Instability of an interface subjected to a perturbed shock: reflected shock effects
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摘要: 通过平面激波绕刚体圆柱的方法形成扰动激波，采用无膜技术形成N2/SF6均匀界面，在竖式激波管中开展了扰动激波冲击界面Richtmyer-Meshkov (RM)不稳定性实验研究。针对3种不同的无量纲距离η(圆柱到界面距离与圆柱直径之比)情形，利用高速纹影技术及平面Mie散射技术，获得了反射激波二次冲击作用下的界面演化图像。前期工作(邹立勇等，2017)显示，入射激波冲击后，界面发展为包括中心气腔和两侧台阶的"Λ"形结构。研究结果表明：反射激波二次冲击后，"Λ"形界面首先经历相位反转，然后扰动逐渐发展增强。在η=2.0情形，界面演化为气泡，而当η=3.3和4.0时，在整体的气泡结构之外，界面中心发展为尖钉结构。获得了反射激波作用后的混合区宽度，并与理论模型结果进行了比较。在界面演化线性阶段，Meyer-Blewett(MB)线性模型结果和实验结果吻合较好。在界面演化非线性阶段，Dimonte-Ramaprabhu (DR)模型结果和实验结果吻合较好。特别地，当η=4.0时，理论与实验结果差别最小。Abstract: The Richtmyer-Meshkov(RM) instability of a N2/SF6 interface subjected to a perturbed shock is investigated experimentally in a vertical shock tube. The perturbed shock is generated by a planar shock diffracting around a rigid cylinder and the initial uniform interface is formed by a membraneless method. Three different dimensionless distances η (the ratio of spacing from the cylinder to the interface over the cylinder diameter) are considered. Dynamic images of the interface evolution after the impact of the reflected shock are obtained using both schlieren and planar Mie scattering techniques. Our previous study (Zou, et al., 2017) indicated that, after the impingement of the incident shock, the interface evolves into a "Λ" shape structure with two interface steps at both sides and a cavity at the center. The results in present paper show that, due to the impingement of the reflected shock, the "Λ" shape structure interface first experiences a fast phase reversal and then the perturbation increases gradually. For η=2.0 case, the interface evolves into an overall bubble structure, while for η=3.3 and η=4.0 cases, a spike appears in the center of the interface besides the overall bubble. The mixing width is further measured from Mie scattering images and compared with the theoretical values. It is found that at the linear stage, the interface width can be predicted well by the linear model proposed by Meyer and Blewett, and at the nonlinear stage, the width can be reasonably estimated by the model proposed by Dimonte and Ramaprabhu. In particular, the distinction between the theoretical prediction and the experimental result is the lowest for the case of η=4.0.
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Key words:
- perturbed shock /
- RM instability /
- reflected shock /
- mixing width /
- nonlinear model
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图 3 高速纹影技术获得的入射阶段和反射阶段N2/SF6界面演化图像(η =4.0)
Figure 3. Schlieren images showing the evolution of N2/SF6 interface in the incident and the reflected stages (η =4.0)
图 4 Mie散射获得的反射激波作用下N2/SF6界面演化图像。实线圈区域为气腔，虚线圆圈区域为台阶，a为混合区宽度
Figure 4. Planar Mie scattering sequences showing the evolution of N2/SF6 interface impacted by the reflected shock. The solid circles indicate the N2 cavity and the dashed circles highlight the interface steps, a refers to the mixing width
图 5 反射激波作用下界面斜压涡量沉积示意图
Figure 5. Schematic of baroclinic vorticity deposition on the interface under the impact of the reflected shock
图 6 反射激波到达前的扰动界面形状
Figure 6. The shape of interface immediately before the arrival of the reflected shock
图 7 混合区宽度随时间变化曲线：实验和MB模型对比
Figure 7. Comparison of mixing width between the experimental results and the MB model
图 8 混合区宽度随时间变化曲线：实验和DR模型对比
Figure 8. Comparison of mixing width between the experimental results and the DR model
表 1 3种情形的实验参数
Table 1. Experimental parameters for three cases
Case d/mm l/mm η 1 10 20 2.0 2 6 20 3.3 3 10 40 4.0 
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表 2 “Λ”形界面参数
Table 2. Parameters of "Λ" shaped interface
η a0/mm λ0/mm k/mm-1 θ0/ (°) a0/λ0 2.0 10.2 65. 9 0.09 116.7 0.15 3.3 7.0 54.7 0.11 125.7 0.13 4.0 8.2 105.8 0.06 145.5 0.08
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表 3 理论模型增长率
Table 3. Growth rate calculated by theoretical model
η v0MB/(m·s-1) R v0DR/(m·s-1) 2.0 53.99 0.82 44.27 3.3 44.83 0.85 38.11 4.0 26.74 0.92 24.60
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