Numerical Simulation of Shock-Turbulence Interactions Using High-Order Shock-Fitting Algorithms

Abstract

High-order methods are critical for reliable numerical simulation of strong-shock and turbulence interaction problems. Such problems are not well understood due to limitations of numerical methods. 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. In our previous work [1, 2] we have shown that algorithms based on shock-fitting methodology can solve the flow with highorder accuracy near as well as away from the shocks without any numerical oscillations. In the current study, we extend the fifth order shock-fitting algorithm to carry out Direct Numerical Simulations (DNS) of interactions of shock waves with realistic isotropic turbulence. Incoming isotropic turbulence is developed in a temporal simulation of solenoidal fluctuations in a periodic box. Using Taylor's hypothesis these fluctuations are prescribed upstream of the shock wave and the flow behind the shock wave is computed using the shock fitting algorithm. In this paper we investigate interactions of isotropic turbulence with normal shock waves of Mach numbers 1 2.0 10.0 M and compare the results against numerical and Linear Interaction Analysis (LIA) results available in the literature. The results follow the trends observed in the previous studies which were only for the weak shocks. It is observed that velocity fluctuations are amplified across the shock wave and almost same amplification in turbulent kinetic energy observed for stronger than Mach 4 shocks. Transverse vorticity fluctuations are significantly increased across the shock and amplifications increase with increasing Mach number. Taylor microscales decrease as flow passes through a shock wave and amplification factor for transverse microscale agree well with the LIA results. Overall, the results generally confirm the findings by earlier numerical simulations and provide results for stronger shocks than those considered by numerical studies in the past. In future, higher Reynolds number flows will be considered with larger computer resources to avoid excessive viscous decay observed in the current study.

Simulations of Turbulent Flows with Strong Shocks and Density Variations

“…We have shown that the shock-fitting implementations that are uniformly high order accurate [30][31][32][33] and suffer no spurious oscillations around the shock as generally observed with shock capturing formulations. We have implemented these shock-fitting methods for shock and isotropic turbulence interaction problems.…”

“…7 for inflow conditions of case II. Some results for inflow of case I were presented in our previous study [30]. It is observed that the jump in the mean turbulent density and pressure is smaller than that observed in the laminar flow.…”

“…Methodology and some of the shock turbulence results presented in this report are presented in more detail in Ref. [30]. With the shock-fitting algorithm for the problem shown in Fig.…”

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

“…Moreover, spurious numerical oscillations have been observed when solving strong-shock and turbulence interaction problems with shock-capturing schemes [7,8]. In our previous work [6,9,10], we presented shock-fitting algorithms that converge with high-order accuracy near as well as away from the shock. These methods were also extended for direct numerical simulation of shock-turbulence interactions [10].…”

“…In our previous work [6,9,10], we presented shock-fitting algorithms that converge with high-order accuracy near as well as away from the shock. These methods were also extended for direct numerical simulation of shock-turbulence interactions [10]. In this paper, we present extensive results to estimate effects of mean Mach number, turbulent Mach number and Reynolds number on post-shock flow in shock-turbulence interactions.…”