Derivation and analysis of a 1D porous medium flow solver embedded in a two-domain model for 2D and 3D transpiration cooling

Abstract

• A 1D porous medium flow solver is derived and analyzed. • The 1D solver is embedded in a two-domain model for 2D/3D transpiration cooling. • Differences between results of the new model and a full 2D/3D model are negligible. • Transpiration cooling problems are solved significantly faster with the new model. For the numerical investigation of transpiration cooling problems, often two-domain models are used. Different systems of governing equations are solved in a hot gas and a porous medium domain, and both domains are coupled with each other by imposing boundary conditions on the interface. This work presents a novel approach which splits the porous medium domain into 1D problems for Darcy-Forchheimer flow under local thermal nonequilibrium. The fluid and solid temperature solutions are computed analytically, and only one ordinary differential equation has to be solved to determine fluid density and Darcy velocity. Unique solutions to the equations of the 1D model are verified to exist under physically reasonable assumptions. The solutions of the 1D problems are assembled to one 2D or 3D solution. In a postprocessing, slip and adiabatic side walls are modeled despite being nonexistent in 1D. Numerical 2D and 3D test cases together with experimental data verify the suitability of the new assembled-1D approach for the simulation of transpiration-cooled hot gas flows with orthogonal cooling gas injection. Furthermore, the test cases demonstrate the significant computational speed-up related to a full-2D/3D approach.