Heat flux on partially catalytic surfaces in hypersonic flows

Abstract

The combined effects of the chemical nonequilibrium and the surface catalysis on the stagnation-point heat flux of a blunt body are investigated by Navier-Stokes calculations on a spherical model under Scirocco Plasma Wind Tunnel conditions. The freestream properties in the test section are found by means of a preliminary nonequilibrium, full Navier-Stokes computation of the nozzle flow expansion. All available numerical heat flux results are correlated as a function of a dimensionless parameter, including the simultaneous effects of the finite-gas and the surface-phase reactions. The proposed parameter, which takes into account simultaneously the nonequilibrium effects in the bulk and surface phases, correlates well with the numerical results over a blunt-body stagnation region. The final correlation formula for the stagnation heat flux can be used to correlate experimental results on different materials with known catalytic coefficients or, conversely, to determine the surface catalytic efficiency of different thermal protection materials. Nomenclature a = speed of sound, m/s c p = specific heat per unit mass at constant pressure, J/kg • K D = diffusion coefficient, m 2 /s D a = homogeneous Damkohler number; Eq. (28) D as = heterogeneous Damkohler number; Eq. (31) E = total energy, J E v = vibrational energy source term, J/s e = specific total energy per unit volume, J/m 3 h = enthalpy per unit mass, J/kg hf" = heat envolved in the formation of component i, J/kg k = Boltzmann constant (1.38022 x 10~2 3 ), J/K k h>r = backward reaction-rate coefficient for reaction r k er = equilibrium constant for reaction r kf >r = forward reaction-rate coefficient for reaction r k w = catalytic reaction-rate constant, m/s M = molecular weight, kg/kg • mole n = normal to the wall coordinate p = pressure, Pa q = stagnation-point heat flux, W/m 2 qm = mole fraction Re = Reynolds number Rt = gas constant of component i r h = body radius Sc = Schmidt number T = absolute temperature, K u = x component of velocity, m/s v = y component of velocity, m/s x = jc-axis component Y = mass fraction y = v-axis component y = recombination coefficient X = thermal conductivity, J/m • s p = density, kg/m 3 r = heat flux correlation parameter a) = catalytic recombination rate, kg/m 2 • s a = atomic species c = conductive term d = diffusive term eq = equilibrium / = frozen few = fully catalytic wall / = i th component of mixture N = atomic nitrogen new = noncatalytic wall ns = number of chemical species nvs = number of vibrational species O = atomic oxygen p = partial derivative with respect to pressure t = partial derivative with respect to time v = vibrational term u; = wall x,y,z = Cartesian components p = partial derivate with respect to density 0 = stagnation conditions 02 = stagnation-point conditions oo = freestream value Superscripts p = reaction order for catalytic reaction + = nondimensional quantities

A review of the mathematical modeling of equilibrium and nonequilibrium hypersonic flows

“…The net mass flux generated by the diffusion of atom s to the surface is given by According to the mass balance on the surface, the net mass flux of species s formed at the surface is zero. The mass flux due to the recombination reactions must be balanced by that of the diffusion to the surface [128], which is expressed as Substituting Eq. ( 134) and Eq.…”

Sensitivity Analysis of the Catalysis Recombination Mechanism on Nanoscale Silica Surfaces

“…For instance, a weak catalytic surface could cause a large decrement in surface heat flux as it prevents the recombination of the dissociated atoms on the surface, hence reducing exothermic heat releases. The determination of the catalytic effect, termed as “recombination coefficient”, becomes crucial [ 14 , 15 , 16 ].…”