[Paper Review] Integrated modeling and validation for phase change with natural convection

K. Schüller, Benjamin Berkels+1 more|arXiv (Cornell University)|Jan 11, 2018

Arctic and Antarctic ice dynamics17 references3 citations

TL;DR

This paper presents an integrated simulation-experiment framework for validating phase change with natural convection in water-ice systems using a fixed-grid enthalpy porosity method in OpenFOAM and high-resolution optical imaging with binary Mumford-Shah segmentation. The approach enables continuous, quantitative comparison between simulated and measured phase interfaces, revealing good qualitative agreement but small quantitative discrepancies likely due to simplified boundary conditions and experimental heat losses.

ABSTRACT

Water-ice systems undergoing melting develop complex spatio-temporal interface dynamics and a non-trivial temperature field. In this contribution, we present computational aspects of a recently conducted validation study that aims at investigating the role of natural convection for cryo-interface dynamics of water-ice. We will present a fixed grid model known as the enthalpy porosity method. It is based on introducing a phase field and employs mixture theory. The resulting PDEs are solved using a finite volume discretization. The second part is devoted to experiments that have been conducted for model validation. The evolving water-ice interface is tracked based on optical images that shows both the water and the ice phase. To segment the phases, we use a binary Mumford Shah method, which yields a piece-wise constant approximation of the imaging data. Its jump set is the reconstruction of the measured phase interface. Our combined simulation and segmentation effort finally enables us to compare the modeled and measured phase interfaces continuously. We conclude with a discussion of our findings.

Motivation & Objective

• To develop a computationally efficient fixed-grid model for simulating phase change with natural convection in water-ice systems.
• To conduct high-spatio-temporal-resolution experiments to capture the evolving water-ice interface dynamics.
• To integrate simulation and experimental data through advanced image segmentation for direct model validation.
• To identify and analyze discrepancies between simulation and experiment to improve model fidelity.
• To establish a flexible, integrated validation strategy for complex multi-physics systems.

Proposed method

• The enthalpy porosity method is employed as a fixed-grid approach based on mixture theory and a phase field formulation to model phase change.
• The resulting system of PDEs, including momentum, energy, and continuity equations with Boussinesq approximation, is solved using finite volume discretization in OpenFOAM.
• A mushy zone constant is introduced to model the transition between solid and liquid phases, with sensitivity analysis indicating high values are necessary for water-ice.
• Optical images of the melting process are acquired with high spatio-temporal resolution to track the phase interface experimentally.
• Binary Mumford-Shah segmentation is applied to the imaging data to reconstruct the phase interface as the jump set of a piecewise-constant approximation.
• The segmented interface is compared directly with the simulated interface at multiple time points to enable quantitative validation.

Experimental results

Research questions

• RQ1 How accurately can the enthalpy porosity method simulate natural convection effects in water-ice phase change with a fixed grid?
• RQ2 To what extent does the simulated phase interface morphology match the experimentally observed interface evolution?
• RQ3 What are the primary sources of discrepancy between simulation and experiment in the phase interface position?
• RQ4 How does the mushy zone constant influence the model's ability to capture physical behavior in water-ice systems?
• RQ5 Can high-resolution image segmentation enable robust, continuous validation of phase change simulations?

Key findings

• The simulation and experiment show good qualitative agreement in the shape and evolution of the water-ice interface, with the interface advancing fastest near the top due to buoyancy-driven convection.
• A small but measurable discrepancy exists in the absolute position of the phase interface between simulation and experiment, particularly at 600 and 900 seconds.
• The initial temperature of the ice has low sensitivity to the interface position, with variations between -25 °C and 0 °C producing minimal model differences.
• The discrepancy is likely caused by non-ideal boundary conditions in the simulation, such as assuming perfectly adiabatic walls and a constant heater temperature, while the actual heater oscillates between 28 °C and 33 °C.
• Experimental heat losses through plexiglas walls, which act as thermal sinks, may further contribute to the mismatch.
• The study demonstrates the feasibility and value of combining high-resolution imaging with advanced segmentation and simulation for integrated model validation in multi-physics systems.