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Understanding the development and breakup of interfacial waves in a two-phase mixing layer between the gas and liquid streams is paramount to atomization. Due to the velocity difference between the two streams, the shear on the interface triggers a longitudinal instability, which develops to interfacial waves that propagate downstream. As the interfacial waves grow spatially, transverse modulations arise, turning the interfacial waves from quasi-two-dimensional to fully three-dimensional. The inlet gas turbulence intensity has a strong impact on the interfacial instability. Therefore, parametric direct numerical simulations are performed in the present study to systematically investigate the effect of the inlet gas turbulence on the formation, development and breakup of the interfacial waves. The open-source multiphase flow solver, PARIS, is used for the simulations and the mass–momentum consistent volume-of-fluid method is used to capture the sharp gas–liquid interfaces. Two computational domain widths are considered and the wide domain will allow a detailed study of the transverse development of the interfacial waves. The dominant frequency and spatial growth rate of the longitudinal instability are found to increase with the inlet gas turbulence intensity. The dominant transverse wavenumber, determined by the Rayleigh–Taylor instability, scales with the longitudinal frequency, so it also increases with the inlet gas turbulence intensity. The holes formed in the liquid sheet are important to the disintegration of the interfacial waves. The hole formation is influenced by the inlet gas turbulence. As a result, the sheet breakup dynamics and the statistics of the droplets formed also change accordingly.
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Branching behaviour of the Rayleigh–Taylor instability in linear viscoelastic fluids
The Rayleigh–Taylor instability of a linear viscoelastic fluid overlying a passive gas is considered, where, under neutral conditions, the key dimensionless groups are the Bond number and the Weissenberg number. The branching behaviour upon instability to sinusoidal disturbances is determined by weak nonlinear analysis with the Bond number advanced from its critical value at neutral stability. It is shown that the solutions emanating from the critical state either branch out supercritically to steady waves at predictable wavelengths or break up subcritically with a wavelength having a single node. The nonlinear analysis leads to the counterintuitive observation that Rayleigh–Taylor instability of a viscoelastic fluid in a laterally unbounded layer must always result in saturated steady waves. The analysis also shows that the subcritical breakup in a viscoelastic fluid can only occur if the layer is laterally bounded below a critical horizontal width. If the special case of an infinitely deep viscoelastic layer is considered, a simple expression is obtained from which the transition between steady saturated waves and subcritical behaviour can be determined in terms of the leading dimensionless groups. This expression reveals that the supercritical saturation of the free surface is due to the influence of the normal elastic stresses, while the subcritical rupture of the free surface is attributed to the influence of capillary effects. In short, depending upon the magnitude of the scaled shear modulus, there exists a wavenumber at which a transition from saturated waves to subcritical breakup occurs.
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- Award ID(s):
- 2025117
- PAR ID:
- 10274248
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 915
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2021.80
