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.

Read more about this topic:  Oblique Shock

Famous quotes containing the words oblique, shock, waves and/or limit:

    “Street lamps come out, and lean at corners, awry,
    Casting black shadows, oblique and intense....”
    —Philip Larkin (1922–1986)

    “Without passion man is a mere latent force and possibility, like the flint which awaits the shock of the iron before it can give forth its spark.”
    —Henri-Frédéric Amiel (1821–1881)

    “Your eyes have pardoned our faults,
    your hands have touched us
    you have leaned forward a little
    and the waves can never thrust us back
    from the splendour of your ragged coast.”
    —Hilda Doolittle (1886–1961)

    “An educational method that shall have liberty as its basis must intervene to help the child to a conquest of liberty. That is to say, his training must be such as shall help him to diminish as much as possible the social bonds which limit his activity.”
    —Maria Montessori (1870–1952)