Mathematical simulation of radiation transfer in the powder bed: application to selective laser sintering

A statistical scattering model is proposed for powder beds with particles of arbitrary shape and dimensions satisfying the conditions of geometrical optics. The model takes into account dependent scattering and can be applied to powder mixtures. The problems of normal incidence on a deep powder bed and on a thin powder layer backed by a reflective substrate are analytically solved in the two-flux approximation. Calculated laser radiation transfer in the Fe-Cu powder mixture agrees in general with the known ray tracing simulation. Due to multiple reflection in an open pore system incident radiation penetrates to the depth of ∼ 10 particle diameters at 1.06 μm wavelength and up to ∼ 20 diameters at 10.6 μm. The calculated effective absorptances of Fe powder at 10.6 μm and that of Cu powder at 1.06 and 10.6 μm agree with experiments while the absorptance of Fe powder at 1.06 μm is overestimated.