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:

    “The jeweled stripes on the window ran straight down when the train stopped and got more and more oblique as it speeded up. The wheels rumbled in her head, saying Man-hattan Tran-sfer Man-hattan Tran-sfer.”
    —John Dos Passos (1896–1970)

    “Civilized society is one huge bourgeoisie: no nobleman dares now shock his greengrocer.”
    —George Bernard Shaw (1856–1950)

    “The waves have now a redder glow—
    The hours are breathing faint and low—
    And when, amid no earthly moans,
    Down, down that town shall settle hence,
    Hell, rising from a thousand thrones,
    Shall do it reverence.”
    —Edgar Allan Poe (1809–1849)

    “Now for civil service reform. Legislation must be prepared and executive rules and maxims. We must limit and narrow the area of patronage. We must diminish the evils of office-seeking. We must stop interference of federal officers with elections. We must be relieved of congressional dictation as to appointments.”
    —Rutherford Birchard Hayes (1822–1893)