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)

    “I was not long since in a company where I wot not who of my fraternity brought news of a kind of pills, by true account, composed of a hundred and odd several ingredients; whereat we laughed very heartily, and made ourselves good sport; for what rock so hard were able to resist the shock or withstand the force of so thick and numerous a battery?”
    —Michel de Montaigne (1533–1592)

    “With these I would be.
    And with water: the waves coming forward, without cessation,
    The waves, altered by sand-bars, beds of kelp, miscellaneous
    driftwood,
    Topped by cross-winds, tugged at by sinuous undercurrents
    The tide rustling in, sliding between the ridges of stone,
    The tongues of water, creeping in, quietly.”
    —Theodore Roethke (1908–1963)

    “There is no limit to what a man can do so long as he does not care a straw who gets the credit for it.”
    —C.E. (Charles Edward)