A new method of modeling the conditional scalar dissipation rate

Devaud, Cécile; Bilger, R.W.; Liu, T.

doi:10.1063/1.1699108

Cited by 43 publications

(15 citation statements)

References 8 publications

(1 reference statement)

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“…The successful implementation of the CMC method depends on the proper modelling of the PDF and the corresponding conditional dissipation rate (Devaud et al, 2004;Mortensen, 2004Mortensen, , 2005Vikhansky and Cox, 2007). In the present work we approximate the PDF by a discrete measure as follows:…”

Section: Discrete-measure Pdfsmentioning

confidence: 99%

Conditional moment closure for self-catalytic reactions

Vikhansky

2010

Chemical Engineering Science

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Section: Discrete-measure Pdfsmentioning

confidence: 99%

Conditional moment closure for self-catalytic reactions

Vikhansky

2010

Chemical Engineering Science

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“…͑27͒ is validated against experimental data and two other ͗N Z ͉ ͘ models which are commonly used in CMC computations: the amplitude mapping closure ͑AMC͒ model 10 ͑sometimes called the inverse error function model͒; and the doubly integrated PDF transport equation model. 8 The alternative models were briefly discussed in Sec. I and a detailed explanation of their performance for the flame conditions considered is given by Sreedhara et al 6 The three conditional scalar dissipation models depend directly ͑MMC and AMC͒ or indirectly ͑PDF integration model͒ on Ñ Z .…”

Section: B Model Validationmentioning

confidence: 99%

“…Simple models which link ͗N Z ͉ ͘ to Ñ Z have been developed but most are inconsistent with the PDF transport equation. 4 Recent CMC based studies 4,[6][7][8][9] derive the conditional scalar dissipation from the double integration of the mixture fraction PDF transport equation, thus enforcing consistency between ͗N Z ͉ ͘ and P Z . Unfortunately this approach suffers from numerical problems in regions of low probability as the final model formula contains P Z in the denominator.…”

Section: Introductionmentioning

confidence: 99%

Modeling of scalar mixing in turbulent jet flames by multiple mapping conditioning

et al. 2009

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This is the published version of the paper.This version of the publication may differ from the final published version. Multiple mapping conditioning ͑MMC͒ combines the probability density function ͑PDF͒ and the conditional moment closure ͑CMC͒ methods via the application of a generalized mapping function to a prescribed reference space. Stochastic and deterministic formulations of MMC exist, and the deterministic implementation has been applied here to a piloted jet diffusion flame ͑Sandia Flame D͒. This paper focuses on the feasibility of MMC and its closures for real ͑laboratory͒ flames and a relatively simple one-dimensional reference space that represents mixture fraction has been used. The remaining chemically reactive species are implicitly conditioned on mixture fraction and their fluctuations around the conditional mean are neglected. This work primarily evaluates the ability of the deterministic form of MMC to provide accurate and consistent closures for the mixture fraction PDF and the conditional scalar dissipation which do not rely on presumed shape functions for the PDF such as the commonly used ␤-PDF. Computed probability distributions agree well with measurements, and a detailed comparison of the modeled conditional and mean scalar dissipation with experimental data and conventional closures demonstrate MMC's potential. Predictions of reactive species and temperature are in good agreement with experimental data and similar in quality to singly conditioned, first-order CMC predictions. MMC therefore provides an attractive-since consistent-alternative approach for the modeling of scalar mixing in turbulent reacting flows. Permanent repository link

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“…20 (An alternative model, valid for homogeneous and inhomogeneous flows, has recently been proposed by Devaud, Bilger, and Liu. 21 ) Taking ͗⑀ ͘ / ͗Ј 2 ͘ to be constant, the time variable can be rescaled. The only remaining parameter to fix in the model is h 1 .…”

Section: B Nonreactive Casementioning

confidence: 99%

A multienvironment conditional probability density function model for turbulent reacting flows

Fox

Raman

2004

Physics of Fluids

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The multienvironment conditional probability density function (MECPDF) model was first proposed by Fox [Computational Models for Turbulent Reacting Flows (Cambridge University Press, Cambridge, 2003)] as a simple extension of multienvironment probability density function models for turbulent reacting flows. Like the conditional moment closure (CMC) and the laminar flamelet model (LFM), the MECPDF model describes the reacting scalars conditioned on the value of the mixture fraction. However, unlike CMC and LFM, the new model provides a consistent description of conditional fluctuations in both the scalar dissipation rate and the reacting scalars, and hence can be used to model partial extinction and reignition in homogeneous turbulent reacting flows. In this work, a general derivation of the MECPDF model is presented for a single reaction-progress variable using the direct quadrature method of moments. Extensions of the model to multiple reaction-progress variables and conditioning on the mixture-fraction vector are also discussed. After deriving the model, the closure assumptions are validated using direct simulations for pure diffusion of two randomly distributed, initially correlated scalar fields. Two homogeneous applications are then considered: nonreactive mixing starting from nontrivial initial conditions, and reactive mixing with partial extinction and reignition. The multienvironment conditional probability density function (MECPDF) model was first proposed by Fox [Computational Models for Turbulent Reacting Flows (Cambridge University Press, Cambridge, 2003)] as a simple extension of multienvironment probability density function models for turbulent reacting flows. Like the conditional moment closure (CMC) and the laminar flamelet model (LFM), the MECPDF model describes the reacting scalars conditioned on the value of the mixture fraction. However, unlike CMC and LFM, the new model provides a consistent description of conditional fluctuations in both the scalar dissipation rate and the reacting scalars, and hence can be used to model partial extinction and reignition in homogeneous turbulent reacting flows. In this work, a general derivation of the MECPDF model is presented for a single reaction-progress variable using the direct quadrature method of moments. Extensions of the model to multiple reaction-progress variables and conditioning on the mixture-fraction vector are also discussed. After deriving the model, the closure assumptions are validated using direct simulations for pure diffusion of two randomly distributed, initially correlated scalar fields. Two homogeneous applications are then considered: nonreactive mixing starting from nontrivial initial conditions, and reactive mixing with partial extinction and reignition. Keywords Center for Turbulence Research Disciplines Chemical Engineering Comments This article is from Physics of Fluids

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A new method of modeling the conditional scalar dissipation rate

Cited by 43 publications

References 8 publications

Conditional moment closure for self-catalytic reactions

Conditional moment closure for self-catalytic reactions

Modeling of scalar mixing in turbulent jet flames by multiple mapping conditioning

A multienvironment conditional probability density function model for turbulent reacting flows

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