Statistical radiative modeling of a porous medium with semi transparent and transparent phases: Application to a felt of overlapping fibres

Abstract A general statistical model of characterisation of the radiative properties of homogenised phases has been developed for a porous medium with a semi transparent absorbing phase a and a transparent one b, characterised by general interfacial reflection and transmission laws. For non Beerian homogenised phases, it is based on successive sets of radiative statistical functions: extinction cumulative distribution functions, scattering cumulative probabilities and general phase functions ab initio determined by a Monte Carlo approach, only from morphological data and interfacial reflection and transmission laws in the last case. Specific sets are associated with isotropic and uniform volume emission by a and with the successive internal and external scattering events within a and b, the emission or scattering source terms of which have been weighted by spatial distribution functions. For a Beerian homogenised phase, a unique set of radiative statistical functions has been determined from random isotropic volume source points. Two Generalised Radiative Transfer Equations (GRTEs), coupled by external scattering source terms are then expressed only vs the radiative statistical functions. It is shown that a radiative Fourier’s model, based on radiative conductivity tensors, is not valid for a medium made of a semi transparent phase and a transparent one, if the particular case for which the semi transparent phase becomes opaque and the trivi-al case of a quasi isothermal medium are excepted. The previous models are applied to a felt of fibres for insulation of high temperature systems. The radiative power field in radiation steady state within a felt of fibres enclosed between parallel opaque walls has been determined by solving the coupled GRTEs by a Monte Carlo method, for different values of the transverse optical thickness of a fibre. The temperature field within the felt has also been determined for two temperatures imposed at the boundaries and for imposed flux and temperature. Finally the optimal conditions of insulation have been determined for a case such that usual conduction can be neglected compared to radiation.