Abstract
The Mach stem height is an important parameter in the Mach reflection of steady supersonic flow. Various experimental, numerical, and theoretical works have been conducted to study this parameter in the past. However, much of the established work focuses around a single set of trailing edge heights. Here, we perform a study to show the dependence of Mach stem height on the trailing edge height for a wider range of geometry. Through numerical simulation for a set of trailing edge heights, we found that the normalized Mach stem height is almost linear with respect to the normalized wedge trailing edge height. The parameter used for normalization can be either the inlet height or the length of the lower wedge surface. The observation of this linear trend is justified through a simplified analysis, which leads to an expression of the Mach stem height that linearly depends on the trailing edge height. The present study extends our knowledge about how the geometry affects the Mach stem height, and provides a basis for future work to elaborate analytical models for Mach stem height.
Highlights
Numerical Simulation for Dependence of Mach Stem Height on the TrailingNumerical results for Mach stem height are obtained through solving the full set of nonlinear Euler equations in gas dynamics, using the second-order Roe scheme based on finite difference approximation and second-order upwinding for the flux [26]
Ministry of Education Key Laboratory of Fluid Mechanics, School of Aeronautic Science and Engineering, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Analytical models of various degrees of accuracy or complexity have been proposed in the past [16,20,21,22,23], none of which have been put into a linear form and have been used to predict the dependence of the Mach stem height on the wedge trailing length
Summary
Numerical results for Mach stem height are obtained through solving the full set of nonlinear Euler equations in gas dynamics, using the second-order Roe scheme based on finite difference approximation and second-order upwinding for the flux [26]. The second order method with grids 400 × 600 and 600 × 900 results in Mach stem heights that are marginally close. Open circles are CFD data obtained using grids different to 400 × 600 points or a first-order accurate method. This supports the previous claim that the use of a second-order method with the grid 400 × 600 is accurate enough.
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