Investigation of Mach Number Independence Principle for a Two-Dimensional Wedge

Oswatitsch's independence principle is of primary importance in aerothermodynamics, particularly for high-speed vehicles. In accordance with this principle, force coefficients measured experimentally for a certain design at Mach 10 (e.g.) hold up under all higher Mach numbers, i.e., Mach> 10, provided the flow is inviscid and perfect gas. In any case, once the surface temperature exceeds a critical point, the independence principle begins to lose its validity. In this paper, a slender 2D wedge is analyzed numerically and theoretically for a range of Mach number $\mathbf{1 < \mathbf{M}_{\infty} < 20}$ for specific aerodynamic properties, namely, pressure coefficient $\boldsymbol{\mathrm{C}_{\mathrm{P}}}$, wave-drag coefficients $\boldsymbol{\mathrm{C}_{\mathrm{D}}}$, and shock wave angle, all of which are vital for designing hypersonic cruise and re-entry vehicles. The independence principle for the two-dimensional wedge is numerically assessed through FLU ENT in the context of an adiabatic wall boundary condition. The numerical results of $\boldsymbol{\mathrm{C}_{\mathrm{P}}, \mathrm{C}_{\mathrm{D}}}$, and shock wave angle computed under different Mach numbers are in relatively good agreement with the theoretical results. Also, for the slender wedge model considered here, at higher Mach numbers, its Mach angle's magnitude corresponds to the maximum deflection angle, which the flow undergoes at the body surface.