Numerical visualization of nappe oscillation
Abstract The unsteady global dynamics of a gravitational liquid sheet interacting with a onesided adjacent air enclosure, typically referred to as nappe oscillation, is addressed, under the assumptions of potential flow and presence of surface tension effects. Preliminary physical insights of the sheet centerline sinuous modes show that the nappe dynamics features the propagation of two wave fronts both directed downstream or one downstream and the other one upstream depending on whether the flow Weber number is greater or less than unity, respectively; moreover, the overall system behaves as a driven damped spring-mass oscillator, where the liquid sheet acts as the mass and the air enclosure as the spring. The findings of the eigenvalues spectral analysis closely agree with direct numerical simulations of the partial differential equation governing in the space-time domain the global evolution of the disturbances, starting from an initial gaussian-like shape.
Global dynamics analysis of nappe oscillation
The unsteady global dynamics of a gravitational liquid sheet interacting with a one-sided adjacent air enclosure, typically referred to as nappe oscillation, is addressed, under the assumptions of potential flow and absence of surface tension effects. To the purpose of shedding physical insights, the investigation examines both the dynamics and the energy aspects. An interesting re-formulation of the problem consists of recasting the nappe global behavior as a driven damped spring-mass oscillator, where the inertial effects are linked to the liquid sheet mass and the spring is represented by the equivalent stiffness of the air enclosure acting on the average displacement of the compliant nappe centerline. The investigation is carried out through a modal (i.e., time asymptotic) and a non-modal (i.e., short-time transient) linear approach, which are corroborated by direct numerical simulations of the governing equation. The modal analysis shows that the flow system is characterized by low-frequency and high...
Surfactant effects on the dynamics of a thin liquid sheet
The dynamics of a free-surface slender two-dimensional stream (liquid sheet) issuing from a nozzle in the gravitational field in still air, under the effect of surface-active agents, are analysed experimentally. The particular test section geometry (the liquid is forced to assume a bidimensional form between two vertical guides and a horizontal plate placed at a certain variable distance from the nozzle exit section) employed in this study gives rise to various flow regimes depending on the governing parameters: liquid flow rate, sheet height, surface pressure, gravity. Two basic phenomena are observed: thinning of the sheet (with recirculating motion inside it) and sheet-threadlines transition. For a certain surfactant (bulk) concentration, there exists a minimum critical flow rate value for which the sheet is seen to thin starting at both of the sheet bottom corners. A ridge, usually referred to as a Reynolds ridge in the literature, separates the sheet from the thin-film regions. The thin films exhibit recirculating flows (caused by the onset of surfactant-induced surface-pressure-driven convection in the gravitational field) and extend to the entire rectangular interface as the flow rate is reduced. At zero flow rate the thinned sheet resembles a plane vertical soap film showing a recirculating cellular structure. These phenomena are linked to the presence of surface-active material adsorbed at the liquid-air interface and occur when the sheet height exceeds a critical value. Otherwise, at a critical flow rate value the liquid sheet breaks up into an array of (more or less regularly distributed) discrete threadlines (vertical jets), whose spacing depends on the surface tension of the test liquid.