Week 5: Prandtl Meyer Shock problem
Shock waves: These are the waves generated in the channel due to the sudden change in pressure between the fluids due to some kind of shark edge or any kind of diversions. Basically, due to these kinds of diversions, an imaginary boundary is generated, which varies the Mach number around its perimeter. As the same fluid of two different Mach numbers (having different velocities) interacts on an interface, that will cause disturbance there. That disturbance at the interface is due to the striking of different velocities of fluids with each other, and waves are generated that are turbulent and variable (in terms of velocities and pressure) and are, therefore, called shock waves.
SGS parameter: SGS stands for Sub-Grid Scale that is the alternative grid size mesh than base grid, which is applied over certain parameter like temprature, pressure, velocity, etc. to analyse the flow in better way at a perticular section than rest of the space.
- As the SGS value decreased, the cell count values increased.
- By reducing the SGS value, we get a more clear and refined view of flow, which is better for predicted result calculations.
For achieving the same, first go for importing the geometry, and in this we downloaded the model file and imported it by dragging the file into CONVERGE-STUDIO. After this, go for the normal checks, which must be pointed in the direction of the flow. Then, a diagnosis is done to check for any kind of geometrical error. After verifying it, the case setup is set as per the given inputs and boundary conditions. In this case, all the basic parameters are selected with specific values, and all these values are setup together as input files for the model. During the case setup, the important thing that we need to keep in mind is to initialise the air input at supersonic speed. Along with this, as the edge of the interface, a lot of the disturbance is expected, so for that also adaptive mesh refinement is required to clarify the physics at the interface in a better manner. So after setting that all up, we need to do case setup validation and then export the input files into the folder.
The simulation that follows can be converging by using the Cygwin interface, which is required for giving the command to the software. In Cygwin, first we go to the directory where the input files are present and then command them for simulation. This simulation can be done automatically at the back end, and the output files are generated in the same folder as the results of the simulation.
Then those output files have to be exported in Paraview to see the results in the different interfaces and also in their plots in the Converge Studio. For importing the output files in Paraview, first we need to convert the data into a ".vtm file," which is done in the "Post-Processing 3-D" option in Converge-Studio. Then all the 3D and 2-D analyses of the results are analysed separately. The rest of the plots can be seen in Converge-studio itself, specifically under the "line-plotting option."
By doing so, I was able to obtain all of the required results for this particular challenge and take screenshots of them. The CFD analysis of this problem is done three times for three different mesh sizes, and the results are attached in a word file. Kindly find it below.
Detailed explanations about the plots:
The cell count in this challenge is constant at the initial condition but for a very short amount of time. After that, as the disturbance is created due to crossing the pre-feed limit of adaptive mesh refinement, the grid adjustment starts. This increases with the increased rate of shock waves. As the mesh size decreases, it increases the cell count, which makes the graph steeper. But after a certain period of time, it will be almost constant, i.e., after 2000 cycles.
The mass flow rate plots appear to be unstable at first touch, but as the flow cycled on, convergence took effect. After achieving the convergence shown in the graph, we observe that the mass of the flow that enters the geometry from the inlet per unit of time is equal to the mass of the flow that exits from the outlet. But due to the sign conventions, the input and output flows are represented, respectively, as positive and negative values for comparison.
Animation link: https://youtu.be/qlwNoiVC66s
Anubhav