A Priori Direct Numerical Simulation Assessment of Algebraic Models of Variances and Dissipation Rates in the Context of Reynolds-Averaged Navier-Stokes Simulations for Low Damköhler Number Partially Premixed Combustion

Abstract

Statistically planar turbulent premixed and partially premixed flames for different initial turbulence intensity are simulated for global equivalence ratio ⟨φ⟩ = 0.7 and 1.0 using three-dimensional simplified chemistry based Direct Numerical Simulations (DNS). For the simulations of partially premixed flames a bimodal distribution of equivalence ratio variation about the prescribed value of ⟨φ⟩ is introduced in the fresh reactants. The simulation parameters are chosen in such a manner that the combustion situation in all the cases represents the thin reaction zones regime with global Damköhler number smaller than unity. The DNS data has been used to analyze the statistics of the variances , covariances (where Y, ξ and c are the fuel mass fraction, mixture fraction, and reaction progress variable, respectively, and tilde and double prime represent the Favre mean and Favre fluctuation of the relevant quantities, respectively), scalar dissipation rates (i.e., and ) of active scalar variances, and the cross-scalar dissipation rates ( and ) of the covariances of active scalar and mixture fraction ξ fluctuations in the context of Reynolds-Averaged Navier-Stokes (RANS) simulations. The performances of different algebraic models for the variances, covariances, scalar dissipation rate of active scalars, and cross-scalar dissipation rates have been assessed with respect to the corresponding values obtained from the DNS database. It has been found that root mean square turbulence velocity fluctuation u′ and global equivalence ratio ⟨φ⟩ have significant effects on the statistics of . The authors found that the maximum values of increase with increasing u′ and ⟨φ⟩ values. Moreover, the modeling parameters of the algebraic models for the quantities , and show significant u′ and ⟨φ⟩ dependence. Based on the a priori DNS assessment, the algebraic models for , which give rise to satisfactory agreement with the corresponding quantities obtained from DNS without any change in model parameters in response to the changes in u′ and ⟨φ⟩, have been identified. It has been found that none of the existing algebraic models for and are capable of predicting corresponding quantities extracted from the DNS data for the complete set of u′ and ⟨φ⟩ values analyzed in the present study.