Topology-based characterization of compressibility effects in mixing layers

Abstract

Direct numerical simulations of high-speed mixing layers are used to characterize the effects of compressibility on the basis of local streamline topology and vortical structure. Temporal simulations of the mixing layers are performed using a finite volume gas-kinetic scheme for convective Mach numbers ranging from $M_{c}=0.2$ to $M_{c}=1.2$ . The focus of the study is on the transient development and the main objectives are to (i) investigate and characterize the turbulence suppression mechanism conditioned upon local streamline topology; and (ii) examine changes in the vortex vector field – distribution, magnitude and orientation – as a function of Mach number. We first reaffirm that kinetic energy suppression with increasing Mach number is due to a decrease in pressure–strain redistribution. Then, we examine the suppression mechanism conditioned upon topology and vortex structure. Conditional statistics indicate that (i) at a given Mach number, shear-dominated topologies generally exhibit more effective pressure–strain redistribution than vortical topologies; and (ii) for a given topology, the level of pressure–strain correlation mostly decreases with increasing Mach number. At each topology, with increasing Mach number, there is a corresponding decrease in turbulent shear stress and production leading to reduced kinetic energy. Further, as $M_{c}$ increases, the proportion of vortex-dominated regions in the flow increases, leading to further reduction in the turbulent kinetic energy of the flow. Then, the orientation of vortical structures and direction of fluid rotation are examined using the vortex vector approach of Tian et al. (J. Fluid Mech., vol. 849, 2018, pp. 312–339). At higher $M_{c}$ , the vortex vectors tend to be more aligned in the streamwise direction in contrast to low $M_{c}$ wherein larger angles with streamwise direction are preferred. The connection between vortex orientation and kinetic energy production is also investigated. The findings lead to improved insight into turbulence suppression dynamics in high Mach number turbulent flows.

Scale-space energy density function transport equation for compressible inhomogeneous turbulent flows

“…DNS data of a temporally evolving mixing layer from the paper by Arun et al. (2019) is chosen to investigate the energy density function and certain turbulence processes in the scale space.…”

“…Further details and validation of the numerical simulations are available in an earlier publication (Arun et al. 2019).…”

Revisiting turbulence small-scale behavior using velocity gradient triple decomposition

“…Aside from Kolář's method, Gao and Liu [12] formulated a "Rortex"-based VGT decomposition for locally fluid-rotational points (VGT has complex eigenvalues) in a turbulent flow field. This method [17] of separating the rigid-body-rotation (Rortex) from shear in vorticity is computationally more reasonable and has been employed in several studies [18][19][20][21] for investigation of coherent vortex structures in turbulent flows. The goal of this study is to examine velocity gradient statistics in turbulence using the decomposition of VGT into normal-strain-rate, rigid-body-rotation and pure-shear tensors.…”

Non-equilibrium time-relaxation kinetic model for compressible turbulence modeling

“…Then, LES studies restart from the filtered DNS solution on unresolved grids. TCPML is initialized by a hyperbolic tangent profile for the streamwise velocity (Arun et al 2019) as…”