Prandtl Meyer Shock problem
Introduction:
In this project, the Prandtl Meyer shock wave phenomena is simulated using Converge Studio. The purpose of this simulation is to understand the effect of SGS parameter on shock location and cell count.
Shock Wave:
A shock wave is a propagating disturbance moving faster than the speed of sound in the medium. The shock wave carries energy in the medium and is characteried by an abrupt change in pressure, velocity, and density in the medium. When the speed of a source exceeds the speed of sound, the wave front lags behind the source in a cone shaped region steming from the vertex. The edge of the cone creates a supersonic wave front with a large amplitude. This is known as a \"shock wave.\" This action causes a \"sonic boom\" heard by the observer. The speed of the sound wave varies with its amplitude. The speed of the shock wave is always greater than the speed of sound in the medium and decreases with the amplitude of the wave. The shock wave dies when the speed it matches the ordinary speed of the wave. The faster an object moves, the narrower the cone of high pressure behind it becomes. The vertex angle of the cone of high pressure can be used to measure the speed of a supersonic object. i.e. a fighter jet.
Boundary Conditions:
The shock wave problem employs a Neumann boundary condition because it is supersonic. A Neumann boundary condition states that the outlet condition is dependent on initial condition flow. The properties of the fluid inside the domain cannot be altered fast enough to match the outlet flow. The wave is supersonic. Case 2 is used to compare a subsonic case.
Case 1 (Supersonic):
Inlet:
Velocity: 680m/s x-direction
Temperature: 286.1K
Fluid: Air
25000 cycles
Density based steady-state solver
Adaptive Mesh Refinement
Case 2 (Subsonic):
Inlet:
Velocity: 100m/s x-direction
Temperature: 286.1K
Fluid: Air
25000 cycles
Density based steady-state solver
Adaptive Mesh Refinement
Geometry:
The geometry for this problem was imported, scaled, and boundaries were flagged.
Mesh:
An adaptive mesh refinement was used to refine the mesh at the location where the shock occurs. Temperature mesh refinement was used. The mesh is refined when the change is greater than each user specified value. In this case SGS paramenters are 0.05, 0.08 and 0.1.
Adaptive mesh refinement uses the following equation:
`Gridsize = ((basegrid)/(2^(embed - \"level\")))`
Results:
Case 1 SGS 0.05:
Case 1 SGS 0.08:
Case 1 SGS 0.1:
Case 2 SGS 0.05:
Results:
Since the adaptive mesh refinement (amr) is dependent on the value of the sub grid scale (SGS), it is observed that the expansion fan becomes wider as the SGS parameter increases. High values of SGS limit the mesh refinement leading to not well-defined and blurred waves. Lower SGS will also cause a larger number of cells.
Conclusion:
This project observed various SGS criterias and found that the temperature contour with the lowest SGS value allows for finer meshs then the others. The Prandtl-Meyer Shock flow require amr in order to simulate the results accurately. This simulation allows for the studies of supersonic flows such as in aircrafts.