Analysis And Comparison Of Analytical And Numerical Solution Of Flowfield In Solid Rocket Motors With Tapered Sidewalls

Exact parameters of internal flowfield are required for the design and fabrication of modern solid rocket motors. The flowfield in solid rocket motors with tapered sidewalls is studied with both analytical method and numerical method in present paper.In the analytical part, based on incompressible Euler equation of two-dimensional flow, vorticity—stream function equation is obtained assuming steady, rotational, inviscid, isothermal, incompressible and non-reactive flow conditions. Then, the nonlinear equation is solved by the method of perturbation in order to obtain the solutions of velocity field, pressure field and vorticity field, and solutions are also shown to be reducible, at the leading order, to Taylor's inviscid solution in the chamber with straight sidewalls. In the numerical part, the laminar model and standard k-εmodel in FLUENT software are adopted separately to solve different problems at different Reynolds number, and the results of numerical simulation are postprocessed.The results indicate that the influence of taper angle of sidewallsαand the length of straight sidewalls L is important. If the model without account for the small taper, not only the pressure drop will be over-predicted but also the other parameters of flowfield will be influenced, and the influence will be obvious in the solid rocket motors with long chamber and large tapered angle. Numerical results are well in agreement with the analytical solutions except at some places where there is a little difference because the analytical solutions are obtained with inviscid model and a series of assumption, and the axial pressure gradients being the main origin of vorticity is further validated. In addition, the analytical solutions will be valid only when the geometric parameters of motors are in certain range. The leading order solution which is concise but inaccurate can be used only in the motors of small tapered domain and taper angle of sidewalls, and better precision can be achieved when the higher-order corrections are added.