Experimental study of the Richtmyer–Meshkov instability of incompressible fluids
Experimental study of the Richtmyer–Meshkov instability of incompressible fluids
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DOI：
10.1017/s002211200300452x
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发表时间：
2003-05
影响因子：
3.7
通讯作者：
C. Niederhaus;J. Jacobs
中科院分区：
文献类型：
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作者：
C. Niederhaus;J. Jacobs
实验研究了低Atwood数互溶双液体系的Richtmyer-Meshkov不稳定性。最初分层的流体包含在安装在滑橇上的矩形罐内，滑橇骑在垂直的一组轨道上。这种不稳定性是由滑橇跌落到螺旋弹簧上产生的，产生一个几乎是脉冲式的向上加速度。当容器在轨道上向上然后向下行进时发生的随后的自由下落允许不稳定性在没有重力的情况下发展。分离两种液体的界面最初具有良好定义的正弦扰动，该正弦扰动在经历脉冲加速度之后快速反转并且然后幅度增长。测量扰动幅度，并与理论预测进行比较。线性稳定性理论给出了很好的协议与测得的初始增长率，$\dot{a}_0$，单模扰动的预测幅度不同的小于10%，从实验测量到一个无量纲的时间$k\dot {a}_0 t = 0.7$，其中$k$是波数。线性稳定性理论也提供了良好的协议，直到界面成为多值的多模初始扰动的各个模式的振幅。与以前发表的弱非线性单模模型的比较显示出良好的一致性高达$k\dot{a}_0 t = 3$，而发表的非线性单模模型提供良好的一致性高达$k\dot{a}_0 t = 30$。研究了雷诺数对界面涡核演化和总增长率的影响。整体振幅的测量被发现是不受雷诺数的范围内的值在这里研究。然而，在较低的雷诺数值进行的实验发现，涡核旋转速率下降。此外，还观察到涡核的不稳定性。当雷诺数减小时，出现这种不稳定性的时间增加。
The Richtmyer–Meshkov instability of a low-Atwood-number miscible two-liquid system is investigated experimentally. The initially stratified fluids are contained within a rectangular tank mounted on a sled that rides on a vertical set of rails. The instability is generated by dropping the sled onto a coil spring, producing a nearly impulsive upward acceleration. The subsequent free-fall that occurs as the container travels upward and then downward on the rails allows the instability to evolve in the absence of gravity. The interface separating the two liquids initially has a well-defined sinusoidal perturbation that quickly inverts and then grows in amplitude after undergoing the impulsive acceleration. Disturbance amplitudes are measured and compared to theoretical predictions. Linear stability theory gives excellent agreement with the measured initial growth rate, $\dot{a}_0$, for single-mode perturbations with the predicted amplitudes differing by less than 10% from experimental measurements up to a non-dimensional time $k\dot {a}_0 t = 0.7$, where $k$ is the wavenumber. Linear stability theory also provides excellent agreement for the individual mode amplitudes of multi-mode initial perturbations until the interface becomes multi-valued. Comparison with previously published weakly nonlinear single-mode models shows good agreement up to $k\dot{a}_0 t = 3$, whereas published nonlinear single-mode models provide good agreement up to $k\dot{a}_0 t = 30$. The effects of Reynolds number on the vortex core evolution and overall growth rate of the interface are also investigated. Measurements of the overall amplitude are found to be unaffected by the Reynolds number for the range of values studied here. However, experiments carried out at lower values of Reynolds numbers were found to have decreased vortex core rotation rates. In addition, an instability in the vortex cores is observed. The time of appearance of this instability was found to increase when the Reynolds number is decreased.