Exact Solution of the Bidirectional Vortex

Abstract

In this paper, we present an inviscid solution that describes the cyclonic motion of a bidirectional vortex in a cylindrical chamber. The study is prompted by the need to characterize the flowfield inside a swirl-driven thrust chamber. This chamber has the advantage of confining mixing and combustion to an inner vortex tube that remains separated from the chamber walls by virtue of an outer stream of swirling, low temperature oxidizer. Our model is based on nonreactive, steady, rotational, axisymmetric, incompressible, and inviscid flow conditions. Unlike other studies of columnar vortices where the axial dependence is not considered, the present model accounts for the chamber's finite body length. In fact, it incorporates the inlet and headwall conditions associated with a swirl-driven cyclone. Based on the resulting formulation, several flow features are captured. Among them is the location of the inner-outer vortex interface where the axial velocity vanishes.