Optimization Design and Parameter Modeling for an Elliptic Shock Wave

Abstract

The elliptic shock wave has potential applications in the design of hypersonic inlets and waveriders. In this study, an optimization design process and a mathematical model for an elliptic shock wave are proposed. An elliptic cone flow field is employed to generate an elliptic shock wave whose shape is predetermined using the value of aspect ratio. The design of the shock wave is transformed into an optimization problem, and an optimization design process with the gas viscosity considered is developed. The elliptic cone is parameterized, and the parameters are adjusted by an optimization algorithm to meet the requirements. The results show that the optimization process can realize the accurate design of an elliptic shock wave. Based on the analysis of the elliptic cone flow field, the shock wave can be well approximated as an elliptic cone, and the aspect ratio of the shock wave is positively correlated with three factors: the aspect ratio and slenderness ratio of the elliptic cone and the incoming Mach number. The relationship between the aspect ratio of the shock wave and these three factors is modeled by a feed-forward neural network with accuracy verified, which is beneficial for the rapid design of elliptic shock waves.