Prandtl Meyer Shock problem

Theory:

Shock wave, strong pressure wave in any elastic medium such as air, water, or a solid substance, produced by supersonic aircraft, explosions, lightning, or other phenomena that create violent changes in pressure

Basically when the velocity increases greater or equal to speed of sound shock waves are generated due to disturbance in pressure.we can determine the type of wave by using mach number: M=v/c (v=velocity of moving aircraft c=speed of sound )

Boundary condition:

Inlet:

Velocity =680 m/s in x direction

Temperature= 286.1 K

Exit:

Pressure- Zero normal gradient

Velocity- Zero normal gradient

Front and Back – 2D ,Top and Bottom Wall – Slip Wall.

Later SGS was changed to 0.5 just to know what it meant.After that velocity of 100m/s was placed .

General study: At high speed fluid flow no- slip condition fails so slip occurs .Also flow becomes compressible so density based steady state solver must be used.M<0.3(INCOMPRESIBLE ) otherwise compresible .

When as we cannot create entire atmosphere and we create a small boundary with area of consideration so the non reflective boundary conditions must be used as the flow should not be disturbed due to wall boundary and various theories are available on internet for it

Simulation Time Parameters:

Start Time: 0 Cyc

End Time: 25000 Cyc

Solver: Density based steady state solver

Fluid under consideration: Air (O2 + N2)

Plots for pressure and velocity are shown .we observe that shock wave creates a sharp boundary and angle can be determined by

Now when sgc was changed from 0.03 to o.4

From the post processing results, it can be observed that the expansion fan tends to become less narrow and distinct as the SGS parameter increase. This is due to the fact that the adaptive mesh refinement is dependent on the value of sub grid scale (SGS). Higher values of SGS of limits the mesh refinement required to capture the expansion waves effectively leading to a blur and not well-defined waves

NOW when the velocity was changed to 100m/s

As the flow is subsonic we do not observe any significant changes in pressure and shock waves are not generated .

Regarding the cell counts

The cell counts were observed to decrease a expected for higher sgc of 0.5 as can be seen from the contour that its accuracy decreases due to less no of cells