Dimensionally adaptive techniques for computationally efficient discrete transfer radiation calculations

Abstract The use of long slender 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 transition 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 therefore seeks to demonstrate the ability of a dimensionally adaptive mesh (i.e. one that transitions from 3D to axisymmetric and, when applicable, 1D) to improve computational speed while still accurately calculating heat flux. The Discrete Transfer Method (DTM) was used to solve the Radiative Transfer Equation (RTE) on both a fully 3D mesh and a dimensionally adaptive mesh. Three techniques were tested for calculating heat transfer across the boundary between 3D and axisymmetric regions. The Single Unweighted Ray (SUR) method uses a single ray to represent the radiative exchange between 3D bounding faces and axisymmetric ring elements. The Multiple Unweighted Ray (MUR) method subdivides the axisymmetric face into a number of sub-faces, with a ray connecting each sub-face with the 3D face, and tracks radiative intensity along each ray. Finally, the Single Weighted Ray (SWR) method tracks intensity along a single ray, with radiative properties averaged from multiple points along several paths. Flux results were compared between the four approaches. The SUR, MUR, and SWR methods agreed with the fully 3D calculations within median percent differences of less than 1%.