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:

    “Besides, our action on each other, good as well as evil, is so incidental and at random, that we can seldom hear the acknowledgments of any person who would thank us for a benefit, without some shame and humiliation. We can rarely strike a direct stroke, but must be content with an oblique one; we seldom have the satisfaction of yielding a direct benefit, which is directly received.”
    —Ralph Waldo Emerson (1803–1882)

    “The pointless ferocities of intellectual life shock businessmen, who kill only to eat.”
    —Mason Cooley (b. 1927)

    “Like as the waves make towards the pebbled shore,
    So do our minutes hasten to their end;
    Each changing place with that which goes before,
    In sequent toil all forwards do contend.”
    —William Shakespeare (1564–1616)

    “It is after all the greatest art to limit and isolate oneself.”
    —Johann Wolfgang Von Goethe (1749–1832)