# Wolf Dynamics - Multiphysics simulations, optimization, and data analytics

## OPENFOAM VALIDATION CASES

Supersonic flow past an expansion corner

In this case, we simulate a supersonic flow past an expansion corner. The equations to be solved are the Euler equations and the air is modeled as an ideal gas. The inlet Mach number is 2.5, inlet pressure is 303961 Pa, inlet temperature is 300 k, and the expansion corner is inclined 15 degrees below the horizontal line.

The exact solution to this problem can be computed using isentropic flow relations and the theory of Prandtl-Meyer expansion waves (expansion fan).

 Left figure: Computational domain and boundary conditions. Right figure: Domain mesh.

 Left figure: Expansion fan visualization using Mach number contours. Right figure: Sampling of Mach number along the sampling line.

TheoreticalOpenFOAMPercent Error (%)
Mach number after expansion fan
 3.2370
 3.2302
0.21

warning  The theoretical value was extracted/interpolated from tables illustrated in the references below.
We can not guarantee the accuracy or precision of this information.

References:

Modern compressible flow: with historical perspective. Third edition. McGraw-Hill.

Compressible aerodynamics calculator. http://www.dept.aoe.vt.edu/~devenpor/aoe3114/calc.html