Week 5: Prandtl Meyer Shock problem
Aim:- To simulate the prandtl mayer shock problem and steady the Effect of SGS parameter on shock location an cell count.
Shock Flow Boundary Conditions: For solving the steady state flow appropriate boundary conditions are needed. It is one of the required components of the mathematical model. On the other hand for solving transient flow appropriate initial condition is required. Boundary condition are generally three types Dirichlet boundary condition ,Neumann boundary condition and mixed boundary condition .If the flow is supersonic, the specified pressure will no longer be used,pressure will be extrapolated from the flow in the interior. When using a dirichlet boundary condition the value of variable is prescribed at the boundary. Neumann boundary condition specifies the value in which derivative of a solution is applied within the boundary of the domain.
What is a shock wave?
When the speed of the moving object or source exceed the speed of sound in medium then the wave front lag behined the source forming a cone shaped region behined with a source vertex. The edge of the cone forms a supersonic waves front with an usually large amplitude called a shock wave.
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 pressure, temperature, and density of the medium.
When a shock wave passes through matter, energy is preserved but entropy increases. This change in the matter's properties manifests itself as a decrease in the energy which can be extracted as work, and as a drag force on supersonic object ; shock waves are strongly irreversible process.
Given cad model is import on the converge studio by dragging method
After importing the geometry check for diagnosis dock
Transform the normal for the inside flow
Case setup
Select predefined material as Air
In run parameter select Steady solver
Simulation time parameter
Solver parameter steady state
Boundaries are flagged as inlet , outlet ,twod-1, twod-2 and slip.
Inlet
Inflow boundary is chosen with neumann bounary condition
Pressure boundary condition- Zero normal gradient
Velocity boundary condition- Specified value 680 m/s
Temperature boundary condition- Specified value 286.1K
Outlet
Zero normal gradient - For both pressure and velocity
Twod-1, Twod-2- Two_D
Slip
Bounary type- Wall
Velocity boundary condition
Wall motion type- Stationary
Surface movement-Fixed
Temperature boundary condition- Zero normal gradient
Turbulent kinetic energy boundary condition- Zero normal gradient
Turbulent model - RNG-K-epsilon
Grid size
dx=0.8m, dy=0.8m, dz=0.8m
Adaptive mesh refinement is applied
Adaptive mesh refinement is applied where the selected property changes its value beyond the specified value. In the above setup temperature based AMR is used. The temperature is monitored and the mesh is changed according to the temperature.
Different values of SGS temperature are impleted and cell count is studied. The number of level of refinement is said to 2.
Result
Case-1
When no Adaptive mesh refinement is used
Case-2
When Adaptive mesh refinement is used
At SGS=0.1
At SGS=0.075
At SGS=0.05
https://www.youtube.com/watch?v=qKqrI1pr4aw
At SGS=0.025
At SGS=0.01
Conclusion
| S.no | SGS Temperature | Maximum cell count |
| 1 | No AMR | 4322 |
| 2 | 0.1 | 5233 |
| 3 | 0.075 | 5887 |
| 4 | 0.050 | 7534 |
| 5 | 0.025 | 12570 |
| 6 | 0.01 | 15858 |
1. Cell count is observed as variable when AMR is applied at different SGS , when SGS temperature value decreases maximum cell count increases.
2. From the above temperature gradient contour we can say that width of expansion slightly changes when refinement applied. Higher the SGS
parameter more spread out because grid is not refined . Lower the value of SGS parameter grid is more refined at the formation of expansion and hence accuracy is greater.
3. The above table shows the cell count is different for different SGS temperature. When the value of the SGS temperature reduses cell count increases because mesh get refined even small changes in curvature.
4. Variation of all temperature , pressure ,mech number and mass flow are observed for all the cases by plot, contour and animation.
Calculation for Grid size 1st level
`Grid size=(Basegrid)/2^(embeded- l evel)`
=`0.8/2^(2-1)`
= 0.4
Calculation for Grid size 2nd level
`Grid size=(Basegrid)/2^(embeded- l evel)`
=`0.4/2^(2-1)`
= 0.2
Calculation for Grid size 3rd level
`Grid size=(Basegrid)/2^(embeded- l evel)`
=`0.2/2^(2-1)`
= 0.1