Radiative heat transfer by alumina smoke particles (molten Al 2 O 3 ) in aluminized solid rocket motor internal flowfields has been investigated by computational simulation. The issue of how to define the alumina dispersion's radiative properties has been addressed to be compatible with existing radiative transfer equation solvers. Individual particleradiativeproperties,whicharenongrayandanisotropicinscattering,areevaluatedfromfundamentalparticle scattering theory for spheres (i.e., Mie theory) and optical constants from the literature, including temperature and spectraldependence.Anintegration procedure overwavelength hasbeenimplemented tomakeuseoftheeffective gray form of two common radiative transfer equation solvers: the finite volume method and Rosseland diffusion radiation model. The internal flowfield has beenmodeled including turbulent multiphase flow with inert radiating particles using commercial computational fluid dynamics software. The simulation has been exercised for a subscale solid rocket motor,the75-lbballistictestandevaluationsystemsmotor.Simulationresultsshowthatthebulkoftheinternalflowfield (the core flow) is very optically thick, so much so as to be amenable to Rosseland diffusion modeling.
Nomenclature
A= projected area a = absorption coefficient D = particle diameter, m fT = blackbody fractional function f pn = particle-scattering factor I = intensity K eI;R = Rosseland extinction coefficient k = absorption index N = particle number density n = refractive index Q a = absorption efficiency Q e = extinction efficiency Q s = scattering efficiency r = particle radius r = position vector s = direction vector s 0 = scattering direction vector T = particle temperature T e = blackbody irradiation temperature V = volume pn = particle extinction efficiency (Rosseland mean) " pn = particle emissivity = single-scattering particle polar angle pn = particle reflectivity p = particle-scattering coefficient = Stefan-Boltzmann constant (5:672 10 8 W=m 2 K 4 ) = phase function 0 = solid angle ! 0 = single-scattering albedo Subscripts a = absorption b = blackbody e = extinction I = isotropic n = particle number p = particle s = scattering = wavelength Superscripts * = nondimensional