Laminar Stagnation-Point Heat Transfer for a Two-Temperature Argon Plasma

Abstract

A theory for the heat transfer to the stagnation-point boundary layer of an axisymmetric blunt body in a subsonic two-temperature argon plasma flow was developed. Two-temperature transport properties were calculated from the rigorous kinetic theory and are employed in solving the multifluid problem formulated with a wall sheath boundary condition. The system of equations is solved numerically for various problem parameters. The effects of parameters on thermal nonequilibrium characteristics of the boundary layer are discussed. Also shown are the variations in the transport properties across the boundary layer.x,y Nomenclature = mobility coefficient = viscosity-density product ratio, p/i/(p/i) 0 = specific heat of mixture : diffusion coefficient = electric field = ion flux = electronic charge --dimensionless normal velocity = specific mixture enthalpy • -enthalpy of specie, j = ionization index, for neutrals i = 1 = current density = Boltzmann constant = pure heat conduction coefficient for electrons and heavies, respectively = reactive heat conduction coefficient for electrons and heavies, respectively = total heat conduction coefficient for electrons and heavies, respectively = constants in Eq. (16) = mass of a particle = molar mass = Avogadro number = total number density = number density of j species = pressure = Prandtl number = heat flux = universal gas constant = Reynolds number = nose radius of blunt body = wall radius from the axis of symmetry = transformation coordinate in x direction, Eq. (14) = Stanton number = temperature = freestream velocity = velocity components in x and y directions, respectively = diffusion velocity of j species = mole fraction of j species = coordinates (Fig. 1) a = degree of ionization j] = dimensionless coordinate in y direction /A = viscosity F = volumetric collision frequency 0 = temperature ratio T e /T h p = density (p = plasma sheath potential a = electrical conductivity 8j 2 = defined in Eqs. (23) and (24) 8y = potential drop in boundary layer, Eq. (25) A =T W /(T 0 -T W ) V = d/dx + d/dy Subscripts amb = ambipolar a,n = neutral atom b = edge of plasma sheath e = electron / = field H = ions plus neutrals h = heavy particle / = ion r = reactive part of heat conductivity coefficient w = wall or surface oo, 0 = freestream condition 17 = differentiation with respect to TJ Superscripts ( )* = dimensionless quantities