On the simulation and modeling of turbulent reacting flows

Abstract

A computational algorithm is described for Direct Numerical Simulation (DNS) of a reactive plume in spatially-evolving, grid turbulence. The chemistry follows the single-step, irreversible, global reaction: $Fuel+(r)Oxidizer\to(1+r)Product+Heat,$ with parameters chosen to match experimental data as far as allowed by resolution constraints. Simulation results are presented for four different cases in order to examine the effects of heat release, Damkohler number, and Arrhenius kinetics on the flow physics. Statistical data from the DNS are compared to theory and wind tunnel data and found in reasonable agreement with regard to growth of turbulent length scales, decay of turbulent kinetic energy, decay of centerline scalar concentration, decrease in scalar rms and spread of plume profile. Reactive scalar statistics are consistent with expected behavior.In addition to the DNS, models are presented for use in Large Eddy Simulations (LES) of non-premixed, turbulent reacting flows. A new chemistry model is derived for predicting filtered chemical species and/or reaction rates. The model is based on laminar flamelet theory and assumes that the subgrid or 'Large Eddy' Probability Density Function (LEPDF) of the mixture-fraction follows a Beta-distribution. The functional form of the scalar dissipation rate is obtained by assuming that the instantaneous local straining fields in the neighborhood of the reaction zones are laminar counterflows. Inputs to the model are the filtered mixture-fraction, its subgrid-scale variance and filtered dissipation rate. The model is evaluated by filtering DNS data to simulate the results of an LES. The DNS data show that the model is reasonably accurate and that the accuracy improves with increasing Damkohler number. Furthermore, as the activation temperature is increased, the accuracy of the model improves relative to that for a model assuming equilibrium chemistry. Finally, it is demonstrated that the assumed counterflow form for the scalar dissipation rate is acceptable and that the chemistry model is insensitive to whether or not unmixed fuel and/or oxidizer are present within an LES grid cell.