Direct Numerical Simulations of Turbulent Flow Interactions with Strong Shocks Using Shock-Fitting Method

Abstract

Canonical problem of interaction of a normal shock and isotropic turbulence is fundamental to many important scientific and engineering applications. Most widely used shock capturing methods for the numerical simulation of compressible flows are inherently dissipative, only first order accurate and may incur numerical oscillations near the shock waves. Since high order methods are critical for direct numerical simulation of turbulent flows, we use a shock-fitting method that has been shown to be fifth-order accurate near as well as away from the shock. Moreover, unlike shock-capturing schemes, there are no spurious oscillations even with very strong shock waves. We carry out Direct Numerical Simulation (DNS) of canonical shock-turbulence interaction problem for 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, Re , 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. Similarly maximum streamwise vorticity fluctuations in post-shock flow first increase and then decrease as mean Mach number is increased. 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. Overall, the results generally confirm the findings by earlier numerical simulations and provide new trends for stronger shocks than those considered by numerical studies in the past.

Effect of compressibility on strong shock and turbulence interactions

“…The extensive DNS studies on strong shock and turbulence interaction of perfect gas flow are similar to those of Rawat and Zhong [29]. The main objective is to obtain more quantitative results.…”

“…4). [29] The above results are quite interesting and exciting. Basically, for very strong shock, new trends of turbulence statistics appear which is never observed in previous researches for weak shocks.…”

“…To avoid such problems in existing numerical simulation tools, Rawat and Zhong [1,29] recently proposed a unique approach of using a high-order shock-fitting and shockcapturing method. The main shock is treated by the shock-fitting method as a sharp boundary of the computational domain.…”

“…The difference between turbulent and laminar values decreases as shock strength is increased. [29]. Figure 3 shows the amplification in streamwise velocity fluctuations for cases with different shock Mach number.…”

“…The amplification in streamwise velocity fluctuations at different shock Mach number[29] (a) vorticity flucuation (b) variation of anisotropy Fig. 4.…”