Mixing In Homogeneous Turbulence Research Articles

Presumed Mapping Functions for Eulerian Modelling of Turbulent Mixing

The mapping closure of Chen et al. [Phys. Rev. Lett., 63, 1989] is a transported probability density function (PDF) method that has proven very efficient for modelling of turbulent mixing in homogeneous turbulence. By utilizing a Gaussian reference field, the solution to the mapping function (in homogeneous turbulence) can be found analytically for a range of initial conditions common for turbulent combustion applications, e.g. for binary or trinary mixing. The purpose of this paper is to investigate the possibility of making this solution a presumed mapping function (PMF) for inhomogeneous flows. The PMF in turn will imply a presumed mixture fraction PDF that can be used for a wide range of models in turbulent combustion, e.g. flamelet models, the conditional moment closure (CMC) or large eddy simulations. The true novelty of the paper, though, is in the derivation of highly efficient, closed algebraic expressions for several existing models of conditional statistics, e.g. for the conditional scalar dissipation/diffusion rate or the conditional mean velocity. The closed form expressions nearly eliminates the overhead computational cost that usually is associated with nonlinear models for conditional statistics. In this respect it is argued that the PMF is particularly well suited for CMC that relies heavily on manipulations of the PDF for consistency. The accuracy of the PMF approach is shown with comparison to DNS of a single scalar mixing layer to be better than for the β-PDF. Not only in the shape of the PDF itself, but also for all conditional statistics models computed from the PDF.

On velocity-conditioned scalar mixing in homogeneous turbulence

Scalar mixing models are required to model turbulent molecular mixing in full probability density function (pdf) simulations of turbulent reacting flows. Despite the existence of direct numerical simulation (DNS) data suggesting the contrary, most scalar mixing models assume that molecular mixing is independent of the instantaneous velocity, i.e., 〈D∇2φ|V,ψ〉=〈D∇2φ|ψ〉. Since in a joint velocity, composition pdf calculation the velocity is known, this assumption is unnecessary and leads to a lack of local isotropy in the scalar field. Moreover, since velocity conditioning offers a numerically tractable approach for including the effects of local anisotropy and mean velocity gradients on scalar mixing, it should be of considerable interest for the numerical simulation of scalar mixing in inhomogeneous turbulent flows. An efficient numerical implementation of velocity-conditioned scalar mixing for full pdf simulations is proposed and verified against DNS data for homogeneous turbulence (isotropic and shear flow) with a uniform mean scalar gradient. A second-moment closure relating the velocity-conditioned scalar dissipation to the scalar fluxes and Reynolds stresses that is exact in the limit of a joint Gaussian pdf is also derived for use with moment closure models.

Inter-Layer Diffusion Model of Scalar Mixing in Homogeneous Turbulence

ABSTRACT A field-parametrized model termed the Inter-Layer Diffusion Model (ILDM) is developed and is implemented for the probabilistic description of scalar mixing in homogeneous turbulent flows. The essential element of the model is based on the lamellar theory of mixing in the context developed by Kerstein (199 la), and proposes that there are two coupled mechanisms by which the mixing process is described. These mechanisms are due to: (1) local events and (2) integrated global events. The mathematical formalities by which the closure is invoked are described and it is shown that the conditional expected diffusion of the scalar field depicted by the model depends more directly on the local events. With the manipulation of each of these two mechanisms, several families of scalar probability density functions (pdf's) are generated. These families include some of the distributions generated by other mixing closures. The similarity of local events imply the similarity of the conditional expected diffusion ...

Multiscalar mapping closure for mixing in homogeneous turbulence

A new methodology to use mapping closures for the mixing of several scalars in homogeneous turbulence is explained. The main idea is the unidimensional mapping for each scalar, with the cross-dissipation handled by a joint reference field. A restricted and a general closure are described. A Monte Carlo code based on a fractional step technique has been developed. As an example, the segregated double-delta two-scalar mixing is analytically and numerically solved and predictions are shown.

A mapping closure for turbulent scalar mixing using a time-evolving reference field

A methodology for modeling passive scalar mixing in homogeneous turbulence using a new mapping closure approach is developed. The physical scalar field φ(y,t) (y-space coordinate, t time) is mapped using a mapping function, X(t), onto a reference scalar field θ(y,t), whose evolution is known. There are two main differences between the present approach and that of Chen et al. [Phys. Rev. Lett. 63, 2657 (1989)]. In the present approach, the reference field is time evolving and not restricted to a Gaussian. The evolution equation of the mapping function is derived for a general reference field. Gaussian and β-pdf reference fields are investigated. Calculations from both reference fields are compared with the heat conduction simulation (HCS) data of Girimaji (NASA Contract. Rep. 4446, 1992). The limits of validity of the mapping closure approach are discussed.

Mixing, Chaotic Advection, and Turbulence

The establishment of a paradigm for mixing of fluids can substantially affect the development of various branches of physical sciences and technology. Mixing is intimately connected with turbulence, Earth and natural sciences, and various branches of engineering. However, in spite of its universality, there have been surprisingly few attempts to construct a general framework for analysis. An examination of any library index reveals that there are almost no works textbooks or monographs focusing on the fluid mechanics of mixing from a global perspective. In fact, there have been few articles published in these pages devoted exclusively to mixing since the first issue in 1969 [one possible exception is Hill’s Homogeneous Turbulent Mixing With Chemical Reaction (1976), which is largely based on statistical theory]. However, mixing has been an important component in various other articles; a few of them are Mixing-Controlled Supersonic Combustion (Ferri 1973), and Mixing in Stably Stratified Waters (Sherman et al. 1978), Eddies, Waves, Circulation, and Mixing: Statistical Geofluid Mechanics (Holloway 1986), and Ocean Turbulence (Gargett 1989). It is apparent that mixing appears in both industry and nature and the problems span an enormous range of time and length scales; the Reynolds number in problems where mixing is important varies by 40 orders of magnitude (see Figure 1). Virtually everyone agrees that mixing is complicated. However, there is no agreement as to the source of the complications; to a rhcologist, the constitutive equation is of paramount importance; to someone in turbu-

Homogeneous Turbulent Mixing with Chemical Reaction

Homogeneous Turbulent Mixing with Chemical Reaction