| Summary: | This paper presents closed analytical solutions for the pressure and velocity �eld of ows in two-dimensional porous media. The ow�eld is modelled through a potential
function which allows the use of the Laplace equation to describe the pressure �eld. The boundary conditions of the porous medium are tailored to represent general cases
encountered in transpiration cooling applications. These include mixed Neumann and Dirichlet boundary conditions to represent a pressurised plenum driving a coolant mass ux, and impermeable sections where the plenum is attached to a non-porous substructure. The external pressure boundary is modelled as an arbitrary function representing
a ow around the porous domain, and the wall thickness of the porous domain can take any arbitrary distribution. General solutions in Cartesian coordinates and Cylindrical
coordinates are provided describing the entire porous domain of a at plate or curved geometry respectively. In addition, special simpli�ed solutions are provided for regions
of particular interest, such as the interface of external ow and porous medium. The obtained solutions are veri�ed through a comparison to a numerical simulation of two
test cases, a rectangular at plate geometry and 90 degree section of a cylindrical case.
|
|---|