Aerodynamic effects in the break-up of liquid jets: on the first wind-induced break-up regime

Abstract

We present both numerical and analytical results from a spatial stability analysis of the coupled gas-liquid hydrodynamic equations governing the first wind-induced (FWI) liquid-jet break-up regime. Our study shows that an accurate evaluation of the growth rate of instabilities developing in a liquid jet discharging into a still gaseous atmosphere requires gas viscosity to be included in the stability equations even for low We g , where We g = ρ g U 2 l R 0 /σ , and ρ g , U l , R 0 and σ are the gas density, the liquid injection velocity, the jet radius and the surface tension coefficient, respectively. The numerical results of the complete set of equations, in which the effect of viscosity in the gas perturbations is treated self-consistently for the first time, are in accordance with recently reported experimental growth rates. This permits us to conclude that the simple stability analysis presented here can be used to predict experimental results. Moreover, in order to throw light on the physical role played by the gas viscosity in the liquid-jet break-up process, we have considered the limiting case of very high Reynolds numbers and performed an asymptotic analysis which provides us with a parameter, α, that measures the relative importance of viscous effects in the gas perturbations. The criterion |α| 1, with α computed a priori using only the much simpler inviscid stability results is a guide to assess the accuracy of a stability analysis in which viscous diffusion is neglected. We have also been able to explain the origin of the ad hoc constant 0.175 introduced by Sterling & Sleicher (J.

Generation and breakup of Worthington jets after cavity collapse. Part 1. Jet formation

“…The characteristic time needed for such perturbations to disrupt the jet into drops is the capillary time, ∼ (ρ R 3 /σ) 1/2 , with R the jet radius. Therefore the jet breakup length, L b , is such that L b /R ∝ (ρ U 2 R/σ) 1/2 if aerodynamic effects are absent [Sterling & Sleicher (1975); Gordillo & Pérez-Saborid (2005)]. Notice that the study of jet breakup in our case is somewhat related to that considered by Rayleigh since the fluid particles conserve their velocities, in a first approach, along the ballistic region of the jet.…”

Model for the initiation of atomization in a high-speed laminar liquid jet

“…At low jet speeds, the Plateau-Rayleigh (Plateau 1873;Rayleigh 1878) instability disintegrates the jet into large droplets at large distances from the nozzle. As the jet speed is increased, aerodynamic forces and the nozzle exit velocity profile affect the jet instability (Chandrasekhar 1961;Batchelor & Gill 1962;Taylor 1963;Mattingly & Chang 1974;Sterling & Sleicher 1975;Lin & Reitz 1998;Gordillo & Pérez-Saborid 2005). For a long nozzle, the nozzle flow becomes turbulent at a certain jet speed.…”

Characterising the heat and mass transfer coefficients for a crossflow interaction of air and water

“…Now, given the complexity of such an interaction, and the absence of simple analytical solutions, it is necessary to provide a flow regime map to aid the design of heat and mass transfer devices involving falling liquids in gaseous crossflows. Numerous studies have examined the behaviour of sheets of falling liquid, in quiescent gas, [15][16][17][18][19][20][21] and similarly a number of studies have examined the behaviour of liquid sheets with gas co-flow and around jets in crossflow [22][23][24]. Bolanos-Jimenez et al [25] performed a theoretical and experimental study on the behaviour of air and water sheets in a parallel flow condition.…”