Rotational Flowfields in Porous Channels with Arbitrary Head wall Injection

摘要

In this paper, Taylor's incompressible and rotational flow in a porous channel with surface mass addition is extended to account for arbitrary headwall injection. Our analysis considers Euler's steady-state equations from which an approximate solution is derived. The resulting mean flow representation satisfies the vanishing axial velocity condition at the blowing walls and is confirmed through comparisons with inviscid finite volume numerical simulations. For a given class of symmetric headwall injection profiles, our solutions are exact at the sidewall and along the midsection plane, where the error in the approximations vanishes identically. The case of uniform injection stands as an exception due to its discontinuity at the sidewall. All solutions become increasingly more accurate in the downstream direction. They hence enable us to approximate the bulk flowfield in both hybrid and sob'd rockets with variable headwall injection.