Abstract
Based on the Zufiria theoretical model, a new model regarding the asymptotic bubble velocity for the Rayleigh-Taylor (RT) instability is presented by use of the complex velocity potential proposed by Sohn. The proposed model is an extension of the ordinary Zufiria model and can deal with non-ideal fluids. With the control variable method, the effect of the viscosity and surface tension on the bubble growth rate of the RT instability is studied. The result is consistent with Cao’s result if we only consider the viscous effect and with Xia’s result if we only consider the surface tension effect. The asymptotic bubble velocity predicted by the Zufiria model is smaller than that predicted by the Layzer model, and the result from the Zufiria model is much closer to White’s experimental data.
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Abbreviations
- A :
-
Atwood number
- Bo :
-
Bond number
- F :
-
complex velocity potential
- Fr :
-
Froude number
- g :
-
gravity acceleration
- k :
-
wave number
- R :
-
curvature radius of bubble
- Re :
-
Reynolds number
- Q :
-
source strength
- U :
-
asymptotic bubble velocity
- η :
-
amplitude of bubble
- θ :
-
stream function
- λ :
-
wave length
- µ :
-
dynamic viscosity coefficient
- υ :
-
kinetic viscosity coefficient
- ρ :
-
fluid density
- σ :
-
surface tension
- φ :
-
velocity potential
References
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Project supported by the National Natural Science Foundation of China (Nos. 11171281 and 11201389)
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Li, M., Zhu, Q. & Li, G. Effect of surface tension and viscosity on bubble growth of single mode Rayleigh-Taylor instability. Appl. Math. Mech.-Engl. Ed. 37, 1607–1614 (2016). https://doi.org/10.1007/s10483-016-2143-8
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DOI: https://doi.org/10.1007/s10483-016-2143-8