[Paper Review] The pear-shaped fate of an ice melting front

James N. Hewett, Mathieu Sellier|arXiv (Cornell University)|May 7, 2017

Icing and De-icing Technologies9 references3 citations

TL;DR

This study numerically simulates the melting of ice around a heated horizontal cylinder near water's density inversion point (4.0 °C), using dynamic meshing with a node shuffle algorithm to track the moving solid-liquid interface. Results show pear-shaped melting fronts due to thermal plumes—upward for T_w > 4.0 °C and downward for T_w < 4.0 °C—confirming natural convection significantly influences melting rates and interface morphology, with good agreement to experimental data on shape and overall melting progression.

ABSTRACT

A fluid-structure interaction problem with the melting of water around a heated horizontal circular cylinder is analysed with numerical simulations. Dynamic meshing was used for evolving the flow domain in time as the melting front extended radially outward from the cylinder; a node shuffle algorithm was used to retain mesh quality across the significant mesh deformation. We simulated one case above the density inversion point of water and one case below, yielding pear-shaped melting fronts due to thermal plumes either rising or falling from the cylinder, respectively. Results were compared with previous experimental studies and the melting front profiles matched reasonably well and melting rates were in agreement. We confirm that natural convection plays a significant role in the transport of energy as the melt zone increases, and needs to be considered for accurately modelling phase change under these conditions.

Motivation & Objective

• To investigate the influence of water's density inversion on the morphology and dynamics of melting fronts during phase change around a heated horizontal cylinder.
• To validate numerical simulation of the Stefan problem with explicit interface tracking under natural convection effects.
• To compare simulated melting front shapes and rates with experimental data for both above- and below-inversion temperature cases.
• To assess the role of natural convection in enhancing heat transfer as the melt zone expands.
• To evaluate the accuracy of a dynamic meshing approach with node shuffling for handling large deformations in moving boundary problems.

Proposed method

• A 2D, incompressible, laminar flow model was used with the Boussinesq approximation to account for buoyancy-driven convection.
• The moving boundary (melting front) was explicitly tracked via dynamic meshing, with mesh quality preserved using a node shuffle algorithm.
• At each time step, the flow field was solved in steady state on the updated mesh, assuming quasi-steady conditions.
• Thermophysical properties of water were assumed constant except for density, which varied linearly with temperature to capture the density inversion effect.
• The interface motion was determined by the local heat flux and Stefan condition, with no artificial phase change source terms.
• Simulations were performed for two wall temperatures: 2.3 °C (below inversion) and 14.1 °C (above inversion), matching experimental conditions.

Experimental results

Research questions

• RQ1 How does water’s density inversion near 4.0 °C affect the shape and evolution of the melting front around a heated horizontal cylinder?
• RQ2 To what extent does natural convection dominate heat transfer as the melt zone expands, and how does this vary above and below the density inversion point?
• RQ3 Can dynamic meshing with node shuffling accurately capture the complex, pear-shaped interface morphology observed experimentally?
• RQ4 Why do simulations show discrepancies in melting rate during the transition from conduction- to convection-dominated regimes compared to experiments?
• RQ5 How do 2D steady-state assumptions affect the prediction of transient flow instabilities and enhanced heat transfer observed in 3D experiments?

Key findings

• Pear-shaped melting fronts emerged in both cases due to thermal plumes: upward for T_w = 14.1 °C and downward for T_w = 2.3 °C, matching experimental observations.
• The Rayleigh numbers were 6700 (inverted) and 7400 (upright), indicating similar convective strength despite different flow structures.
• Natural convection became the dominant heat transfer mechanism as the melt volume increased, significantly influencing interface evolution.
• The interface shape matched experimental profiles reasonably well across the entire simulation period, confirming model validity.
• Discrepancies in melting rates during the regime transition (τ ≈ 0.3) were attributed to unsteady 3D effects and transient instabilities absent in the 2D steady-state model.
• The upright pear-shape exhibited more complex flow features, including counter-rotating vortices above the cylinder, due to the inclusion of the density inversion point.