Dynamic evolution of Rayleigh-Taylor bubbles from sinusoidal, W-shaped, and random perturbations.
Dynamic evolution of Rayleigh-Taylor bubbles from sinusoidal, W-shaped, and random perturbations.
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DOI：
10.1103/physreve.97.033108
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发表时间：
2018-03
期刊：
影响因子：
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通讯作者：
Zhiqin Zhou;You-sheng Zhang;Bao-lin Tian
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文献类型：
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作者：
Zhiqin Zhou;You-sheng Zhang;Bao-lin Tian
不同密度比下二维Rayleigh-Taylor不稳定性的隐式大涡模拟（即，Atwood数A=0.05，0.5和0.9）来研究气泡的后期动力学。为了产生一个充满有界，半有界和混沌气泡的流场，三个问题与不同的扰动进行了模拟：（I）周期性正弦扰动，（II）孤立的W形扰动，和（III）随机短波扰动。的高度h，速度v，和直径D的（占主导地位的）气泡随时间t的演变制定和分析。在问题Ⅰ中，在准定常阶段，数值模拟证实了Goncharov的终端速度v_{∞}=Frsqrt[Agλ/（1+A）]的预言，其中Fr=1/sqrt[3π]。此外，发现该阶段的直径D与初始扰动波长λ成正比，即D <$λ。这与Daly的模拟结果D=λ（1+A）/2不同。在问题II中，设计了W形扰动以产生类似于问题III中的混沌气泡的气泡环境。我们得到与上述类似的终端速度关系，但Fr被Fr_{w} 0.63代替。在问题III中，模拟结果表明h随气泡加速常数α <$h/（Agt^{2}）<$0. 05呈二次增长，D以稳定的长宽比β <$D/h <$（1+A）/2自相似地膨胀，这与现有理论不同。因此，根据自相似增长的机制，我们导出了β=4α（1+A）/Fr_{w}^{2}的关系，将问题III中的混沌泡的演化与问题II中的半有界泡的演化联系起来.这种关系的有效性突出了这样一个事实，即问题III中的混沌气泡的动力学类似于问题II中的半有界孤立气泡，但不类似于问题I中的有界周期气泡。
Implicit large eddy simulations of two-dimensional Rayleigh-Taylor instability at different density ratios (i.e., Atwood number A=0.05, 0.5, and 0.9) are conducted to investigate the late-time dynamics of bubbles. To produce a flow field full of bounded, semibounded, and chaotic bubbles, three problems with distinct perturbations are simulated: (I) periodic sinusoidal perturbation, (II) isolated W-shaped perturbation, and (III) random short-wave perturbations. The evolution of height h, velocity v, and diameter D of the (dominant) bubble with time t are formulated and analyzed. In problem I, during the quasisteady stage, the simulations confirm Goncharov's prediction of the terminal speed v_{∞}=Frsqrt[Agλ/(1+A)], where Fr=1/sqrt[3π]. Moreover, the diameter D at this stage is found to be proportional to the initial perturbation wavelength λ as D≈λ. This differed from Daly's simulation result of D=λ(1+A)/2. In problem II, a W-shaped perturbation is designed to produce a bubble environment similar to that of chaotic bubbles in problem III. We obtain a similar terminal speed relationship as above, but Fr is replaced by Fr_{w}≈0.63. In problem III, the simulations show that h grows quadratically with the bubble acceleration constant α≡h/(Agt^{2})≈0.05, and D expands self-similarly with a steady aspect ratio β≡D/h≈(1+A)/2, which differs from existing theories. Therefore, following the mechanism of self-similar growth, we derive a relationship of β=4α(1+A)/Fr_{w}^{2} to relate the evolution of chaotic bubbles in problem III to that of semibounded bubbles in problem II. The validity of this relationship highlights the fact that the dynamics of chaotic bubbles in problem III are similar to the semibounded isolated bubbles in problem II, but not to that of bounded periodic bubbles in problem I.