Modeling Of Turbulent Mixing At Density Discontinuities In Nonsteady Compressible Flows

This document describes a theoretical modeling of turbulent mixing at density discontinuities in nonsteady compressible flows. It is shown that when density and pressure gradients are large and have opposite signs (e.g., near the combustion products/air contact surface in blast waves driven by high-explosive sources), flow perturbations will be amplified, leading to local turbulent mixing. The applicability of using a turbulence model to simulate this process is examined. The conservation laws (for mass, momentum, energy and species) are presented in mass-averaged form, the k-epsilon model of turbulence is applied. The relevant term for the generation of turbulent kinetic energy, the term of dominant importance in this problem, is derived by two independent approaches. This generation term is driven by gradients of pressure and density normal to the interface between the high-explosive products of combustion and the shocked air, and not by shear. The present work is thought to represent the first description of a turbulence model for flows driven by such normal gradients. (Author).

The analysis of turbulent mixing in complex turbulent flows is a challenging task. The effective mixing of entrained fluids to a molecular level is a vital part of the dynamics of turbulent flows, especially when combustion is involved. The work has shown the limitations of the steady-state simulations and acknowledged the need of applying high-fidelity unsteady methods for the calculation of flows with pronounced unsteadiness promoted by large-scale coherent structures or other sources.

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In this volume, compressible turbulent mixing is discussed from the viewpoints of experiment, numerical simulation and theoretical models. The major problem areas include Rayleigh-Taylor and Richtmyer-Meshkov instabilities, and multiphase mixing problems. A variety of initial configurations are discussed, including single and multiple mode perturbations and nonlinear geometries in both two and three dimensions. The effects of experimental and numerical artifacts are also considered.

Turbulence, mixing and the mutual interaction of turbulence and chemistry continue to remain perplexing and impregnable in the fron tiers of fluid mechanics. The past ten years have brought enormous advances in computers and computational techniques on the one hand and in measurements and data processing on the other. The impact of such capabilities has led to a revolution both in the understanding of the structure of turbulence as well as in the predictive methods for application in technology. The early ideas on turbulence being an array of complicated phenomena and having some form of reasonably strong coherent struc ture have become well substantiated in recent experimental work. We are still at the very beginning of understanding all of the aspects of such coherence and of the possibilities of incorporating such structure into the analytical models for even those cases where the thin shear layer approximation may be valid. Nevertheless a distinguished body of "eddy chasers" has come into existence. The structure of mixing layers which has been studied for some years in terms of correlations and spectral analysis is also getting better understood. Both probability concepts such as intermittency and conditional sampling as well as the concept of large scale structure and the associated strain seem to indicate possibilities of distinguishing and synthesizing 'engulfment' and molecular mixing.

This book allows readers to tackle the challenges of turbulent flow problems with confidence. It covers the fundamentals of turbulence, various modeling approaches, and experimental studies. The fundamentals section includes isotropic turbulence and anistropic turbulence, turbulent flow dynamics, free shear layers, turbulent boundary layers and plumes. The modeling section focuses on topics such as eddy viscosity models, standard K-E Models, Direct Numerical Stimulation, Large Eddy Simulation, and their applications. The measurement of turbulent fluctuations experiments in isothermal and stratified turbulent flows are explored in the experimental methods section. Special topics include modeling of near wall turbulent flows, compressible turbulent flows, and more.

Direct numerical simulations (DNS) of compressible turbulent mixing layer are performed for subsonic to supersonic Mach numbers. Each simulation achieves the self-similar state and it is shown that the turbulent statistics during this state agree well with previous numerical and experimental works. The DNS data is used to extract the physics of compressible turbulence and to perform a priori analysis for subgrid scale (SGS) closures. The flow dynamics in proximity of the turbulent/non-turbulent interface (TNTI), separating the turbulent and the irrotational regions, is analyzed using the DNS data. This interface is detected by using a certain threshold for the vorticity norm. The conditional flow statistics based on the normal distance from the TNTI are compared for different convective Mach numbers. It is shown that the thickness of the interface layer is approximately one Taylor length scale for both incompressible and compressible mixing layers, and the flow dynamics in this layer differs from deep inside the turbulent region. Various terms in the transport equations for total kinetic energy, turbulent kinetic energy, and vorticity are examined in order to better understand the transport mechanisms across the TNTI in compressible flows. The DNS data is also employed to analyze the local flow topology in compressible mixing layers using the invariants of the velocity gradient tensor. The topological and dissipating behaviors of the flow are analyzed in two different regions: near the TNTI, and inside the turbulent region. It is found that the distribution of various flow topologies in regions close to the TNTI differs from inside the turbulent region, and in these regions the most probable topologies are non-focal. The occurrence probability of different flow topologies conditioned by the dilatation level is presented and it is shown that the structures in the locally compressed regions tend to have stable topologies while in locally expanded regions the unstable topologies are prevalent. In order to better understand the behavior of different flow topologies, the probability distributions of vorticity norm, dissipation, and rate of stretching are analyzed in incompressible, compressed and expanded regions. The DNS data is also used to perform a priori analysis for subgrid scale (SGS) viscous and scalar closures. Several models for each closure are tested and effects of filter width, compressibility level, and Schmidt number on their performance are studied. A new model for SGS viscous dissipation is proposed based on the scaling of SGS kinetic energy. The proposed model yields the best prediction of SGS viscous dissipation among the considered models for filter widths corresponding to the inertial range. For the range of Mach numbers and Schmidt numbers studied in this work, the SGS scalar dissipation model based on proportionality of turbulent time scale and scalar mixing time scale produces the best results in the filter widths corresponding to the inertial subrange. For both viscous and scalar SGS dissipation models, two dynamic approaches are used to compute the model coefficient. It is shown that if the dynamic procedure based on global equilibrium of dissipation and production is employed, more accurate results are generated compared to the conventional dynamic method based on test-filtering.

The book provides an original approach in the research of structural analysis of free developed shear compressible turbulence at high Reynolds number on the base of direct numerical simulation (DNS) and instability evolution for ideal medium (integral conservation laws) with approximate mechanism of dissipation (FLUX dissipative monotone OC upwindOCO difference schemes) and does not use any explicit sub-grid approximation and semi-empirical models of turbulence. Convective mixing is considered as a principal part of conservation law.