Stationary rotary force waves on the liquid–air core interface of a swirl atomizer

A one-dimensional wave equation, applicable to the waves on the surface of the air-core of a swirl atomizer is derived analytically, by analogy to the similar one-dimensional wave equation derivation for shallowwater gravity waves. In addition an analogy to the flow of water over a weir is used to produce an analytical derivation of the flow over the lip of the outlet of a swirl atomizer using the principle of maximum flow. The principle of maximum flow is substantiated by reference to continuity of the discharge in the direction of streaming. For shallowwater gravity waves, the phase velocity is the same expression as for the critical velocity over the weir. Similarly, in the present work, the wave phase velocity on the surface of the air-core is shown to be the same expression as for the critical velocity for the flow at the outlet. In addition, this wave phase velocity is shown to be the square root of the product of the radial acceleration and the liquid thickness, as analogous with the wave phase velocity for shallow water gravity waves, which is the square root of the product of the acceleration due to gravity and the water depth. The work revisits the weirs and flumes work of Binnie et al. but using a different methodology. The results corroborate with the work of Binnie. High speed video, Laser Doppler Anemometry and deflected laser beam experimental work has been carried out on an oversize Perspex (Plexiglas) swirl atomizer. Three distinctive types of waves were detected: helical striations, low amplitude random ripples and low frequency stationary waves. It is the latter wave type that is considered further in this article. The experimentally observed waves appear to be stationary upon the axially moving flow. The mathematical analysis allows for the possibility of a negative value for the phase velocity expression. Therefore the critical velocity and the wave phase velocity do indeed lead to stationary waves in the atomizer. A quantitative comparison between the analytically derived wave phase velocity and that measured experimentally, for this stationary pulsating wave, show very good agreement within a few percent

Wave patterns generated by an axisymmetric obstacle in a two-layer flow

Gravity waves generated by a moving obstacle in a two-layer stratified fluid are investigated. The experimental configuration is three-dimensional with an axisymmetric obstacle which is towed in one of the two layers. The experimental method used in the present study is based on a stereoscopic technique allowing the 3D reconstruction of the interface between the two layers. Investigation into the wave pattern as a function of the Froude number, Fr, based on the relative density of the fluid layers and the velocity of the towed obstacle is presented. Specific attention is paid to the transcritical regime for which Fr is close to one. Potential energy trapped in the wave field patterns is also extracted from the experimental results and is analyzed as a function of both the Froude number, Fr, and the transcritical similarity parameter Γ. In particular, a remarkable increase in the potential energy around Fr = 1 is observed and a scaling allowing to assemble data resulting from different experimental parameters is proposed

Axisymmetric waves in electrohydrodynamic flows

The formation of nonlinear axisymmetric waves on inviscid irrotational liquid jets in the presence of radial electric fields is considered. Gravity is neglected but surface tension is considered. Electrohydrodynamic waves of arbitrary amplitude and wavelength are computed using finite-difference methods. Particular attention is paid to nonlinear traveling waves. In the first class of problems, an electric field generated by placing the liquid jet inside a hollowcylindrical electrode held at constant voltage, its axis coinciding with that of the jet, is studied. The jet is assumed to be a perfect conductor whose free surface is stressed by the electric field acting in the hydrodynamically passive annulus. In the second class of problems, the annular gas is a perfect conductor that transmits a constant voltage onto the liquid/gas surface. The liquid axisymmetrically wets a constant-radius cylindrical rod electrode placed coaxially with respect to the hollow outer electrode, and held at a different constant voltage. The fluid dynamics and electrostatics need to be addressed simultaneously in the inner region. Axisymmetric interfacial waves influenced by surface tension and electrical stresses are computed in both cases. The computations are capable of following highly nonlinear solutions and predict, for certain parameter values, the onset of interface pinching accompanied with the formation of toroidal bubbles. For given wave amplitudes, the results suggest that, for the former case, the electric field delays bubble formation and reduces wave steepness, while for the latter case the electric field promotes bubble formation, all other parameters being equal