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浙江大学学报(工学版)  2026, Vol. 60 Issue (10): 2099-2108    DOI: 10.3785/j.issn.1008-973X.2026.10.003
工程力学     
不同韦伯数下马蹄涡与自由界面的相互作用
曾威远(),熊诗颖*()
浙江大学 航空航天学院,浙江 杭州 310027
Interaction between horseshoe vortex and free surface at different Weber numbers
Weiyuan ZENG(),Shiying XIONG*()
School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China
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摘要:

通过直接数值模拟研究不同韦伯数下马蹄涡与自由界面之间的相互作用. 采用分段线性界面重构方法结合体积分数法,求解不可压Navier-Stokes方程,并引入连续表面力模型,对韦伯数0.24~0.84范围内的流动过程进行模拟. 通过对流场中总动能、耗散率、总螺旋度及表面能的演化进行定量分析,揭示了韦伯数对涡环与自由界面相互作用的影响. 在低韦伯数情况下,表面张力占主导地位,相界面保持紧凑的环状结构,涡量场稳定且螺旋度几乎不变;在高韦伯数下,惯性力主导,界面经历显著的拉伸、断裂和重联过程,涡结构发生破碎,动能衰减加速,出现明显的能量耗散峰值,螺旋度持续减小. 研究结果揭示了韦伯数在涡环与界面作用的能量传递与耗散机制中具有重要作用,可为多相流界面动力学特性提供理论支撑,并为跨界面航行器设计这类工程应用提供指导.

关键词: 自由表面马蹄涡自由界面韦伯数涡动力学表面张力    
Abstract:

Direct numerical simulations were performed to investigate the interaction between a horseshoe vortex and a free surface at various Weber numbers. The incompressible Navier-Stokes equations were solved using the volume-of-fluid method coupled with the piecewise linear interface construction scheme. The continuum surface force model was incorporated to account for surface tension effects during interface deformation. The simulations covered a range of Weber numbers from 0.24 to 0.84. By quantitatively analyzing the evolution of total kinetic energy, dissipation rate, total helicity, and surface energy, the influence of Weber number on the vortex-interface interaction was elucidated. At low Weber numbers, surface tension dominated, maintaining the interface as a coherent ring-like structure and suppressing deformation and topological changes, while the vorticity field remained stable with negligible variations in helicity. Conversely, at high Weber numbers, inertial forces dominated over capillary effects, leading to significant interface deformation, breakup, and reconnection. This process resulted in vortex breakdown, accelerated kinetic energy decay, distinct peaks in energy dissipation, and a continuous decrease in helicity. These findings underscored the critical role of the Weber number in energy transfer and dissipation mechanisms, providing theoretical support for multiphase flow dynamics and guidelines for engineering applications such as the design of surface and trans-media vehicles.

Key words: free-surface horseshoe vortex    free surface    Weber number    vortex dynamics    surface tension
收稿日期: 2025-12-31 出版日期: 2026-07-28
CLC:  O 359  
基金资助: 国家自然科学基金资助项目(12302294, 12432010).
通讯作者: 熊诗颖     E-mail: zengweiyuan@zju.edu.cn;shiying.xiong@zju.edu.cn
作者简介: 曾威远(1998—),男,硕士生,从事两相流/涡动力学数值模拟研究. orcid.org/0009-0003-0752-2266. E-mail:zengweiyuan@zju.edu.cn
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引用本文:

曾威远,熊诗颖. 不同韦伯数下马蹄涡与自由界面的相互作用[J]. 浙江大学学报(工学版), 2026, 60(10): 2099-2108.

Weiyuan ZENG,Shiying XIONG. Interaction between horseshoe vortex and free surface at different Weber numbers. Journal of ZheJiang University (Engineering Science), 2026, 60(10): 2099-2108.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2026.10.003        https://www.zjujournals.com/eng/CN/Y2026/V60/I10/2099

Case$ \sigma $$ We $$ {N}^{3} $$ {\rho }_{{\mathrm{l}}}/{\rho }_{{\mathrm{g}}} $$ {\mu }_{{\mathrm{l}}}/{\mu }_{{\mathrm{g}}} $$ Re $
13500.24512310001001000
23000.28512310001001000
32500.34512310001001000
42000.42512310001001000
51500.56512310001001000
61000.84512310001001000
表 1  自由表面马蹄涡算例参数
图 1  算例设置示意图
图 2  不同网格分辨率下归一化总动能$ {\boldsymbol{E}}_{\rm{k}}\text{/}{\boldsymbol{E}}_{\rm{k,0}} $随无量纲时间的演化
图 3  表面张力驱动下低黏度液滴演化对比
图 4  不同韦伯数下的相界面分布
图 5  $ We=0.42 $下的相界面与涡量场演化
图 6  不同$ \boldsymbol{We} $数下总动能$ {\boldsymbol{E}}_{\rm{k}} $随无量纲时间的演化
图 7  不同$ \boldsymbol{We} $数下$ \boldsymbol{x=}\mathbf{0.5}\boldsymbol{L} $切面局部动能密度分布时间演化图
图 8  不同$ \boldsymbol{We} $数下平均耗散率随无量纲时间的演化
图 9  不同$ \boldsymbol{We} $数下左半域总螺旋度与右半域总螺旋度随无量纲时间的演化
图 10  不同$ \boldsymbol{We} $数下$ \boldsymbol{y=}\mathbf{0.5}\boldsymbol{L} $切面局部螺旋度密度分布时间演化图
图 11  不同$ \boldsymbol{We} $数下归一化表面能随无量纲时间的演化
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