TY - JOUR
T1 - Joint probability density function models for multiscalar turbulent mixing
AU - Perry, Bruce A.
AU - Mueller, Michael E.
N1 - Funding Information:
The authors sincerely appreciate funding for this work provided by NASA under grant NNX16AP90A. B.A.P . is thankful to be supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE1148900 . The authors also gratefully acknowledge valuable support in the form of computational time on the TIGRESS high performance computing center at Princeton University, which is jointly supported by the Princeton Institute for Computational Science and Engineering (PICSciE) and the Princeton University Office of Information Technology’s Research Computing Department.
Funding Information:
The authors sincerely appreciate funding for this work provided by NASA under grant NNX16AP90A. B.A.P. is thankful to be supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE1148900. The authors also gratefully acknowledge valuable support in the form of computational time on the TIGRESS high performance computing center at Princeton University, which is jointly supported by the Princeton Institute for Computational Science and Engineering (PICSciE) and the Princeton University Office of Information Technology's Research Computing Department.
Publisher Copyright:
© 2018 The Combustion Institute
PY - 2018/7
Y1 - 2018/7
N2 - Modeling multicomponent turbulent mixing is essential for simulations of turbulent combustion, which is controlled by mixing of fuel, oxidizer, combustion products, and intermediate species. One challenge is to find functions that can reproduce the joint probability density function (PDF) of scalar mixing states using only a small number of parameters. Even for mixing with only two independent scalars, several statistical distributions, including the Dirichlet, Connor–Mosimann (CM), five-parameter bivariate beta (BVB5), and statistically-most-likely distributions, have previously been proposed for this purpose, with minimal physical justification. This work uses the concept of statistical neutrality to relate these distributions to each other, relate the distributions to physical mixing configurations, and develop a systematic approach to model selection. This approach is validated by comparing the ability of these distributions to reproduce the evolution of the scalar PDF from Direct Numerical Simulations of three-component passive scalar mixing in isotropic turbulence with 11 different initial conditions that are representative of a wide range of mixing conditions of interest. The approach correctly identifies whether the Dirichlet, CM, and BVB5 distributions, which are increasingly complex bivariate generalizations of the beta distribution, can accurately model the joint PDFs, but knowledge of the mixing configuration is required to select the appropriate distribution. The statistically-most-likely distribution is generally less accurate than the appropriate bivariate beta distribution but still gives reasonable predictions and does not require knowledge of the mixing configuration, so it is a suitable model when no single mixing configuration can be identified.
AB - Modeling multicomponent turbulent mixing is essential for simulations of turbulent combustion, which is controlled by mixing of fuel, oxidizer, combustion products, and intermediate species. One challenge is to find functions that can reproduce the joint probability density function (PDF) of scalar mixing states using only a small number of parameters. Even for mixing with only two independent scalars, several statistical distributions, including the Dirichlet, Connor–Mosimann (CM), five-parameter bivariate beta (BVB5), and statistically-most-likely distributions, have previously been proposed for this purpose, with minimal physical justification. This work uses the concept of statistical neutrality to relate these distributions to each other, relate the distributions to physical mixing configurations, and develop a systematic approach to model selection. This approach is validated by comparing the ability of these distributions to reproduce the evolution of the scalar PDF from Direct Numerical Simulations of three-component passive scalar mixing in isotropic turbulence with 11 different initial conditions that are representative of a wide range of mixing conditions of interest. The approach correctly identifies whether the Dirichlet, CM, and BVB5 distributions, which are increasingly complex bivariate generalizations of the beta distribution, can accurately model the joint PDFs, but knowledge of the mixing configuration is required to select the appropriate distribution. The statistically-most-likely distribution is generally less accurate than the appropriate bivariate beta distribution but still gives reasonable predictions and does not require knowledge of the mixing configuration, so it is a suitable model when no single mixing configuration can be identified.
KW - Direct numerical simulation
KW - Multiscalar turbulent mixing
KW - Presumed probability density function
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U2 - 10.1016/j.combustflame.2018.03.039
DO - 10.1016/j.combustflame.2018.03.039
M3 - Article
AN - SCOPUS:85045387323
SN - 0010-2180
VL - 193
SP - 344
EP - 362
JO - Combustion and Flame
JF - Combustion and Flame
ER -