Compressible Flow

```Compressible Flow: possible topics to
cover in CFD class.
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Bocal 1D (Anderson – Comp Fluid Dyn.)
Supersonic jet expansion
Prandtl Mayer compression/expansion
Supersonic flat plate
NACA 0012 transonic (Marco Antônio tese)
Blunt body shok wave
Explore Sub-sonic potential Flow
• Look if it is possible to explore supersonic
potential flow.
• How one can handle transonic potential flow. This
is a big issue because M < 1 ellipitc equation,
M>1 hyperbolic equation. Pherhaps a way to go is
to use transient approach which is a marching
procedure capable to capture shocks.
• How to set up compressible potential flow in
phoencs. Use bernouli to get pressure.
Bocal 1d
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Already developed in c-v-nozzle. The nozzle shape was developed in a fitting
using excel. The area porosities derived from this fit and were inserted in
phoenics using inform.
The nozzle has heat addition but no-friction (yet).
The model does not have diffusive terms. It uses quick scheme. The pressure
term due wall inclination still have to be discussed. According to IM250
homework there is a term but according to Anderson’s book it does not have
see pg 292, eq. 7.25.
Actually the momentum equation and energy equation have to be clearly
stated in 1D form before going to cfd. It has to be done in a document.
The flow in the nozzle is isoentropic. The heating is done upstream the nozzle.
The theoretical isoentropic relationship have to be developed to check the
numerical solution.
The shock capture have to be explored. What is conserved, what changes
along the shock. The shock thickness and it grid dependecy.
Shock Tube 1d
• It has to explore the time step in a shock tube.
tube solutions.
Shock Tube 1d
• It has to explore the time step in a shock tube.
tube solutions.
Supersonic Jet Expansion
• It introduces the use of ‘parabolic’ model to a
2D flow capable to handle hyperbolic flow
because it is a marching procedure.
• The main issue is the parabolic set up in
phoenics including the special inform
commands.
Prandt Mayer Expansion
• Parabolic /hyperbolic model in phoenics
• Compare with analytical/numerical solution
given in Anderson pg. 174
Supersonic Flat Plate
• Challenging problem because there is nonviscous flow with a boundary layer viscous
flow and shock interaction.
• The energy equation has to consider the
dissipation term which will increase the air
temperature near the wall.
• See discussion in Anderson, pg. 449 and also
in the analytical solution (kamotani class)
Transonic NACA 0012
• Get the MS thesis of Marco Antônio
Blunt Body
• A challenge. I don´t have any material to start
with.
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