Modeling and experimentation of conductive and radiative transfer through heterogeneous insulators in high-flux environments

Heterogeneous materials are used in a wide range of applications involving high heat flux environments such as concentrated solar reactors, high-temperature furnaces, or thermal protection systems of space vehicles. The thermal response of heterogeneous materials is driven by coupled conduction, convection, and radiation heat transfer and, depending on the material composition, also by thermochemical processes. The thermal properties of such materials can be determined by using experimental methods. One challenge lies in the choice of the modeling approach to consider radiative transport. Modeling the heterogeneous media by an equivalent homogeneous media with an effective thermal conductivity (ETC) accounting for a radiative transport is computationally simple but requires accurate knowledge of the temperature-dependent ETC and can lead to errors. To provide more accuracy, models that solve the radiative transfer equation (RTE) separately from conduction are used. This type of method is computationally intensive and it is unclear in which condition one approach or the other is needed. First, a novel combined experimental-numerical method, that allows for the determination of the ETC for a large temperature range (288 K to 1473 K) utilizing one experiment only, is imple- mented. The experiment includes transient and locally-resolved temperature measurements of porous ceramics samples with different porosities exposed to high radiative fluxes in EPFL’s high-flux solar simulator (HFSS). The pseudo-inverse methodology uses the porous material analysis toolbox based on OpenFOAM (PATO). Second, a more advanced thermal response model calculating the radiative contribution by the separate solution of the RTE and its contribution to the energy equation through a source term is implemented. The development of this PATORAC algorithm includes the implementation of a path-length based Monte-Carlo (MC) ray-tracing code. The MC solver was coupled to the energy equation solver through specifically coded boundary conditions and source terms. A quantitative comparison between the two methods is given as a function of the transport properties, morphology, and boundary conditions. Quantitative guidelines are established to provide recommendations for the choice of the most adapted approach. Finally, the developed tools and guidelines are applied to a carbon-phenolic composite ma- terial (ZURAM) that is used as a thermal protection system in space applications. Tests performed with ZURAM samples in a high convective flux environment (VKI’s Plasmatron) and in EPFL’s HFSS are numerically rebuilt using the ETC method, providing information on the temperature-dependent thermal diffusivity. The investigations show that the pseudo inverse approach developed for the determination of the temperature-dependent ETC is useful for conditions that are not dominated by incoming radiation. It should be used to simulate the thermal behavior of heterogeneous materials that present relatively high conductivities and extinction coefficient. The coupled radiation- conduction approach, on the other hand, must be used in conditions with low-absorbing and low-conducting media in highly radiating environments. The comparison between tests in VKI’s Plasmatron and the HFSS widens the testing possibilities of such materials. Indeed, facilities like the HFSS are easier to implement and prove to be an alternative for space composites testing.