Prandtl Meyer Shock problem
Aim- To study the flow characteristics of fluid passing over an expansion corner and to see how the SGS parameter affects the simulation results.
Governing equation- The equation used to solve this case is Navier-Stokes Unsteady equations. It comprises of 5 equations continuity, x-momentum, y-momentum, z-momentum, and energy equation.
Objective- The objective of this problem is to simulate fluid flow over an expansion corner at different SGS parameters.
Description- First the geometry to be simulated is imported in Converge Studio and then the geometry is checked for any errors. The geometry is grouped into faces so that respective boundary conditions can be assigned and then the case setup is done. This is a steady-state simulation with end cycle 20,000. It is a turbulent flow simulation hence the RNG k-epsilon turbulence model is selected. The mesh size used is 0.8m in all directions. In this project, temperature AMR was provided with maximum embedding level of 2 and sub-grid scale criteria as 0.05 and then results are compared with different SGS parameters.
Geometry-
Material- Fluid: Air
Boundary Condition-Inlet: Velocity 680m/s
Outlet: Pressure Zero normal gradient
Top_bottom: Fixed wall no slip.
2D: TWO_D
Initial Condition- Pressure:50000.0 Pa and temperature:300K
Mesh- Mesh size:0.8m with temperature AMR was provided with maximum embedding level of 2 and sub-grid scale criteria as 0.01, 0.05, 0.07, and 0.09.
SGS 0.01
SGS 0.05
SGS 0.07
SGS 0.09
Results-
Cell count
The above plot shows how the cell count varies as the throttle position changes. The max cell count is between 2-4ms when the throttle is at max angle of 25deg and then it gradually decreases as the throttle comes back to its original position of 0deg.
1.) 100 m/s
SGS 0.01
Pressure
Temperature
Velocity
SGS 0.07
Pressure
Temperature
Velocity
SGS 0.09
Pressure
Temperature
Velocity
2.) 680 m/s
SGS 0.01
Pressure
Temperature
Velocity
SGS 0.05
Pressure
Temperature
Velocity
SGS 0.07
Pressure
Temperature
Velocity
SGS 0.09
Pressure
Temperature
Velocity
Conclusion
As the SGS parameter decreases the cell count increases and hence we get accurate results. The temperature and pressure decrease whereas the velocity increases after the expansion corner which is the characteristic of the Prandtl Meyer flow.