High-resolution simulations of temporally evolving mixing layers, for convective Mach numbers ranging from . These reduced spatial scales serve to reduce the effective velocity scale for turbulent motions, suppressed Reynolds stresses, turbulent kinetic energy (TKE) production and dissipation, and the mixing-layer thickness growth rate.

Internal regulation in compressible turbulent shear layers

Turbulent mixing of passive scalars is studied in the canonical shock–turbulence interaction configuration via shock-capturing direct numerical simulations, varying the shock Mach number (. Mixing enhancement for different flow topologies across the shock is studied from changes in the PDFs of velocity gradient tensor invariants and conditional distributions of scalar dissipation. The proportion of the stable-focus-stretching flow topology is the highest among all the topologies in the flow both before and after the shock. Unstable-node/saddle/saddle topology is the most dissipative throughout the flow domain, despite variations across the shock. Preshock and postshock distributions of the alignment between the strain-rate tensor eigenvectors and the scalar gradient, vorticity and the mean streamwise vector conditioned on flow topology are studied. A novel barycentric map representation is introduced for a more direct visualization of the alignments and conditioned scalar dissipation distributions. Interaction with the shock increases alignment of the scalar gradient with the most extensive eigenvector, decreasing it with the most compressive, which is still dominant. The barycentric map of the passive scalar gradient also reveals that, across the shock, the most probable alignment between scalar gradient and strain eigendirections converges towards the alignment that provides the most dissipation. This also leads to an enhancement of scalar dissipation immediately downstream of the shock.

/pdf/parametric-numerical-study-of-passive-scalar-mixing-in-shock-57dzt355ll.pdf

Parametric numerical study of passive scalar mixing in shock turbulence interaction

Abstract The effects of compressibility on the statistics and coherent structures of a temporally developing mixing layer are studied using numerical simulations at convective Mach numbers ranging from $M_c=0.2$ to $1.8$ and at Taylor Reynolds numbers up to 290. As the convective Mach number increases, the streamwise dissipation becomes more effective to suppress the turbulent kinetic energy. At $M_c=1.8$, the streamwise dissipation increases much faster than the other two components in the transition region, even larger than pressure–strain redistribution, correlating with the streamwise elongated vortical structures at a higher level of compressibility. We confirm the existence of the large-scale high- and low-speed structures in the mixing layers, which accompany the spanwise Kelvin–Helmholtz rollers at low convective Mach number and dominate the mixing layer at higher convective Mach number. Conditional statistics demonstrate that the large-scale low-speed structures are lifted upwards by a pair of counter-rotating quasi-streamwise rollers flanking the structures. The small-scale vortical structures have an apparent preference for clustering into the top of the low-speed regions, which is directly associated with high-shearing motions on top of the low-speed structures. The high-speed structures statistically exhibit central symmetry with the low-speed structures. The statistics and dynamics of large-scale high- and low-speed structures in the compressible mixing layers resemble those in the outer region of the turbulent boundary layers, which reveals the universality of the large-scale structures in free shear and wall-bounded turbulence. A conceptual model is introduced for the large-scale high- and low-speed structures in turbulent mixing layers.

/pdf/compressibility-effects-on-statistics-and-coherent-29jlkwdj.pdf

Compressibility effects on statistics and coherent structures of compressible turbulent mixing layers

Scale-space energy density function, $E(\mathbf{x}, \mathbf{r})$, is defined as the derivative of the two-point velocity correlation. The function E describes the turbulent kinetic energy density of scale r at a location x and can be considered as the generalization of spectral energy density function concept to inhomogeneous flows. We derive the transport equation for the scale-space energy density function in compressible flows to develop a better understanding of scale-to-scale energy transfer and the degree of non-locality of the energy interactions. Specifically, the effects of variable-density and dilatation on turbulence energy dynamics are identified. It is expected that these findings will yield deeper insight into compressibility effects leading to improved models at all levels of closure for mass flux, density-variance, pressure-dilatation, pressure-strain correlation and dilatational dissipation processes.

Detailed derivation of scale-Space Energy Density Transport Equation for Compressible Inhomogeneous Turbulent Flows

Recent analysis of direct numerical simulations of compressible homogeneous shear flow turbulence has unraveled some of the energy transfer mechanisms responsible for the decrease of kinetic energy growth when the flow becomes more compressible. In this complementary study, attention is focused on the rate of strain tensor. A Helmholtz decomposition of the velocity field leads to a consideration of a solenoidal and an irrotational rate of strain tensor. Their eigenvalue distributions, eigenvector orientations, and the relative alignment between the eigenvectors and the vorticity and pressure gradient vectors are examined with the use of probability density functions. The irrotational rate of strain tensor is found to have a preferred structure in regions of strong dilatation. This structure depends on the mean shear, and is quite different from that of the solenoidal rate of strain tensor. Compressibility strongly affects the orientation properties of the pressure gradient vector.

Statistical analysis of the rate of strain tensor in compressible homogeneous turbulence

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 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.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112019004348

Topology-based characterization of compressibility effects in mixing layers

The structure of vorticity field in compressible mixing layers is studied using direct numerical simulations of temporally evolving mixing layers. The probability distribution of the inclination angles of vorticity vector with respect to various axes are analyzed. Spanwise projections of vorticity vectors have a tendency to align at angles -45lsupgol/supg and 135lsupgol/supg with respect to the streamwise direction. On streamwise and transverse planes the projected vorticity vectors tend to align at very small angles with respect to the mean vorticity vector. These distributions are uninfluenced by changes in compressibility. Orientations of vortex filaments which are dominant contributors to the vorticity covariances are also identified. These orientations are independent of the transverse location within the turbulent core. The orientations of the projections of these filaments on to different planes are found out. Compressibility has no effect on the orientation of vorticity vectors contributing most to covariances.

https://iopscience.iop.org/article/10.1088/1402-4896/ab0aad/pdf

S. Arun

Papers

Topology-based characterization of compressibility effects in mixing layers

Detailed derivation of scale-Space Energy Density Transport Equation for Compressible Inhomogeneous Turbulent Flows

Structure of vorticity field in compressible turbulent mixing layers