HIGHER-ORDER SPHERICAL HARMONICS TO MODEL RADIATION IN DIRECT NUMERICAL SIMULATION OF TURBULENT REACTING FLOWS

The exact treatment of the radiative transfer equation (RTE) is difficult even for idealized situ-ations and simple boundary conditions. A number of higher-order approximations, such as the moment method, discrete ordinates method and spherical harmonics method, provide efficient solution methods. A statistical method, such as the photon Monte Carlo method, solves the RTE by simulating radiative processes such as emission, absorption, and scattering. Although ac-curate, it requires large computational resources and the solution suffers from statistical noise. The third-order spherical harmonics method (P3 approximation) used here decomposes the RTE into a set of 16 first-order partial differential equations. Successive elimination of spherical harmonic tensors reduces this set to six coupled second-order partial differential equations with general boundary conditions, allowing for variable properties and arbitrary three-dimensional geometries. The tedious algebra required to assemble the final form is offset by greater accu-racy because it is a spectral method as opposed to the finite difference/finite volume approach of the discrete ordinates method. The radiative solution is coupled with a direct numerical so-lution (DNS) of turbulent reacting flows to isolate and quantify turbulence–radiation interac-tions. These interactions arise due to nonlinear coupling between the fluctuations of temperature