Computational multi-phase convective conjugate heat transfer on overlapping meshes: a quasi-direct coupling approach via Schwarz alternating method

We present a new computational framework to simulate the multi-phase convective conjugate heat transfer (CHT) problems emanating from realistic manufacturing processes. The paper aims to address the challenges of boundary-fitted and immersed boundary approaches, which cannot simultaneously achieve fluid-solid interface accuracy and geometry-flexibility in simulating this class of multi-physics systems. The method development is built on a stabilized Arbitrary Lagrangian-Eulerian (ALE)-based finite element thermal multi-phase formulation, which is discretized by overlapping one boundary-fitted mesh and non-boundary-fitted mesh with a quasi-direct coupling approach via Schwarz alternating method. The framework utilizes a volume-of-fluid (VoF)-based multi-phase flow model coupled with a thermodynamics model with phase transitions to capture the conjugate heat transfer between the solid and multi-phase flows and the multi-stage boiling and condensation phenomena. The quasi-direct coupling approach allows the exact and automatic enforcement of temperature and heat-flux compatibility at the fluid-solid interface with large property discontinuities. From the perspective of method development, the proposed framework fully exploits boundary-fitted approach’s strength in resolving fluid-solid interface and boundary layers and immersed boundary approach’s geometry flexibility in handling moving objects while circumventing each individual’s limitations. From the perspective of industry applications, such as water quenching processes, the resulting model can enable accurate temperature prediction directly from process parameters without invoking the conventional empirical heat transfer coefficient (HTC)-based approach that requires intensive calibration. We present the mathematical formulation and numerical implementation in detail and demonstrate the claimed features of the proposed framework through a set of benchmark problems and real-world water quenching processes. The accuracy of the proposed framework is carefully assessed by comparing the prediction with other computational results and experimental measurements.