Higher Flowfield Approximations for Solid Rocket Motors with Tapered Bores

Current ballistics analyses require detailed information regarding the key characteristics of the flowfields present in the combustion chambers of solid rocket motors. In this study, our purpose is to develop an internal flowfield applicable to circular-port solid rocket motors with tapered bores. Our analysis is based on the vorticity-stream function method, allowing one to resolve the resulting problem under isothermal, inviscid, rotational and steady-state conditions. Here, the approach employed in Clayton’s original investigation of tapered motors is implemented with the aim of producing an approximate solution that reflects the behavior of the flowfield at higher orders as well as combined geometric configurations. In the advent of a nonlinear governing equation, an initial solution is sought with the use of regular perturbations. Additionally, an analytical solution is explored using the method of variation of parameters; its outcome will be shown to be identical to the leading order solution obtained by asymptotic analysis. In an effort to validate the approximations used throughout this work, a numerical simulation is performed and compared to the analytical results.

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