Space-streamline-based method of characteristics for inverse design of three-dimensional super/hypersonic flows

Abstract

The inverse design of super/hypersonic flows is widely utilized in aerospace, especially in waveriders, inlets, and nozzles. However, most of the existing methods are intended for the two-dimensional (2D) problem. The inverse method for generalized three-dimensional (3D) supersonic flows is still immature and is the main purpose of the space-streamline-based method of characteristics (SMOC) presented in this paper. The key of SMOC is to integrate an additional Euler predictor–corrector algorithm for pressure gradients in the unit calculation process. In this way, the temporary orientation of the osculating plane (OP) of the space streamline is determined, and the conventional 2D axisymmetric method of characteristics can be adopted in the OP. Three common unit processes of SMOC and the posedness are introduced, and the astringency is demonstrated by corresponding algebraic calculations. With this method, inviscid super/hypersonic flows can be solved on the basis of specified flow features, such as a 3D shock surface or a 3D wall pressure distribution. The accuracy and efficiency of SMOC are verified by using an inverse design example, that is, the flow produced by an elliptic conical surface at a freestream Mach number of 6. The numerical simulation of the inverse design result indicates that the 3D shock wave geometry and the 3D wall pressure distribution match the targets completely. The relative root-mean-squared error of the surface geometry is 10−3 magnitude, and the computation time cost of the inverse design is less than that of the general direct Euler solver.