Wake transitions and melting dynamics of a translating sphere in warm liquid

TL;DR

This study uses simulations to analyze the melting behavior and wake dynamics of a sphere in warm liquid, revealing multiple flow regimes and introducing a predictive surface-area model, with implications for natural and industrial processes.

Contribution

It provides a comprehensive analysis of melting regimes and flow dynamics of a sphere in warm liquid, introducing a new surface-area based predictive model and exploring buoyancy effects.

Findings

Four melting regimes identified based on Reynolds number.

A new surface-area formulation accurately predicts volume evolution.

Buoyancy effects significantly influence wake stability and shape.

Abstract

We investigate the three-dimensional melting dynamics of an initially spherical particle translating in a warmer liquid using sharp-interface simulations that fully resolve both solid and fluid phases with the Stefan condition. A wide parameter space is explored, spanning initial Reynolds number ($Re_0$), Stefan number ($St$), and Richardson number ($Ri$). In the absence of buoyancy ($Ri= 0$), the interface evolution is governed by canonical wake bifurcations. Four regimes are identified: an axi-symmetric regime ($Re_0<212$) with a rounded front and planar rear; a steady-planar-symmetric regime ($212<Re_0<273$) with an inclined rear plane; a periodic-planar-symmetric regime ($273<Re_0<355$) where vortex shedding emerges in the wake; and a chaotic regime ($Re_0>355$) with fluctuating stagnation points and a more rounded rear. Despite these differences, all regimes exhibit a tendency toward melt-rate homogenisation over time. Besides, we introduce an aspect-ratio-based surface-area formulation that yields a predictive model, accurately capturing volume evolution across regimes. Hydrodynamic loads also reflect the coupling between shape and flow: drag follows rigid-sphere correlations only at moderate $Re_0$; planar rears enhance drag at higher $Re_0$; lift appears only in symmetry-broken regimes and reverses late in time; torque reorients the rear plane toward vertical, consistent with free-body experiments. When buoyancy is included, assisting configurations ($Ri>0$) suppress recirculation and maintain quasi-spherical shapes, whereas opposing or transverse buoyancy ($Ri<0$) destabilises wakes and promotes tilted planar rears. These results provide a unified framework for convection-driven melting across laminar, periodic, and chaotic wakes, with implications for geophysical and industrial processes.