Dynamic evolution of Rayleigh-Taylor bubbles from sinusoidal, W-shaped, and random perturbations

Physical Review. E
Zhi-Rui ZhouBao-Lin Tian

Abstract

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...Continue Reading

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