Prandtl-Meyer Flow

cavity_flow_image.png

This tutorial will cover the basics of setting up and running a Prandtl-Meyer expansion fan problem. Files for running the case yourself can be found here: LOCI-STREAM RUN FILES

The Prandtl-Meyer expansion fan is a situation where a supersonic changes direction in such a way that the flow bends away from itself. In this problem a compressible flow with a Mach number of 2.5 flows left to right and bends around the corner, which produces the Prandtl-Meyer expansion fan.


ComputatIOnal Domain

 
Simulation_domain.png

The domain is a simple rectangular geometry with an edge that bends away at 15 degrees. The mesh is extruded in the z-direction to create a 3D geometry with a single cell thickness.


To see the Loci-Stream control file click for this case click HERE.


Running the Code

Loci-Stream is an MPI based parallel code, so execution of the code is started with a call to mpirun. A template call is shown below where the terms in brackets(<>) are replaced by the specifics of your case.
mpirun -np <np> <path_to_stream_exec> --scheduleoutput -q solution <casename> <restart> > /dev/null >run.out 2>&1 &

For this example the call is:
mpirun -np 4 /home/user/Loci-Stream/bin/stream --scheduleoutput -q solution prandtl  > /dev/null >run.out 2>&1 &


Results

The 'extract' utility is used to view the results of a simulation. For this case we view the simulation at the 10,000th time step. In the run directory extract the solution using: extract -vtk prandtl 10000 P v r t m . This will generate a solution directory with files in the Paraview VTK format which can be opened by Paraview. The case name is 'prandtl' and the timestep is '10000', and the variables to extract are the pressure(P), velocity(v), density(r), temperature(t), and mach number(m).

Above on the left is a contour plot of the velocity magnitude within the cavity. On the right is a stream traced plot of the velocity field. A set of secondary vortices in the corners can be seen as well as the formation of tertiary vortices.