Direct Numerical Simulation of a Turbulent Reactive Plume on a Parallel Computer

A computational algorithm is described for direct numerical simulation (DNS) of a reactive plume in spatially evolving grid turbulence. The algorithm uses sixth-order compact differencing in conjunction with a fifth-order compact boundary scheme which has been developed and found to be stable. A compact filtering method is discussed as a means of stabilizing calculations where the viscous/diffusive terms are differenced in their conservative form. This approach serves as an alternative to nonconservative differencing, previously advocated as a means of damping the 2δ waves. In numerically solving the low Mach number equations the time derivative of the density field in the pressure Poisson equation was found to be the most destabilizing part of the calculation. Even-ordered finite difference approximations to this derivative were found to be more stable (allow for larger density gradients) than odd-ordered approximations. Turbulence at the inlet boundary is generated by scanning through an existing three-dimensional field of fully developed turbulence. In scanning through the inlet field, it was found that a high order interpolation, e.g., cubic-spline interpolation, is necessary in order to provide continuous velocity derivatives. Regarding pressure, a Neumann inlet condition combined with a Dirichlet outlet condition was found to work well. The chemistry follows the single-step, irreversible, global reaction: Fuel + (r) Oxidizer → (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, Damköhler 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.