Pseudopotential Lattice Boltzmann Method for boiling heat transfer: a mesh refinement procedure

TL;DR

This paper introduces a mesh refinement methodology for pseudopotential Lattice Boltzmann simulations of boiling heat transfer, ensuring convergence and sensitivity analysis of the numerical results with respect to grid parameters.

Contribution

It proposes a novel mesh refinement procedure that relates physical parameters to lattice parameters, improving the accuracy of phase-change heat transfer simulations using LBM.

Findings

The methodology achieves convergent results across different boiling problems.

Convergence order varies with the complexity of the phenomena.

The approach enhances the reliability of LBM in simulating boiling heat transfer.

Abstract

Boiling is a complex phenomenon where different non-linear physical interactions take place and for which the quantitative modeling of the mechanism involved is not fully developed yet. In the last years, many works have been published focusing on the numerical analysis of this problem. However, a lack of numerical works assessing quantitatively the sensitivity of these numerical simulations to grid parameters can be identified, especially for the Lattice Boltzmann method (LBM). The main goal of this work is to propose a mesh refinement methodology for simulating phase-change heat transfer problems by means of the pseudopotential LBM. This methodology was based on relating the physical parameters to their lattice counterparts for an arbitrary mesh under the viscous regime (where $\Delta t \propto \Delta x ^2$). A suitable modification of the EOS parameters and the adjusting of thermodynamic consistency and surface tension for a certain $\Delta x$ were the main steps of the proposed methodology. A first ensemble of simple simulations including the droplet vaporization and the Stefan problems was performed to validate the proposed method and to assess the influence of some physical mechanisms. Global norms in space and time were used to evaluate the variations of both the density and temperature fields for pool boiling simulations when the lattice discretization is refined. It was observed that the proposed methodology provides convergent results for all the problems considered, and the convergence orders depend on the complexity of the simulated phenomena.