Mechanism of early-stage drop deformation in shock induced flow at limited Weber numbers
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摘要: 以实验结合数值模拟与理论分析的方法，研究韦伯数在2 100~2 700区间内，不同组合流动参数对液滴破碎初期变形的影响与作用机制。实验中通过高速摄影捕捉到一系列具有明显差异的液滴变形模态，表明在相近韦伯数下液滴的初期变形仍受到气流速度、密度等具体流动参数的显著影响。以刚性球体替代液滴进行外流数值模拟，利用球体表面气动力分布推算出的液滴表面变形趋势与实际变形形态吻合，表明液滴的初期变形特征与外流流动分离和涡特征具有一致性。对流场和理论变形数据的分析显示，流动分离发展阶段和稳定阶段对液滴作用力以及它们所诱导的液滴变形特征存在很大差异；分离发展与液滴变形过程的特征时间之比可由气液密度比的平方根表示，它决定了液滴早期变形的基本形态。分离发展阶段所占时间比例越高，即实验中气液密度比越高，则液滴更倾向于发展出单个显著的环形突起，反之则趋于形成多个相对均衡的突起。Abstract: Early-stage deformation of water drops under Weber numbers ranging from 2 100 to 2 700 is investigated by experimental, numerical and theoretical methods, to reveal the influences of primary flow parameters on drop deformation as well as the mechanism behind them. Images of the drop deformation with noteworthy differences under different test conditions are captured with high-speed photography technique, demonstrating that though the Weber numbers are similar, drop deformation can be largely affected by the involved primary flow parameters, such as gas velocity, gas density and drop diameter. By substituting the liquid drop with a rigid sphere body, the gas flow field is numerically simulated, and the aerodynamic forces acting on sphere surface are distilled based on which the drop deformation is theoretically computed. The results show a good agreement between the theoretical and experimental deformation trends. The early-stage deformation of the drop is found to be in coherence with the flow separation and vortex distribution characteristics of the gas flow. Evolution of the gas flow field can be divided into a transient separation developing period and a following globally steady period. The pressure distribution exerted by the gas flow and the radial acceleration induced by it exhibit large differences in the two periods. The characteristic time of the separation development relative to the drop deformation, which can be represented by the square root of gas-liquid density ratio, is found to be a dominant parameter determining the drop deformation pattern in early stage of aero-breakup. A higher gas density leads to a higher occupation of the separation developing period in the whole drop deformation process, and the drop tends to develop a single ridge on its rear surface; on the contrary, multiple ridges with similar amplitude are more likely to happen when the gas density is lower, reflecting the characteristics of the outer flow in the globally stable period.
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Key words:
- drop /
- aero-breakup /
- early-stage deformation /
- high-speed photography /
- drop rear-surface
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图 3 t/td, 0~0.2时刻相近We条件下的液滴变形图像
Figure 3. Deformation images of water drops under limited We conditions at t/td, 0~0.2
图 4 基于外流数值模拟不同变形形态的理论预测
Figure 4. Theoretical prediction of different deformation patterns based on numerical simulation of outer flow
图 5 圆球表面剪切与压力发展过程
Figure 5. Development of shear stress and pressure distribution on the sphere surface
图 6 流场建立初期的激波绕射
Figure 6. Shock diffraction in the early stage of flow field establishment
图 8 分离发展过程中球体表面压力系数分布(工况Ⅰ)
Figure 8. Pressure coefficient distribution on the sphere surface in the flow field establishment of Case Ⅰ
图 9 分离发展过程中液滴表面径向加速度分布(工况Ⅰ)
Figure 9. Radial acceleration distribution on the sphere surfacein the flow field establishment of Case Ⅰ
图 10 不同流动条件下二次涡(涡B)的出现时间
Figure 10. Occurrence time of secondary eddy (eddy B) in different flow conditions
图 11 工况Ⅰ条件下变形各组分的量纲一加速度
Figure 11. Non-dimensional acceleration of deformation components in Case Ⅰ
图 13 κ对液滴变形的影响(We=2 370，Re=4.2×104，Mag=0.483，对应实验工况Ⅰ)
Figure 13. Influence of κ on drop deformation patterns (We=2 370, Re=4.2×104, Mag=0.483, corresponding to Case Ⅰ)
表 1 实验参数
Table 1. Experimental parameters
Cases d0/mm Mas ug /(m·s-1) ρg /(kg·m-3) We Re Oh ts, 0/μs td, 0/μs κ Ⅰ 3.76 1.37 186.2 1.312 2 370 4.2×104 1.9×10-3 20.2 557.7 3.62×10-2 Ⅱ 2.66 1.89 396.3 0.460 2 670 1.9×104 2.3×10-3 6.7 312.9 2.14×10-2 Ⅲ 2.82 1.91 399.6 0.346 2 142 1.5×104 2.2×10-3 7.1 379.5 1.87×10-2 Ⅳ 3.04 2.36 560.3 0.162 2 118 8.9×103 2.1×10-3 5.4 426.9 1.26×10-2 Ⅴ 2.61 2.60 641.0 0.164 2 421 8.3×103 2.3×10-3 4.1 317.7 1.29×10-2 
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