Eccentric Effect on Evolution of Shock-Accelerated Double-Layer Gas Cylinder
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摘要: 实验与数值研究了平面激波诱导下双层气柱的演化规律.利用肥皂膜技术生成了3种双层气柱，通过固定内、外层气柱半径，改变内层气柱在流向方向上的位置，研究了双层气柱偏心效应对流场演化的影响.结果表明，当内层气柱向上游偏移时，外层气柱的上游界面在后期会产生朝向上游的"射流"；当内层气柱向下游偏移时，下游两道界面会较早地耦合在一起.获得了内、外层气柱上游界面的线性速度，发现压力等因素对内、外层气柱上游界面分别有抑制和促进作用，且作用大小与偏心程度密切相关.稀疏波的作用会明显改变外层气柱上游界面的运动行为，使其线性运动阶段延长或缩短.外层气柱的宽度在偏心时均被促进，高度随着内层气柱靠近下游逐渐减小；内层气柱向上游偏移时，其自身的宽度被抑制，但高度没有明显变化.对双层气柱的界面面积和平均体积分数的定量分析表明内层气柱向上游偏移时会促进物质混合.获得了环量随时间的变化规律，发现在演化早期双层气柱的环量可以通过已有模型的线性叠加得到较好的预测.
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关键词:
- Richtmyer-Meshkov不稳定性 /
- 双层气柱界面 /
- 肥皂膜技术 /
- 环量模型 /
- 激波管实验
Abstract: Evolution of a double-layer gas cylinder induced by a planar shock wave was investigated experimentally and numerically. Three double-layer gas cylinders were generated based on the soap film technology. By fixing the radii of the inner and outer gas cylinders, and changing the position of the inner gas cylinder in the stream-wise direction, the eccentric effect on the double-layer gas cylinder evolution has been highlighted. The results show that when the inner gas cylinder is positioned upstream, a 'jet' toward the upstream interface of the outer cylinder is generated at the late stage. When the inner gas cylinder is positioned downstream, the coupling effect between two downstream interfaces occurs earlier. The linear velocities of the upstream interfaces of the inner and outer gas cylinders are obtained. It is found that the pressures inhibit and promote the upstream interfaces of the inner and outer gas cylinders respectively, and the pressure magnitude is closely related to the position of the inner cylinder. The rarefaction wave impact changes the movement behaviour of the upstream interface of the outer cylinder, and the linear phase will be prolonged or shortened. The outer gas cylinder width is promoted when the eccentricity exists, and its height gradually decreases as the inner one approaches downstream initially. When the inner gas cylinder is positioned upstream, the inner cylinder width is inhibited but its height changes little. The interfacial area and mean volume fraction of the double-layer gas cylinder were extracted from computations, and the results show that the mixing between gases will be promoted when the inner gas cylinder is positioned upstream. Finally, the time-variation of the circulation is obtained. It is found that the circulation of the double-layer gas cylinder at the early stage can be well predicted by the linear superposition of the existing models. -
图 1 双层气柱生成装置示意图
Figure 1. Schematic of the device to generate interfaces and the cases in this work
图 3 不同网格尺寸下, 激波冲击气柱后146 μs时, 沿双层气柱中心线的密度分布情况
Figure 3. Density profiles with different mesh sizes along the center line of the double-layer gas cylinder at 146 μs after shock impact
图 4 工况Ⅰ双层SF6气柱被平面激波冲击后实验与数值的纹影图
Figure 4. Experimental and numerical schlieren images of a double-layer SF6 cylinder impacted by a planar shock for case Ⅰ
图 5 工况Ⅱ双层SF6气柱被平面激波冲击后实验与数值的纹影图
Figure 5. Experimental and numerical schlieren images of a double-layer SF6 cylinder impacted by a planar shock for case Ⅱ
图 6 工况Ⅲ双层SF6气柱被平面激波冲击后实验与数值的纹影图
Figure 6. Experimental and numerical schlieren images of a double-layer SF6 cylinder impacted by a planar shock for case Ⅲ
图 7 工况Ⅰ在不同时刻的波系示意图
Figure 7. Schematics of wave patterns at different times for case Ⅰ
图 10 外层气柱宽度与高度的变化情况
Figure 10. Evolution of the width and the height of the outer cylinder
图 11 内层气柱宽度与高度的变化情况
Figure 11. Evolution of the width and the height of the inner cylinder
图 12 各工况下气柱总面积和气柱内的平均体积分数随时间的变化情况
Figure 12. Evolution of the total interfacial area and mean volume fraction of the shocked cylinder for three cases
图 13 3种工况下中心线上方界面沉积的正环量、负环量和总环量随时间的变化情况
Figure 13. Time-variation of the positive, negative and total circulations deposited on the shocked cylinders at the upper half plane for three cases
表 1 各组工况的物理参数
Table 1. Physical parameters for each case
cases Ma d/mm VF1 VF2 Ⅰ 1.28 -7 0.56 0.07 Ⅱ 1.27 0 0.5 0.05 Ⅲ 1.28 +7 0.5 0.06 
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表 2 外层气柱上游极点的速度
Table 2. Velocities of the upstream poles of inner and outer cylinders for all cases
cases Vi ΔV VRM V0 Ⅰ-out 96.5 108.1 -35.8 24.2 Ⅱ-out 95.0 105.3 -33.2 22.9 Ⅲ-out 96.1 109.9 -34.3 20.5 Ⅰ-in 133.9 129.3 21.4 -19.5 Ⅱ-in 130.7 125.6 21.7 -16.6 Ⅲ-in 140.5 130.4 21.2 -11.1
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表 3 各组工况数值结果的环量值(Γsim)与4种组合模型的环量预测值(环量的单位为m2/s)
Table 3. Comparison of circulations from the numerical simulations (Γsim) and theoretical predictions by the models for each case(the unit of circulation is m2/s)
cases Γsim ΓSZ+ΓPB relative error/(%) ΓSZ+ΓYKZ relative error/(%) ΓPB+ΓYKZ relative error/(%) ΓPB+ΓPB relative error/(%) Ⅰ -5.99 -5.95 0.67 -6.69 11.69 -6.52 8.85 -5.78 3.51 Ⅱ -5.38 -5.36 0.37 -6.05 12.45 -5.70 5.95 -5.02 6.69 Ⅲ -5.58 -5.56 0.36 -6.26 12.19 -5.99 7.35 -5.29 5.20
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