Variance consistent mean shift particle model for treating differential molecular diffusion in transported PDF methods for turbulent reactive flows

Pei Zhang; Haifeng Wang

doi:10.1016/j.compfluid.2018.04.021

Variance consistent mean shift particle model for treating differential molecular diffusion in transported PDF methods for turbulent reactive flows

Pei Zhang, Haifeng Wang

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

A mean shift (MS) particle model has been developed before to account for molecular diffusion in the transported probability density function (PDF) methods for turbulent reactive flows (McDermott and Pope, Journal of Computational Physics, 2007, 226, 947–993). The MS model is superior over the traditional random walk model for its capabilities to incorporate differential molecular diffusion and to yield a consistent DNS limit of scalar variance production/dissipation. The MS model, however, yields inconsistent transport of the scalar variance because of the missing molecular diffusion in the resultant variance transport equation. To yield fully consistent transport of scalar mean and variance, a variance consistent mean shift (VCMS) model is developed in this work. The VCMS model formulations are developed for both a single-scalar system and a multi-scalar system. Boundedness violation of particle scalars exists in both the MS and VCMS models and causes a realizability issue of the models. A correction algorithm (called MP correction by McDermott and Pope) has been developed before to correct the boundedness violation in the MS model. The MP correction is found to produce overcorrection to the particles, resulting in an underprediction of the scalar variance. In addition, it is only applicable to the IEM mixing model. In this work, three new boundedness correction algorithms are developed based on the strategies of a least-decay factor (LDF), clipping at scalar bounds (CSB), and clipping with paired mixing (CPM). The accuracy and consistency of the VCMS models are examined and validated thoroughly in a turbulent mixing layer problem. The effectiveness and accuracy of the different boundedness correction algorithms are also examined and assessed in the mixing layer problem. The applicability of the CPM correction to other mixing models (MCurl and EMST) is also demonstrated.

Original language	English
Pages (from-to)	53-76
Number of pages	24
Journal	Computers and Fluids
Volume	170
DOIs	https://doi.org/10.1016/j.compfluid.2018.04.021
State	Published - Jul 15 2018
Externally published	Yes

Funding

This paper is based upon work supported by the National Science Foundation under Grant No. CBET-1336075. This research was supported in part through computational resources provided by Information Technology at Purdue University, West Lafayette, Indiana. We are thankful to Mr. Chao Han for providing the simulation data for the Sandia piloted jet flame D in Table 5 and helpful discussions. This paper is based upon work supported by the National Science Foundation under Grant No. CBET-1336075 . This research was supported in part through computational resources provided by Information Technology at Purdue University, West Lafayette, Indiana. We are thankful to Mr. Chao Han for providing the simulation data for the Sandia piloted jet flame D in Table 5 and helpful discussions.

Funders	Funder number
National Science Foundation	CBET-1336075
Purdue University

Keywords

Boundedness correction algorithms
Differential molecular diffusion
Mean shift particle model
Model consistency
Transported PDF methods

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10.1016/j.compfluid.2018.04.021

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title = "Variance consistent mean shift particle model for treating differential molecular diffusion in transported PDF methods for turbulent reactive flows",

abstract = "A mean shift (MS) particle model has been developed before to account for molecular diffusion in the transported probability density function (PDF) methods for turbulent reactive flows (McDermott and Pope, Journal of Computational Physics, 2007, 226, 947–993). The MS model is superior over the traditional random walk model for its capabilities to incorporate differential molecular diffusion and to yield a consistent DNS limit of scalar variance production/dissipation. The MS model, however, yields inconsistent transport of the scalar variance because of the missing molecular diffusion in the resultant variance transport equation. To yield fully consistent transport of scalar mean and variance, a variance consistent mean shift (VCMS) model is developed in this work. The VCMS model formulations are developed for both a single-scalar system and a multi-scalar system. Boundedness violation of particle scalars exists in both the MS and VCMS models and causes a realizability issue of the models. A correction algorithm (called MP correction by McDermott and Pope) has been developed before to correct the boundedness violation in the MS model. The MP correction is found to produce overcorrection to the particles, resulting in an underprediction of the scalar variance. In addition, it is only applicable to the IEM mixing model. In this work, three new boundedness correction algorithms are developed based on the strategies of a least-decay factor (LDF), clipping at scalar bounds (CSB), and clipping with paired mixing (CPM). The accuracy and consistency of the VCMS models are examined and validated thoroughly in a turbulent mixing layer problem. The effectiveness and accuracy of the different boundedness correction algorithms are also examined and assessed in the mixing layer problem. The applicability of the CPM correction to other mixing models (MCurl and EMST) is also demonstrated.",

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N2 - A mean shift (MS) particle model has been developed before to account for molecular diffusion in the transported probability density function (PDF) methods for turbulent reactive flows (McDermott and Pope, Journal of Computational Physics, 2007, 226, 947–993). The MS model is superior over the traditional random walk model for its capabilities to incorporate differential molecular diffusion and to yield a consistent DNS limit of scalar variance production/dissipation. The MS model, however, yields inconsistent transport of the scalar variance because of the missing molecular diffusion in the resultant variance transport equation. To yield fully consistent transport of scalar mean and variance, a variance consistent mean shift (VCMS) model is developed in this work. The VCMS model formulations are developed for both a single-scalar system and a multi-scalar system. Boundedness violation of particle scalars exists in both the MS and VCMS models and causes a realizability issue of the models. A correction algorithm (called MP correction by McDermott and Pope) has been developed before to correct the boundedness violation in the MS model. The MP correction is found to produce overcorrection to the particles, resulting in an underprediction of the scalar variance. In addition, it is only applicable to the IEM mixing model. In this work, three new boundedness correction algorithms are developed based on the strategies of a least-decay factor (LDF), clipping at scalar bounds (CSB), and clipping with paired mixing (CPM). The accuracy and consistency of the VCMS models are examined and validated thoroughly in a turbulent mixing layer problem. The effectiveness and accuracy of the different boundedness correction algorithms are also examined and assessed in the mixing layer problem. The applicability of the CPM correction to other mixing models (MCurl and EMST) is also demonstrated.

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Variance consistent mean shift particle model for treating differential molecular diffusion in transported PDF methods for turbulent reactive flows

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