Analytical investigation of 1D Darcy-Forchheimer flow under local thermal nonequilibrium

Abstract

In the context of transpiration cooling, a 1D porous medium model consisting of a temperature system and a mass-momentum system is derived from the 2D/3D Darcy-Forchheimer equations. The temperatures of the coolant and the solid are assumed to be in local nonequilibrium. This system is analytically verified to have a unique solution. Transpiration cooling simulations are performed by a two-domain approach, coupling the assembled 1D porous medium solutions with 2D solutions of a hot gas flow solver. A comparison of results obtained by applying the 1D porous medium model with the temperature system either including or neglecting fluid heat conduction justifies the use of the latter simplified system.