Effect of linear-anisotropic scattering on spectral emission from cylindrical plumes

Abstract

The corresponding integral form of the equation of radiative transfer in absorbing, emitting, linear-anisotropic scattering media is used to compute the spectral hemispherical and the spectral plume emissivities of a onedimensional cylinder. The solution is based on using power series representations of the temperature and incident radiation profiles. The expansion coefficients for the temperature are assumed known, whereas the expansion coefficients for the incident radiation are solved for by the application of a collocation strategy based on the zeros of the Chebyshev polynomials. The method of solution is employed to study primarily the interaction between an absorbing/emitting gas phase and an absorbing/emitting/scattering particle phase. The numerical results indicate that the plume emissivity is enhanced by as much as 20% by the presence of purely scattering particles. Nomenclature Aj-expansion coefficients to Planck function a = linear anisotropic scattering coefficient BI = expansion coefficients to G(r) C = interaction parameter D m , n (r) = functions defined in the Appendix dA l = elemental surface area on plume dA 2 -elemental surface area of detector dQ lx = flux from elemental strip d 2 Q\\ -flux from elemental surface dA l dfl u = solid angle E m , n (r) = functions defined in the Appendix G(r) = incident radiation H = height or length of plume / = order of expansion of incident radiation I b (T) -dimensional Planck function /"(*) = modified Bessel function of the first kind 7(r,0,<£)= radiation intensity 7*(r,0,<j(>) = /(r,0,<£)// fc (r), normalized radiation intensity / = order of expansion of Planck function K n (x) = modified Bessel function of the second kind L m , n ( r ,x) -kernels in integral equations n -index of refraction h -outward normal unit vector P(0) = -1 + a cos 0, scattering phase function q(r) = net radiation heat flux in r-direction R = (a s + K P + Kg)R ph , optical radius of plume R g = K g R ph , spectral optical radius of plume due to participating gases R p = (cr s + K p )R ph , spectral optical radius of plume due to particles R ph = physical radius of plume r = optical radial variable r k = collocation point S -distance between plume and detector T m = mean temperature of plume T(r) = temperature of medium X* = functions defined in the Appendix