Advances In Particle/Finite Volume Algorithms For Turbulent Reactive Flows

In the field of turbulent reactive flow simulations, hybrid particle/finite volume large eddy simulation/probability density function (LES/PDF) methods have been shown to be highly accurate in simulating laboratory-scale flames. Their strengths lie in the combination of the large eddy simulation procedure's ability to resolve the large, non-universal scales of turbulence, combined with the fact that probability density function models for turbulent combustion require no closure for the highly non-linear chemistry source term. This work presents advances in such hybrid particle/finite volume LES/PDF algorithms for turbulent reactive flows. New time stepping, interpolation, and coupling schemes have been proposed with the goal of reducing particle mass consistency (PMC) error (defined as the discrepancy between particle mass density and resolved finite volume density) and overall simulation error. The Multi-step Second-order Runge-Kutta (MRK2) integration scheme is an ODE integration scheme designed for reducing PMC errors when applied to discontinuous velocity fields. When applied to a discontinuous velocity field such as might be produced by a state-of-the art velocity interpolation scheme, MRK2 preserves the continuity of the Lagrangian position mapping and is second-order convergent in time, as opposed to a standard second-order Runge-Kutta scheme, which is only first-order convergent in time when applied to a discontinuous velocity field. The Direct Richardson p-th order (DRp) is a conceptually new family of SDE integration schemes which are weakly p-th order accurate in time, where p is an arbitrary positive integer. Unlike standard SDE integration schemes, which are based on matching appropriate terms in the Ito-Taylor expansion of the stochastic process, the DRp schemes work via Richardson extrapolation between the probability density functions of a set of first-order accurate Euler approximations with differing time steps. In the context of the Large Eddy Simulation/Probability Density Function (LES/PDF) code developed by the Turbulence and Combustion Group at Cornell University, a PDF to LES density coupling scheme via a transported specific volume (TSV) has been developed. While coupling approaches similar to TSV have been used previously in LES/PDF application, the present implementation is the first to allow overall second-order accuracy of the LES/PDF code in space and time. New implicit and explicit schemes for PMC error reduction schemes have been developed and tested in the context of the Sandia-Sydney bluff-body flame. Implicit PMC preservation schemes include new velocity and diffusivity interpolation algorithms, and explicit PMC error correction is achieved via a corrective velocity. While corrective velocity schemes have been used previously, the present algorithm, featuring a smoothed version of the PMC error field, is capable of maintaining the same PMC error levels with a corrective velocity of lower magnitude. Finally, the LES/PDF algorithm, developed by the Turbulence and Combustion group at Cornell, is applied to the Sandia-Sydney bluff-body flames. Comparison is made with experimental data, and the new code is in better agreement with experiment than previous simulations of the same series of flames