Effects of Rotational Energy Relaxation in a Modular Particle-Continuum Method

Amodular particle-continuum method is extended to include thermal nonequilibrium between translational and rotational energy modes to simulate hypersonic steady-state flows that exhibit small regions of collisional nonequilibrium in a mainly continuum flowfield. This method loosely couples an existing direct-simulation Monte Carlo code to a Navier–Stokes solver (computational fluid dynamics) while allowing both time step and cell size to be completely decoupled between each method. By limiting the size of the direct-simulation Monte Carlo region to only areas in collisional nonequilibrium, the modular particle-continuummethod is able to reproduce full direct-simulationMonte Carlo results for flows with global Knudsen numbers of 0.01 and 0.002 while decreasing the computational time required by factors of 2.94 and 28.1, respectively. The goal of the present study is to include consistent models that separate rotational and translational modes in both flow modules. Inclusion of rotational relaxation decreases the computational cost of the modular particle-continuum method. Nomenclature Ch = heat transfer coefficient Cp = pressure coefficient C = shear stress coefficient d = diameter, m e = energy per unit mass, J=kg f = probability density function g = relative speed, m=s k = Boltzmann constant, 1:38 1023 J=K m = molecular mass, kg n = number density, 1=m3 P = average probability p = pressure, Pa Q = flow quantity q = heat flux,W=m2 S = internal relaxation source term T = temperature, K u = velocity, m=s w = source term Z = collision number " = energy, J = number of internal degrees of freedom = characteristic temperature, K = mean free path, m = coefficient of viscosity, kg=ms; reduced mass, kg = mean collision frequency = mass density, kg=m3 = reference cross section, m2 = relaxation time, s = subrelaxation weight = variable probability! = variable hard sphere viscosity temperature exponent Subscripts ROT = rotation ref = reference s = species TRA = translation W = wall 1 = freestream I.