DSMC results

for quite large overall Knudsen numbers along

the forebody; and (9) for the generic flight test

cases which involve substantial dissociation, the

calculated forebody and afterbody heating for

the reacting solutions are substantially less

than for the corresponding nonreacting cases.

Readily evident from the above findings and

the comparisons with the OREX flight

measurements is a demonstrated capability of

the DSMC method to calculate complex flow

features including surface heating to good

accuracy when compared to experimental

measurements, both ground based and flight.

References

1Anon., "Hypersonic Experimental and

Computational Capabilities: Improvement and

Validation," AGARD AR-319, vol. 1, May 1996.

2Allegre, Jean and Bisch, Daniele, "Blunted

Cone at Rarefied Hypersonic Conditions -

Experimental Density Flow fields, Heating

Rates, and Aerodynamic Forces," CNRS Report

RC 95-2, September 1995.

3Legge, Hubert, "Heat Transfer and Forces

on a Blunted 70 Deg. Haft Angle Cone Measured

in Hypersonic Free Jet Flow," DLR Report IB

222-93 A 33, November 1993.

4Legge, H.; von Roden, G.; Klotzbach, A.;

and Rammenzwieg, D., "Calibration Data of

V2G with a Conical Ma - 15 Nozzle," DLR

IB 223-94A 11, 1994.

5Legge, Hubert, "Patterson Probe

Measurements in the Wake of a 70 Deg. Half

Angle Cone in Hypersonic Rarefied Flow," DLR

Report-IB 223-94 A 15, December 1994.

6Legge, Hubert, "Flow Visualization and

Pitot Probe Measurements in Hypersonic

Rarefied Flow Around a 70 Deg. Half Angle

Cone," DLR Report IB 223-95 A 01, February

1995.

7Legge, H., "Experiments on a 70 Degree

Blunted Cone in Rarefied Hypersonic Wind

Tunnel Flow," AIAA Paper 95-2140, June 1995.

8Danckert, A. and Legge, H., "Wake

Structure of a 70 Degree Blunted Cone, DSMC

Results, and Patterson Probe Measurements,"

AIAA Paper 95-2141, June 1995.
9Legge,H.;Rammenzweig, D.;and

Klotzbach,A.,"HeatTransferMeasurementson

a Blunted70DegHalfAngleConein High

EnthalpySmallReynoldsNumberFlow,"DLR

ReportIB 223-95A22,March1996.

10Holden,M.;Kolly,J.; andChadwick,K.,

"Calibration,Validation,andEvaluation

Studiesin theLENSFacility,"AIAAPaper

95-0291,1995.

11Holden,M.S.;Chadwick,K.M.;Gallis,

M.A.;andHarvey,J. K.,"ComparisonBetween

ShockTunnelMeasurementsona Planetary

ProbeConfigurationandDSMCPredictions,"

20thISSW,CalTech,July 1995.

12Moss,J. N.;Mitcheltree,R.A.;Dogra,V.

K.;andWilmoth,R.G.,"DirectSimulation

MonteCarloandNavier-StokesSimulationsof

Blunt BodyWakeFlows,"AIAA Journal, vol. 32,

no. 7, 1994, pp. 1399-1406.

13Wilmoth, R. G.; Mitcheltree, R. A.; Moss,

J. N.; and Dogra, V. K., "Zonally Decoupled

Direct Simulation Monte Carlo Solutions of

Hypersonic Blunt-Body Wake Flows," Journal of

Spacecraft and Rockets, vol. 31, no. 6,

Nov. - Dec. 1994, pp. 971-979.

14Moss, J. N.; Dogra, V. K.; and Wilmoth, R.

G., "DSMC Simulations of Mach 20 Nitrogen

Flows about a 70 ° Blunted Cone and its Wake,"

NASA TM-107762, August 1993.

15Moss, J. N.; Price, J. M.; and Dogra, V. K.,

"DSMC Calcualtions for a 70 ° Blunted Cone at

3.2 km/s in Nitrogen," NASA

TM-109181, January 1995.

16Dogra, V. K.; Moss, J. N.; Taylor, J. C.;

Hash, D. B.; and Hassan, H. A., "Rarefaction

Effects on Blunt-Body Wake Structure,"

R_rCfiCd Gas Dynamics 19, edited by J. Harvey

and G. Lord, Oxford University Press, 1995,

pp. 1154-1160.

17Moss, J. N.; Dogra, V. K.; Price, J. M.; and

Hash, D. B., "Comparison of DSMC and

Experimental Results for Hypersonic External

Flows," AIAA Paper 95-2028.

18Gallis, M. A. and Harvey, J. K.,

"Comparison of the Maximum Entropy DSMC

Code with Flow field Measurements," AIAA

Paper 95-0413, 1995.

19Gallis, M. A. and Harvey, J. K.,

"Validation of DSMC Computations for the

Flowfield Around a 70 o Blunted Cone," Rarefied

Gas Dynamics 19, edited by J. Harvey and G.

Lord, Oxford University Press, 1995, pp. 1284-

1290.

20Marriott, R. M. and Bartel, T. J.,

"Comparison of DSMC Flow Field Predictions

using Different Models for Energy Exchange

and Chemical Reaction Probability," Rarefied

Gas Dynamics 19, edited by J. Harvey and

G. Lord, Oxford University Press, 1995,

pp. 413-419.

21Gilmore, Martin R., "Rarefied Flow Over

a Blunt Body," DRA/DWS/WX7frR 95 189,

February 1995.

22Coron, F. and Harvey, J. K., "Synopsis for

Test Case 6 - Rarefied 70 ° Spherically Blunted

Cone,' 4th European High-Velocity Database

Workshop, ESTEC, Noordwijk, The

Netherlands, Nov. 1994.

23pallegoix, J. F., "Workshop ESTEC--Test

Case No. 6--Rarefied Spherically Blunted Cone,"

Paper presented at 4th European High-Velocity

Database Workshop, ESTEC, Noordwijk, The

Netherlands, November 1994.

24Dogra, V. K.; Moss, J. N.; Wilmoth, R. G.;

Taylor, J. C.; and Hassan, H. A., "Effects of

Chemistry on Blunt-Body Wake Structure,"

AIAA Journal, vol. 33, no. 3, 1995, pp. 463-469.

9
25Dogra,V.K.;Moss,J. N.;Wilmoth,R. G.;

Taylor,J. C.;andHassan,H.A.,"BluntBody

RarefiedWakesforEarthEntry,"Journal of

ThermoDhvsics and Heat Transfer, vol. 9, no. 3,

July - Sept., 1995, pp. 464-470.

26Gallis, M. A. and Harvey, J. IL,

"Implementation of a Maximum Entropy

Method in Monte Carlo Direct Simulations,"

AIAA Paper 95-2094.

27Gallis, M. A. and Harvey, J. K., "Analysis

of Non-Equilibrium in Mars Atmosphere Entry

Flows," AIAA Paper 95-2095.

28NAL/NASDA Joint Research Report.

OREX, March 1995 (in Japanese).

29Inouye, Y., "OREX Flight- Quick Report

and Lessons Learned," Invited paper 4, 2nd

European Symposium on Aerothermodynamics

of Space Vehicles, ESTEC, Nov. 1994.

30yamamoto, Y. and Yoshioka, M., "CFD

and FEM Coupling Analysis of OREX

Aerothermodynamic Flight Data," AIAA

Paper 95-2087, June 1995.

31yamamoto, Y., Private Communication,

Aerodynamics Division, National Aerospace

Lab., Tokyo-182, Japan, Dec. 1995.

32Gupta, R. N., Moss, J. N., and Price, J.

M., "Assessment of Thermochemical

Nonequilibrium and Slip Effects for Orbital

Reentry Experiment (OREX)," AIAA

Paper 96-1859, June 1996.

33Moss, J. N. and Price, J. M., "DSMC

Calculations of OREX Entry," 20th

International Symposium on Rarefied Gas

Dynamics, Beijing, China, August 1996.

34Gnoffo, P. A., "An Upwind-Biased, PointImplicit Relaxation Algorithm for Viscous

Compressible Perfect-Gas Flows," NASA

TP-2953, February 1990.

35Gnoffo, P. A.; Gupta, R. N.; and Shinn, J.

L., "Conservation Equations and Physical

Models for Hypersonic Air Flows in Thermal

and Chemical Nonequilibrium," NASA TP-2867,

Feb. 1989.

36Olynick, D. R. and Hassan, H. A., "New

Two-Temperature Dissociation Model for

Reacting Flows," Journal of ThermoDhvsics and

Heat Transfer, vol. 7, no. 4, Oct. - Dec. 1993,

pp. 687-696.

37Olynick, D. R.; Taylor, J. C.; and Hassan,

H. A., "Comparisons Between DSMC and the

Navier-Stokes Equations for Reentry Flows,"

AIAA Paper 93-2810, July 1993.

38Gupta, R. N.; Scott, C. D.; and Moss, J.

N., "Slip-Boundary Equations for

Multicomponent Nonequilibrium Airflow,"

NASA TP-2452,

Nov. 1985.

39Holden, M. S., Personal Communication,

May 1995, Calspan Corporation, Buffalo,

New York.

40Bird, G. A., Molecular Gas Dynamics and

the Direct Simulation of Gas F|QWS, Clarendon

Press, Oxford, 1994.

41Gupta, R. N., "Viscous Shock-Layer Study

of Thermochemical Nonequilibrium," Journal of

ThermoDhvsics and Heat Transfer, vol. 10, no.

2, 1996, pp. 257-266.

10
Table1. ExperimentalTestConditions

Test TO Po Moo Re_/cmp_ x 105Voo T_ _,oo Tw

Case (K) (bars) (kg/m3) (m/s) (K) (mm) (K)

Gas

(a) SR3 Wind Tunnel, CNRS Meudon; d b = 5 cm

1 1100 3.5 20.2 285 1.73 1502 13.3 1.59 300 N2

2 1100 10.0 20.0 838 5.19 1502 13.6 0.54 300 N2

3 1300 120.0 20.5 7277 46.65 1633 15.3 0.06 300 N2

(b) V2G Wind Tunnel, DLR GSttingen; db = 5, 2.5, and 0.5 cm

1 575 2 15.6 719 6.70 1082 11.6 0.39 490 N2

2 675 5 16.5 1233 11.02 1173 12.2 0.25 565 N2

3 775 10 16.8 1935 17.25 1257 13.4 0.16 635 N2

(c) V3G Wind Tunnel, DLR GSttingen, db = 0.5 cm

1 295 0.163 9.0 859 14.22 759 17.2 0.16 variable N2

2 295 0.0549 9.0 286 4.74 759 17.2 0.48 variable N2

3 295 0.0163 9.0 86 1.42 759 17.2 1.60 variable N2

4 295 0.0054 9.0 29 0.47 759 17.2 4.80 variable N2

(d) HEG, DLR GSttingen; db = 0.5 cm

1 6713 576.0 10.1 7043 408.5 4539 489.9 0.017 300 Air

2 9244 385.0 9.5 2498 156.4 6075 856.4 0.044 300 Air

(e) LENS, Calspan Buffalo; db = 15.24 cm

1 4351 74.1 15.6 578 13.06 3246 103.7 0.35 294 N2

Table 2. Flight Test Conditions*

Quantity Earth Entry Mars Entry

Number density, m "3 1.654 x 1020 1.654 x 1020

Temperature, K 180.65 141

Velocity 7.0 7.0

Mole fraction N 2 0.7628 0.05

Mole fraction O 2 0.2372 .....

Mole fraction CO2 ..... 0.95

*70 ° blunted cone with base diameter of 2 m and a noncatalytic surface with a wall

temperature of 1000 K.

11
Rn/R b = 0.50, Rc/R b = 0.05, Rs/R b = 0.25, RffR b = 0.083

/ _\ Location

._ Rc _ 1

5

..... --' i 7

s///-- .o

i zN

1R_ _'_ 1 _R S

7

_n

0.349

2.043

2.166

2.323

3.557

3.817

4.223

Fig. 1 70 ° spherically blunted cone configuration•

101 .

-- DSMC

..... N S. (LAURA)with slip

100q _._-_ 2 O Exp, SR3

i

r--3 O

q 10-1 __..

W/cm 2 _ . -

10 -2

lO3 .......... 7-211 ii _ ,

0 2 4 6 8 10 12 14

s/R n

(b) Case 2.

Fig. 3 Continued•

200

leoi

150

140

120

8O

60

40

20

/BflSR3

I I

M_/_/Re_, d = 0.1 tJ

//

i

/ 0.2

J //

s • LENS ,,"

i /1

_ /t V2G ,/

-- i III B "J•

,," HEGss/ r_ 0.4

_ C'" - -- -- - "1.0

5 10 15 20 25 30

M_

Fig. 2 Low-density test conditions in terms of the

rarefaction parameter Moo/R_oo, d'

101

100

q, 10 "1

W/cm 2

10-2 '

' OCI_#r 2 -- DSMC -- - -- N S. (Hash)with slip

O Exp, SR3 ..... N.S (LAURA)with Ilip

I

....l_____............... __.....

0 2 4 6 8 10 12 14

S,,'Rn

(c) Case 3.

Fig. 3 Concluded.

101

100'

10 -1

q, 10 -2

Wtcm 2

10-3

10-4

10-5

0

-- DSMC

2 ..... NS (LAURA)w_h _lp

3 _ Exp, SR3

2 4

.... i .... i .... i .... i .... i .... i .... i

2 4 6 8 10 12 14

_R n

(a) Case 1.

Fig. 3 Comparison of SR3 experimental 2 and computed 17

heating rate results (d b = 5.0 cm ).

C H

l°°L 

10 "1 Iu't:7_O _

10"2_

10 "3 I

ii i!

0 Experimental

CNRS, SR3

-- DSMC

O

I I I I t

2 4 6 8 10

S/FI n

(a) Incidence = 0°.

Fig. 4 Comparison of SR3 experimental 2 and computed 23

heating rate distributions for Case 2

12
C H

10 0

10 "1

10 "2

10-3 --

10-4 _

10-51

0

O Experimental

CNRS, SR3

-- DSMC, windward

..... DSMC, leeward

2 4 6 8

SIR n

(b) Incidence = lO °.

Fig 4 Continued.

J

10

3,0

25

20

C D 1.5

1.0

(15

13.0

10" 2

o

o

O Experimental

[] DSMC

1_ 1 100 101

Kn 0

(a) Drag coefficient.

Fig. 6 Comparison of experimental 3 and DSMC 18-19

results for V3G tests with model at zero incidence.

C H

100-

i

10 "1 _

J

i

i

10"2

10 .3 '

10 -4 _

O Experimental

CNRS, SR3

-- DSMC, windward

..... OSMC, leeward

10 "5

0

; J I I

4 6 8 10

SIR n

(c) Incidence = 20 °.

Fig 4 Concluded.

0.20

0.15

0.10

C H 0.05

0.00

-0.05

-0.10

10 -2

o

©

E3

o

© Experimental

[] OSMC

J ........ J

10 -1 100

Kn0

(b) Overall heat transfer coefficient.

Fig. 6 Concluded.

I

101

100

80

60

40

y, mm 20

0

-20

-40

-40 -20

p/p_ 1 1_

I_I_\r 032\3\_ -°e

__"o S. Exp., SR3

0 20 40 60 80 100 120

x, mm

Fig. 5 Comparison of measured 2 and calculated 17 density

for SR3 test Case 2.

0.20

0.15

0.10

nu

(nv)®0.05

0.00

.0.1 00:0 ,................. 015 110 1.5 2.0

x/d b

f

-- DSMC

O Exp.,V2G

i .... i

2.5 3.0

Fig. 7 Measured 2 and calculated 17 number flux along

centerline of near wake for V2G test Case 2.

13
4000<_, HEG

• "- test Case V_, km/s Exp. DSMC

_,_ ", 1 4.55 C)

300u_ "_ • 2 608 O ....

(P\

f\ $-- ....

q' 2000

1000 O _,,

0 I .... i .... i i I J

0.0 0.5 1.0 1.5 2.0 2.5

s/R n

Fig. 8 Measured 7-9 and calculated 17 heating rates for two

HEG tests using 5 mm base diameter models.

lO2

101

q, 100

W/cm 2

,o-t .... <j o,oo .,

_,_ ....... DSMC Nonreacting Air

/----4 ..... N.S., Slip, Reacting Air

, , I , , , , I I , I

10"2 1 3 4 5

eft:l n

Fig. I 1 Calculated 24 heating rate distributions for Earth

entry (Alt = 85 km, Voo = 7 km/s, db = 2.0 m).

1°2F

2 4

101 o

q' = t

W/cm 2 -3 f _)

10 o

-- DSMC

10"1 = o Exp., LENS

........ N S. (Hash) with slip i

10 "2_,, , , = .... _ .... ' .... = , ,,, J , , , , I , , ,

2 4 6 8 10 12

s/R n

Fig. 9 Measured 10 and calculated 15 heating rate distributions

for LENS test Case 1.

103

lO2

q,

W/cm 2

101

-- DSMC, Reacting CO2/N 2

....... DSMC, Nonreacting CO2/N 2

.,

100 I I I I I )

0 0.4 0.8 1.2 1.6 2 2.8

s/R n

Fig. ! 2 Calculated 27 heating rate distributions for Mars

entr7 (Alt = 68 km, V_ = 7.0 kin/s, db = 2.0 m).

Cp

1°1I •

100 -2

...................Rn 61 ______.

10"1

-3 5 _.A _'_

10 -2 y eJ_ - DSMC

Experiment, LENS

--4 ........ N S. (Hash) with s lip

I0-3 .... , .... _ .... _ .... , .... , .... _ .... ,

0 2 4 6 8 10 12 14

s/R n

Fig. 10 Measured 10 and calculated 15 pressure distributions

for LENS test Case 1.

a,g

10 0

10 -1

10-2

10-3

10 -4

10 °5

75

DSMC

i i I I i

100 125 150 175 200

AIt, km

Fig. 13 Comparison of calculated 33 and measured 29

OREX axial acceleration.

14
q,

W/cm 2

5O

-- Inferred from flight

"" -- * - VSL calculations

_,' o '_ O Navier-stokes calculations

20 I • DSMC calculations

10

2 I I

7300 7350 7400 7450 7500 7550

Time, s

Fig 14. Comparison of flight inferred 30 stagnation-point

heating rates with calculations using

VSL32 NS 31 and DSMC 32

15