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Abstract
While the mean and unconditional variance are to be predicted well by any reasonable turbulent combustion model, these are generally not sufficient for the accurate modelling of complex phenomena such as extinction/reignition. An additional criterion has been recently introduced: accurate modelling of the dissipation timescales associated with fluctuations of scalars about their conditional mean (conditional dissipation timescales). Analysis of Direct Numerical Simulation (DNS) results for a passive scalar shows that the conditional dissipation timescale is of the order of the integral timescale and smaller than the unconditional dissipation timescale. A model is proposed: the conditional dissipation timescale is proportional to the integral timescale. This model is used in Multiple Mapping Conditioning (MMC) modelling for a passive scalar case and a reactive scalar case, comparing to DNS results for both. The results show that this model improves the accuracy of MMC predictions so as to match the DNS results more closely using a relatively-coarse spatial resolution compared to other turbulent combustion models.
Acknowledgements
The author is grateful to Prof. A. Y. Klimenko and Dr N. S. A. Smith for their assistance and advice in the preliminary stages of this paper.
Notes
1This is similar to [Citation54, Equation (2.42)], but the second term on the RHS of [Citation54, Equation (2.42)] is exactly zero (not ‘very small’ as had been assumed) since ⟨⟨Z|ξ⟩Z′′′|ξ⟩=⟨Z|ξ⟩⟨Z′′′|ξ⟩=0, therefore its integral over P ξ dξ must also be zero.