A Dimensionally Adaptive Technique for Computationally Efficient Cylindrical Discrete Ordinates Radiation Calculations

Abstract The use of high aspect ratio cylindrical pressure vessels and rotationally periodic burners in Pressurized Oxy-Coal (POC) furnaces leads to physical behavior that is 3D periodic near the burner, but which transitions to axisymmetric towards the outlet. A fully 3D model would consume unneeded resources, and an axisymmetric model would fail to capture periodic features of the near burner region, such as recirculation zones. The present work evaluates the ability of a dimensionally adaptive mesh (i.e., one that transitions from 3D to axisymmetric and 1D) to improve computational speed while still accurately calculating heat flux for such cylindrical systems. The Discrete Ordinates Method (DOM) was used to solve the cylindrical Radiative Transfer Equation (RTE) on both a dimensionally adaptive mesh and a fully 3D mesh. The effects of both spatial and angular refinement on speedup and agreement between the adaptive and fully 3D mesh were studied. For the four cylindrical combustor configurations studied, speedups ranged from 46.6% on a coarse adaptive mesh to 49.1% on a fine mesh. Increasing angular resolution decreased speedups from 48.0% at S2 to 37.1% at S8. Increasing angular resolution from S2 to S4 reduced the overall percent difference between adaptive and 3D meshes from 0.656% to 0.381%. Increasing angular resolution beyond S4 did not significantly improve agreement between mesh types.