An advanced numerical radial sub-resolution technique to correct heat fluxes in the vicinity of bubbles at saturation

Abstract

This work explores the use of a thermal sub-resolution technique applied on coarse grids to better estimate the temperature gradient in the vicinity of a bubble at saturation as part of a DNS-Front-Tracking framework. By refining locally the solution and realigning it with the bubble’s interface normal direction, the temperature and fluxes prediction are notably enhanced. The refined profiles computed by Finite-Difference in a local spherical frame of reference are then transmitted to the fixed grid using several coupling methods both identified from the literature. Coupling methods overriding the fixed grid temperature are interesting in terms of ease of implementation and robustness whereas face fluxes methods are conservative, but they may cause underestimation of quantities and may require local smoothing like neighbouring averaging. In pure diffusion, these coupling approaches show a good agreement with the theoretical Nusselt number profile. However, the quasi-static hypothesis is difficult to satisfy at the beginning of the simulation which causes a permanent bias. Results are promising on a rising bubble case, reducing the error on the heat transfer prediction below 6.5% with a reduction in computation cost by a factor of 1300 compared to a reference simulation.