# Prandtl Meyer Shock problem using Converge CFD

**OBJECTIVE-** Simulate Prandtl Meyer Shock problem and look at the effect of SGS temperature value on cell count and the shock location.

**Case-1: For SGS value- 0.02 k (supersonic flow)**

**Case-2:** **For ****SGS value- 0.05 k (supersonic flow)**

**Case-3:** **For ****SGS value****– 0.1 k (supersonic flow)**

**Case-4:** **For ****SGS value****– 0.2 k (supersonic flow)**

**Case-5: For SGS value- 0.05 k (subsonic flow)**

**SHOCK WAVE:**

Shock waves are generated when an object moves faster than the speed of sound(supersonic speed), and there is an abrupt change in the flow area or diversion, the flow process is irreversible and the entropy increases.

Shock waves are very small regions in the gas where the gas properties change by a large amount. Across a shock wave, the static pressure ,temperature and gas density increases almost instantaneously.

**Shocks are basically of tree types**:

**Normal Shock:**

Occurs when shock is 90° (perpendicular) to the shock medium’s flow direction.

**Oblique Shocks:**

Occurs when shock is at a certain angle to the shock medium’s flow direction.

**Bow Shocks:**

Occurs upstream of the front of a blunt object when the upstream flow velocity exceeds Mach 1.

**Boundary conditions in shock flows:**

In case of Shock flow problems Neumann boundary conditions are used at the outlet.As outer bounadry has no influence on the inner nodes, in nuemann boundary conditions the values at the outlet is extrpolated from the inner nodes.Neumann boundary conditions include derivative of the solution at the boundary.

At the inlet Dirichlet boundary condition is provided.Dirichlet boundary condition specifies the values that a solution needs to take along the boundary of the domain.

**Prandtl Meyer Shock problem**

When a supersonic flow encounters a convex corner, it forms an expansion fan, which consists of an infinite number of expansion waves centred at the corner.A illustrative diagram is shown below.

**Geometry-**A 3D geometry was exported to the converge studio.

**Setup-**

**Applications-**

-General flow

**Materials-**

-Air

**Simulation Parameters:**

-Density based steady state solver

-Start time-0, End time-25000 cycle

-Intial time step=minimum time step=1e-7 s

-Maximum time step=1 s

**Boundary conditions- **

-Inlet- INFLOW-velocity-680 m/s

-Outlet- OUTFLOW-pressure & velocity-Zero normal gradient

-Top & bottom- Wall-slip

-Front- 2D

-Back – 2D

**Regions & Initialization:**

Boundaries are assigned to region

Velocity and pressure set to 680 m/s and 50000 pa

Species-Air

**Base grid**– dx=dy=dz=0.8 m

**Adaptive mesh refinement**-SGS value-0.02,0.05,0.1 & 0.2.

**Mesh-**

**Total cell count for different SGS value:**

From the below graph it seen that with increase in SGS value from 0.02 to 0.2 the no of cell count decreases.

**Case-1: SGS- 0.02 K (supersonic flow)**

**Mesh-**

For SGS -0.02 K the adaptive mesh refinement is the maximum and mesh is very fine in shock region.

**Results-**

Results show that the flow properties like teperature ,pressure ,velocity and mach no. has changed across the shock wave.

Temperature Contour:

From the temperature contour below it can be seen that there is a temperature fall across the expansion wave ie. T1 > T2.

**For SGS -0.02 **

**Velocity Contour:**

From the velocity contour below it can be seen that there is a increase in velocity across the expansion wave ie. V1< V2

**Pressure Contour:**

From the Pressure contour below it can be seen that there is a pressure fall across the expansion wave ie. P1 > P2

**Mach Number at inlet and outlet:**

We can see that the Mach no. has increased from 2 to 2.16 across the shock wave indicating an increase in velocity.

**Case-1: SGS- 0.05 K (supersonic flow)**

**Mesh-**

For SGS -0.05 K the adaptive mesh refinement is less than the SGS 0.02.

**Results-**

Results show that the flow properties like teperature ,pressure ,velocity and mach no. has changed across the shock wave.

**Temperature Contour:**

**Velocity Contour:**

**Pressure Contour:**

**Mach Number at inlet and outlet:**

We can see that the Mach no. has increased from 2 to 2.16 across the shock wave indicating an increase in velocity.

**Case-1: SGS- 0.1 K (supersonic flow)**

**Mesh-**

For SGS -0.1 K the adaptive mesh refinement is very less as result the cell count is also less.

**Results-**

Results show that the flow properties like teperature ,pressure ,velocity and mach no. has changed across the shock wave.

From the below results we can see that for SGS 0.1 the mesh is very coarse in AMR region and the contours for the mach cone is hazy.

**Temperature Contour:**

**Velocity Contour:**

**Pressure Contour:**

**Mach Number at inlet and outlet:**

We can see that the Mach no. has increased from 2 to 2.16 across the shock wave indicating an increase in velocity.

**Case-4: SGS- 0.2 K (supersonic flow)**

**Mesh-**

For SGS -0.2 K the adaptive mesh refinement is the lowest as result the cell count is also less.

**Results-**

From the below results we can see that for SGS 0.2 the mesh is very coarse in the shock region and the contours for the mach cone is very hazy.

The angle of shock also is slightly at a higher angle to the horizontal.

**Temperature Contour:**

**Velocity Contour:**

**Pressure Contour:**

**Case-5: For SGS value- 0.05 k (subsonic flow)**

**Inlet velocity=100 m/s**

**Setup-**

**Applications-**

-General flow

**Materials-**

-Air

**Simulation Parameters:**

-Density based steady state solver

-Start time-0, End time-25000 cycle

-Intial time step=minimum time step=1e-7 s

-Maximum time step=1 s

**Boundary conditions- **

-Inlet- INFLOW-velocity-100 m/s

-Outlet- OUTFLOW-pressure & velocity-Zero normal gradient

-Top & bottom- Wall-slip

-Front- 2D

-Back – 2D

**Regions & Initialization:**

Boundaries are assigned to region

Velocity and pressure set to 680 m/s and 50000 pa

Species-Air

**Base grid**– dx=dy=dz=0.8 m

**Adaptive mesh refinement**-SGS value=0.05

**Total cell count:**

Total cell count is around 4500 and AMR has no change in cell count as no skock waves are generated in subsonic flows.

**Results-**

**Temperature Contour:**

The temperature contour indicate that for subsonic inlet we dont see shock waves and AMR is also of no use in subsonic flows

**Velocity Contour:**

The velocity contour indicate that for subsonic inlet we dont see shock waves and AMR is also of no use in subsonic flows

**Pressure Contour:**

The pressure contour indicate that for subsonic inlet we dont see shock waves and AMR is also of no use in subsonic flows

**Animation of shock wave:**

**Conclusion:**

1. The Prandtl Meyer Shock problem was simulated successfully for four different SGS value.

2. With decrease in from 0.2 to 0.02 the the number of cell count increased due to more mesh refinement.

3. With lower SGS value the contours were smooth with prominent shock wave and results were more accurate.

4. For subsonic flow no shock wave were formed.