[论文解读] Transition from classical to ultimate melting

Edoardo Bellincioni, Kevin Zhong+5 more|arXiv (Cornell University)|Jan 10, 2026

Lattice Boltzmann Simulation Studies被引用 0

一句话总结

论文展示了湍流中的融化转变：小尺度（经典）融化的 Nu ~ Re_D0^{1/2} 转变为大尺度（极限）融化的 Nu ~ Re_D0^{0.8–1}，通过在对象尺寸跨越四个数量级的实验和 DNS 观测到。

ABSTRACT

Melting is omnipresent in nature and technology, with applications ranging from metallurgy, biology, food science, and latent thermal energy storage to oceanography, geophysics, and climate science, and occurring on all scales from sub-millimeter to global scales. The key objective is to understand the rate at which an object melts as a function of its size and of the ambient conditions. To achieve this it is important to be able to extrapolate from small scale experiments and observations to large or even global scales. This is done by scaling laws. However, these are only meaningful if there is no transition from one scaling relation to another one. Here we show, however, that for both fixed and freely-advected melting objects immersed in a turbulent flow a melting transition does exist, namely from slow melting at the small scales to fast melting at the large scales. We do so by controlled melting experiments and corresponding direct numerical simulations, covering four orders of magnitude in scale. The transition corresponds to the transition from a laminar-type boundary layer around the melting object to a turbulent-type boundary layer, i.e., from so-called classical turbulence to ultimate turbulence, with its enhanced transport properties. Our results thus provide a quantitative understanding of the flow physics of the melting process and thereby enable a better extrapolation and prediction of melt rates on large scales such as relevant in geophysics, oceanography, and climate science.

研究动机与目标

• 了解在固定和自由被载物体的情况下，融化速率如何随对象尺寸和环境湍流变化而标度。
• 确定融化是否在不同湍流边界层之间存在转变。
• 量化转变点及其对雷诺数和流动参数的依赖。
• 提供一个框架，将实验室尺度的融化率外推到地球物理尺度，以用于气候建模和能量存储等应用。

提出的方法

• 在统计上稳定的同质各向同性湍流中进行受控的冰球融化实验，改变对象尺寸。
• 在 HIT 中使用嵌入边界方法进行直接数值模拟，以追踪自由对流中的融化（包括拉格朗日融化）。
• 通过 Stefan 条件分析融化速率，并将其与水侧对流的 Nusselt 数相关联。
• 比较 Eulerian（固定）与 Lagrangian（自由对流）融化情形，以评估边界层效应。
• 汇编并再分析来自先前研究的数据，在 Re_D0 的四个数量级范围内建立广泛的标度趋势。

Figure 1: Present experimental and numerical setups (a) Experimental setup: twenty independently-controlled electric motors mounted on the vertices of a $\approx$ \qty 210 dodecahedral water tank drive propellers to generate HIT in the tank center. (b) Volume contours of instantaneous temperature in

实验结果

研究问题

• RQ1 在小尺度（经典）与大尺度（极限）融化中，融化速率（Nu）与以尺寸为基准的雷诺数（Re_D0）之间的标度关系是什么？
• RQ2 在湍流中，是否存在由层流型与湍流型边界层之间的转变来支配融化速率？
• RQ3 转变点（就 Re_D0 或 Re_λ 而言）如何依赖于普朗特、斯特凡数与流动条件？
• RQ4 在 Eulerian 与 Lagrangian 融化配置中，融化速率行为差异有多大？
• RQ5 是否有一个统一模型，能够在地球物理和工业背景下预测跨越巨大神尺度的融化速率？

主要发现

• 融化表现出两种两性：在较小的 Re_D0 时，Nu ∝ Re_D0^{1/2}（边界层呈层流样式），在较大 Re_D0 时，Nu ∝ Re_D0^{γ}，其中 0.8 ≤ γ ≤ 1（边界层为湍流型）。
• 两种情形之间的转变发生在 Re_D0 约为 4000 左右，对应约为边界层剪切雷诺数约 60。
• 极限区域遵循 Nu ∝ Re × L(Re) 的形式，且有对数修正，在所研究范围内等效地给出 Nu ∝ Re_D0^{0.8}。
• 融化强烈依赖于 Re_D0（对象尺度的涡），但对 Re_λ（整体流动涡）基本不敏感，暗示局部涡相互作用主导融化。
• Eulerian 融化比 Lagrangian 稍快，因为在 Eulerian 情况下对象表面沿面的剪切率更高。
• 该研究覆盖 Re_D0 的四个数量级，并结合实验、DNS 以及文献数据，确立了转变与标度规律。

Figure 2: Reynolds number controls melting rate of ice balls in both experiments and DNS Snapshots of a freely-advected melting ice ball at two different times at fixed $\textit{Re}_{\lambda}$ and fixed $\textit{Re}_{D_{0}}$ (as noted) and temporal evolution of the volume-equivalent radius for vario