The Bidirectional Vortex. Part 1: An Exact Inviscid Solution

Abstract

In this paper, we derive an exact solution that describes the bulk fluid motion of a bidirectional coaxial vortex appropriate of a liquid propellant combustion chamber. The study is prompted by the need to characterize the flow inside a laboratory-scale 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 an outer stream of swirling, low temperature oxidizer. Our mathematical model is based on steady, rotational, axisymmetric, incompressible, and inviscid flow conditions. In contrast to other studies of columnar vortices (where the axial dependence is ignored), our model accounts for the chamber’s finite body length. In fact, it incorporates the proper inlet and head-end flow conditions associated with a bipolar swirl-driven combustor. Based on the exact solution, several important flow attributes are illuminated. Among them is the location of the nontranslating vortex layer known as the mantle. This cylindrical layer separates the outer and inner vortex tubes (i.e., the updraft and the downdraft) and is confirmed using computational fluid dynamics and flow visualization.