Density effects on post-shock turbulence structure and dynamics

Abstract

Turbulence structure resulting from multi-fluid or multi-species, variable-density isotropic turbulence interaction with a Mach 2 shock is studied using turbulence-resolving shock-capturing simulations and Eulerian (grid) and Lagrangian (particle) methods. The complex roles density play in the modification of turbulence by the shock wave are identified. Statistical analyses of the velocity gradient tensor (VGT) show that the density variations significantly change the turbulence structure and flow topology. Specifically, a stronger symmetrization of the joint probability density function (PDF) of second and third invariants of the anisotropic velocity gradient tensor, PDF(Q * , R * ), as well as the PDF of the vortex stretching contribution to the enstrophy equation, are observed in the multi-species case. Furthermore, subsequent to the interaction with the shock, turbulent statistics also acquire a differential distribution in regions having different densities. This results in a nearly symmetrical PDF(Q * , R * ) in heavy fluid regions, while the light fluid regions retain the characteristic tear-drop shape. To understand this behavior and the return to "standard" turbulence structure as the flow evolves away from the shock, Lagrangian dynamics of the VGT and its invariants are studied by considering particle residence times and conditional particle variables in different flow regions. The pressure Hessian contributions to the VGT invariants transport equations are shown to be not only affected by the shock wave, but also by the density in the multi-fluid case, making them critically important to the flow dynamics and turbulence structure. arXiv:1908.05327v1 [physics.flu-dyn]

Reynolds stress anisotropy in shock/isotropic turbulence interactions

“…Other recent studies have explored related topics in the context of SITI such as mixing of passive scalars (Boukharfane, Bouali & Mura 2018; Gao, Bermejo-Moreno & Larsson 2020), variable density and multi-fluid flows (Tian et al. 2017; Tian, Jaberi & Livescu 2019), reacting shock waves (Huete et al. 2017) and specialized studies on post-shock thermodynamic fluctuations (Sethuraman, Sinha & Larsson 2018; Sethuraman & Sinha 2020 a , b ), temperature–velocity correlations (Quadros, Sinha & Larsson 2016 a ) and turbulent energy flux (Quadros, Sinha & Larsson 2016 b ) to inform turbulence model development.…”

Turbulence topology evolution in weakly turbulent premixed flames

“…At this level, it must emphasized that similar LEE can be readily derived for the invariants of the traceless VGT A * , as it is shown in Appendix A. The traceless VGT is indeed often considered to analyze non-reactive turbulent flows featuring compressibility and/or dilatational effects 29,30,46,51 . At this level, it must also be emphasized that some similarities are expected between the present reactive flows featuring local premixed flame fronts and other turbulent flows featuring sharp density variations, e.g., shock waves, detonations, or two-phase flows featuring mass transfer (evaporation).…”

“…The present study is focused on the analysis of the influence of thermal expansion on the dynamics of the velocity gradient tensor (VGT) and associated flow topologies. The study of flow topology and dilatation effects is a topic of relevance to scalar mixing in turbulent flows [27][28][29][30] .…”

“…From the above set of definitions, the Lagrangian evolution equations (LEE) of the VGT invariants can be derived 30,47 . The starting point of such a derivation is the transport equation of the VGT component, which is given by [47][48][49][50] Ȧij ≡…”

Physics-Informed Machine Learning of the Lagrangian Dynamics of Velocity Gradient Tensor

“…The analysis has been performed using data extracted from Direct Numerical Simulation (DNS) corresponding to various fully developed turbulent flows, such as isotropic turbulence, turbulent boundary layer, mixing layers, and more complex flows, such as shock-turbulence interaction [e.g. [10][11][12][13][14][15][16][17][18][19]. To accurately represent Lagrangian dynamics of the VGT, reduced empirical models have been proposed to capture the important dynamics without solving the full Navier-Stokes equations.…”