COMPUTATIONAL STUDIES OF THE VIRGINIA TECH
HYPERSONIC WIND TUNNEL
Rui Chen
Department of Aerospace & Ocean Engineering, Virginia Tech, Blacksburg, VA
Abstract
Introduction
This paper presents steady-state (viscous) and timeaccurate (inviscid) numerical solutions of the flowfield
inside the Virginia Tech Hypersonic Wind Tunnel
(VTHST) with a Mach 4 nozzle. The numerical
solutions are obtained using a computational fluid
dynamics (CFD) solver named GASP. Comparisons
between the steady-state CFD solutions and available
experimental data are also presented in this paper. The
first objective of my research is to study the steadystate flowfield characteristics of the VTHST. The
second objective of my research is to simulate the
supersonic wind tunnel starting process, which has
seldom been simulated using CFD. I was able to obtain
reasonable Mach contours with my steady-state CFD
calculations. However, I determined that steady-state
CFD calculations cannot accurately predict the
flowfield inside the VTHST because much higher
pressure ratios (the total pressure in the settling
chamber divided by the back pressure at the diffuser
exit) are required to start the VTHST in steady-state
CFD calculations than those required to start the actual
tunnel. Currently, I am running time-accurate
calculations for the VTHST with a Mach 4 nozzle.
Although the calculations are still in progress, it seems
that the VTHST can start at the correct pressure ratio in
the time-accurate calculations.
The Virginia Tech Hypersonic Wind Tunnel
(VTHST) shown in Figure 1 is a unique intermittent
blowdown tunnel designed and built by the Institute of
Theoretical and Applied Mechanics (ITAM) in
Novosibirsk, Russia. It is capable of creating Mach 2 to
Mach 7 flow inside its test section for approximately
1.5 seconds per run. The VTHST has been used for
researches related to direct-measuring skin friction gage
and Scramjet. However, the ITAM only provided
limited experimental and calculated flowfield data to
researchers at Virginia Tech. Therefore, one objective
of my research is to use a computational fluid dynamics
(CFD) solver to calculate the characteristics of the
flowfield inside the VTHST, such as the Mach number
and pressure profiles inside the test section to help
researchers design their experiments.
Heater Settling Chamber Nozzle
Test Chamber
Diffuser
Silencer
Gas Storage Bottles
Notation
pb
poc
Q
T
Diffuser (movable)
= pressure at the diffuser exit (atmospheric)
Figure 1: The VT HST and Its Test Chamber
= settling chamber total pressure
CFD is an ideal tool to study the flowfield inside the
VTHST since it enables one to obtain the flow
properties at any position inside the tunnel. However,
sometimes it can be difficult to get the CFD solution to
converge. Even if the solution converges, it may not be
the correct one. For example, although I was able to
obtain steady-state solutions for the VTHST with Mach
4, 6 and 7 nozzles, the pressure ratios ( poc / pb )
= conservative variable
= time
required to start the tunnel are much higher in my
steady-state CFD calculations than those required to
start the real tunrrrnel.
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time. This modification should not change the overall
flow characteristics of the tunnel significantly. The
diffuser is inside the test chamber, and it is 200mm
from the nozzle exit. Figure 3 shows the grid of the test
chamber for the steady-state calculation. The grid for
the entire VTHST model for the steady-state calculation
has 166400 cells.
The supersonic wind tunnel starting process is a
complex phenomenon. After the Mach number at the
nozzle throat becomes 1.0, a nearly normal shockwave
moves from the diverging part of the nozzle into the test
chamber. Eventually, the diffuser will “swallow” the
shock and the flow inside the test chamber achieves the
designed conditions. Since the supersonic wind tunnel
flow is inherently an unsteady process, another way to
obtain the steady-state flowfield solution is to perform
time accurate calculations. Although flowfield solutions
take longer to obtain using time-accurate calculations
than steady-state calculations, time accurate calculation
should approximate more closely the physics of wind
tunnel flow. In addition, the results of time-accurate
calculations can be used to study the supersonic wind
tunnel starting process, which has seldom been
simulated using CFD.
This paper presents the results of viscous steadystate CFD calculations for the VTHST with a Mach 4
nozzle, as well as some results of the inviscid timeaccurate calculation with the Mach 4 nozzle, which is
still in progress Viscous effects are not included in the
time-accurate calculation because it is believed that
viscous effects do not play a significant role in the
supersonic wind tunnel starting process. However, in
my future studies, I would like to verify this
assumption. The Mach number profile at the nozzle
exits obtained using steady-state calculation is also
compared with available experimental data.
Nozzle Test Chamber
Diffuser
Figure 2: Boundary of the Grid for Steady-state
Calculation
Figure 3: Test Chamber Grid for Steady-state Calculation
As shown in Figure 4, for the inviscid time-accurate
calculation, a conical settling chamber is added in front
of the axi-symmetrical Mach 4 nozzle, test chamber and
diffuser assembly. The position of the diffuser is the
same as that in the steady-state calculation. The real
settling chamber consists of a constant area duct
followed by a converging nozzle. However, since the
exact geometry of the real settling chamber is not
available, a conical settling camber with approximately
the same volume is used in the CFD calculation. Figure
5 shows the grid of the test chamber for the timeaccurate calculation. The grid for the entire VTHST
model for the time-accurate calculation has 10477 cells.
The VTHST and Grid Generation
Introduction to the VTHST
The VTHST is an intermittent blowdown wind
tunnel. The overall length of the VTHST is 13 feet, and
it features a 14X7.9X8.9in. enclosed free-jet test
chamber. All parts of the VTHST are axi-symmetric
except for the test chamber. Before each run, the eight
storage bottles (11.3ft.3) are filled with working gas to
pressures ranging from 130 to 150atm. A time control
device switches on the main valve, and gas enters the
heater, and exhausts into the room. The VTHST also
features six replaceable nozzles with an exit diameter of
3.9in. designed for Mach 2.0 to 7.0 flows. The diffuser
can be moved back and forth inside the test chamber to
accommodate a variety of model sizes.
Settling Chamber Nozzle Test Chamber
Diffuser
Figure 4: Boundary of the Grid for Time-accurate
Calculation
Figure 5: Test Chamber Grid for Time-accurate
Calculations
Grid Generation
The grids for my CFD calculations are generated
using Pointwise’s Gridgen 15. For the viscous steadystate calculations, as shown in Figure 2, the grid
consists of axi-symmetrical Mach 4 nozzle, test
chamber and diffuser. The rectangular test chamber is
modeled as axi-symmetric to reduce computational
Flowfield Modeling
The CFD calculations are performed using
AeroSoft’s GASP (General Aerodynamic Simulation
Program), which solves the Reynolds Averaged NavierStokes Equations (RANS). GASP has been used in a
wide variety of applications such as Scramjet
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contour). To make the calculation as realistic as
possible, the boundary condition at the diffuser exit is
set to “Pback Subsonic Outflow” before the working
gas starts to exit the diffuser. Then the boundary
condition is set to “1st Order Extrapolation”. As will be
shown in the next section, the tunnel will not start if the
“Pback Subsonic Outflow” boundary condition is used
alone. In addition, “1st Order Extrapolation” cannot be
used alone because the back pressure influences the
flow properties inside the tunnel before the flow exits
the diffuser. When the gas starts to exit the diffuser,
exhaust plume near the boundary occurs outside of the
computational domain, and thus may alter the boundary
condition. Using “1st Order Extrapolation” will enable
the calculation to continue realistically without having
to model the exhaust plume.
The inviscid flux scheme used in my calculation is
Roe. First order spatial accuracy is used to make the
solution converge faster and more easily. Implicit dual
time stepping algorithm with 2nd order temporal
accuracy is used to obtain the time-accurate solutions.
Gauss Seidel is used for both implicit and inner
iteration schemes.
combustors and re-entry vehicle aerodynamics
simulations. For my calculations, GASP was run on 8
processors in a SGI Origin 2000 parallel computer. In
all the CFD calculations, the working gas is air, and it is
assumed to be a perfect gas.
Steady-state Calculation
At the nozzle inlet, the Q (density, products of
density and two components of velocity, and the
internal energy) is fixed, but the turbulence variables
are not fixed. This boundary condition at the inlet is
referred to as “Fixed Q (not turbulence)” in GASP. This
boundary condition requires the user to specify the
pressure and Mach number at the boundary. Another
boundary condition called “P0-T0 Subsonic Inflow”
which fixes the total pressure and total temperature at
the nozzle inlet could also have been used. But this
boundary condition does not work well if the geometric
contour near the boundary has large gradient such as
that shown in Figure 2. The boundary condition at the
tunnel walls are set to “no-slip and adiabatic”. Two
boundary conditions are suitable for the diffuser exit.
The first one is “Pback Subsonic Outflow”, which fixes
the pressure at the diffuser exit at a user-specified
value. This boundary condition can be used because the
tunnel exhausts gas into the room atmosphere, and the
flow inside the tunnel depends on the back pressure at
the diffuser exit. The second option is to use “1st Order
Extrapolation” boundary condition, which extrapolates
the flow properties at the boundary from interior cells.
By not enforcing a back pressure, the flow is not forced
to slow down by adverse pressure gradient, thus the
tunnel should be more likely to start. I have tried both
boundary conditions in my calculations.
The inviscid flux scheme used in my calculation is
Roe, with 3rd order spatial accuracy and Van Albada
limiter. The turbulence model used is Wilcox (1998)
k − ω model. Gauss Seidel is used for both implicit
and inner iteration schemes.
Results and Discussions
Steady-state calculation
The back pressure is set to 94800Pa (0.93atm), the
atmospheric pressure at Virginia Tech. The “Fixed Q
(not turbulence)” boundary condition requires the user
to input the pressure and the Mach number at the
boundary. The Mach number at the nozzle inlet is set to
0.05 using the area-Mach number relation for quasi-1D
flow. To start the tunnel, the pressure at the inlet is set
to 27atm. This pressure is well above the settling
chamber total pressure of 15atm, at which the real
tunnel starts1. Figure 5 shows the Mach contour inside
the test section when poc =15atm. Although the flow
inside the nozzle achieves Mach 4, an oblique shock
stands in the test chamber, and the tunnel is not started.
Time-accurate Calculations
Since disturbances can travel downstream of the
diffuser exit before supersonic flow occurs in the
nozzle, using the “P0-T0 Subsonic Inflow” boundary
condition at the nozzle inlet should most closely
approximate the physical situation. However, this
boundary condition will not work with the geometry
used for steady-state calculations as described in the
previous section. So a conical settling chamber with a
relatively small gradient in its contour is added in front
of the nozzle inlet as shown in Figure 4. Since viscous
effects are ignored in the time-accurate calculations, the
boundary condition at the walls is set to “tangency” (the
velocity vectors at the walls are tangent to the wall
Figure 5: Test Chamber Mach Contour (
poc = 15 atm )
Figure 6 shows that the VTHST is still not started
when poc is increased to 20atm. However, when the
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VTHST to verify the Mach number profile at the nozzle
exit.
Poc is increased to 27atm, the tunnel is started as shown
in Figure 7. The streamlines in Figure 7 shows that the
flowfield is uniform in the Mach 4 region of the test
section. The flow expands to Mach 6.0 after the Mach 4
region, and then slows down through an oblique shock
at the diffuser inlet. Although the Mach contour in
Figure 7 looks reasonable, the condition that produced
the flow is far from the realistic condition.
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Experimental Data (Ref. 1)
CFD Prediction
4.5
4
3.5
y(cm)
3
2.5
2
1.5
1
0.5
0
2.5
3
3.5
4
4.5
5
Mach#
Figure 6: Test Chamber Mach Contour (
Figure 8: Mach Number Profile at the Nozzle Exit
for the Steady-state Calculation
poc = 20atm )
T=0.0004sec.
T=0.001sec.
T=0.0018sec.
Figure 7: Test Chamber Mach Contour and Streamlines
(
T=0.0028sec.
poc = 27 atm )
T=0.0038sec.
To make the tunnel start, I also tried to set the
diffuser exit boundary condition to “1st Order
Extrapolation”, while leaving the nozzle inlet condition
unchanged. However, the solution diverged before it
reaches steady-state, and the Mach contour looked
similar to that in Figure 5.
The reason that the model tunnel cannot start at the
correct poc may be caused by the fact that the tunnel
T=0.004sec.
T=0.0043sec.
T=0.0083sec.
starting process is inherently unsteady. A steady-state
calculation cannot capture all the physics in the
unsteady tunnel starting process, such as the moving
shockwave, starting vortices and the change in
boundary condition described in the flowfield modeling
section.
Figure 8 shows a comparison between experimental
Mach number profile at the nozzle exit and the
numerical prediction. As shown in Figure 8, the
experimental and computed Mach number profiles
outside of the boundary layer seem to agree. However,
the measured boundary layer thickness is greater than
that predicted by CFD. This discrepancy could either
be due to errors in the experimental results presented in
Ref. 1, or the turbulence model used in my CFD
calculation. Experiments need to be performed in the
T=0.015sec.
T=0.020sec.
T=0.0266sec.
Figure 9: Flow Development in Time
Time-accurate calculation
The total pressure and total temperature for the “P0T0 Subsonic Inflow” boundary condition are set to
15atm (as in a real experiment) and 15oC respectively.
The Mach number at the settling chamber inlet is set to
4
The time-accurate calculation is performed
assuming inviscid flow because I believe that viscous
effects do not play a significant role in wind tunnel
starting process. However, in Ref. 3, Pope states that
viscous effects are extremely important in the tunnel
starting process. Thus, viscous effects will be modeled
in my future studies to determine the importance of
viscous effects in the supersonic wind tunnel starting
process.
0.009 using the area-Mach number relation for quasi1D flow. The solution is saved every 0.0001 seconds.
The flow reaches the diffuser exit at T=0.0031 seconds.
Thus, the boundary condition from T=0.0001sec. to
T=0.0031sec. is set to “Pback Subsonic Outflow”. “1st
Order Extrapolation” boundary condition is used after
T=0.0031sec. Figure 9 shows the Mach contour inside
the VTHST from T=0.0008sec. to T=0.0266sec. As
shown in Figure 9, the flow oscillates between the
diverging section of the nozzle and the front of the test
chamber from T=0.0018sec. to T=0.0043sec. After
T=0.0043sec., the oblique shock starts to move toward
the diffuser. At T=0.0266sec., the oblique shock is
“swallowed” by the diffuser. But if the Mach contour at
T=0.0266sec. is compared to Figure 7, one can see that
the tunnel is still not started completely at T=0.0266sec.
Experimental data from Ref. 1 shows that the timeaccurate calculation should be run until T=0.1sec. for
the VTHST to achieve steady-state flow. Currently, the
time-accurate solution diverges at T=0.0266sec. I am
still trying to determine the cause of the divergence.
One possible cause may be that the boundary conditions
are still incorrect. There could also be some subtle
problems with the grid.
Figure 9 shows that, if the calculation is able to
continue until T=0.1sec., time-accurate calculations
may indeed make the VTHST start at a realistic
pressure ratio. Before obtaining the solution shown in
Figure 9, I run the time-accurate calculation with only
the “Pback Subsonic Outflow” boundary condition, and
3rd order spatial accuracy instead of 1st order spatial
accuracy. The solution diverged at T=0.026sec., and the
Mach contour at T=0.026sec. is shown in Figure 10.
From the time-accurate solution, the oblique shock seen
in Figure 10 moves back and forth between the nozzle
exit and its current position in Figure 10. As shown in
Figure 10, if the “1st order Extrapolation” boundary
condition is not used, there is little hope that the model
tunnel can start.
(a) 3rd Order Spatial Accuracy
(b) 1st Order Spatial Accuracy
Figure 11: Velocity Vector Near the Nozzle Inlet at
T=0.0008sec.
Conclusions
Viscous steady-state and inviscid time-accurate
CFD solutions of the flowfield inside the VTHST with
a Mach 4 nozzle were presented in this paper. It is
found that steady-state CFD calculations cannot
accurately predict the flowfield inside the VTHST
because much higher pressure ratios are required to
start the VTHST in steady-state CFD calculations than
those required to start the actual tunnel. Although
currently the solution for the time-accurate calculation
Figure 10: Mach Contour at T=0.026sec. Without using
“1st Order Extrapolation” Boundary Condition
Another interesting phenomenon associated with
the tunnel starting process is starting vortex, which
occurs when liquid or gas is starting to move around
obstacles2. Figure 11 shows that one should use 3rd
order spatial accuracy to capture starting vortices.
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diverges at T=0.026sec., the time-accurate calculation
seems to be able to make the tunnel start at the correct
pressure ratio if the calculation could be run past
T=0.026sec. It is also found that 3rd order spatial
accuracy is needed to capture starting vortices near the
nozzle inlet. Starting vortices do not occur in
calculations with 1st order spatial accuracy.
Currently, I am trying to make the time-accurate
calculation run past T=0.026sec. Once I can get the
inviscid and 1st order spatially accurate calculation to
reach steady-state, I will add viscous effects into the
computational model to investigate the importance of
viscous effects in the supersonic wind tunnel starting
process. In addition, 3rd order spatial accuracy will
eventually be used to make my CFD simulation more
realistic.
Acknowledgement
This research is supported by Virginia Space Grant
Consortium (VSGC). I would like to thank my advisor
Dr. Joseph Schetz for his help in my research, and Dr.
Reece Neel of AeroSoft Inc. for his help in running
GASP.
References
1.
2.
3.
ITAM, “Description and Specification of VT
HST”, Novosibirsk, Russia, 2002.
Luo, X and van Dongen M. E. H., “Strong Starting
Vortices”,
http://www.fluid.tue.nl/GDY/vortex/vortex.html.
Pope, Alan and Goin, Kennith L., “High-Speed
Wing Tunnel Testing”, John Wiley & Son Inc,
1965.
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