Oblique Shock - Oblique Shock Waves and The Hypersonic Limit

Oblique Shock Waves and The Hypersonic Limit

As the Mach number of the upstream flow becomes hypersonic, the equations for the pressure, density, and temperature after the oblique shock wave reach a mathematical limit. The pressure and density ratios can then be expressed as:

$\frac{p_2}{p_1} \approx \frac{2\gamma}{\gamma+1}M_1^2\sin^2\beta$

$\frac{\rho_2}{\rho_1} \approx \frac{\gamma+1}{\gamma-1}.$

For a perfect atmospheric gas approximation using γ = 1.4, the hypersonic limit for the density ratio is 6. However, hypersonic post-shock dissociation of O₂ and N₂ into O and N lowers γ, allowing for higher density ratios in nature. The hypersonic temperature ratio is:

$\frac{T_2}{T_1} \approx \frac{2\gamma(\gamma-1)}{(\gamma+1)^2}M_1^2\sin^2\beta.$

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