Numerical study on flow separation and shock wave interaction over a flat plate with facing step

Abstract

Results of a numerical investigation on a transonic compressible flow over a flat plate with facing steps are presented. The study has been performed by solving Two-Dimensional Navier- Stokes equations. The system of governing equations has been solved, using an explicit Harten- Yee Non- MUSCL Modified flux type TVD scheme and a zero-equation algebraic turbulence model to calculate the eddy viscosity coefficient. Simulations for backward and forward facing step have been done over a range of Mach numbers from 0.8 to 1.2 for four different step heights (0.025, 0.05, 0.075 and 0.10). The results show the details on pressure, temperature and velocity field, together with recirculation length, expansion shock, reattached shock, oblique shock, detached shock and interaction among shock waves of flow field. The flow field characteristics with the change of facing step, Mach numbers and heights of the step are also reported. The main objective of this study is to disclose the effect of forward and backward facing step, Mach numbers and heights of the step on the flow pattern of a transonic compressible flow over a flat plate which would be helpful for the subsequent construction in reality. The various parameters of the calculation are (i) the type of the facing step (ii) the height of the step and (iii) Mach number of the incoming flow. Due to the variation of type of step, four different shocks appear in the flow field; corner expansion shock and reattached shock appear in backward facing step, on the other hand leading edge oblique shock and detached shock appear in forward facing step. In both cases, recirculation is found on the flow field which is located behind the backward facing step and in front the forward facing step, respectively. It can be found that the change of step heights and Mach numbers changes the feature of different shocks, the dynamic behavior of the flow field, affects the temperature and pressure field, and modifies the length and strength of recirculation regions.