Session MC: Turbulence Simulations III

Simulation of Strong Shock and Turbulence Interactions using High-Order Shock-Fitting Algorithms

We present results for Direct Numerical Simulations (DNS) of interactions of shock waves with realistic isotropic turbulence using shock-fitting schemes that are highly accurate and stable even for very strong shocks. We consider interaction of normal shocks of mean Mach numbers $M_1 =2-20$ with incoming isotropic turbulence of turbulent Mach number, $M_t =0.12-0.38$, and Reynolds number based on Taylor microscale, $Re_\lambda =7-40$. New trends are observed in turbulent statistics for the shocks stronger than those considered in previous studies. Amplifications in streamwise Reynolds stress values downstream of the shock are found to be initially decreasing as Mach number is increased but for stronger than Mach 8 shocks this trend reverses. We also observe that vorticity fluctuations return to isotropy behind the shock, but increasing Mach number of incoming flow delays this return to isotropy. Taylor microscales decrease as flow passes through a shock wave and amplification factors agree well with the linear theory results. Overall, the results generally confirm the findings by earlier studies but show new trends for stronger shocks than those considered by studies in the past.   

DNS of Shock / Isotropic Turbulence Interaction

We discuss DNS of Shock / Isotropic Turbulence Interactions (SITI). We vary the incoming turbulence Mach number up to 0.8 and the convective Mach number up to 5 in order to determine their effects on the interaction. These cases are challenging due to the presence of shocklets in the incoming turbulence as well as significant motion of the main shock. Shock-capturing must be used at all points while still maintaining low enough numerical dissipation to preserve the turbulent fluctuations. We use the linearly- and nonlinearly-optimized Weighted Essentially Non-Oscillatory (WENO) method[1,2]. Particular attention is paid to the inflow boundary condition, where we find the use of snapshots of ``frozen" turbulence from decaying isotropic box simulations to be unsatisfactory. We instead use time-varying inflow data generated by a separate forced isotropic turbulence simulation with a specified convection speed. This allows us to access flow conditions where the assumptions of Taylor's Hypothesis are not met. \\ 1.) Mart\'{\i}n, M.P., Taylor, E.M., Wu, M., and Weirs, V.G., JCP 220(1) 270-89, 2006. \\ 2.) Taylor, E.M., Wu, M., and Mart\'{\i}n, M.P., JCP 223(1) 384-97, 2007.   

Large-eddy simulations of the shock-turbulence interaction canonical problem

We present results of large-eddy simulations of the interaction between a nominally planar shock wave and incoming isotropic turbulence passing through it. The numerical hybrid method in use combines fifth-order WENO and sixth-order central finite-difference schemes in a structured grid, with a sensor that switches between both schemes near shock waves. We compare results obtained with different SGS models, focusing on their performance in the relaxation region immediately downstream of the shock wave, where the effects of non-equilibrium and anisotropy are most noticeable. SGS models under evaluation include pure and mixed dynamic eddy-diffusivity models (with gradient and similarity mixed terms, and different types of eddy-diffusivities), as well as the structure-based stretched-vortex model. Extensions of existing models are proposed to improve their performance, evaluated through comparison of time-averaged turbulence quantities with filtered DNS results (see Phys. Fluids 21, 126101 (2009)).   

Inflow Turbulence Generation and Oblique Shock / Turbulent Boundary Layer Interaction

Large-eddy simulation of an oblique shock impinging on a supersonic turbulent boundary layer ($M_{\infty }$ = 2.28, \textit{$\varphi $} = 8\r{ }, Re$_{\theta }$ = 1800, 5100) is carried out with a high-order compact differencing scheme using localized artificial diffusivity for shock capturing. Solution sensitivity is investigated with regards to mesh resolution, spanwise domain, Reynolds number, and inflow turbulence boundary conditions. Through analysis of the spectral content of the wall pressure in the separation bubble, the expected low-frequency motion is identified with a time scale $\sim $O(100\textit{$\delta $}/$u_{\infty })$. When using a standard recycling/rescaling method for inflow turbulence generation, it is shown that spurious correlations associated with the recycling frequency are introduced in the incoming boundary layer. We describe an improvement that eliminates spurious correlations in the inflow turbulence and the creation of an LES database which is used to investigate the high-frequency \textit{flapping} and low-frequency \textit{breathing} physics of oblique STBLI.   

Simulations of High Speed Turbulent Jets in Crossflow

Numerical simulations are used to study an under-expanded sonic jet injected into a supersonic crossflow and an over-expanded supersonic jet injected into a subsonic crossflow, where the flow conditions are based on Santiago {\it et al.}'s (1997) and Beresh {\it et al.}'s (2005) experiments, respectively. A finite volume compressible Navier--Stokes solver developed by Park \& Mahesh (2007) for unstructured grids is used. The simulations successfully reproduce experimentally observed shock systems and flow vortical structures such as the barrel shock, Mach disk, horseshoe vortices that wrap up in front of the jet and the counter rotating vortex pair (CVP) downstream of the jet. The dynamics of these flow structures are discussed, as well as the influence of grid resolution and the effect of inflow turbulence. The time averaged flow fields are compared to the experimental results, and reasonable agreement is observed.   

The decay of forced rescaling modes in a Mach 3 turbulent boundary layer

We introduce a new, Mach $3$, compressible, turbulent boundary layer (TBL) spatial direct numerical simulation (SDNS), with a streamwise length of $50\delta_{inlet}$. The simulation has an inlet $Re_{\theta}$ of $2500$, increasing to $4000$ at the outlet, with the boundary layer thickness, $\delta$, nearly doubling from the inlet to the outlet. The inflow is computed using an auxiliary DNS with a rescaling length of $8\delta$. We examine the evolution of turbulence statistics as the boundary layer grows. In particular, we scrutinize the effects of rescaling and the non-stationarity of the flow. We wish to determine how far downstream the flow must travel to sufficiently ``forget'' the effects of rescaling. The effect of rescaling is of particular interest when investigating low frequency and large scale phenomena, such as coherent flow structures. These large coherent structures are on the order of $10\delta$ in streamwise extent, and have been found at similar conditions to the present study.\footnote{Ringuette, Wu~\&~Mart\'in \emph{J. Fluid Mech.}, 594:59-69, 2008.} With this data set we will address and quantify the role of rescaling and the rate at which the flow will forget this artificial forcing.   

DDES of shock wave/ turbulent boundary layer interaction

The detached-eddy simulation (DES) model, which is a hybrid RANS and LES method, aims to solve the intensive CPU requirement of LES. Thus, near the solid surface within a wall boundary layer, the unsteady RANS model is realized, while away from the wall surface, the model automatically converts to LES. The delayed-detached-eddy simulation (DDES) was proposed by Spalart in 2006 to improve the DES model previously developed. The transition from the RANS model to LES in DES is not grid spacing independent, therefore a blending function is introduced to the recently developed DDES model to make the transition from RANS to LES grid spacing independent. The present research concern the study of the shock/wave turbulent boundary layer interaction using delayed-detached-eddy simulation (DDES) model with a low diffusion E-CUSP (LDE) scheme with fifth-order WENO scheme. The first case studied using DDES is a 3D transonic channel with shock/turbulent boundary layer interaction. The second case studied consists of a 3D transonic inlet-diffuser. Both results are compared with experimental data. The computed results of the transonic channel agree well with experimental data. The results show that DDES simulation provides improved results for the shock wave/turbulent boundary layer interaction compared to those of its predecessor the detached-eddy simulation.