Development of closures of scalar dissipation rate for large eddy simulation of turbulent premixed combustion using direct numerical simulation data

Abstract

In turbulent premixed combustion, the mean reaction rate can be modelled based on scalar dissipation rate (SDR) in the context of both Reynolds Averaged Navier-Stockes (RANS) and Large Eddy Simulations (LES) simulations. The SDR, which characterises the mixing rate of the unburnt reactants and hot burnt products, itself requires modelling as well. The SDR based reaction rate closure has been studied extensively in the context of RANS. However, modelling of SDR and SDR based reaction rate closure are yet to be addressed in the context of LES for turbulent premixed combustion. There are two major approaches for SDR based reaction rate modelling, which are algebraic closure and SDR transport equation based closure respectively. Several Direct Numerical Simulation (DNS) databases, part of which were generated by this study, have been explicitly filtered using a Gaussian filter for both a-priori analysis of Favre filtered SDR and filtered SDR transport equation and a-posteriori assessment of the SDR based reaction rate closure. In the a-priori DNS analysis, a three-dimensional DNS database of freely propagating statistically planar flames for a range of different heat release parameter, global Lewis number and turbulent Reynolds number has been LES filtered using a Gaussian filter. An existing SDR based reaction rate closure for RANS simulations has been extended for LES and a satisfactory performance of this LES closure is observed for a range of filter widths, covering both laboratories scale to practical scales. When the generation and destruction of the scalar gradient are at equilibrium, it is viable for an algebraic SDR model in the context of LES. A-priori DNS assessment of algebraic SDR closures based on passive scalar mixing model and a power-law has been conducted, which have been found unsuitable for the reactive turbulent flows of premixed flames. Subsequently, a new algebraic model of Favre-filtered SDR has been proposed by extending a popular algebraic model of RANS averaged SDR into the context of LES. The performances of the newly proposed algebraic closure were assessed with respect to Favre-filtered SDR directly extracted from the DNS datasets. It has been found that the newly proposed SDR model for LES predicts both local and volume-averaged behaviours of SDR satisfactorily. However, when the generation and destruction of the scalar gradient are not at equilibrium, the Favre-filtered SDR transport equation need to be modelled for both RANS and LES. The statistical behaviours of the SDR transport equation have been studied for different global Lewis number, turbulent Reynolds number and heat release parameter at different filter widths. Based on the scaling analysis of all the unclosed terms in the Favre-filtered SDR transport equation, models are proposed for those terms in the context of LES and their performances have been assessed with respect to their corresponding values obtained from explicitly filtered DNS data. These newly proposed models are found to satisfactorily predict both the qualitative and quantitative behaviours of these unclosed terms for a range of different values of filter widths, heat release parameter, global Lewis number and turbulent Reynolds number. The newly proposed algebraic closure and transport equation based closure of Favrefiltered SDR in the context of LES, which were proposed based on simple chemistry DNS database, are assessed by a v-flame detail chemistry DNS database as a-posteriori assessment. The algebraic model is found to capture both qualitative and quantitative behaviours of SDR with reaction progress variable defined based on both deficient reactants and products. The models of the unclosed terms of SDR transport equation are found to capture the behaviours of the explicitly filtered terms of the detail chemistry DNS database in an order-of-magnitude sense. Further improvement is required in order to address the effects of diffusivity gradient, the gradients of reaction rate and molecular dissipation of SDR.