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The Lagrangian Spectral Relaxation Model Of The Scalar Dissipation In Homogeneous Turbulence, Rodney O. Fox

#### The Lagrangian Spectral Relaxation Model Of The Scalar Dissipation In Homogeneous Turbulence, Rodney O. Fox

*Rodney O. Fox*

Lagrangian pdf methods are employed to extend the spectral relaxation (SR) model of the scalar dissipation of an inert, passive scalar (1⩽Sc) in homogeneous turbulence. The Lagrangian spectral relaxation (LSR) model divides wavenumber space into a finite number (the total number depending on the Taylor-scale Reynolds numberRλ and the Schmidt number Sc) of wavenumber bands whose time constants are determined from the mean turbulent kinetic energy and instantaneous turbulent energy dissipation rate. The LSR model accounts for the evolution of the scalar spectrum (viz., pdf) from an arbitrary initial shape to its fully developed form. The effect of turbulent-frequencyfluctuations ...

On Velocity-Conditioned Scalar Mixing In Homogeneous Turbulence, Rodney O. Fox

#### On Velocity-Conditioned Scalar Mixing In Homogeneous Turbulence, Rodney O. Fox

*Rodney O. Fox*

Scalar mixing models are required to modelturbulent 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 ...

Modeling Multiple Reactive Scalar Mixing With The Generalized Iem Model, Kuochen Tsai, Rodney O. Fox

#### Modeling Multiple Reactive Scalar Mixing With The Generalized Iem Model, Kuochen Tsai, Rodney O. Fox

*Rodney O. Fox*

An outstanding feature of the amplitude mapping closure is its ability to relax an arbitrary initial probability density function (PDF) to a Gaussian PDF asymptotically. Due to the difficulties in computing either the analytical or numerical solution, the mapping closure has never been applied to multiple scalars with finite reaction rates. In this work, the generalized IEM (GIEM) model is combined with the mapping closure to model the molecular mixing terms in the PDF balance equation. The GIEM model assumes a linear relationship between the rates of change of the reactive scalars and an inert scalar (shadow scalar) during the ...

The Spectral Relaxation Model Of The Scalar Dissipation Rate In Homogeneous Turbulence, Rodney O. Fox

#### The Spectral Relaxation Model Of The Scalar Dissipation Rate In Homogeneous Turbulence, Rodney O. Fox

*Rodney O. Fox*

A model for the effect of scalar spectral relaxation on the scalar dissipation rate of an inert, passive scalar (Sc>1) in fully developed homogeneous turbulence is presented. In the model, wave-number space is divided into a finite number [the total number depending on the turbulence Reynolds number Re, and the Schmidt number (SC)] of intermediate stages whose time constants are determined from the velocity spectrum. The model accounts for the evolution of the scalar spectrum from an arbitrary initial shape to its fully developed form and its effect on the scalar dissipation rate for finite Re, and Sc>1 ...

Improved Fokker–Planck Model For The Joint Scalar, Scalar Gradient Pdf, Rodney O. Fox

#### Improved Fokker–Planck Model For The Joint Scalar, Scalar Gradient Pdf, Rodney O. Fox

*Rodney O. Fox*

The joint scalar, scalar gradient probability density function (PDF) of an inert nonpremixed scalar diffusing in a one-dimensional system of random-sized lamellas is investigated by numerical simulation. The form of the scalar PDF, at a given RMS value, is nearly identical to that predicted by direct numerical simulation (DNS) of scalar mixing in isotropic turbulence and the mapping closure, and the moments of both the scalar and the scalar gradient suggest that their limiting marginal PDF are Gaussian. The joint scalar, scalar gradient PDF is found to be restricted to a bounded region in the scalar-scalar gradient plane, whose form ...

The Fokker–Planck Closure For Turbulent Molecular Mixing: Passive Scalars, Rodney O. Fox

#### The Fokker–Planck Closure For Turbulent Molecular Mixing: Passive Scalars, Rodney O. Fox

*Rodney O. Fox*

A turbulent-molecular-mixing closure for passive scalar mixing is derived based on the theory of diffusion in layerlike lamellar structures. The closure is formulated in terms of the Fokker- Planck (FP) equation (or an equivalent stochastic differential equation), and is to be employed in conjunction with the probability density function (pdf) balance equation appearing in the pdf methods for modeling turbulent reactive flows. Like the mapping closure, the FP closure predicts a limiting Gaussian pdf for the passive scalar concentration in isotropic turbulence. In addition, the FP closure models the joint pdf of the scalar concentration and the scalar gradient and ...