A method for predicting Mach stem height in steady flows

Abstract

The prediction of Mach stem height can be important in the design of supersonic intake in supersonic and hypersonic flows. It is also important because of the progress in aircraft and rocket engines. An analytical method of predicting the Mach stem height is necessary in theoretical field of shock reflection and is the basis of the comparable computational fluid dynamics (CFD) method. A method for predicting the Mach stem height in steady flows is performed based on the earlier models. In this article, an analytical model for predicting the Mach stem height is improved based on two main assumptions: one is the calculation of the triple point deflection angle when the Mach stem is an oblique shock and the other is about the shape of the free part of the slip line. Under these assumptions, the relations predicting of Mach stem height in two-dimensional steady flow are derived based on the advanced averaging method of the subsonic flow region. The Mach stem heights are decided solely for the incoming flow Mach numbers and the wedge angles by the improved analytical model. As a result, the Mach stem heights by the model of this article are found to agree well with experimental results at lower Mach numbers, but there are relative errors at higher Mach numbers. The convexity of the slip line is also considered.