New method for solving one-dimensional transonic reacting flows of a scramjet combustor

A new solution method is proposed to solve the one-dimensional transonic reacting flows of a scramjet combustor, which represents a mathematical singularity in the governing equations when the flow velocity approaches the speed of sound. The governing equations of the one-dimensional transonic flows are rewritten by using a variable transformation method and, in this way, the singularity of the governing equations is eliminated. Subsequently, a forward iterative shooting method is introduced to deal with the numerical problem appearing in the flow that includes finite-rate chemistry and high-temperature gas properties. Comparative analysis is performed to evaluate the method presented in this paper and previous methods. The results show that it has a wider applicability and better stability in solving the one-dimensional transonic reacting flows than previous methods. One major advantage of this method is that, as a result of the elimination of the singularity using variable transformation and the introduction of a forward iterative shooting method, a smooth and stable numerical calculation for transonic reacting flows can be ensured.