Newtonian jet stability: The role of air resistance

Abstract

The stability of high speed laminar Newtonian jets is studied as a function of ambient air pressure. For Weber numbers less than 5.3 (based on air density) air pressure has no effect on stability. Ambient viscosity, through the effect of shear stresses acting on the jet surface, gives rise to the maximum in the breakup curve. For large Weber numbers ambient pressure effects can alter, and eventually control, the appearance of the maximum.Liquid jets ejected from long capillaries break up into droplets in a manner determined by the physical properties of the liquid and the ambient medium. In an earlier study ( 2 ) jets of Newtonian fluids were ejected into stagnant air at atmospheric pressures, and attention was confined to the properties and dynamics of the jet. In the present work we examine the role played by the ambient medium in destabilizing the jet, and in particular, the effect of ambient pressure.Jet stability is usually characterized through a breakup curve, which shows the dependence upon jet velocity of the coherent length of the jet. At low velocities no dependence on ambient pressure is observed, and the breakup length increases linearly with velocity. As the jet velocity is increased the effect of the ambient medium is observed in the appearance of a pressure dependence of the breakup curve. A maximum breakup length occurs for each pressure, the low pressure curves being the more stable. All these observations seem quite reasonable, and one might think that the effect of the ambient medium is well established in view of the long history of studies of jet stability. (For a historical surve , see reference 1).which one may determine quantitatively the effect of the ambient medium on jet stability.Two theories exist which have relevance to this study.Weber (11) examined the stability of a laminar Newtonian jet ejected into a stagnant inviscid atmosphere. The effect of the interaction between the jet and its surroundings is the establishment of a pressure distribution which accelerates the growth of certain disturbances. Weber's theory predicts the existence of a maximum in the breakup curve and attributes the existence of the maximum to aerodynamic pressure effects. Grant's experiments (2) showed that Weber's theory is not quantitatively accurate, and, in fact, is quite bad under typical experimental conditions. Tomotika (10) examined the stability of a stationary cylinder of liquid surrounded by a second liquid, both liquids being viscous. Thus the viscosity of the ambient medium was accounted for. However, since the jet was assumed stationary, the effect of viscous drag on the jet was not accounted for, and Tomotika's theory would lead to a linear breakup curve showing no maximum. Tomotika's theory does allow an estimate of the importance of the viscosity of the ambient medium to be made, and Meister and Scheele (6) have recently reviewed this work. It is a fact, however, that no brea h up data exist fromIn considering the interaction of a jet with its surroundings, and in trying to plan a well-defin...

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

“…In this theory, the strong instability arises from a large velocity difference U between the liquid and gas phases. However, several experimental observations (Fenn & Middleman 1969;Davies & Young-Hoon 1974;Phinney 1975;Hoyt & Taylor 1977;Arai, Shimizu & Hiroyasu 1985;Karasawa et al 1992;Wu, Miranda & Faeth 1995), including those shown in figure 1, indicate that aerodynamic effects on turbulent atomization are of secondary…”

Effect of helium atmospheres on abrasive suspension water jets

“…But as it can be seen with a literature review there have been many different results. For example, Fenn and Middleman [3], working with jet velocities ranging between 2 m/s and 70 m/s, and ambient pressures within 7 hPa and 980 hPa, Weber numbers between 600 and 188000 and Reynolds numbers between 500 and 3000, concluded that the jet stability is affected by atmospheric pressure only when the atmospheric Weber 1 is greater than 5.3. Davies and Young [4] studied jets with a velocity of 11 m/s in air atmospheres from 100 hPa to 1000 hPa, a Weber number of 3800 and a Reynolds of number of 25000.…”

“…They found, among others, that the structure of the studied jets was affected by the density of the surrounding gas, but the jet velocity did not show a detectable consistent effect on it. Authors like Fenn and Middleman [3], Eddingfield and Albrecht [7], and McCarthy and Molloy [8] reported changes in the tendency of the behavior of the jet coherence according to the jet velocity. This can explain the variety on the results of the studies mentioned above (including even the independency between the jet structure and jet velocity for certain ranges).…”

Einfluss der Absorption von Ammoniak auf die Form schwingender Wasserstrahlen in Anwesenheit von n‐Pentanol

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