Sawan Suman

Velocity gradient invariants and local flow-field topology in compressible turbulence

The effect of compressibility on velocity gradient structure and the related flow-field patterns/topology is investigated using direct numerical simulation data. To clearly isolate compressibility effects, the behavior is investigated as a function of local level of dilatation. Importantly, dilatation-conditioned behavior is found to be independent of Mach and Reynolds numbers. Not surprisingly, at low dilatation level, velocity gradient structure and local flow topology are similar to incompressible turbulence. At high dilatation levels, however, the behavior is quite different. A recently developed velocity gradient evolution equation – Homogenized Euler Equation (HEE) – qualitatively captures many of the observed features of compressible turbulence.

Homogenized Euler equation: a model for compressible velocity gradient dynamics

Along the lines of the restricted Euler equation (REE) for incompressible flows, we develop homogenized Euler equation (HEE) for describing turbulent velocity gradient dynamics of an isentropic compressible calorically perfect gas. Starting from energy and state equations, an evolution equation for pressure Hessian is derived invoking uniform (homogeneous) velocity gradient assumption. Behaviour of principal strain rates, vorticity vector alignment and invariants of the normalized velocity gradient tensor is investigated conditioned on dilatation level. The HEE results agree very well with the known behaviour in the incompressible limit. Indeed, at zero dilatation HEE reproduces the incompressible anisotropic pressure Hessian behaviour very closely. When compared against compressible direct numerical simulation results, the HEE accurately captures the strain rate behaviour at different dilatation levels. The model also recovers the fixed point behaviour of pressure-released (high-Mach-number limit) Burgers turbulence.

Rapid distortion analysis of high Mach number homogeneous shear flows: Characterization of flow-thermodynamics interaction regimes

In high-speed shear flows the nature of flow-thermodynamics interactions, and consequently the character of transition/turbulence, changes markedly with Mach number. We identify and characterize three different regimes of interactions in terms of acoustic frequency-to-shear magnitude ratio employing the linear rapid distortion analysis. We begin with an analysis of the pressure equation and demonstrate that acoustic frequency grows monotonically with time in this initial value problem whereas the shear magnitude is imposed to be constant. Initially when acoustic frequency is smaller than shear magnitude, fluctuations grow rapidly as the velocity field evolves unrestrained by pressure. This corresponds to Regime 1 wherein there is no significant flow-thermodynamics interaction. Flow-thermodynamics interactions commence in Regime 2 as acoustic frequency grows to the level of imposed shear rate. Dilatational velocity and pressure fields in the flow-normal direction are generated. The two fields are coupled a...

Velocity gradient dynamics in compressible turbulence: Characterization of pressure-Hessian tensor

Pressure-Hessian tensor produces the most significant difference between incompressible and compressible velocity gradient dynamics in turbulent flows. Characterization of pressure-Hessian tensor as a function of the level of compressibility is therefore of much interest. Using direct numerical simulation results, we demonstrate that the pressure-Hessian tensor behavior can be most exclusively characterized in terms of the compressibility parameter δ which is defined to be the growth-rate of dilatation-rate. A key compressibility effect is the distinct change in the alignment between pressure-Hessian and velocity gradient tensors with increasing δ. In incompressible turbulence, the pressure-Hessian eigenvectors exhibit a mild tendency to align at 45° angle with the principal directions of strain rate. With increasing δ, the pressure-Hessian tensor shows progressively stronger tendency to align along principal directions of the local strain-rate tensor. We show that this change in pressure-Hessian orientat...

Velocity-gradient dynamics in compressible turbulence: influence of Mach number and dilatation rate

The onset of compressibility effects brings about profound changes in the nature of pressure and its consequent influence on velocity-gradient evolution in turbulent flows. In this work we examine the changing action of pressure on velocity-gradient evolution with varying levels of compressibility in decaying isotropic turbulence. The degree of departure from incompressibility is characterized in one of the following three ways: (1) local turbulent Mach number, which is indicative of local balance between inertial and pressure effects; (2) local relative dilatation, which is a measure of the level of compression/expansion rate of a fluid element and (3) global turbulent Mach number, which is a global measure of compressibility of a homogeneous turbulent flow field. It is found that the pressure-Hessian inhibits velocity-gradient steepening at incompressible and subsonic local Mach numbers. In contrast, at higher local Mach numbers, the pressure-Hessian becomes the dominant driver of gradient steepening. E...

Partially Averaged Navier Stokes (PANS) Method for Turbulence Simulations: Theory and Practice

Variable-resolution (VR) turbulence simulations possess ideal attributes for engineering applications as they purport to yield the best accuracy possible for any prescribed level of computational effort. However, at the current time, these accuracy-on-demand approaches are not considered theoretically rigorous. It is argued that pragmatic considerations that motivate the formulation of VR methods automatically preclude a theoretically rigorous approach. In this paper, we argue that VR approaches can be based on strong theoretical underpinnings without sacrificing numerical robustness and practical utility. We demonstrate that the partially-averaged Navier-Stokes (PANS) VR approach is based on strong physical and mathematical foundation and yet is robust enough for complex practical flows. We present important PANS theoretical attributes followed by results from complex flow computations.

A direct numerical simulation-based investigation and modeling of pressure Hessian effects on compressible velocity gradient dynamics

The pressure Hessian tensor plays a key role in shaping the behavior of the velocity gradient tensor, and in turn, that of many incumbent non-linear processes in a turbulent flow field. In compressible flows, the role of pressure Hessian is even more important because it represents the level of fluid-thermodynamic coupling existing in the flow field. In this work, we first perform a direct numerical simulation-based study to clearly identify, isolate, and understand various important inviscid mechanisms that govern the evolution of the pressure Hessian tensor in compressible turbulence. The ensuing understanding is then employed to introduce major improvements to the existing Lagrangian model of the pressure Hessian tensor (the enhanced Homogenized Euler equation or EHEE) in terms of (i) non-symmetric, non-isentropic effects and (ii) improved representation of the anisotropic portion of the pressure Hessian tensor. Finally, we evaluate the new model extensively by comparing the new model results against k...

On the use of reduced chemical kinetics for hypersonic transition and breakdown to turbulence computations

In high temperature hypersonic boundary layers, chemical reactions among air constituents can aect transition and subsequent breakdown to turbulence. It is vital that the chemical kinetic sets used in hypersonic transition and turbulence computations not only be adequately accurate, but also be computationally viable. Reduced chemical kinetic schemes, if applicable, can substantially reduce the computational stiness of owchemistry interaction calculations. In this work, we attempt to establish that the commonly used ve-species, seventeen-reaction chemical kinetic set posses a strongly attracting slow manifold that can be exploited for the purpose of reduced chemistry. Further, we evaluate two reduction methods: (i) quasi-steady state approximation (QSSA), and (ii) locally linear approximation (LLA) to approximate the slow manifold of a high temperature air mixture. While the performance of QSSA is good only near the equilibrium point, the performance of LLA is excellent over a wide range of temperature. Overall, our results indicate that hypersonic external computations can benet from chemistry reduction strategies.

Pressure Hessian Evolution in Compressible Turbulence

The pressure Hessian tensor plays a crucial role on the dynamics of velocity gradient tensor. Therefore, understanding the evolution mechanism of pressure Hessian in compressible turbulence is of much interest. Using the results of direct numerical simulation (DNS) of compressible decaying isotropic turbulence, we present the complete budget of pressure Hessian evolution equation. The relative significance of various mechanisms responsible for pressure Hessian evolution is closely examined. This study is expected to directly contribute toward the development of improved closure models for the Lagrangian stochastic method.