General Reynolds Analogy for Blunt-Nosed Bodies in Hypersonic Flows

Abstract

proportional factor of the analogy relation; Eq. (6) f 0 = nondimensional velocity along x axis; u∕u e g = nondimensional total enthalpy; H∕H e H = total enthalpy per unit mass, J∕kg k = thermal conductivity, W∕m · K M ∞ = Mach number in freestream n = index of the power-law shape leading edge Pr = Prandtl number p = wall pressure, N∕m 2 p 0 = pressure gradient parameter at the stagnation point; −d 2 p∕p 0 ∕dθ 2 θ0 p = normalized pressure distribution function; Eq. (13) _ q w = heat flux to the wall, W∕m 2 r 0 = section radius of the body of revolution, m; Eq. (1) R = curvature radius of the surface, m R c = radius of the inscribed circle of the base of the body, m Re l = local Reynolds number; ρ ∞ U ∞ R∕μ ∞ Re ∞ = freestream Reynolds number; ρ ∞ U ∞ R c ∕μ ∞ T = temperature, K T 0 = stagnation temperature in freestream, K U ∞ = velocity in freestream, m∕s u, v = flow velocity along x and y, m∕s W r = rarefied flow criterion; M 2ω ∞ ∕Re l x, y = local coordinate in physical space, m β = gradient parameter; 2dln u e ∕dln ξ Γ 1;2 = coefficients in Eq. (19) γ = specific heat ratio η, ξ = local coordinate in Lees-Dorodnitsyn transformation space θ = slope angle of the surface θ c = surface slope angle at the base of the body μ = viscosity, kg∕m · s ρ = density, kg∕m 3 ς = normalized heat transfer distribution function; Eq. (13) τ w = skin shear stress, N∕m 2 ω = index of the viscosity-temperature power law Subscripts e = boundary-layer edge condition free = free molecular flow condition r = reference state w = wall condition 0 = stagnation point condition ∞ = freestream condition Superscripts(1) = first-order approximation based on Navier-Stokes-Fourier equations (2) = second-order correction based on Burnett equations

Current Status and Applications of Bluff Body Aerodynamics Theorem

“…The cause of the crash was that the thermal insulation material fragments on the shuttle's outer storage box dropped off under the action of severely aerodynamic forces during launch and hit the left-wing front edge of Colombia, damaging the shuttle's thermal insulation system that provides protection during reentry phase, causing the reentry thermal tile to disengage. High-temperature airflow enters and destroys the internal structure of the wing through tiny holes in the wing during the reentry phase, leading the shuttle to disintegrate rapidly in the air, causing the misfortune of seven astronauts [10].…”