Simulations of Turbulent Flow Interactions with Strong Shocks Using Shock-Fitting Methods.

摘要

Canonical problem of interaction of a normal shock and isotropic turbulence is fundamental to many important scientific and engineering applications. This problem, however, is not well understood despite several research efforts. Shock capturing methods have been the method of choice for numerical simulation of compressible flows. However, most of such methods are only first order accurate and may incur numerical oscillations near the shock. On the other hand, direct numerical simulations of turbulent flows require highly accurate methods to resolve all the scales in the flow. In this study, we explore shock-fitting algorithms for the canonical shock turbulence interaction problem as an alternative which can achieve uniform high-order accuracy and can avoid possible spurious oscillations incurred in shock-capturing methods by treating shocks as sharp interfaces. We first evaluate several different ways of implementing shock-fitting algorithms and then use the best suited method for canonical shock and turbulence interaction problems.;The assessment of the numerical methods is carried out for one-dimensional and two-dimensional canonical problems. We explore two ways for shock-fitting: conventional moving grid set-up and a new fixed grid set-up with front tracking. In the conventional shock-fitting method, a moving grid is fitted to the shock, whereas in the newly developed fixed grid set-up, the shock front is tracked using Lagrangian points and is free to move across the underlying fixed grid. We carry out a rigorous grid-convergence analysis on different variations of shock-fitting methods with both moving and fixed grids. We show that true fifth-order convergence is achieved for a canonical one-dimensional shock-disturbance interaction problem when fifth-order upwind finite difference scheme or shock-capturing WENO schemes is applied with conventional shock-fitting. A high-order front-tracking implementation of shock-fitting is also presented in this study. Nominal rate of convergence is shown and results are validated by comparing to results from the conventional shock-fitting method.;Based on assessment studies, a fifth order upwind shock-fitting method is used for direct numerical simulation of interaction of isotropic turbulence with a nominally normal shock. We consider flows with mean Mach numbers ranging from 2 to 20 and turbulent Mach number varying from 0.12 to 0.38. A Reynolds number based on Taylor microscale, Relambda, of up to 40 is used, requiring more than 30 million grid points per simulation. Such high mean Mach number values have never been considered in past for study of shock turbulence interactions. Some new trends are observed in turbulent statistics as mean Mach number is increased. Maximum value of streamwise velocity fluctuations downstream of the shock is found to be initially decreasing as Mach number is increased but for stronger than Mach 8 shocks this trend reverses. We observe that vorticity fluctuations return to isotropy behind the shock for some cases. Increasing mean Mach number and Reynolds number leads to delay in the return to isotropy in the vorticity fluctuations.