Theoretical analysis of Rayleigh-Taylor instability on a spherical droplet in a gas stream. (English) Zbl 1481.76245
Summary: A linear analysis of the Rayleigh-Taylor (R-T) instability on a spherical viscous liquid droplet in a gas stream is presented. Different from the most previous studies in which the external acceleration is usually assumed to be radial, the present study considers a unidirectional acceleration acting on a spherical droplet with arbitrary initial disturbances and therefore can provide insights into the influence of R-T instability on the atomization of spherical droplets. A general recursion relation coupling different spherical modes is derived and two physically prevalent limiting cases are discussed. In the limiting case of inviscid droplet, the critical Bond numbers to excite the instability and the growth rates for a given Bond number are obtained by solving two eigenvalue problems. In the limiting case of large droplet acceleration, different spherical modes are asymptotically decoupled and an explicit dispersion relation is derived. For given Bond number and Ohnesorge numbers, the critical size of stable droplet, the most-unstable mode and its corresponding growth rate are determined theoretically.
MSC:
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
| 76E17 | Interfacial stability and instability in hydrodynamic stability |
Keywords:
Rayleigh-Taylor instability; spherical droplet; linear analysis; non-radial acceleration; secondary atomizationReferences:
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