Week 5: Prandtl Meyer Shock problem
Shock Wave and Boundary Conditions
Shock wave or shock is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a medium but is characterized by an abrupt, nearly discontinuous, change in temperature, pressure and density of the medium. The boundary conditions used are Dirichlet boundary condition, Neumann boundary Conditions and Mixed boundary condition.
Objective
To simulate Prandtyl Meyer Shock problem with variations in the SGS parameter for a velocity of 680 m/s at the inlet.
Geometry
Above is the geometry with the following dimensions 65,45.1525 and 8.151 in x,y,and z directions.
Boundary Conditions of Case 1
Inlet
Boundary type - Inlet
Pressure BC-Zero Normal Gradient
Velocity BC- 680m/s
Temperature BC- 286.1 K
Outlet
Boundary type -Outlet
Pressure BC- Zero Normal Gradient
Velocity BC- Zero Normal Gradient
Front and Back
Boundary type -2-D
Top and Bottom
Boundary type - Wall
Velocity BC- Slip
Temperature BC- Zero Normal Gradient
Mesh
For the mesh the control is given as follows base size of 0.8m with adaptive mesh refinement is activated. Above figure show the mesh grid.
Temperature AMR
Maxmium Cell - 200000
Embed type - Sub-Grid Scale Size
Max Embeddind Level- 2
Sub Grid Criterion-0.05,0.025 and 0.01.
Case 1- 0.05 SGS
Cell Count
With the SGS of 0.05 the cell count reached about 7682 cells at the end of the cycle.
Temperature
Above are the temperature plot and its contour during the the simulations.The Temperature at the inlet remains same 286.1K through the entire simulation. At the Outlet the started higher about 300K and begins to decrease as throughout the cycles because the flow spreads from a minute point to a braod area. The spreading can be viewd in the contour plots.
Animation of case 1 with 0.05 SGS
Case 1-0.025 SGS
The Sub Criterion - 0.025.
Cell Count
The Cell count for this case at the end of the simulation is 12673 cells with fluctations in the cycle during the simulation.
Temperature
From the temperature plots and from the contour we can see that the inlet temperature remains the same in the whole cycle. But the outlet temperature oscillates tremendously reaching the about 467 K of max temperature and falls down to 268 K at the end.
The SGS parameter is little bit more finer than the pervoius paramter setting which can be seen in the final mesh.
Animation of case 1 with 0.025 SGS
case 1 -0.01 SGS
The Sub Criterion for this case is 0.01.
Cell Count
The cell count for this case is at the end of the cycle is 15984 cells with a maximum cell count of 30878 cells during the cycle.
Temperature
During the simulation the temperature attains the max temperarure of 502 K and decreases to minimium of 268 K which less than the inlet temperature which was at a constant of 286.1 K.
The SGS parameter for this case is extremely finer compared to the other SGS parameter with the same Boundary conditons applied.
Animation of case 1 with 0.01 SGS
Case 2 - 0.05
This second case with changes in the inlet velocity.
Boundary Conditions of Case 2
Inlet
Boundary type - Inlet
Pressure BC-Zero Normal Gradient
Velocity BC- 100 m/s
Temperature BC- 286.1 K
Outlet
Boundary type -Outlet
Pressure BC- Zero Normal Gradient
Velocity BC- Zero Normal Gradient
Front and Back
Boundary type -2-D
Top and Bottom
Boundary type - Wall
Velocity BC- Slip
Temperature BC- Zero Normal Gradient
Temperature AMR
Maxmium Cell - 200000
Embed type - Sub-Grid Scale Size
Max Embeddind Level- 2.
Sub Grid Criterion- 0.05.
Cell Count
For this case the cell count reaches a maximium of 9595 cells and at the end simulation the cell count is about 7626 cells.
Temperature
The temperature for this case reached a maximium of 467 K at the outlet boundary falls down to 268 K till the end of the simulation this is because the temperature falls down as the flow spread vastly. The Inlet temperaure remains the same of 286.1 K.
The SGS parameter in this case is similar to the case 1 parameter.
Animation of case 2 with 0.05 SGS
Conclusion
In comparing the SGS parameter for the the inlet velocity of 680 m/s the 0.01 SGS value is more effective when compared to the other SGS values.
Smaller the SGS value higher the Cell Count with smooth distribution.