A computational algorithm is described for direct numerical simulation (DNS) of a reactive plume in spatially evolving grid turbulence. Reynolds numbers, since such flows can be computed by The algorithm uses sixth-order compact differencing in conjunction direct numerical simulation (DNS). In DNS, the exact govwith a fifth-order compact boundary scheme which has been develerning equations are solved in order to gain insight into oped and found to be stable. A compact filtering method is disthe turbulence and combustion phenomena. In performing cussed as a means of stabilizing calculations where the viscous/ a DNS, it is important to select the proper numerical diffusive terms are differenced in their conservative form. This approach serves as an alternative to nonconservative differencing, method for treating the flow of interest. Since turbulent previously advocated as a means of damping the 2อณ waves. In flows contain a wide range of length scales, spectral methnumerically solving the low Mach number equations the time derivods are a natural choice for DNS due to their high accuracy ative of the density field in the pressure Poisson equation was found and their ability to correctly represent a broad range of to be the most destabilizing part of the calculation. Even-ordered finite difference approximations to this derivative were found to be wavenumbers. The application of spectral methods to turmore stable (allow for larger density gradients) than odd-ordered bulent reacting flows was initiated by Riley et al. [1] and approximations. Turbulence at the inlet boundary is generated by was continued by McMurtry et al. [2], Givi et al. [3], and scanning through an existing three-dimensional field of fully devel-Leonard and Hill [4].
oped turbulence. In scanning through the inlet field, it was found Spectral methods are employed by expanding the depenthat a high order interpolation, e.g., cubic-spline interpolation, is necessary in order to provide continuous velocity derivatives. Re-dent variables in truncated series of orthogonal basis funcgarding pressure, a Neumann inlet condition combined with a tions satisfying the required boundary conditions. Spatial
Dirichlet outlet condition was found to work well. The chemistry derivatives are evaluated locally in the transformed dofollows the single-step, irreversible, global reaction: Fuel ุ (r) main, while nonlinear products are evaluated locally in the Oxidizer ว (1 ุ r)Product ุ Heat, with parameters chosen to match physical domain. The most common expansion used is experimental data as far as allowed by resolution constraints. Simulation results are presented for four different cases in order to examine Fourier series, although Chebyschev polynomials, Legthe effects of heat release, Damko ยจhler number, and Arrhenius kinetics endre polynomials, Jacobi polynomials, and other series on the flow physics. Statistical data from the DNS are compared to have sometimes been employed [5]. With Fourier methods, theory and wind tunnel data and found in reasonable agreement the mapping between physical space and spectral space with regard to growth of turbulent length scales, decay of turbulent can be performed efficiently using a fast Fourier transform kinetic energy, decay of centerline scalar concentration, decrease in scalar rms, and spread of plume profile. Reactive scalar statistics are (FFT) algorithm. Spectral and pseudo-spectral methods consistent with expected behavior.