Combined effect of viscosity and vorticity on single mode Rayleigh–Taylor instability bubble growth

Banerjee, Rahul; Mandal, Labakanta; Roy, Sunipa; Khan, Manoranjan; Gupta, Manash Ranjan

doi:10.1063/1.3555523

Cited by 30 publications

(13 citation statements)

References 8 publications

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“…In our previous works [14,[20][21][22][23], we have considered η 1 (t) = 0 due to the absence of velocity shear parallel to the unperturbed interface. However, in presence of streaming motion of the fluids, the tip of the bubble moves parallel to unperturbed interface with velocityη 1 (t).…”

Section: Basic Mathematical Modelmentioning

confidence: 99%

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Influence of surface tension on two fluids shearing instability

Banerjee¹,

Kanjilal²

2014

Pap. Phys.

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Using extended Layzer's potential flow model, we investigate the effects of surface tension on the growth of the bubble and spike in combined Rayleigh-Taylor and Kelvin-Helmholtz instability. The nonlinear asymptotic solutions are obtained analytically for the velocity and curvature of the bubble and spike tip. We find that the surface tension decreases the velocity but does not affect the curvature, provided surface tension is greater than a critical value. For a certain condition, we observe that surface tension stabilizes the motion. Any perturbation, whatever its magnitude, results stable with nonlinear oscillations. The nonlinear oscillations depend on surface tension and relative velocity shear of the two fluids.

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Section: Basic Mathematical Modelmentioning

confidence: 99%

“…According to the extended Layzer model [10,11,14,20], the velocity potentials describing the motion for the upper (heavier) and lower (lighter) fluids are assumed to be given by…”

Section: Basic Mathematical Modelmentioning

confidence: 99%

Influence of surface tension on two fluids shearing instability

Banerjee¹,

Kanjilal²

2014

Pap. Phys.

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“…Following the linear growth stage, the single-mode RTI would evolve with constant velocity, implying that the flow has been transformed into the nonlinear stage. The nonlinear stage has been investigated by many analytical models [16][17][18][19][20][21][22][23][24]. An important early contribution was attributed to Layzer [16], who theoretically analyzed the motion of the fluid-vacuum interface in the gravitational field and proposed the first poten-tial flow model for describing the RTI evolution with limiting Atwood number of 1.…”

Section: Introductionmentioning

confidence: 99%

“…It is noticed that the viscosities of the fluids are neglected in above potential flow models. Sohn [23] and Banerjee [24] then analyzed the role of viscosity and anticipated the increased skin-friction drag between viscous bubble and spike. To this end, the modified potential flow models combining the viscosity effect and the vorticity [24] or the surface tension force [23] were established for saturated velocity stage.…”

Section: Introductionmentioning

confidence: 99%

Late-time description of immiscible Rayleigh-Taylor instability: A lattice Boltzmann study

Huang¹,

Xia²,

Liang³

et al. 2020

Preprint

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In this paper, the late-time description of immiscible Rayleigh-Taylor instability (RTI) in a long duct is investigated over a comprehensive range of the Reynolds numbers (1 ≤ Re ≤ 10000) and Atwood numbers (0.05 ≤ A ≤ 0.7) based on the mesoscopic lattice Boltzmann method. We first reported that the instability with a moderately high Atwood number of 0.7 undergoes a sequence of distinguishing stages at a high Reynolds number, which are termed as the linear growth, saturated velocity growth, reacceleration and chaotic development stages. The spike and bubble at the secondary stage evolve with the constant velocities and their values agree well with the analytical solutions of the potential flow theory. The duration of the spike saturated velocity stage is very shorter than that of the bubble, implying the asymmetric developments between the spike and bubble fronts. Owing to the increasing strengths of the formed vortices, the movements of the spike and bubble are accelerated such that their velocities exceed than the asymptotic values and the evolution of the instability then enters into the reacceleration stage. Lastly, the curves for the spike and bubble velocities have some fluctuations at the chaotic stage and also a complex interfacial structure with large topological change is observed, while it still preserves the symmetry property with respect to the central axis. To determine the nature of the late-time growth, we also calculated the spike and bubble growth rates by using five popular statistical methods and two comparative techniques are recommended, resulting in the spike and bubble growth rates of about 0.13 and 0.022, respectively. When the Reynolds number is gradually reduced, some later stages such as the chaotic and reacceleration stages cannot be reached successively and the structure of the interface in the evolutional process becomes relatively smooth. The influence of the fluid Atwood number is also examined on the late-time RTI development at a large Reynolds number.It is found that the sustaining time for the saturated velocity stage decreases with the Atwood number. The spike late-time growth rate shows an overall increase with the Atwood number, while it has little influence on the bubble growth rate being approximately 0.0215.

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“…Sharma et al [15] analyzed the RT instability of two superposed fluids taking the effect of small rotation, suspended dust particles and surface tension. Rahul Banerjee et al [16] investigated the combined effect of viscosity and vorticity on the growth rate of the bubble associated with single mode RT instability. To cite but a few.…”

Section: Introductionmentioning

confidence: 99%

Viscosity, heat conductivity, and Prandtl number effects in the Rayleigh–Taylor Instability

Chen¹,

Zhang

2016

Front. Phys.

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Two-dimensional Rayleigh-Taylor(RT) instability problem is simulated with a multiplerelaxation-time discrete Boltzmann model with gravity term. The viscosity, heat conductivity and Prandtl number effects are probed from the macroscopic and the non-equilibrium views. In macro sense, both viscosity and heat conduction show significant inhibitory effect in the reacceleration stage, and the inhibition effect is mainly achieved by inhibiting the development of Kelvin-Helmholtz instability. Before this, the Prandtl number effect is not sensitive. Based on the view of non-equilibrium, the viscosity, heat conductivity, and Prandtl number effects on non-equilibrium manifestations, and the correlation degrees between the non-uniformity and the non-equilibrium strength in the complex flow are systematic investigated.

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Combined effect of viscosity and vorticity on single mode Rayleigh–Taylor instability bubble growth

Cited by 30 publications

References 8 publications

Influence of surface tension on two fluids shearing instability

Influence of surface tension on two fluids shearing instability

Late-time description of immiscible Rayleigh-Taylor instability: A lattice Boltzmann study

Viscosity, heat conductivity, and Prandtl number effects in the Rayleigh–Taylor Instability

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