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A direct numerical simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different values of Karlovitz number Ka, turbulent Reynolds number Ret, heat release parameter τ, and global Lewis number Le has been used to assess the models of the tangential strain rate term in the generalised flame surface density (FSD) transport equation in the context of Reynolds averaged Navier Stokes (RANS) simulations. The tangential strain rate term has been split into contributions arising due to dilatation rate TD and flame normal strain rate (-TN). Subsequently, TD and (-TN) were split into their resolved (i.e., TD1 and (-TN1)) and unresolved (TD2 and (-TN2)) components. Detailed physical explanations have been provided for the observed behaviours of the components of the tangential strain rate term. This analysis gave way to the modelling of the unresolved dilatation rate  and flame normal strain rate contributions. Models have been identified for TD2 and (-TN2) for RANS simulations, which are shown to perform satisfactorily in all cases considered, accounting for the variations in Ka, Ret, τ and Le. The performance of the newly proposed models for the FSD strain rate term have been found to be either comparable to or better than the existing models

mathematical problems in engineering

Modelling of the Tangential Strain Rate Term in the Flame Surface Density Transport Equation in the Context of Reynolds Averaged Navier Stokes Simulations: A Direct Numerical Simulation Analysis