Instability regimes in the primary breakup region of planar coflowing sheets

Abstract

This article investigates the appearance of instabilities in two planar coflowing fluid sheets with different densities and viscosities via experiments, numerical simulation and linear stability analysis. At low dynamic pressure ratios a convective instability is shown to appear for which the frequency of the waves in the primary atomization region is influenced by both liquid and gas velocities. For large dynamic pressure ratios an asymptotic regime is obtained in which frequency is solely controlled by gas velocity and the instability becomes absolute. The transition from convective to absolute is shown to be influenced by the velocity defect induced by the presence of the separator plate. We show that in this regime the splitter plate thickness can also affect the nature of the instability if it is larger than the gas vorticity thickness. Computational and experimental results are in agreement with the predictions of a spatio-temporal stability analysis.

Air entrainment and bubble statistics in breaking waves

“…The DNS has been limited to two-dimensional evolution of periodic unstable waves with relatively small wavelengths, providing numerical data on wave dissipation and the splashing processes (Chen et al 1999;Song & Sirviente 2004;Iafrati 2011;Deike et al 2015). Three dimensional simulations of breaking waves have recently become available, both DNS (Fuster et al 2009) and LES (Derakhti & Kirby 2014;Lubin & Glockner 2015). They are indeed necessary to investigate bubble and spray formation, which are fundamentally three-dimensional processes.…”

“…The Dirac delta, δ s , expresses the fact that the surface tension term is concentrated on the interface, where γ is the surface tension coefficient, κ and n the curvature and normal to the interface. This solver has been successfully used in multiphase problems like atomization (Fuster et al 2009;Agbaglah et al 2011;Chen et al 2013), the growth of instabilities at the interface (Fuster et al 2013), wave breaking in two (Deike et al 2015) and three dimensions (Fuster et al 2009), capillary wave turbulence (Deike et al 2014) and splashing (Thoraval et al 2012). …”

Two mechanisms of droplet splashing on a solid substrate

“…It suggests that an instability mechanism involving gas inertia is enhanced by the gas density. When the jet is initiated before the contact (jet-splash regime), we can consider that the droplet is spreading and skating on a thin layer of air and it is tempting to draw an analogy with the atomization of liquid jets (Boeck & Zaleski 2005;Fuster et al 2013). In fact, it has been already suggested and demonstrated experimentally that in this case, the rapid skating of the liquid on a thin gas layer can develop a Kelvin-Helmholtz (KH) like instability that generates the splash (Kim et al 2014;Liu et al 2015).…”

“…In particular Liu et al (2015) has shown that the splash could be suppressed by draining the air layer beneath the drop near the contact location, emphasizing the role of the skating of the liquid on the gas layer. The KH instability involves the density ratio as well as the viscosity ratio in the growth rate of the instability (Villermaux 1998;Yecko & Zaleski 1999;Yecko et al 2002;Boeck & Zaleski 2005;Fuster et al 2013), and although the shear flow induced by the skating has a complex structure, such an instability should be present in the dynamics prior to the contact. To quantify the shear induced by the dynamics, we measure the vorticity (ω = ∂ z u − ∂ r v) in the gas layer beneath the droplet.…”

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

“…To further elucidate the rich dynamics of vertical counter-current gas-liquid flows, we therefore use simulations of the full Navier-Stokes equations together with the semi-analytical methods described above. It is worth noting that applying a low to moderate density contrast to this type of flow is popular in the simulation literature for a number of reasons, such as less complex system dynamics, which helps to pinpoint dynamically relevant mechanisms, but also numerical convenience, see, e.g., the works by Scardovelli and Zaleski, 25 Boeck et al 26 and Fuster et al 27 In this respect, we will make contact to the existing literature by considering low and high density contrasts in our analysis and report on its influence on the system behaviour.…”