DTIC ADA455442: CFD Validation for Hypersonic Flight: Hypersonic Double-Cone Flow Simulations

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(c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

CFD Validation rfo Hypersoni c Fligh:t
Hypersonic Double-Cone Flow Simulations
Graham V. Candler,* loannis Nompelis,** Marie-Claude Druguet'
Aerospace Engineering and Mechanics & Army HPC Research Center
University of Minnesota, Minneapolis MN 55455
Michael S. Holder^ Timothy P. Wadhams^
Calspan- University at Buffalo Research Center, Buffalo NY 14225
lain D. Boyd,§ Wen-Lan Wang**
Department of Aerospace Engineering
University of Michigan, Ann Arbor MI 4&109
Abstract Introduction
At the 2001 AIAA Aerospace Sciences Meeting At the 2001 AIAA Aerospace Sciences Meeting,
there was a blind comparison between computational there was a session dedicated to a CFD code validation
simulations and experimental data for hypersonic study. A number of computational researchers used
double-cone and hollow cylinder-flare flows. This code their methods to predict the flow over several hyper-
validation exercise showed that in general there was sonic configurations, and then the experimental data
good agreement between the continuum CFD sim- were revealed and compared to the computations. Two
ulations and experiments. Also, in general, there geometries were tested: a hollow-cylinder / flare that
was good agreement between direct simulation Monte produces a weak viscous interaction, and a double-cone
Carlo (DSMC) calculations and the experiments in re- that produces a much more complicated flow field with
gions of attached flow. However, in almost all of the a stronger viscous-inviscid interaction. The test con-
computations, the heat transfer rate on the forebody ditions were chosen so that the free-stream conditions
of the cone was over-predicted by about 20%. The would be well characterized and the flows would be
purpose of this paper is to report on our analysis of entirely laminar. Also to reduce the complexity of the
this difference. We perform CFD simulations of the computational analysis, nitrogen was used as the test
hypersonic nozzle flow to assess the importance of vi- gas.
brational nonequilibrium on the test conditions. We This blind code validation study resulted in sev-
then recompute the flows using a new set of vibrational eral key conclusions: First, the comparisons between
nonequilibrium conditions and consider the effects of the continuum computations and experiments were
a slip boundary condition at the model surface. Ad- generally very good. For example, consider Fig. 1
ditionally, we analyze new heat transfer rate data on which is taken from the paper of Harvey, Holden, and
sharp and blunt 25° cones over a wider range of test Wadhams.1 The predicted surface pressure and heat
conditions. This analysis appears to explain the dis- transfer rate are plotted against the experimental data
crepancy between the previous calculations and the at two test conditions. Note that the pressure matches
experiments. well on the cone forebody, through the separation zone,
in the region of high pressure due to the shock-shock
interaction, and on the second cone. Similarly for
* Professor, AIAA Associate Fellow (candlerQaem.umn.edu)
the heat transfer rate, with very good agreement in
** Graduate Research Assistant, AIAA Student Member
the separation zone, the shock interaction region, and
t Research Fellow, also IUSTI-CNRS 6595, Marseille, France,
on the second cone. The main differences are that
AIAA Member
* Program Manager, AOEC, AIAA Associate Fellow the heat transfer rate on the cone forebody is over-
» Aeronautical Engineer predicted by about 20% and the separation zone is
3 Associate Professor, AIAA Senior Member slightly too large, which results in the peak of pressure
and heat transfer being too far downstream. The con-
Copyright © 2002 by Graham V. Candler. Published by the
tinuum computations by the other researchers showed
American Institute of Aeronautics and Astronautics, Inc. with
permission. essentially the same features, and additional calcula-
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CFD Validation for Hypersonic Flight : Hypersonic Double-Cone Flow
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2 AIAA 2002-0581
tions at different flow conditions were generally similar
to those described here.
A second conclusion of the study was that the
hollow-cylinder / flare geometry computations also
showed similarly good agreement with the experi-
ments. However, in general all of the computations
showed a small over-prediction in the heat transfer rate
on the cylinder surface upstream of the separated flow
region.
Comparisons between the experimental Schlieren
images and the computed flow fields showed remark-
ably good agreement. The computations reproduced X/L
(a)
all of the visible features, including inflections in the
bow shocks, separation shock locations, and shock
interaction points. There is even evidence in the
Schlieren of the predicted under-expanded jet that
runs down the surface of the second cone.
Finally, the agreement between the Direct Simu-
lation Monte Carlo (DSMC) calculations and experi-
ments was not as good as the continuum calculations.
Generally, DSMC is able to capture the surface pres-
sure and heat transfer rate in the attached regions.
However, in most cases, the DSMC calculations also
over-predict the heat transfer rate on the cone and
cylinder forebodies, as in the continuum calculations.
(b)
DSMC apparently fails to predict the correct separa-
FIGURE 1. Normalized surface pressure and heat
tion zone size for the massively separated flows, re-
transfer rate for the sharp double-cone for (a) Run 28
sulting in poor predictions of the flow in these regions.
(Moo = 9.59, fleoo = 1.31 x I05m~l) and (b) Run 35
This is not surprising since the flows are characterized
(Moo = 11.30, #600 = 1.33 x 105m~1) Computations
by a low Knudsen number, making them difficult to
by Candler et al.2 Taken from Ref. 1.
compute with DSMC.
In this paper, we focus on the main discrepancy be-
tween the computations and experiments, namely the Effect of Vibration on Test Conditions
over-prediction of the heat transfer rate on the cone
One of the most important uncertainties in code
and cylinder forebodies. We first evaluate how the
validation is the specification of the free-stream con-
free-stream conditions are inferred from the measured
ditions. This is particularly true in a hypersonic wind
conditions during the experiments, and simulate the
tunnel where high-temperature and pressure gas is ex-
flow within the experimental facility nozzle. We are
panded to a high Mach number. Non-ideal effects such
then able to predict the conditions of the experiment
as intermolecular force effects, chemical reactions, and
and determine the influence of vibrational nonequi-
vibrational excitation may affect the free-stream con-
librium on the experimental conditions. Using these
ditions. Additionally, it is not clear how one infers the
conditions, we then recompute the four cases that we
test conditions from the quantities that can be mea-
considered in our previous paper and compare to ex-
sured in the test stream. In an impulse facility such as
periments. These cases are Runs 28 and 35, which are
the shock tunnel used in the present experiments, the
sharp double-cones at Mach 9.5 and 11.3, and Runs 11
pressure and enthalpy in the reflected shock region are
and 14, which are hollow-cylinder / extended flares at
known. The test-section pitot pressure can be mea-
the same Mach numbers. We also perform the same
sured easily, and the heat transfer rate to a reference
analysis on new 25° cone heat transfer rate data from
probe can also be measured.
Holden.
In Holden's experiments, calibration runs are per-
formed before the actual test conditions to verify the
uniformity of the section flow. Then the tests are per-
formed at the same nominal conditions as the cali-
8 - 2 RTO-TR-AVT-007-V3
(c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.
AIAA 2002-0581 3
bration. Additional pitot pressure measurements are Thus, we expect that the effect of vibrational freez-
made during the test to verify that the test conditions ing in the nozzle test-section is to lower the axial ve-
are consistent with the calibration run. To determine locity and increase the density. We can show this
the free-stream conditions, a quasi-one-dimensional more quantitatively if we numerically integrate an adi-
code is run using the measured post-reflected shock abatic flow while enforcing isentropic conditions from
stagnation conditions as reservoir conditions. Because the reservoir conditions to the measured pitot pres-
the effective area ratio of the nozzle is not known due sure. The relevant equations are:
to nozzle wall boundary layer displacement, the code is rT
run to the point where the pitot pressure matches the h0 = h+±u2 = \ cpdT+^u2
Jo
measured pitot pressure. Then, the test conditions are
dT _ dp
taken to be those given by the quasi-one-dimensional ds = c —-R-t=0
p1 p
code. This approach has been used successfully for
where c is a function of temperature. Using the reser-
a long time, but usually for air rather than nitrogen, p
voir conditions for Run 35 of p = 547 psi = 3.77MPa
and at higher pressures than considered in the present 0
and h = 4.12 x 107ft2/sec2 = 3.83MJ/kg, we com-
experiments. 0
pute an equilibrium reservoir temperature of T =
It should be noted that in the hypersonic limit, the 0
3176 K and density of p = 3.998 kg/m3. At these
Rayleigh pitot pressure formula 0
conditions, there is only a very small amount of disso-
ciation, which is neglected.
If we then expand the reservoir gas to the measured
pitot pressure of 0.541 psi using the above equations
and assuming an equilibrium simple harmonic oscil-
reduces to
lator, we obtain the test-section conditions given in
Table 1. If instead, we assume that the gas freezes at
Po2 =
the throat temperature, we obtain a different set of
conditions, also given in the table.
&,
O A Note that in the above equation and in Table 1,
27 47
the Mach number is computed with the frozen speed
where p is the measured pitot pressure and oc de-
o2 of sound. It should be noted that to obtain these re-
notes free-stream conditions. Thus, the pitot pressure
sults, we have used one additional piece of informa-
is simply a measurement of the kinetic energy per unit
tion, namely we must be able to compute the pitot
volume, or the axial- direct ion momentum flux.
pressure from the vibrational nonequilibrium condi-
Note that in an ideal adiabatic expansion to hyper-
tions. We have performed CFD simulations of the
sonic conditions, we have
flow over the pitot probes used in the experiments
using a two-temperature, finite-rate relaxation model
— r T 4- ln2 ~ !?
— Cp-L i 2 — 2 for nitrogen. These calculations show that under the
conditions of interest, the Rayleigh pitot pressure for-
where we have assumed that ^u2 ^> c T. Thus given
p
mula gives the correct value of pitot pressure, p ^. For
the reservoir enthalpy, we know the value of u2 at all lo- 0
example, the CFD simulation at the nonequilibrium
cations in the inviscid portion of the nozzle flow. Now,
since the pitot pressure measurement gives us p^u^,
all we have effectively measured is the free-stream den-
TABLE 1. Computed test-section conditions for Run
sity in an ideal expansion.
35 conditions using equilibrium and frozen flow as-
Now consider what happens if there is vibrational
sumptions. Adiabatic, isentropic expansion.
energy frozen in the flow during the expansion. We
have Case Equilibrium Frozen
•^u — h, — 6 , TOO (K) 133.9 99.38
o V
T,oo (K) 133.9 2768
where e* is the vibrational energy per unit mass frozen Poo (g/m3) 0.548 0.612
in the flow. Thus for this non-ideal expansion, the
UOQ (m/s) 2716 2571
kinetic energy will be lower than in an ideal expan-
11.51 12.65
Moo
sion. And therefore, to achieve the same measured
AX>T& (Pa) 4044 4045
pitot pressure, the free-stream density will have to be
Poot& (W/cm2) 1098 1040
larger.
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(c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.
4 AIAA 2002-0581
conditions given in Table 1 gives a pitot pressure of Initial simulations of the nozzle flow were discour-
Po2 = 0.541 psi, which is the value obtained from the aging, with the centerline pitot pressure significantly
Rayleigh pitot pressure formula at these conditions. over-predicted. This is caused by the turbulence model
This analysis of adiabatic, isentropic expansions over-predicting the boundary layer displacement thick-
with equilibrium and frozen vibration shows that for ness in the nozzle exit plane. This may be a result
a given pitot pressure, vibrational freezing reduces the of a deficiency in the turbulence model at high Mach
axial velocity and increases the density. We can es- numbers and low densities, or some other effect. Pre-
timate how this difference in the test-section condi- vious simulations of hypersonic nozzles showed signif-
tions will affect the surface pressure and heat transfer. icant variations in the computed test-section condi-
To first order, the surface pressure scales with Poo^, tions depending on the choice of the turbulence model,
while the heat transfer rate scales with pooU^. Table with the Baldwin-Lomax model typically giving inter-
1 gives these quantities for the two conditions consid- mediate values for the boundary layer displacement
ered. Note that there is virtually no change in the thickness.8 In any case, we were therefore forced to
dynamic pressure, as expected from the pitot pressure perform parametric studies where we allowed the flow
scaling argument given above. However, since the ve- to "relaminarize" (which is a fancy term for turning
locity is lower, the kinetic energy flux is reduced by off the turbulence model) at different locations. This
5.3%; this reduction will likely result in a lower heat may not be completely arbitrary given that there is
transfer rate in the nonequilibrium case. a very strong favorable pressure gradient and the test
conditions are at a low density. With this approach,
we were able to adjust the relaminarization location to
Nozzle Flow Simulations
match the measured displacement thickness for most
The preceding analysis shows that vibrational freez- of the test conditions.
ing is likely to reduce the measured heat transfer rate.
For example, consider Fig. 2 which plots the mea-
However, a more complete analysis is required to de-
sured pitot pressure for the Run 35 calibration run
termine how much vibrational freezing occurs and to
with the results of two nozzle simulations. Again, note
assess the additional non-ideal effects in the nozzle
that the fully turbulent calculation over-predicts the
flow. Thus, we have performed a series of CFD simu-
displacement thickness, resulting in a smaller effective
lations of the nozzle flows. We solve the axisymmet-
area ratio and a larger pitot pressure. When the flow
ric compressible Navier-Stokes equations, along with
is assumed to relaminarize at 2.2m from the throat
a vibrational energy conservation equation. We al-
(for a nozzle of just over 6m in length), the displace-
low finite-rate vibrational energy relaxation using Mil-
ment thickness matches the experiment much better.
likan and White rates.3 Nitrogen dissociation and re-
As a result, the computed pitot pressure agrees much
combination is included with standard rate constants,
better with the measurements.
but under the present conditions the dissociation lev-
els are so low that they can be neglected. The Blot-
0.8
tner curve-fits for viscosity4 are used, and because the
nozzle wall boundary layer is turbulent, we use the
Baldwin-Lomax turbulence model.5 A second-order
0.6
accurate modified Steger-Warming flux vector split-
ting approach6 is used, along with the Data-Parallel
3
Line-Relaxation method.7
I
The nozzle grids are constructed directly from the CO 0.4
CAD files of the nozzle contours. Typical grids use Q_
1786 points in the axial direction and 128 points in O
Ql
the surface normal direction, with stretching at the
0.2
surface. The nozzle throats are elongated, making the Experiment
Fully Turbulent
specification of the sonic line difficult. Thus the flow
Relaminarization at 2.2 m
is computed from the constant diameter driven tube
section, through the throat, and to the test-section. 0.0 -20 -10 0 10 20
y (inch)
Thermo-chemical equilibrium was assumed at the in-
flow, and care was taken to specify the subsonic inflow FIGURE 2. Run 1302 (calibration for Run 35) pitot
conditions so that the total enthalpy is conserved in pressure in the nozzle exit plane compared with ax-
the computed flow. isymmetric nozzle computations.
8 - 4 RTO-TR-AVT-007-V3
(c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.
AIAA 2002-0581 5
With this relaminarization location, we then ran a the exit-plane pitot pressure for this case. We have
nozzle simulation with the actual Run 35 reservoir con- matched the boundary layer displacement thickness,
ditions. The results of this simulation are tabulated in but the radial variation of the pitot pressure is much
Table 2. The resulting dynamic pressure and kinetic larger in the computation than in the experiment. The
energy flux are also given; note that the computed reason for this is presently unknown, and as will be
values are lower than the nominal conditions. This is shown below, this is the only case for which this lack of
a result of matching the experimental pitot pressure agreement was obtained. Table 3 summarizes the com-
profile, rather than a single mean value. As a result, puted free-stream conditions for the four cases consid-
the computed value of Poo^o is 14% lower than the ered.
nominal conditions. It is also interesting to note the
similarity in the results of the CFD calculations with 1.0
the simple adiabatic and isentropic expansion. Note
that the vibrational temperature freezes at slightly less
0.8
than the throat temperature in the CFD simulation,
which accounts for some of the differences in the two
(0
Q.
calculations.
0.6
A similar analysis was carried out for the other test
conditions with similar agreement between the pitot
pressure surveys and the computations. However, we 0.4
o
were unable to obtain good agreement for the cali- GL
bration run corresponding to Run 28. Figure 3 plots
0.2 » Experiment
Computed
TABLE 2. Nominal and computed test-section condi-
0.0
-20 -10 0 10 20
tions for Run 35 reservoir conditions. CFD solution
Radial Location (inch)
with relaminarization at 2.2m from throat.
FIGURE 3. Run 1304 (calibration for Run 28) pitot
Case Nominal Nonequilibrium
pressure in the nozzle exit plane compared with ax-
138.9 98.27
TOO (K) isymmetric nozzle computations.
T (K) 138.9 2562
voo
Poo (g/m3) 0.5515 0.5848
Run 35 Analysis
Uoo (m/s) 2713 2545
With the test conditions predicted by CFD, we re-
11.30 12.59
computed the test cases. Let us first focus on the
Poo<4 (Pa) 4059 3788
forebody of the sharp double-cone at Run 35 condi-
Ax>t& (W/cm2) 1101 964
tions to see how the modified conditions affect the sur-
face quantities. We use the same CFD code described
TABLE 3. Nominal and computed nonequilibrium free- above and in our previous work.2 We use the results
stream conditions for the 25-55° sharp double-cone of the grid resolution studies that we performed in the
and hollow-cylinder with extended flare flows. past to select a grid that is certain to be fine enough
to resolve the gradients in the tip region. For the first
Nominal Run lla Run 14a Run 28b Run 35b
5 cm of the tip, we use a grid of 260 x 256 points. We
TOO (K) 128.9 156.1 185.6 138.9
also performed DSMC calculations of this flow field,
Poo (g/m3) 0.5066 0.7937 0.6545 0.5515
similar to those performed in Ref. 9.
UQQ (m/s) 2609 2432 2664 2713
Figure 4 plots the computed heat transfer rate and
11.10 9.50 9.59 11.30
Moo
surface pressure based on the nominal Run 35 con-
Nonequilibrium Run 11 Run 14 Run 28 Run 35
ditions and the nonequilibrium conditions computed
TOO (K) 98.69 114.1 140.0 99.38
with CFD. As expected because of the lower value of
T (K) 2497 2269 2589 2768
voo pooU^, the heat transfer rate is lower for the nonequi-
Poo (g/m3) 0.5866 0.7506 0.7372 0.6120
librium test conditions. Our continuum results still
UQO (m/s) 2485 2327 2538 2571
over-predict the heat transfer rate by about 10%, and
12.27 10.69 10.52 12.65
Moo the DSMC results are generally higher still. The mod-
aHollow-cylinder with extended flare ified conditions produce a better agreement with the
bSharp 25-55° double-cone surface pressure, due to the lower free-stream dynamic
RTO-TR-AVT-007-V3 8 - 5
(c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.
6 AIAA 2002-0581
pressure predicted by the nozzle calculation (see Table If we extend that standard Maxwell slip model to
2). The source of the discrepancy between the CFD represent vibrational energy slip (or perhaps more
and DSMC calculations is not known. Interestingly, commonly "jump"), we have
the computed surface pressures agree with one another
very well, and thus it is likely that there is a difference v \ v
slip — Av— —
in the effective surface energy exchange mechanism. OH wall
In our previous work, we considered the effects of a
where a is the accommodation coefficient for vibra-
surface slip boundary condition. We found that there v
tion and X is the mean-free-path that character-
was some change in the predicted heat transfer, but v
izes transport of vibrational energy. Because vibra-
not a significant level. However with the new free-
tional energy is independent of the translational en-
stream conditions, we need to reconsider this issue be-
ergy modes in our model, we use the value of X for the
cause a substantial fraction of the energy is frozen in v
transport of momentum, namely X = 2///pc, where c
the vibrational energy modes. With the elevated vi- v
is the mean thermal speed of the gas, ^/SRT/7r. This
brational temperature in the free-stream gas and the
simple extension of the slip model is based on the work
relatively slow relaxation of the gas within the flow
of Gokcen et a/.10 for example. The value of the vi-
field, it is possible that vibrational energy slip is im-
brational energy accommodation coefficient is not well
portant.
known, but previous calculations11 have used values of
a as low as 0.1.
50 v
Experiment Figure 5 plots the computed heat transfer rate us-
Nominal CFD ing this vibrational slip model with a varied from 0.1
v
Nominal DSMC
^40 to 0.85. Also plotted is a simulation with no vibra-
Noneq. CFD
Noneq. DSMC tional accommodation (an adiabatic surface condition
for vibration). These calculations include momentum
£30 and temperature slip at the surface using the model
CO
DC of Gokcen,10 and accommodation coefficients of 0.85.
CD Clearly, the calculations predict a significant effect of
120 vibrational energy slip on the heating rates. This is
not surprising because at the nonequilibrium test con-
ditions, 11% of the total energy is frozen in the vibra-
I 10
tional modes. Note that there is very little change in
the predicted heat transfer rate for a > 0.3, and be-
v
cause of the uncertainty in the value of a , we used a
v
value of 0.5 for the remainder of the calculations.
These calculations show that the heat transfer rate
to the tip of the cone is reduced by two effects. The
Experiment
Nominal CFD vibrational modes of the gas freeze near the throat
Nominal DSMC temperature, thereby reducing the test-section veloc-
Noneq. CFD
ity. Secondly, due to the elevated vibrational temper-
Noneq. DSMC
ature in the free-stream gas and the slow vibrational
relaxation in the shocklayer, the effects of slip in vi-
brational energy at the surface are enhanced. Thus,
much of the vibrational energy remains stored in the
gas as it flows over the cone tip. This effect can be
seen in Fig. 6, which plots the computed temperature
profiles normal to the surface at axial location of 2 cm
from the cone tip. Note that with the nominal free-
stream conditions, there is essentially no vibrational
excitation within shocklayer. But with nonequilibrium
conditions, the vibrational temperature remains frozen
2 3
(b) x (cm) except in the near-wall region. The effect of slip is also
FIGURE 4. Heat transfer rate (a), and surface pressure clear, with the vibrational temperature highly elevated
(b) near the tip of the 25° cone at Run 35 conditions. at the surface for the slip boundary condition.
8 - 6 RTO-TR-AVT-007-V3
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AIAA 2002-0581 7
Based on these results, we performed CFD simula- Figure 9 plots the computed pitot pressure near the
tions of the entire double-cone flow field at the non- nozzle exit plane at the Run 35 conditions. Because
equilibrium Run 35 conditions. Figure 7 shows the the contours are separated by only 0.025 psi, they ac-
computed translational-rotational temperature and vi- centuate the non-uniformities in the flow. But, there
brational temperature distributions in the flow field. is variation in the flow properties on the scale of the
Similar to Fig. 6, we see that the vibrational tem- model (diameter is 10cm). Therefore, we extracted
perature remains frozen in the inviscid portion of the a line of data at the location where the model is lo-
shocklayer. The gas is close to equilibrium in the sep- cated in the test section, and used this non-uniform
aration zone because of its long residence time. The data as upstream conditions for complete double-cone
heat transfer rate results are plotted in Fig. 8. The simulation. These results are plotted in Fig. 10. The
modified test conditions and the surface slip model do non-uniform conditions reduce the size of the separa-
not change the separation and reattachment locations, tion zone, and improve the agreement on the second
and as a result do not significantly alter the heat trans- cone. This excellent agreement may well be fortuitous,
fer to the second cone. but it is clear that even a small level of non-uniformity
in the free-stream conditions is important for this flow.
50
Experiment
Noneq. no-slip
cCTMO
f
230
CO
DC
CD
120
10
1 2 3
x(cm)
FIGURE 7. Temperature distributions in the flow field
FIGURE 5. Variation of heat transfer rate on 25° cone
of Run 35 at nonequilibrium conditions.
with vibrational energy accommodation coefficient.
. IV ————— Nominal J I
Experiment
fS^>^^^ ————— Noneq T I
Nominal CFD
- | ^^^^X ————— Noneq slip T j
- i > ! _ _ _ _. Nominal T j Noneq. CFD
v
0.15 • i _ _ _ _ . Noneq T Noneq. CFD slip
v
i _ _ _ _ Noneq slip T .
v
-v : ! 11 ;
I 0.1
0.05
°() 500 1000 1500 2000 2500 3000
T(K) x (cm)
FlGURE 6. Temperature distribution normal to the FIGURE 8. Heat transfer rate on the full double-cone
surfa(:e at x — 2.0 cm. at nominal and nonequilibrium Run 35 conditions.
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AIAA 2002-0581
Nominal CFD
Noneq. CFD slip
Experiment
5.5 6.5
x(m)
FIGURE 9. Pitot pressure contours (psi) in the test-
section at Run 35 conditions. x(cm)
FIGURE 11. Heat transfer rate on the full double-cone
at nominal and nonequilibrium Run 28 conditions.
Experiment
Nominal CFD
New 25° Cone Data Analysis
Nonuniform CFD slip
Recently, Holden performed a new set of experi-
ments designed to focus on the heat transfer rate to
the forebody region of the 25° cone and on the cylin-
drical portion of the hollow-cylinder flare. Many dif-
ferent test conditions were run, with the total enthalpy
varied from 2.41 MJ/kg to 3.72 MJ/kg; the stagnation
pressure was also varied by a factor of about six, re-
sulting in test-section densities varying by a factor of
about 15. All runs were at the same nominal Mach
number of 11.3. In contrast to the previous experi-
ments, a pitot pressure survey was performed at the
same time as the experiments so that additional cali-
bration runs were not required. See Ref. 12 for more
x(cm)
details on these new experiments.
FIGURE 10. Heat transfer rate on the full double-cone
We simulated the nozzle flows for the new experi-
with a non-uniform free-stream at Run 35 conditions.
ments and obtained similar results to those discussed
above. The level of agreement between the CFD sim-
Run 28 Analysis
ulations and the pitot pressure survey is illustrated in
Figure 11 plots the computed heat transfer rate Fig. 12; generally there is a very good prediction of the
for the full double-cone at Run 28 conditions. The boundary layer displacement thickness and pitot pres-
nonequilibrium test conditions result in a lower heat sure variation. The nominal and predicted nonequilib-
transfer rate near the cone tip that still slightly over- rium test conditions are given in Table 4. Again, there
predicts the experimental data. However there is now is a substantial degree of vibrational nonequilibrium in
a larger separation zone, which makes the agreement the flows. However, in spite of the large variation in
on the second cone worse than the previous results. the reservoir conditions, the ratio of vibrational en-
Figure 3 showed that the nozzle simulation gave rela- ergy to the total energy of the test gas varies from
tively poor agreement with the experiment pitot pres- only 8.1% in Run 12 to 10% in Run 25. Thus all of
sure survey. Thus, our predicted test conditions may the runs have about the same level of nonequilibrium
still be in error for this case. It should be noted that in the free-stream. Table 4 also gives the free-stream
Run 28 is the only case where such poor agreement mean-free-path, AQQ, which varies by a factor of 16
was obtained, including eight new runs to be discussed across the runs.
below.
8 - 8 RTO-TR-AVT-007-V3
(c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.
AIAA 2002-0581 9
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Radial Location (inch) Radial Location (inch) Radial Location (inch)
FIGURE 12. Pitot pressure in the nozzle exit plane compared with axisymmetric nozzle computations.
The results of the nozzle calculations were then used vibrational nonequilibrium playing a larger role in the
to simulate the flow over the 25° cone geometry. These lower density and large mean-free-path flows.
calculations were "blind" in the sense that no attempt Also plotted in Fig. 13 is a case with a blunt tip on
was made to go back and modify the predicted test the cone, shown as "Run 24 Blunt". In the case, the
conditions after the data were compared with exper- same cone geometry is used, but a 0.288 inch radius
iments. Figure 13 summarizes the results. In all but nose replaces the sharp cone tip. The CFD results for
one of the eight runs simulated, the nonequilibrium this case over-predict the heating rate for both condi-
test conditions along with the slip boundary condition tions, even with the slip surface boundary condition.
show a better agreement with the experiments. Run 12 It should be noted that the measurements merge with
is the exception, with a slight under-prediction of the one another at the last transducer location, indicating
heat transfer rate with the modified conditions. The self-consistency in the data.
importance of the slip modeling scales with the free-
Overall, given the stated uncertainty in the reser-
stream mean-free-path, AQO, which is tabulated in Ta-
voir conditions of approximately ±5%, the agreement
ble 4. Interestingly, the difference between the predic-
for these widely varying test conditions is very encour-
tions using the two free-stream conditions also appears
aging.
to increase with increasing AOO. This is consistent with
RTO-TR-AVT-007-V3 8 - 9