Correlation for Species Concentration on a Hypersonic Stagnation Point with Mass Injection

Abstract

This paper presents a correlation to obtain the surface species concentration on a stagnation point with mass injection for hypersonic flow. The correlation can be used to determine surface recombination heat fluxes and oxidation levels for ablatives or actively cooled heat shields in thermochemical equilibrium flow. It explicitly expresses the wall species concentration as a function of freestream conditions, coolant properties and the stagnation point geometry, revealing the direct effect of the above parameters on the desired quantity. The method was compared against the numerically obtained self-similar solution and showed an accuracy of ±4%. The concentration depends on the boundary layer edge pressure, temperature and velocity gradient, as well as the wall temperature and injected mass flux. The molar mass and diffusion coefficient are further needed for scaling if the injected gas differs from the freestream gas.

Measuring the Concentration of Freestream Species on a Hypersonic Transpiration-Cooled Stagnation Point

“…Ref. [11] showed analytically and numerically that the mass transfer reduction is related to the mass blowing parameter 𝐵 𝑚 = 𝐹 𝑆𝑡 𝑚0 , which is the blowing ratio, normalised by the uncooled mass Stanton number. The blowing ratio denotes the ratio of coolant to freestream mass flux, 𝐹 = 𝜌 𝑐 𝑢 𝑐 𝜌 ∞ 𝑢 ∞ , while the uncooled Stanton number is defined as the uncooled mass transfer coefficient to the freestream velocity, 𝑆𝑡 𝑚0 = 𝐾 𝑚0 𝑢 ∞ .…”

“…The mass Stanton number at the stagnation point in the absence of blowing was derived as [11] 𝑆𝑡 𝑚0 = 0.89…”

“…In this calculation, it was assumed that the mole fraction of air at the surface, 𝑦 air;𝑤 , was that predicted by the semi-analytical correlation [11]. It can be seen from Eq.…”

“…This can be achieved numerically using the self-similar laminar boundary layer equations [10] or a full CFD solver. Alternatively it can be found using a semi-analytical correlation [11], which is reviewed in section II.…”

Oxidation Response of Transpiration-Cooled ZrB2 on a Hypersonic Stagnation Point

“…The oxygen concentration on a hemispherical transpiration cooled hypersonic stagnation point can be obtained for any freestream condition, nose radius and injection parameters, using the correlation developed in Ref. [17]. It requires knowledge of the viscosity, density and velocity gradient at the boundary layer edge, as well as the Schmidt number and the mass flux at the wall, all of which are readily available.…”