Prandtl Meyer Shock problem using Converge CFD

1:- Types of Boundary Conditions Used in CFD:

• Dirichlet Boundary Condition
• Neumann Boundary Condition
• Mixed Boundary Condition
• Robin Boundary Condition

1.1:- Boundary Condition Applicable for shock flow:

For a successful simulation of this Project, proper boundary parameters must be applied to the solver. Here for this simulation, we have to choose between Dirichlet Boundary Condition and Neumann Boundary Condition. This simulation must be done with a density-based solver as we know that the density of compressible fluids tends to vary at high-velocity flow. For this simulation, we can't give a fixed value for outlet pressure/velocity so for this we implement Neumann boundary condition so that the outlet pressure & outlet velocity is based on the initial condition.

2:- Shock Wave:

When the velocity of an object exceeds the local velocity of sound (343 m/s) it causes a cone-shaped expansion fan along the convex corner of the object's profile. This cone-shaped expansion fan is called shock wave. In this condition, the initial Mach number will be greater than 1. This shock wave carries energy & can be spread to the medium which has the characteristics of change in pressure, temperature & density with the familiar sound of a sonic boom.

Procedures:

1. Preparing a channel to stimulate simple flow using Converge CFD.
2. Setting up the boundary conditions & simulation setup.
3. Base Grid meshing is to be
   • dx = dy = dz = 0.8m.
4. Adaptive mesh to be implemented with the following Sub-Grid Scale criteria(SGS) conditions,
   • Case_1: SGS=0.5
   • Case_2: SGS=0.01
   • Case_3: SGS=1.0
5. Using CYGWIN to execute the CFD solver.
6. Use Converge CFD to post convert the output files to ParaView format.
7. Paraview to Post Processing the results.

Inputs:

• Inlet Pressure = ( Based on Initial Conditions )
• Outlet Pressure = ( Based on Initial Conditions )
• Channel Length L = 65 m
• Flow type = Shock Flow ( Turbulent )
• Fluid Medium = Air (Nitrogen, Oxygen)
• For super-sonic flow Inlet Velocity = 680 m/s
• For sub-sonic flow Inlet Velocity = 100 m/s
• Total No of cycles = 25000
• Solver Type = Density Based Solver
• Initial Pressure = 50000 Pa

Pre-Processing & Setting up Boundry Conditions:

Processing for Case-1:

Meshing without SGS:

Adaptive Meshing with SGS=0.05

Adaptive Meshing with SGS=0.01

Adaptive Meshing with SGS=0.10

Super Sonic Flow for Case:1

Velocity Contour:

Pressure Contour:

Sub-Sonic Flow for Case:1

Velocity Contour:

Pressure Contour:

Post_Processing for Case-Super Sonic Flow (SGS=0.05):

Average Velocity Plot:

Mass Flow Rate plot:

Pressure Plot:

Mach No Plot:

Temperature Plot:

Plot for Total Cells Count :

3:- Effects of SGS on Shock Location:

• From the SGS figure of all the three cases, we can see that at the lower Sub-Grid Scale (SGS=0.01) the mesh gets two-stage finer and more detailed so that is can provide us the accurate simulation along the shock flow region. Whereas for higher scale (SGS = 0.10) the mesh is coarse which results in inaccurate simulation patterns.
• The lower Sub-Grid Scale takes more time to solve which also generate higher number of cells when compared to high Sub-Grid Scale simulations which has fever number of cells.
• The lower Sub-Grid Scale simulation provides us finer mesh along most of the expansion fan areas while the higher number SGS simulation provides finer mesh only near the convex corner of the flow channel.

From the mass flow rate plots, we can see that the inlet profile is inversely proportional to the outlet profile. This shows us that the flow is conservative as masses were conserved during the flow.