The Taylor Profile in Porous Channels with Arbitrary Headwall Injection

Abstract

*† In a recent study, Taylor’s incompressible and rotational core flow in a cylindrical porous chamber was extended by the authors to account for arbitrary headwall injection. In this study, we construct the solution for the two-dimensional planar case while incorporating variable headwall injection. The resulting representation is especially well suited to model the non-reactive gaseous motion in slab hybrid rockets and in two-dimensional channels with porous walls. Our analysis employs Euler’s steady-state equations from which an approximate solution is derived. The mean flow approximation that ensues satisfies the no slip boundary condition at the walls. It is confirmed through comparisons with numerical simulations evolving from a pressure-based finite volume solver. The analytical solutions are compared to the numerical results under inviscid flow conditions. Interestingly, they become exact at the wall and along the midsection plane where the error in the approximations vanishes identically. Furthermore, our solutions become increasingly more accurate in the downstream direction. The final formulations enable us to approximate the flowfield in both hybrid and solid rockets with variable headwall injection patterns.