New Framework for Modeling the Bidirectional Vortex Engine Flowfield with Arbitrary Injection

Abstract

*† In this study, an exact solution is derived for the bidirectional vortex field in a rightcylindrical chamber. The cyclonic motion is assumed to be axisymmetric, steady, inviscid and incompressible, with no accounting for reactions or heat transfer. Our approach is based on the Bragg-Hawthorne equation (BHE), which can be solved in our situation under conditions leading to linearity. Using separation of variables, we are able to identify a set of eigensolutions that may be associated with this problem. The linearity of the resulting BHE enables us to superimpose these eigensolutions while making use of orthogonality to the extent of accommodating different injection configurations that may be imposed at the open boundaries. By way of confirmation, the extended formulation is used to regenerate physical configurations corresponding to five different analytical models found in the literature. The results illustrate how the present idealization may be applied to a variety of incompressible representations of cyclone-driven industrial flow separators, vacuum chambers, furnaces, plasma generators, and liquid rocket engines.