Thermal boundary layer modelling for heat flux prediction of bubbles at saturation: A priori analysis based on fully-resolved simulations

Abstract

This study presents and investigates uni-directional thermal sub-layer enhancement techniques within the context of an interface tracking method for simulating bubbly flows at saturation. Current discretisation methods on structured and fixed Cartesian grids tend to spread the bubbles' interface region, creating a trade-off between the freely moving nature of the bubble to the detriment of accurately capturing the discontinuous aspect of the interface and variations of properties and fluxes crossing it. Although robust techniques have been described in the literature to ensure energy conservation, less research has been undertaken to develop a methodology to retrieve the non-linear behaviour of quantities in the interface vicinity at a reasonable computational cost. In this study, the discretised bubble surface is used as a basis for addressing several quasi-static radial sub-problems that are bounded by an interfacial constant saturation temperature and a CFD temperature field value. A first approach, based on an analytical solution fitted at each time step using underlying Eulerian field values, has been developed to incorporate near-interface physics. This includes the tangential effect, incoming fluid velocity, and local mean curvature (first order surface approximation). A semi-analytical approach needs to meet certain assumptions to be valid. This is due to its derivation from a simplified plane boundary-layer development or from a spherical diffusion problem which limits its applicability range. Therefore, a second approach based on a uni-directional sub-resolution fed carefully by interpolated velocity and tangential source terms demonstrates promising results as it aligns with the principal variations of the solution. Both methodologies have been applied onto DNS data of a steady rising bubble configuration at low and moderate Reynolds {3.6;62.5} and Prandtl {1;2.5;5} numbers with a constant interfacial temperature after an extensive analysis of the advection-diffusion terms hierarchy. The key aspects to maximise the effectiveness of the sub-resolution method have been clearly identified and discussed. The Sub-resolution shows better applicability to our case study on moderately large thermal layers. The newly predicted interfacial temperature gradient and temperature profile could be re-employed for Eulerian fluxes correction.