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A99933894

AIAA 99-3493

Computation of HYFLEX Aerodynamic Heating at HEK Shock-Twine1 Test Conditions

Toru Shimada Nissan Motor Co., Ltd. Gunma, Japan

Yukimitsu Yamamoto, Naoki Hirose, Shuichi Ueda National Aerospace Laboratory Tokyo; Japan

Katsuhiro Itoh National Aerospace Laboratory. Miyagi, Japan

33rd. Thermophysics Conference ” 28 June - 1 July, 1999 / Nbrfolk, VA : I.

For pei-mission,.Io copy or to republish, contact the American Institute of Aeronautics and i\stronautics; 1801 Alexander Bell Drive, Suite 500, Reston, VA, 201914344.

(c)l999 American Institute of Aeronautics & Astronautics

AIAA-99-3493

COMPUTATION OF HYFLEX AERODYNAMIC HEATING AT HEK SHOCK-TUNNEL TEST CONDITIONS

Toru Shimada’ Nissan Motor Co., Ltd.

Gunma, Japan

Yukimitsu Yamamoto’ National Aerospace Laboratory

Tokyo, Japan

Naoki Hirose’ National Aerospace Laboratory

Tokyo, Japan

Shuichi Ueda”

National Aerospace Laboratory Tokyo, Japan

Katsuhiro Itoh” National Aerospace Laboratory

Miyagi, Japan

Computations of three-dimensional thermo-chemical non-equilibrium flows around a scale model of the HYFLEX re-entry vehicle have been conducted. Major concern of the simulation is to verify the simulation code by comparison with the measurement data of the HEK shock-tunnel experiments. A modified Equilibrium Flux Method is devised to evaluate the convective terms in an aicurate and stable manner. A non-dimensional parameter is deduced from dimensional analysis to correlate the stagnation-point heating rate with parameters such as the total enthalpy and the binary-scaling parameter. Four cases of free-stream conditions are computed. Computed and measured results are compared on the

’ Senior Engineer, Aerospace Div., Senior Member, AIAA. ’ Group Leader, Fluid Science Research Center, Member AIAA * Senior Research Scientist, Computational Science Div., Associate Fellow, AIAA p Senior Researcher, Space Project and Research Center 1 Head of High Enthalpy Shock Tunnel Laboratory, Kakuda Research Center

Copyright 0 1999 American Institute of Aeronautics and

Astronautics, Inc. All rights reserved.

stagnation-point heating and the heating rate distribution. Computed normalized heat flux distributions do not vary much among the test cases considered. As for stagnation-point heat flux, while computed results show similar tendency to Detra- Kemp-Riddell correlation, they show rather large discrepancy with the experimental data.. Both experimental and computational aspects of reasons for the discrepancy have been discussed.

One of major topics in developing space transportation systems is the aerothermodynamics of re-entry vehicles. Although research in this field has more than four decades of history, quite a few points remain to be investigated. These investigations have been conducted utilizing facilities such as hypersonic wind tunnels, shock tunnels, and so on. Because of high-speed and high-enthalpy nature of re-entry flows, experimental facilities tend to be costly and limited in the availability. The capability of reproducing circumstances during re-entry is also limited for the ground-based facilities. Flight experiments, therefore, are veti important, though the availability of them is further limited.

Numerical simulations of computational fluid dynamics (CFD) have shown remarkable progress and are expected to supplement the limitation of experimental approaches. For the purpose to be

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fulfilled, a computer code and a mathematical model should be verified by comparison with experimental data.

The Hypersonic Flight Experiment (HYFLEX) project ’ , a joint project of the National Aerospace Laboratory (NAL) and the National Space Development Agency of Japan (NASDA), was successfully performed on Feb. 12, I996 as a re-entry experiment prior to the planned HOPE, unmanned orbiting plane. Figure 1 shows HYFLEX vehicle configuration. The aerodynamic heating to the region of C/C hot structure and ceramic tile was measured during the flight.

Recently, NAL has constructed a free-piston driven shock tunnel (HIEST)’ at the Kakuda research center. Major objective of HIEST is to research the hypervelocity flow regime where significant air dissociation occurs. The total length of the HIEST is about 80m which is the world largest. The total enthalpy and the total pressure are 25MJ/kg and 15OMpa at the maximum, respectively. The testing duration is 2.0msec or more. Generally speaking, measurement of severe aerodynamic heating is expected to have some difficulties due to short testing duration and thermo-chemically severe environment. The medium size free-piston shock tunnel (HEK), therefore, was built as the pilot facility for the HlEST to verify the technologies that would be utilized in HlEST and to develop reliable techniques of the heat flux measurement. The configuration of HEK shock tunnel is shown in Figure 2.

In 1997, Ueda et al.’ conducted experimental investigation on aerodynamic heating of HYFLEX model in HEK high-enthalpy shock tunnel. A 6% scale model of 240mm in body length was used and twenty-six heat flux sensors were installed on the nose and on the windward side of the model. The test conditions were selected along the HYFLEX flight trajectory and experimental results have been compared with the flight data. In the report, effects of enthalpy and binary scaling parameter on the heat flux are discussed along with possibility of normalization using a stagnation-point heat flux correlation formula.

Studies using computational fluid dynamics (CFD) have been conducted to investigate the flowfield and aerodynamic heating around HYFLEX. The High Enthalpy Flow Workshop 4-6 held at NAL was where such computational studies were presented and synthesized. In the workshop, numerical solutions of three-dimensional therrno-chemical non-equilibrium flow, obtained by several independent CFD codes, were presented and synthesis on the results was given’. The free-stream condition, common to each solution, was picked up from the flight data at the altitude of 48km and the Mach number of I I. The boundary conditions corresponding to the in-flight, hot-wall situation were considered. The specitied

2

Figure

.._ .-.. -.-.a .- ..__~ -.

z~ji?q-l

: I : Configuration of HYFLEX

2°C P.*.r”oir l”CII,. N.., OIlcaP Ta...

I., *, n 5 :0.

Figure 2: HEK Shock Tunnel

surface temperature distribution was picked up from results of another numerical analysis in which flow field was solved coupled with the thermal response of the structure. 8

Recently, the authors have conducted another set of numerical analyses to evaluate the aerodynamic heating of the cold-wall HYFLEX model at the HEK test conditions. In this paper, details of the simulation, the computational results, and the comparison with the experimental data are described. For the purpose of comparison, correlation of the stagnation-point heating is discussed as well.

The facility, which consists of the driver section (an air reservoir and a compression tube), the shock tube, and the nozzle/test section, operates in the following sequence. Firstly, the high-pressure air in the reservoir pushes a piston to compress and heat up the driver gas (pure Helium or a Helium-Argon mixture) in the compression tube. The primary diaphragm at the downstream end of the tube ruptures when the designed pressure is reached. Then, the shock wave formed propagates down and reflects at the shock- tube end. Finally, the gas being highly compressed and heated up behind the reflected shock ‘wave expands through the nozzle to serve the free stream in the test section. The testing duration is l-2 msec depending on operational conditions. . . HYFI.EX Test Condltrons A 6% scale model, body length of 240mm, was used in the experiments. Heat flux sensors, co-axial thermocouples, were installed on the nose and the

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-. Entbby (MJW . .

Figure 3: Test conditions of HYFLEX experiments at HEK shock tunnel. Test condition numbers with the nozzle exit diameter are indicated.

Table I : Test Conditions Case # 284 288 294 296

Condition # 12 18 19 15 Reservoir

P,, WW 23.5 24.5 37.1 390

H,, (MJkg) 10.9 7.9 8.7 12.1

Diameter. (mm) 10 10 18 18 P, &Pa) 0.33 0.30 2.44 2.96

P, (kg/m’) 2.3e-3 2.6e-3 I I .3e-3 9.3e-3

u, (m/S) 4272 3724 3859 4421

M, 8.8 9.3 7.1 6.8

H: (MJkg) 9.6 7.3 8.2 10.9

eyolds No. 1.4 2.1 6.4 4.7

Table 2: Mass Fraction of Free Stream

Case N2 02 N 0 NO _.._.......-.-..... ._.. . . . . . ..” ,_.........._.............,...,.,,.,..,.............. .._,_,..,,_.......... 284 0.7324 0.1472 0 0.0497 0.0707 288 0.7283 0.182 0 0.0138 0.0759 294 0.7324 0.1866 0 0.0 I 17 0.0693 296 0.7346 0.1578 0 0.0424 0.0652

windward wall. The locations of the sensors were chosen so that comparison with flight data was possible. The heat flux was calculated from measured surface temperature by the method of Schultz and Jones9,‘0

As shown in Figure 3, test conditions were determined by selecting typical pairs of values of the total enthalpy and the binary scaling parameter sampled along the HYFLEX flight path and HOPE-X planed path. Four typical cases are picked up for numerical simulation and their conditions are

Figure 4: Computational Grid

summarized in Table I. Values of flow variables

calculated by NENZF,” a at the nozzle exit are quasi-one-dimensional,

one-temperature, chemically non-equilibrium flow

code. For reference, the total enthalpy HI is given

assuming specific heat ratio y is I .4.

. . Free Stream and Boundary Condlw There is redundancy of the flow definition. In simulation, the density, the static pressure, and the Mach number are specified at the free-stream boundary using the values of the nozzle exit plane. The angle of attack is 50 deg. for all cases. The mass fractions of the chemical species are given in Table 2. Currently, the mass fraction of Argon is neglected, though its amount might be of the same order of atomic oxygen.

The temperature of the HYFLEX surface is assumed 300K and isothermal condition is used on the surface. The wall is assumed fully catalytic. A reflection boundary condition is enforced along the symmetry plane.

G ‘d Systa Computational grid syL:em consists of 40, 60, and 89 points in 4, q, and s directions, respectively, as

shown in Figure 4. The minimum spacing of the grid at the surface of the body is about 5 ,D m. The cell-

Reynolds number for the length is shown in Table I.

With minor modification, the basic mathematical model is similar to that presented in Ref.12. The governing ,equations consist of mass conservation

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equations of eleven chemical species (N, 0, N,, O,, NO, N’, O’, NZ+, 02+, NO’, and e-), three momentum equations, and two energy conservation equations. A two-temperature thermal model is employed, where one equation for the total energy and the other for vibrational-electric energy are solved. The translational and rotational internal energy modes are assumed fully excited. The enthalpy at the thermal equilibrium is evaluated from JANAF tables. The Chemical kinetic model employed is Park-1987 model 13. The energy relaxation between vibrational and translational mode is modeled by Landau-Teller equation and the relaxation time is evaluated by Milikan-White’s correlation with Park’s collision limiting modification. The electric-translational energy relaxation is described by Appleton-Bray model dealing with relaxation times of both Coulomb collisions between ions and electrons and elastic collisions between neutral species and electrons. Transport properties of the high-temperature gas mixture are evaluated using Yos’ formula which has been extended to the two-temperature model. The effective diffusion coefficients are evaluated by the expression of Curtiss and Hirschfelder.

No attempt is made here to incorporate a turbulence model.

1Yumed.c.d Method The governing equations are discretized by a cell- centered finite volume method. At each cell boundary, inviscid and viscous fluxes are evaluated. The source terms are evaluated at the cell center. The temporal evolution of the cell-averaged conservative variables at each cell is calculated until a steady-state solution is obtained. An explicit time integration is carried out with an upwind-residual-averaging method and a point-implicit method for kinetic source terms. The time-step size at each step is determined as 50%-80% amount of the positivity-preservation limit. The viscous terms are evaluated in a central-difference fashion.

The inviscid numerical flux scheme used, here is called “AUSM-DV for Equilibrium Flux” (AUSM- DV-EF).“’ The AUSM-DV-EF scheme is a modified Pullin’s “Equilibrium Flux Method” (EFM) ” which is a kinetic-based flux vector splitting method. The left- going or right-going numerical flux of EFM is determined by the equilibrium-gas fluxes of molecular quantities such as the mass, the momentum, and the energy flowing though a cell interface in the negative or positive direction.

For simplicity, let us describe a one-dimensional EFM numerical flux at a cell interface as;

A,2 = f* (Q,. k J" (Q,t ) (1)

EF =lferf

r I

l!!

E, =;“f exp[; ’ Y u2 -- 2 c2

)

The function erf() is the error function.

(2)

(3)

(4)

Then, let us consider a stationary contact discontinuity where pL f pR , pL = pR = p, and

u,, = 24)’ = 0. The subscripts L and R denote,

respectively, the values of the left and the right sides of the interface. The numerical flux across the contact discontinuity is calculated by Eqs.( l-4) as

w[

\

0 k. - VCR fi/2 = P + 2 0 (5)

0 Y+l

2Ycv - 1) (5 --CR>

/

Apparently, in this case, the rigorous flux vector is

f =(O,p,O)’ Th e equation (5) shows that the EFM

numerical flux brings dissipation into solution at a contact discontinuity because, in general, cL # cR .

This numerical dissipation is known to generate erroneous profile of boundary layer when the scheme is used in viscous-flow computations. A simple remedy for this defect is to introduce a common speed of sound in order to enforce the flux offset. This approach is similar to that of AUSM-DV scheme (Advection upstream Splitting Method, mixture of flux-Difference biased scheme and flux- Yector biased scheme). I6 For example, the common speed of sound can be determined by

c,, = max(c, , cx ) (6)

The Figure 5 shows. the solutions of self-similar viscous hypersonic flow around a 20 degree-angle cone obtained by. EFM, AUSM-DV-EF, and Roe’s schemes, respectively. Comparison shows that the current remedy works well for securing correct adiabatic-wall temperature as well as correct temperature profile in viscous region.

The V-type scheme for AUSM-DV-EF is written as

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’ f”,,2=[~3~~~~~;j+[~*]+g (7)

where

In Eq.(7), the separation of the velocity and that of the pressure are given, respectively, by

ui =&w% -~*(%9P,dIP/Jr (9b)

where the functions with tilde are defined by Eqs.(3- 4) with c replaced by c,,, .

The function g works as an anti-diffusion in the

energy flux at non-linear waves. Although neglecting g brought about a little smearing effect at shock

waves, we currently use the scheme with g = 0 because this treatment enhances the robustness

of the scheme. Next, the D-type scheme is written as

Theoretical Value IJ9

(11)

As for the normal-momentum flux, mixing of the D-type and the V-type schemes is defined by the same way as in AUSM-DV scheme, i.e.,

A so-called “shock-fix” is applied employing the V- type scheme Eq.(7) as the dissipative partner.

A straightforward approach is taken to extend the above scheme to a three-dimensional, two- temperature, multi-species gas mixture version. The only additional treatment is to introduce a common effective specific heat ratio y, . The definition of the

effective specific heat ratio is

(1%

The value of y, is given the value of the side of

- AUSM-DV-EF

M, = 7.95

Re* =4.2x105

Pr =I.0

I 11 12 13 14 15

Angle 0 (deg)

Figure 5: Comparison of numerical solutions of self-similar flow around a cone

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which c, is given its value. In Eqs.(3-4), y and c

are replaced by y, and c, , respectively.

The final form of the scheme is given as

where p = x2, P, , and the subscripts n , t, , and 1,

denote the normal and the tangential components, and

M35 + f,“‘” fob,2 = fv I I 2

s = l,...,N,

U IIL

21 “R PI/l

U ‘I R

0 + 0 ’

(14b) U

‘2 R

eVR 0

HR / i”,

where fvm" = cEfy The values of the left and the right sides of the cell

interface are evaluated by an interpolation assuming peace-wise linear distribution in a cell with minmod limiter function, so that a second-order spatial accuracy is secured in the smooth region.

-tation The computations have been conducted on the Numerical Wind Tunnel (NWT) of NAL employing domain-decomposition parallel computing strategy. The method, in this case, decomposes the computational flow field into I6 domains. Each domain is covered by one processing element (PE), which has its own memory. The communication between the PE’s is established via fast crossbar switching network.

Practically, a convergent solution is obtained after 15,000 or 20,000 iterations. In Figure 6, history of

Iteration Number

Figure 6: Convergence History for Case294

convergence is depicted for case 294 by plotting the L2-norm of the total energy residual. The abrupt jump in the residual seen around 4,000-th iteration is due to a raise of CFL number.

. . . ure Dlstrlbutlonck-Wave S~IIJE

In Figure 7, computed pressure distribution in the plane of symmetry is shown and the shock-wave shape is compared with a Schlieren photograph taken for Case288. From the comparison, the computed shock-wave configuration agrees with the Schlieren picture.

. . . lstrlbutron The surface heat flux obtained for Case294 is shown in Figure 8. Each heating rate distribution along the centerline normalized by each stagnation-point value is depicted in Figure 9, where the experimental data are also shown.

It is noted that the normalized profiles computed for four cases do not differ very much among each other. Notable discrepancy between computation and experiment is seen at around x=0.024(m) on the windward surface.

The experimental data are shown with error bars of flO%, which is recognized as a reference level. The reason for the reference level is described later in the paper.

Correlaticm of Stagnation-Point

In order to investigate the correlation of the stagnation-point heating rate over a variety of test conditions typically shown in Table 3, it is thought beneficial to use non-dimensional similarity parameters.

Let us start by assuming the stagnation-point heating rate is a function of the total enthalpy

H (= Hz ), the binary scaling parameter B , the post-

shock stagnation pressure /‘, , the free-steam

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Figure 7: Computed pressure distribution and Schlieren photograph for Case288. a) Computed result is superimposed on Schliren photograph. b) Schliren photograph is superimposed on computed result.

Figure 8: Surface Heating Rate (W/m2) for Case 294 d 0.00 002 0.04 0.06 008 o.io

X Cm> Figure 9: Surface heating rate distribution along the centerline normalized by stagnation-point value. Error level of + 10% is shown as a reference.

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viscosity p , and the nose radius R, (0.024m).

Namely,

q=f(H,B,?,,~,R,). (15)

The binary scaling parameter B is defined as the product of the free-stream density by the nose radius.

By employing dimensional analysis, a non- dimensional relationship for Eq.( 15) is obtained as

P, I P2BW . (16)

For simplicity, for the time being, let us assume the thermal relationship of the calorically perfect gas. Then, the post-shock stagnation pressure is expressed

by

On the other hand, the total enthalpy and the free- stream pressure is related by the equation,

By using these relations, we obtain

Table 3: Typical Test Conditions Case# P. u, bfz T H P Re

(g/m‘) (km/s) (K) (M.l/kg) (,&.s) ~10~’

282 3.19 3.35 9.83 288 5.89 Il.9 14.3 283 1.79 4.28 9.86 469 9.63 25.5 7.20 284 I .97 4.21 8.82 584 9.71 29.6 6.82 285 3.42 3.35 9.82 289 5 90 17.9 15.3 286 3.00 3.35 981 291 5.91 18.0 13.4 287 2.18 3.94 9.09 468 8.24 25.5 8.03 288 2.62 3.72 9.32 397 7.33 22.7 IO.3 293 2 53 3.70 9.37 388 7.23 22.3 IO.1 294 Il.3 3.81 7.13 729 8.18 34.2 30.6 295 18.2 3.12 7.89 390 5.27 22.4 60.8 296 9.29 4.42 6.76 1060 10.8 43.1 22.9 297 13.6 3.83 7 I4 717 8.07 33.8 37.0 300 6.69 3.91 7.12 750 8.39 34 8 18.0 301 7.71 3.74 7.25 662 7.66 32.2 21.5

P, p2 B-‘R,

= HG(M,) B-2/.l2

Then, Eq.( 16) can be replaced by

4 p3 B-2R,’

Moreover, since we have the relations such as,

H -=ReZU, B-2p2 uf

Eqs.( 17) can be re-written as

rf’ q Re-’ p,lJi

=& M,), (18)

H where 4 I Re’- .

u:

At first, let us look at the functional form of ~(4) in

several iso-Mach number planes. Consider pairs of free-stream conditions of p, and U, listed in Table

3 at a common free-stream Mach number, and calculate the stagnation-point heat fluxes employing the Detra-Kemp-Riddell (D-K-R) correlation (Eq.(22)). Then one can get ‘a({) in each considered

iso-Mach number plane. As a result, for the range of the Mach number considered, the relationship

is found to hold as shown in Figure IO. It is, therefore, appropriate to assume the functional form for

d&M,) be

q=v(5, M_)=x(M,~‘.*‘. (19)

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Assuming x is a linear function of M, and fitting

the data obtained by D-K-R correlation, the fimction x is determined as

x(M,) = 0.43 I M, + 0.9873. (20)

Equations (19) and (20) can be re-written by the following equation for the Stanton number C,, ,

where h is the static enthalpy of the free stream. Considering the relation

h --MM,‘, u:

it is found that Eq.(21) behaves as

when the Mach number is high with the Reynolds

l.E+06 l.E+07 l.E+OB l.E+09 l.E+lO

4

Figure IO: Functiqnal form of ~(6) at several Mach

numbers.

Table 4: Stagnation-Point Heating Rate (MW/m’)

Case 284 288 294 296 CFD 4.04 2.53 7.22 11.7

D-K-R 3.91 3.05 7.1 I 9.57 3.3% -17% 1.5% 22%

v-s 4.50 3.43 8.43 II.7 -10% -26% -14% 0%

Experiment 5.85 4.30 II.4 15.7 -31% -41% -37% -25%

number small or intermediate. This observation does not conflict with the fact that the Stanton number is proportional with the viscous interaction parameter

k/JR e as rarefied gasdynamic effects become

stronger.

&u.warison of Stagnatlon-Polnt Error in ~eMeasUrcJ.IXnI Currently, it is hard to evaluate measurement error, especially of the stagnation-point heat flux. Because of difficulty in this kind of experiments, detailed error analysis was not available. Major error sources could be found in temporal variation of the heat flux, the repeatability of experiment, and change in sensor characteristics. The averaged value of heat flux was affected by how to define a smoothing method. The repeatability was hard to be quantified because number of runs was too small for statistical treatment. Sensors could not be kept in fresh conditions, namely some sensors might change in sensitivity or some might be damaged during the course of experiments. Calibration for such change in sensor characteristics was not done. Although we anticipate that each of these three errors might be more or less 5 to IO%, it is hard, at present, to put the total measurement error at a certain numerical value. Therefore, the error bars of *IO% amount shown in Figure 9 and Figure I2 mean only a reference level of error which is typically discussed among researchers dealing with this kind of shock tunnels.

Ion-Point Hea- The computed and measured stagnation-point heating rates are summarized in Table 4. Also, included in the table are, stagnation-point heating rates estimated by a well-known correlation of Detra-Kemp-Riddell (D-

K-R),

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and relatively new correlation of Verant-Sagnier (V-

S) “9

qvms = 23.,,( “‘;+$ )“‘E. (23)

The latter is added because it has been used as reference data in the experiment.

In Table 4, discrepancies of CFD results, compared with each evaluation method, are given. Good agreement is obtained for Case284 and Case294 with D-K-R and for Case296 with V-S. The amount of f20% error is seen with D-K-R and -26% with V-S for the other cases. The experiment results show highest values among all. The CFD results deviates at maximum 40% with the experimental data. This discrepancy is substantial and not comparable to 10% error.

The reason for this discrepancy is currently not clear. In the simulation, the free stream condition is given values of the nozzle exit. This assumption might bring about some discrepancy between the simulation and the experiment, since the flow expands from the nozzle exit in the test section’* and the front end of the model is placed IOmm downstream from the nozzle exit plane for the case of the angle of attack 50 degrees.

From purely computational reason, grid convergence of numerical solution should be investigated. As shown in Table 1, cell-Reynolds number for the minimum spacing near stagnation- point is of the order of unity. Because of the cold wall

‘condition of the current problem, this cell-Reynolds number might not be small enough to resolve a strong temperature gradient. In order to investigate this problem, computations using finer grids are underway. The results of these new computation and the grid convergence study will be presented somewhere else.

From the present dimensional analysis, Equation

(19) : rj = ,@( )p was obtained as a functional

form for the non-dimensional heat flux q. Equation

(20) is an example of the function x(M, ). The

present correlation is tested by experimental data, V- S results, and CFD results as plotted in Figure I I. It should be noted that D-K-R, V-S, and the present correlation are basically the same, namely the exponent of < equals to 1.25 - 1.26, while it is 1.28 for CFD results and 1.30 for the experiment. Correlation of S-number at St- Equation (2 I), obtained directly from Eqs.( 19) and (20), is rewritten in a slightly different form as below,

1 .E+12

1 .E+l 1

% \ E

1 .E+l 0

--Find CYI. (Ew.l. ./x=0.55.!-1.30

..... Fitted CW. (CFD) t,/x*.OZC-l28

1 .E+O9 J

l.E+07 l.E+08 l.E+09 l.E+lO

c

Figure I I Stagnation-Point Heating Rate Correlation.

8 6

8 d

0’ 0” d

0

0.005 0.010 0.015 0.020 0.025 0.030 0.035

x *(H/U’)‘= / Reo5

Figure 12: Correlation of the Stanton Number at the Stagnation Point. Reference error of flO% is shown.

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(24)

In Figure 12, Eq.(24) is checked for experiments and calculations, as well as their regression lines. The error bars off 10% are shown for reference purpose.

It seems that,, there’ is rather large discrepancy between the experiment and the computations. The errors from the regression estimates.for experimental data vary between -10% to +32%. This suggests considerable amount of dispersion in the measurement. Also, significant bias from each other is seen between the experiment and the computations. The reason for this systematic error is not clear at present.

Summary In this paper, three-dimensional thermo-chemical non-equilibrium CFD simulations are. conducted about aerodynamic heating around HYFLEX model tested in HEK shock tunnel. A modified Equilibrium Flux Method is devised to solve the current problem. Computed normalized heat flux distributions do not vary much among the test cases considered. As for stagnation-point heat flux, while computed results show similar tendency to D-K-R correlation, they show rather large discrepancy with the experimental data. Both experimental and computational aspects of reasons for the discrepancy have been discussed. One of the latter is grid convergence which will be clarified in the future.

wledvmea Part of the work has been conducted as joint.research in the framework of the contract (June ‘98 - March ‘00) between the National Aerospace Laboratory and the Aerospace Division of Nissan Motor Co., Ltd.

References [I] Shirouzu, M. and, Watanabe, S., “On the

Hypersonic Flight Experiment (HYFLEX) for the Development of HOPE,” AIAA Paper 93- 5080, 1993.

[2] Itoh, K., “Tuned operation of free piston shock tunnel,” Proceedings of the 201h International Symposium on Shock Waves (ISSW), Pasadena, 1995.

[3] Ueda, S., Komuro, T:, Sato, K., Takahashi, M., and Itoh, K., “Aerodynamic Heating Experiments on HYFLEX Model in the HEK High Enthalpy Shock Tunnel,” 2 I” ISSW, Great Keppel Island, Australia, 1997.

[4] Takaki, R., and Yamamoto, Y., “Numerical Analysis of Three-dimensional Hypersonic Non-equilibrium Flows around Re-entry Vehicles,” NAL, SP-37, pp.l21-126, 1998.

[5] Kurotaki, T., and Yamamoto, Y., “3-D Real Gas Flow Analysis around Space Vehicles,” NAL, SP-37, pp.l27-132, 1998.

[6] Shimada, T., Yamamoto, Y., Hirose, N., “Numerical Simulations of Hypersonic Real- Gas Flows around Re-Entry Vehicles,” NAL, SP-37, pp.l33-138, 1998.

[7] Yamamoto, Y., “Summary of Three- dimensional High-Enthalpy Flow Workshop for Space Transportation Vehicle,” NAL, SP-37, pp.l39-146, 1998.

[8] Yamamoto, Y., “HYFLEX Computational Fluid Dynamic Analysis,” NAL, SP-37, pp. I 15-126, 1998.

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II American Institute of Aeronautics and Astronautics