A Finite Volume Based Method for Narrow-Band Simulations of Thermal Radiation from Participating Media

Abstract

An approach is proposed to improve numerical modeling of directional thermal radiation originating from absorbing, emitting and scattering media. In this approach, the finite volume method for radiation transfer is applied on the narrow-band basis to evaluate the source function of the radiative transfer equation. The emission in a given direction is then predicted through integration of the transfer equation with evaluated source functions along lines-of-sight through the medium. The correlated-k model is coupled with the radiative transfer solvers to ensure accurate spectral modeling of gas radiative properties. The method performance is demonstrated by comparison with solutions obtained using the basic finite volume method with various directional discretizations. This comparison was done for infrared radiation from a participating medium contained in a three-dimensional enclosure. Nomenclature Latin symbolsA = area, m 2 a = coefficient in the discretization equation of transfer b = source term in the discretization equation of transfer v f = volume fraction I = intensity, W/(m 2 sr µm) k = absorption index, or absorption coefficient, m -1 L = number of control angles in a given direction M = number of control volumes, or number of species N = number of discrete directions, or number of quadrature points n  = refractive index n = face normal p = total pressure, atm S = source function, W/(m 2 sr µm) s  = direction of radiation propagation s = geometric path coordinate, m T = temperature, K V = volume, m 3 , , x y z = Cartesian coordinates, m x = mole fraction Greek symbols  = coefficient in Eq. (19)  = extinction coefficient, m -1  = emissivity  = zenith angle  = wavelength, µm s  = scattering coefficient, m -1 AIAA Aviation  = scattering phase function  = azimuth angle  = solid angle, sr  = quadrature weight Superscripts n = iteration index ' = directional value, or dummy variable  = vector quantity  = averaged quantity Subscripts 0 = boundary condition b = blackbody g = gas, or at a given k-distribution value , i j = angular directions, or quadrature point, or species index mix = mixture P = control volume center , , , , , E W N S B T = east, west, north, south, bottom, and top neighbours of P , , , , , e w n s b t = east, west, north, south, bottom, and top control volume faces p = particle ,   = in a given angular direction  = at a given wavelength