The pulsation bubble dynamics near a free surface have significant engineering applications. Based on the finite volume method, a front tracking method coupled with an extrapolation technique is applied to study the transient characteristics of the pulsation bubble near the free surface with the different stand-off distance parameter γ and buoyancy parameter δ (the parameters are defined in Sec. II D). By comparison, the numerical results agree well with the results from the spark-generated bubble experiment. For the cases with small δ, (i) the phenomenon that the bubble top is elongated is no longer obvious while γ > 2.0, (ii) with the decrease in γ, the bubble centroid at the minimum volume is gradually away from the free surface except for migrating upward while 0.85 1.2, the free surface begins to fall with the bubble collapse after rising during the expansion stage and almost falls back to its original position while γ > 2.4. For the cases with γ = 1.0–1.13, (i) while δ > 0.2293, the jet penetrates the bubble before the bubble reaches its minimum volume, and both are contrary while δ 0.4636, the free surface begins to fall with the bubble collapse after rising during the expansion stage, and (iii) the bubble is always migrating toward the free surface while δ > 0.4109. Meanwhile, the phenomena such as the inward jet formed inside the toroidal bubble, the toroidal bubble split, and the water skirt are also analyzed.

中文翻译：

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基于有限体积法和前向跟踪法的自由面附近脉动气泡瞬态特性研究

自由表面附近的脉动气泡动力学具有重要的工程应用。在有限体积法的基础上，采用前向跟踪法结合外推技术，研究了具有不同间距参数γ和浮力参数δ的自由面附近脉动气泡的瞬态特性（参数定义在第二节 D)。相比之下，数值结果与火花产生气泡实验的结果非常吻合。对于δ较小的情况，(i)当γ>2.0时，气泡顶部被拉长的现象不再明显，(ii)随着γ的减小，最小体积处的气泡质心逐渐远离自由表面除了向上迁移而 0.85 1.2，自由面在膨胀阶段上升后随着气泡的坍塌开始下降，当γ>2.4时几乎回落到原来的位置。对于 γ = 1.0-1.13 的情况， (i) 当 δ > 0.2293 时，射流在气泡达到最小体积之前穿透气泡，两者相反，当 δ 0.4636 时，自由表面随着气泡坍塌开始下降在膨胀阶段上升，并且 (iii) 当 δ > 0.4109 时，气泡总是向自由表面迁移。同时，对环泡内部形成的向内射流、环泡裂开、水裙等现象进行了分析。射流在气泡达到最小体积之前穿透气泡，两者相反，而δ 0.4636，自由表面在膨胀阶段上升后随着气泡坍塌开始下降，（iii）气泡总是向自由迁移表面，而 δ > 0.4109。同时，对环泡内部形成的向内射流、环泡裂开、水裙等现象进行了分析。射流在气泡达到其最小体积之前穿透气泡，两者相反，而δ 0.4636，自由表面在膨胀阶段上升后随着气泡坍塌开始下降，并且（iii）气泡总是向自由迁移表面，而 δ > 0.4109。同时，对环泡内部形成的向内射流、环泡裂开、水裙等现象进行了分析。