Closure of the Transport Equation for the Probability Density Funcfion of Turbulent Scalar Fields

Janicka, J.; Kolbe, W.; Kollmann, W.

doi:10.1515/jnet.1979.4.1.47

Cited by 336 publications

(168 citation statements)

References 16 publications

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“…One example is that by Song, 23 which used a function of the velocity to determine the amount of mixing for paired particles in a modified Curl's model. 19,20 By contrast, in the current model the amount of mixing is controlled by another passive scalar and the velocity is effectively used to determine which particles are paired. A further example is explicit conditioning on the velocity in the interaction by exchange with the conditional mean ͑IECM͒ model.…”

Section: ͑27͒mentioning

confidence: 97%

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Hybrid binomial Langevin-multiple mapping conditioning modeling of a reacting mixing layer

Wandel

Lindstedt

2009

Physics of Fluids

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A novel, stochastic, hybrid binomial Langevin-multiple mapping conditioning ͑MMC͒ model-that utilizes the strengths of each component-has been developed for inhomogeneous flows. The implementation has the advantage of naturally incorporating velocity-scalar interactions through the binomial Langevin model and using this joint probability density function ͑PDF͒ to define a reference variable for the MMC part of the model. The approach has the advantage that the difficulties encountered with the binomial Langevin model in modeling scalars with nonelementary bounds are removed. The formulation of the closure leads to locality in scalar space and permits the use of simple approaches ͑e.g., the modified Curl's model͒ for transport in the reference space. The overall closure was evaluated through application to a chemically reacting mixing layer. The results show encouraging comparisons with experimental data for the first two moments of the PDF and plausible results for higher moments at a relatively modest computational cost.

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Section: ͑27͒mentioning

confidence: 97%

“…In light of the above comments, the modified Curl's model 19,20 was applied for S and pairs of particles selected so that they are close in reference space according to…”

Section: =0 ͑21͒mentioning

confidence: 99%

Hybrid binomial Langevin-multiple mapping conditioning modeling of a reacting mixing layer

Wandel

Lindstedt

2009

Physics of Fluids

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“…In many cases, when the probability of A ∼ B is zero, the exact treatment of competitive equivalence does not matter. Another possible generalization, which may resemble modification of Curl's mixing model [16,17], is random selection of the winner for all mixing couples with probability determined by competition. In reacting flows, non-conservative mixing can be interpreted as the joint influence of physical mixing (which is conservative) and a premixed source term (which generates or destroys scalars).…”

Section: Dissipative; Mixing Reduces Differences Betweenmentioning

confidence: 99%

Conservative mixing, competitive mixing and their applications

Klimenko¹

2010

Phys. Scr.

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In many of the models applied to simulations of turbulent transport and turbulent combustion, the mixing between particles is used to reflect the influence of the continuous diffusion terms in the transport equations. Stochastic particles with properties and mixing can be used not only for simulating turbulent combustion, but also for modeling a large spectrum of physical phenomena. Traditional mixing, which is commonly used in the modeling of turbulent reacting flows, is conservative: the total amount of scalar is (or should be) preserved during a mixing event. It is worthwhile, however, to consider a more general mixing that does not possess these conservative properties; hence, our consideration lies beyond traditional mixing. In non-conservative mixing, the particle post-mixing average becomes biased towards one of the particles participating in mixing. The extreme form of non-conservative mixing can be called competitive mixing or competition: after a mixing event, the loser particle simply receives the properties of the winner particle. Particles with non-conservative mixing can be used to emulate various phenomena involving competition. In particular, we investigate cyclic behavior that can be attributed to complex competing systems. We show that the localness and intransitivity of competitive mixing are linked to the cyclic behavior.

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“…A number of differential diffusion models for transported probability density function (PDF) 2, 3 methods are available in the literature. Chen and Chang 1 develop a method for stochastic mixing models and demonstrate its application in the context of the modified Curl's 4 and interaction by exchange with the mean (IEM) 5 mixing models. A differential diffusion form of the Lagrangian spectral relaxation (LSR) model is developed by Fox.…”

Section: Introductionmentioning

confidence: 99%

A multiple mapping conditioning model for differential diffusion

2014

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This work introduces modeling of differential diffusion within the multiple mapping conditioning (MMC) turbulent mixing and combustion framework. The effect of differential diffusion on scalar variance decay is analyzed and, following a number of publications, is found to scale as Re−1/2. The ability to model the differential decay rates is the most important aim of practical differential diffusion models, and here this is achieved in MMC by introducing what is called the side-stepping method. The approach is practical and, as it does not involve an increase in the number of MMC reference variables, economical. In addition we also investigate the modeling of a more refined and difficult to reproduce differential diffusion effect – the loss of correlation between the different scalars. For this we develop an alternative MMC model with two reference variables but which also makes use of the side-stepping method. The new models are successfully validated against DNS results available in literature for homogenous, isotropic two scalar mixing.

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Closure of the Transport Equation for the Probability Density Funcfion of Turbulent Scalar Fields

Cited by 336 publications

References 16 publications

Hybrid binomial Langevin-multiple mapping conditioning modeling of a reacting mixing layer

Hybrid binomial Langevin-multiple mapping conditioning modeling of a reacting mixing layer

Conservative mixing, competitive mixing and their applications

A multiple mapping conditioning model for differential diffusion

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