Assumed β-pdf Model for Turbulent Mixing: Validation and Extension to Multiple Scalar Mixing

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Abstract
Many engineering calculations of turbulent reacting flows employ the assumed-pdf approach. On the form of the assumed pdf, however, there has been little consensus and the choice has often been ad hoc. The objective of this work is to investigate the validity of the assumed β-pdf model for the case of the inert mixing of two scalars and extend the applicability of the model to multiple scalar mixing. By comparing the β-pdf model favorably with the two-scalar mixing data obtained from direct numerical simulations (DNS), it is demonstrated that the use of this model is justified for all stages of the mixing process in statistically-stationary, isotropic turbulence. It is also shown analytically that during the final stages of mixing the model β-pdf reduces to a Gaussian-pdf, consistent with the observations from experiments and DNS, The suggested multivariate β-pdf model for multiple-scalar mixing relates algebraically, The mean scalar concentrations and the turbulent scalar-energy—to the joint pdf of the scalar concentrations. The model requires that only one extra transport equation—for the turbulent scalar-energy—be solved, apart from the mean equations. The model can be used in conjunction with any model for the turbulence velocity field and is expected to provide a simple method for calculating scalar mixing in turbulent flows.

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