Week 5: Prandtl Meyer Shock problem

Types of boundary conditions

1)Dirichlet boundary condition -it indicates the value of the unknown function of that long domain.

2)Neumann boundary condition- it indicates the derivative of the solution is normal to the boundary domain.

3)Robins Boundary layer -its combination of Dirichlet and Neman boundary layer in all parts of the boundary.

4)Mixed boundary layer -it's also a combination of Dirichlet and Neman boundary layers but only valid for some part of the boundary.

5)Cauchy boundary condition - it will tell both functional value and normal derivative on the boundary of the domain.

shock wave

shock wave is a compression wave

the shock wave is propagating disturbance /noise which travels faster than the speed of sound in an air 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 pressure, temperature, and density of the medium.

types shock wave

1. Normal shock wave -shock created at 90 degrees, normal shock wave changes the supersonic flow in lower subsonic flow, increase pressure

2. Oblique shock wave -shock created at an angle as per body deflection angle, where it also change supersonic flow higher subsonic flow

3. Bow shock -shock created when flow velocity exceeds Mach 1. its mainly seen in aircraft, where it acts both normal and oblique shock wave

Prandtl Meyer shock problem

A supersonic expansion fan, known as Prandtl Meyer expansion, two dimensional simple waves, is a centered expansion process that occurs when a supersonic flow turns around the convex corner, when a flow turns around a smooth and circular corner this wave can be extended backward to met at a point.

the expansion is isentropic since the expansion waves take place across a continuous succession of Mach waves and also there is no change in entropy for each match wave .as the flow passes through the expansion waver, the Mach number increases, and the pressure, density, and temperature

mesh

temperature

velocity

pressure

case 2

scg=0.01

case3

scg=0.001

conclusion

the cell count increases when we decrease the temperature subgrid scale criteria

the pressure , temperature decrease across each wave and velocity increase