Novel Quasi-One-Dimensional Analysis of a Choked Transonic Reacting Flow with Finite-Rate Chemistry

Abstract

A numerically accurate method for solving quasi-one-dimensional transonic flow with a system of ordinary differential equations (ODEs) has been developed to estimate the performance of a high-speed propulsion system. Specifically, ramjet engines are thermally choked in the combustor region. for which the solution processes undergo a mathematical singularity problem. This singularity incurs various numerical difficulties because the derivatives are indeterminate at the sonic condition and the solution cannot march in the streamwise direction, requiring special numerical treatment. To overcome this issue, two solution processes are augmented in the ODE system: coordinate transform, and solution extrapolation from the equivalent subsonic system. An additional variable is defined to convert the spatial coordinate into a dependent variable that characterizes the transonic flow only by the solution curve passing through the critical point. After the transformation, solution variables are extrapolated from the subsonic solutions obtained with a predicted critical (sonic) condition via a forward iterative shooting method such that the flow properties are smoothly varying both upstream and downstream of the critical point. As a result, there is a good agreement in the predicted critical point with the theoretical location. Moreover, the new method successfully yields the transonic solution without any abrupt or discontinuous changes in flow properties including species fractions, which is almost impossible with existing methods.