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Macro and micro issues in turbulent mixing

Science China(Technological Sciences) 2013年第10期56卷 2355-2360页

作者： MELVIN j KAUFMAN R LIM H KAMAN T RAO P glimm j Department of Applied Mathematics and Statistics Stony Brook UniversityStony Brook NY 11794 USA

Numerical prediction of turbulent mixing can be divided into two subproblems: to predict the geometrical extent of a mixing region and to predict the mixing properties on an atomic or molecular scale, within the mixing region. The former goal suffices for some purposes, while important problems of chemical reactions(e.g. flames) and nuclear reactions depend critically on the second goal in addition to the first one. Here we review recent progress in establishing a conceptual reformulation of convergence, and we illustrate these concepts with a review of recent numerical studies addressing turbulence and mixing in the high Reynolds number limit. We review significant progress on the first goal, regarding the mixing region, and initial progress on the second goal, regarding atomic level mixing properties. New results concerning non-uniqueness of the infinite Reynolds number solutions and other consequences of a renormalization group point of view, to be published in detail elsewhere, are summarized *** notion of stochastic convergence(of probability measures and probability distribution functions) replaces traditional pointwise convergence. The primary benefit of this idea is its increased stability relative to the statistical "noise" which characterizes turbulent flow. Our results also show that this modification of convergence, with sufficient mesh refinement, may not be needed. However, in practice, mesh refinement is seldom sufficient and the stochastic convergence concepts have a *** to this circle of ideas is the observation that turbulent mixing, in the limit of high Reynolds number, appears to be non-unique. Not only have multiple solutions been observed(and published) for identical problems, but simple physics based arguments and more refined arguments based on the renormalization group come to the same *** of the non-uniqueness inherent in numerical models of high Reynolds number turbulence and mixing, we also include here numeri

关键词：湍流混合数值预测高雷诺数微观宏观概率分布函数湍流输送系数混合性能

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Chaos,Transport and Mesh Convergence for Fluid Mixing

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Acta Mathematicae Applicatae Sinica 2008年第3期24卷 355-368页

作者： H. Lim Y. Yu j. glimm X.L. Li D.H. Sharp Department of Applied Mathematics and Statistics Stony Brook University Stony Brook NY 11794-3600 USA Computational Science Center Brookhaven National Laboratory Upton N~ 11793-6000 USA Los Alamos National Laboratory Los Alamos NM USA

Chaotic mixing of distinct fluids produces a convoluted structure to the interface separating these fluids. For miscible fluids （as considered here）, this interface is defined as a 50% mass concentration isosurface. For shock wave induced （Richtmyer-Meshkov） instabilities, we find the interface to be increasingly complex as the computational mesh is refined. This interfacial chaos is cut off by viscosity, or by the computational mesh if the Kolmogorov scale is small relative to the mesh. In a regime of converged interface statistics, we then examine mixing, i.e. concentration statistics, regularized by mass diffusion. For Schmidt numbers significantly larger than unity, typical of a liquid or dense plasma, additional mesh refinement is normally needed to overcome numerical mass diffusion and to achieve a converged solution of the mixing problem. However, with the benefit of front tracking and with an algorithm that allows limited interface diffusion, we can assure convergence uniformly in the Schmidt number. We show that different solutions result from variation of the Schmidt number. We propose subgrid viscosity and mass diffusion parameterizations which might allow converged solutions at realistic grid levels.

关键词： Schmidt number mass diffusion turbulence multiphase flow

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A MATHEMATICAL THEORY FOR LES CONVERGENCE

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Acta Mathematica Scientia 2012年第1期32卷 237-258页

作者： H.Lim T.Kaman V.Mahadeo j.glimm S.Dutta D.H.Sharp B.Plohr Department of Applied Mathematics and Statistics Stony Brook University College of St.Catherine Los Alamos National Laboratory

Practical simulations of turbulent processes are generally cutoff, with a grid resolution that stops within the inertial range, meaning that multiple active regions and length scales occur below the grid level and are not resolved. This is the regime of large eddy simulations （LES）, in which the larger but not the smaller of the turbulent length scales are resolved. Solutions of the fluid Navier-Stokes equations, when considered in the inertial regime, are conventionally regarded as solutions of the Euler equations. In other words, the viscous and diffusive transport terms in the Navier-Stokes equations can be neglected in the inertial regime and in LES simulations, while the Euler equation becomes fundamental. For such simulations, significant new solution details emerge as the grid is refined. It follows that conventional notions of grid convergence are at risk of failure, and that a new, and weaker notion of convergence may be appropriate. It is generally understood that the LES or inertial regime is inherently fluctuating and its description must be statistical in nature. Here we develop such a point of view systematically, based on Young measures, which are measures depending on or indexed by space time points. In the Young measure du（ξ）x,t, the random variable ξ of the measure is a solution state variable, i.e., a solution dependent variable, representing momentum, density, energy and species concentrations, while the space time coordinates, x, t, serve to index the *** evidence suggests that convergence via Young measures is suifficiently weak to encompass the LES/inertial regime; numerical and theoretical evidence suggests that this notion may be required for passive scalar concentration and therm degrees of freedom. Our objective in this research is twofold： turbulent simulations without recourse to ad- justable parameters （calibration） and extension to more complex physics, without use of additional models or parameters, in both cases with

关键词： numerical methods turbuent mixing

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