Modeling the spatio-temporal evolution of permeability during coking of porous material
Résumé
Transpiration cooling is one of the most efficient cooling techniques, but one which generates complex phenomena that are difficult to model, and this all the more in that a reactive fluid such as an endothermic fuel is used. Above a certain temperature, such fuel is pyrolysed and, thanks to its endothermic behaviour, this ensures the active cooling of the hot walls of the combustion chamber. However, one of the consequences of this thermal decomposition is the unwanted formation of coke which blocks the porous material (both on the surface and in the interior). This gradual blocking reduces the material's permeability and thus the efficiency of the cooling system. Modelling the permeability distribution of porous materials is thus a key parameter in better understanding transpiration cooling. The present article shows several models intended to estimate the variation in time and space of the permeability of a material (stainless steel) during its coking. The fluid circulating in this porous material is n-dodecane that is maintained at a high temperature. Following a presentation of the measurement device and the measured experimental data of the mean permeability, two categories of model are studied, notably discontinuous mesh models (with 2 and 3 meshes) and continuous analytical models (linear and exponential). The results obtained show that discontinuous models with 2 and 3 meshes are very close in measuring the temporal evolution of the thickness of the coked zone of the porous material. They also revealed that the exponential model is more appropriate than the linear model in estimating the spatiotemporal evolution of the permeability. Additionally, the evolution of the coking rate in the porous material was determined as a function of time and the results show behaviour similar to that indicated in the literature. Lastly, the average Darcy permeability was linked to the mass of coke deposit in the porous material, the result of which reveals a quasi-linear decrease. Nomenclature Latin letters e = Sample thickness e j [m] = Thickness of each layer j K = Hydraulic conductivity tensor K D = Darcian's permeability K Davg = Average Darcian permeability K D0 = Initial Darcian permeability K F = Forchheimer's permeability K j = Darcian permeability of each layer j P = Pressure ΔP = Pressure drop t = time T = temperature V = Mean fluid velocity Greek Letters ε = Overall open porosity μ = Dynamic viscosity ρ = Fluid density ø = Diameter
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