An Adaptive Physics-Driven Deep Learning Framework for a Two-Phase Stefan Problem

TL;DR

This paper introduces a physics-driven deep learning framework that accurately models complex phase change processes in thermal energy storage systems, reducing computational costs compared to traditional methods.

Contribution

The study develops a multi-network deep learning approach constrained by physical laws to efficiently simulate moving boundary Stefan problems without meshing, enhancing modeling of PCM-based TES systems.

Findings

High accuracy in interface and temperature prediction validated against analytical benchmarks.

Effectively captures geometrical influences on solidification and thermal performance.

Eliminates need for mesh regeneration, reducing computational effort.

Abstract

Thermal Energy Storage (TES) using Phase Change Materials (PCMs) represents a critical technology for sustainable energy management and grid stability. This study presents a novel Physics-Driven Deep Learning (PDDL) framework for modeling the complex solid-liquid phase transition in a two-dimensional PCM-based TES system integrated with finned heat exchangers. The system operates under transient forced convection with cooling air, presenting a challenging Moving Boundary Problem (MBP) characterized by intricate phase interface dynamics and strong geometrical dependencies. Conventional numerical methods for such Stefan problems face significant computational burdens due to repeated meshing requirements at the evolving interface. To overcome these limitations, we develop a multi-network PDDL approach that simultaneously predicts the solid phase temperature field, fin temperature distribution, and the moving phase boundary position. The architecture employs three specialized deep neural networks operating in parallel, constrained by the governing physical laws of energy conservation and interface conditions. Comprehensive validation against established analytical benchmarks demonstrates the framework's exceptional accuracy in predicting interface evolution and temperature distributions across various aspect ratios. The model successfully captures the parametric influence of geometrical parameter on solidification rates and thermal performance without requiring mesh regeneration. Our approach provides an efficient computational paradigm for optimizing PCM based TES systems and offers extensibility to three-dimensional configurations and multi-material composites, presenting significant potential for advanced thermal energy system design.