Wall-function treatment in pdf methods for turbulent flows

Dreeben, Thomas D.; Pope, Stephen B.

doi:10.1063/1.869381

Cited by 29 publications

(29 citation statements)

References 19 publications

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“…31 The constant C controls the Lagrangian autocorrelation time in homogeneous turbulence. Here we use the value found by Dreeben and Pope 32 (C is equivalent to C 3 in their model͒ to yield the correct turbulent dissipation flux in near-wall turbulent flows. As shown in our earlier work, 20 the stretched-exponential model yields good agreement with DNS data 31 for one-point, one-time statistics of the scalar dissipation rate.…”

Section: ͑34͒mentioning

confidence: 99%

The Lagrangian spectral relaxation model for differential diffusion in homogeneous turbulence

Fox

1999

Physics of Fluids

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The Lagrangian spectral relaxation ~LSR! model is extended to treat turbulent mixing of two passive scalars (fa and fb) with different molecular diffusivity coefficients ~i.e., differential-diffusion effects!. Because of the multiscale description employed in the LSR model, the scale dependence of differential-diffusion effects is described explicitly, including the generation of scalar decorrelation at small scales and its backscatter to large scales. The model is validated against DNS data for differential diffusion of Gaussian scalars in forced, isotropic turbulence at four values of the turbulence Reynolds number (Rl538, 90, 160, and 230! with and without uniform mean scalar gradients. The explicit Reynolds and Schmidt number dependencies of the model parameters allows for the determination of the Re ~integral-scale Reynolds number! and Sc ~Schmidt number! scaling of the scalar difference z5fa2fb . For example, its variance is shown to scale like ^z2& ;Re20.3. The rate of backscatter (bD) from the diffusive scales towards the large scales is found to be the key parameter in the model. In particular, it is shown that bD must be an increasing function of the Schmidt number for Sc<1 in order to predict the correct scalar-to-mechanical time-scale>ratios, and the correct long-time scalar decorrelation rate in the absence of uniform mean scalar gradients. Disciplines Catalysis and Reaction Engineering | Chemical Engineering CommentsThis article is from Physics of Fluids11(1999) The Lagrangian spectral relaxation ͑LSR͒ model is extended to treat turbulent mixing of two passive scalars ( ␣ and ␤ ) with different molecular diffusivity coefficients ͑i.e., differential-diffusion effects͒. Because of the multiscale description employed in the LSR model, the scale dependence of differential-diffusion effects is described explicitly, including the generation of scalar decorrelation at small scales and its backscatter to large scales. The model is validated against DNS data for differential diffusion of Gaussian scalars in forced, isotropic turbulence at four values of the turbulence Reynolds number (R ϭ38, 90, 160, and 230͒ with and without uniform mean scalar gradients. The explicit Reynolds and Schmidt number dependencies of the model parameters allows for the determination of the Re ͑integral-scale Reynolds number͒ and Sc ͑Schmidt number͒ scaling of the scalar difference zϭ ␣ Ϫ ␤ . For example, its variance is shown to scale like ͗z 2 ͘ ϳRe Ϫ0.3 . The rate of backscatter (␤ D ) from the diffusive scales towards the large scales is found to be the key parameter in the model. In particular, it is shown that ␤ D must be an increasing function of the Schmidt number for Scр1 in order to predict the correct scalar-to-mechanical time-scale ratios, and the correct long-time scalar decorrelation rate in the absence of uniform mean scalar gradients.

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Section: ͑34͒mentioning

confidence: 99%

The Lagrangian spectral relaxation model for differential diffusion in homogeneous turbulence

Fox

1999

Physics of Fluids

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“…͑23͔͒ were found to yield good agreement with DNS. Dreeben and Pope 34 were the first to propose C 1 ϭ5 ͑denoted C 3 in their work͒, albeit based on other physical constraints. However, use of this value would cause the autocorrelation time of * to disagree with the autocorrelation time from DNS.…”

Section: Conditional Statisticsmentioning

confidence: 99%

Improved Lagrangian mixing models for passive scalars in isotropic turbulence

Fox

Yeung

2003

Physics of Fluids

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Lagrangian data for velocity, scalars, and energy and scalar dissipation from direct numerical simulations are used to validate Lagrangian mixing models for inert passive scalars in stationary isotropic turbulence. The scalar fluctuations are nearly Gaussian, and, as a result of production by uniform mean gradients, statistically stationary. Comparisons are made for Taylor-scale Reynolds numbers in the range 38 to about 240 and Schmidt numbers in the range 1/8 to 1. Model predictions for one-point, one-time Eulerian statisticsEulerian correspondence! and one-particle, two-time Lagrangian statistics ~Lagrangian correspondence! are examined. Two scalar mixing models, namely the Lagrangian Fokker-Planck model and the Lagrangian colored-noise ~LCN! model, are proposed and written in terms of stochastic differential equations ~SDE! with specified drift and diffusion terms. Both of these models rely on statistics of the scalar field conditioned upon the energy dissipation, as provided by the Lagrangian spectral relaxation ~LSR! model. With the exception of the scalar dissipation, the models are shown to capture the Reynolds and Schmidt-number dependence of the Lagrangian integral time scales. However, the LCN model provides a more realistic description of the Lagrangian scalar fluctuations as differentiable time series having the correct form of the scalar autocorrelation function. Further extensions of the new mixing models to non-Gaussian scalars are conceptually straightforward, but require a closure for the scalar-conditioned scalar dissipation rate matrix. Likewise, accurate prediction of joint statistics for differential diffusion between different scalars with unequal molecular diffusivities will require the formulation of a multiscale SDE similar to the LSR model. Disciplines Aerospace Engineering | Chemical Engineering CommentsThis article is from Physics of Fluids, 15 (2003) Lagrangian data for velocity, scalars, and energy and scalar dissipation from direct numerical simulations are used to validate Lagrangian mixing models for inert passive scalars in stationary isotropic turbulence. The scalar fluctuations are nearly Gaussian, and, as a result of production by uniform mean gradients, statistically stationary. Comparisons are made for Taylor-scale Reynolds numbers in the range 38 to about 240 and Schmidt numbers in the range 1/8 to 1. Model predictions for one-point, one-time Eulerian statistics ͑Eulerian correspondence͒ and one-particle, two-time Lagrangian statistics ͑Lagrangian correspondence͒ are examined. Two scalar mixing models, namely the Lagrangian Fokker-Planck model and the Lagrangian colored-noise ͑LCN͒ model, are proposed and written in terms of stochastic differential equations ͑SDE͒ with specified drift and diffusion terms. Both of these models rely on statistics of the scalar field conditioned upon the energy dissipation, as provided by the Lagrangian spectral relaxation ͑LSR͒ model. With the exception of the scalar dissipation, the models are shown to capture the Reynolds and Schmi...

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“…A direct dissipation calculation, as suggested in Dreeben and Pope (1997), requires that all scales experiencing dissipation must be resolved. These scales include eddies at the Kolmogorov microscale which are typically less than a millimeter.…”

Section: Turbulence Closurementioning

confidence: 99%

“…Naturally, it remains to provide an equation for ω , which is defined in Dreeben and Pope (1997) as:…”

Section: Turbulence Closurementioning

confidence: 99%

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Stochastic downscaling method: application to wind refinement

Bernardin

Bossy

Chauvin

et al. 2008

Stoch Environ Res Risk Assess

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In this article, we propose a new stochastic downscaling method: provided a numerical prediction of wind at large scale, we aim to improve the approximation at small scales thanks to a local stochastic model. We first recall the framework of a Lagrangian stochastic model borrowed from S.B. Pope. Then, we adapt it to our meteorological framework, both from the theoretical and numerical viewpoints. Finally, we present some promising numerical results corresponding to the simulation of wind over the Mediterranean Sea.

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Wall-function treatment in pdf methods for turbulent flows

Cited by 29 publications

References 19 publications

The Lagrangian spectral relaxation model for differential diffusion in homogeneous turbulence

The Lagrangian spectral relaxation model for differential diffusion in homogeneous turbulence

Improved Lagrangian mixing models for passive scalars in isotropic turbulence

Stochastic downscaling method: application to wind refinement

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