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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2512.16117 |
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| _version_ | 1866911325527998464 |
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| author | Xue, Zhong-Han Zhang, Jie |
| author_facet | Xue, Zhong-Han Zhang, Jie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16117 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wake transitions and melting dynamics of a translating sphere in warm liquid Xue, Zhong-Han Zhang, Jie Fluid Dynamics 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. |
| title | Wake transitions and melting dynamics of a translating sphere in warm liquid |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2512.16117 |