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By Tracie J. Barber, University of New South Wales, Australia
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The simulation of high Mach number flows is difficult
experimentally, and actual flight tests are not
feasible. CFD is a convenient method to use to
study this type of flow and predict flight performance.
Other advantages include the ability to predict flow
properties that are difficult to capture experimentally,
such as detailed pressure and temperature distributions.
At the University of New South Wales (UNSW), experimental,
computational, and theoretical results were
recently compared for two cases that exhibit quite different
shock behavior - a cone and an Apollo module.
This preliminary work will form the first stage of
ongoing research into re-entry vehicle and rocket flight
analysis. The two cases chosen represent two fairly simple
bodies, exhibiting quite different shock behavior.
The Apollo module model is well-known to have a curved,
non-attached shock wave before it in supersonic flow.
The cone is a well-studied body in supersonics and exhibits
an attached shock. The variation in the shock waves
produced by the two bodies proves a useful test of the
CFD modeling capability, while also allowing the flow
in the base region to be studied.
The first body studied is a 15° cone, traveling at zero angle of attack,
and outfitted with two pressure taps. The second is a 1/30th scale model
of the Apollo re-entry vehicle, also traveling at zero angle of attack,
and outfitted with four pressure taps. Visualization of the shock waves
on the actual bodies was performed using the Schlieren method at the UNSW
supersonic wind tunnel facility at a Mach number of 3.05. At this Mach
number, the static pressure is found to be The first body studied is a
15° cone, traveling at zero angle of attack, and outfitted with two pressure
taps. The second is a 1/30th scale model of the Apollo re-entry vehicle,
also traveling at zero angle of attack, and outfitted with four pressure
taps. Visualization of the shock waves on the actual bodies was performed
using the Schlieren method at the UNSW supersonic wind tunnel facility
at a Mach number of 3.05. At this Mach number, the static pressure is
found to be 11.32kPa in the test section. Temperature was calculated to
be 102.5K, local density 0.3848 kg/m3, and the local speed of sound found
to be 202.9 m/s. Reynolds numbers for the two cases, based on model characteristic
length, were found to be approximately 8.52x105.
Comparison of CFD and exparimental shockwave locations
for the Cone model
The Schlieren method makes use of the high density gradients present
in flows exhibiting shock characteristics to enable visualization of the shock
waves. Simulations of the two vehicles were performed using FLUENT 6.
The Spalart-Allmaras turbulence model was used, and converged results
were obtained using adapted meshes and second order upwind differencing.
For computational efficiency, both cases were run as axisymmetric models.
Although the vehicles are indeed axisymmetric, the wind tunnel test
section in which they are studied is not. Therefore any shock waves reflecting
off the simulated tunnel walls, or their subsequent effects, are not correctly
captured by the 2D models.
For the 15° cone, the photographic Schlieren result and the CFD result both
show an attached shock wave that can be seen as the dark straight lines
coming off the very front of the cone. The shock wave angle measured from
the experimental image is 25.5° and from the CFD image is 25.1°. Pressure
coefficient values found from the experimental pressure taps and from
corresponding CFD locations match well.
Pressure coefficient values predicted by FLUENT for the
15° cone are in good agreement with experiment
For the Apollo module scale model, the unattached shock wave in the photographic
Schlieren result appears as a gradient in the image, off the front of
the body. The CFD predictions for the size and location of the shock wave
are in good agreement with experiment. Pressure coefficient values are
also calculated for the locations of the four pressure taps, and with
the exception of one site, good agreement is obtained. The site where
the agreement is poorest is located at the base of the model. As this
measurement location is found just after a sharp corner, where the flow
is subsonic, it is likely that the turbulence model used is not accurate
enough to capture the recirculating flow in this region. Further work
is planned to investigate other turbulence models as the prediction of
the effects on the afterbody are also of interest.
Pressure coefficient values predicted by FLUENT for the
Apollo scale model
are in good agreement with experiment
Comparison of CFD and experimental shockwave locations
for the Apollo model Comparison of CFD and experimental shockwave locations
for the Apollo model
The theoretical downstream properties expected for the flow, based on
the equations for normal shockwave relations, can also be computed from
the FLUENT results and compared to a theoretical value. For the Apollo model,
the ratios of downstream to upstream (relative to the shock wave) values
of pressure, temperature, and density were found at the front central location
of the model. For the most part, these ratios were found to be in good
agreement with the values calculated theoretically (from standard shockwave
relationships). In particular, the good comparison for the temperature
ratio across the shock (1.1%) is a useful indication of the validity
of the CFD model since no experimental data for the temperature was
available.
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