Enhanced advancing front techniques for mesh generation in radiative heat transfer problem

Abstract

Mesh generation is a mathematical technique to produce meshes in the form of triangle and rectangles on a given domain for approximating values such as heat, temperature and pressure. The values are approximated using numerical methods such as finite element, finite difference and finite volume based on some given boundary conditions. In our work, a conceptual model has been designed for allowing a set of sensors to be deployed along the wall of an ethylene cracker furnace. The main function for the deployment is to provide input in the form of boundary values for approximating the temperatures of flue gas and the radiative heat flux distribution inside the furnace. New models called Enhanced Advancing Front Techniques (EAFT) have been proposed which improve on the existing standard advancing front in the form of element creation procedure, internal gradation control as well as the post-processing procedure for mesh quality improvement. EAFT is applied to discretise the domain of the conceptual model of the ethylene furnace with the requirements of having the location of sensors deployed along the wall as boundary nodes as well as forming boundary elements, generating nodes at a certain boundary with linearly different lengths of boundary edges using layer concept as interior gradation controls and constructing the triangular element directly in every iteration without having to re-order the front or delete the existing elements. The quality of the initial mesh is determined using the normalized measure of skewness provided by the GAMBIT software. The final mesh is obtained once the post-processing procedure of improving the mesh quality has been applied to the initial mesh. EAFT provides the framework for the heat to be approximated using the discrete ordinate method, which is a variant of the finite volume method. Simulation results produced using FLUENT support our findings for effectively approximating the flue gas temperature distribution, the circumferential radiative heat flux incident at the reactor coils as well as the circumferential reactor coil temperature in the conceptual model of ethylene furnace at the end of the study.