Breakup length

In the breakup regime, spray characteristics include film angle, film velocity and thickness, breakup length, breakup rate, surface wave frequency, wavelength, growth rate, and penetration distance. These quantities, however, are extremely difficult to measure on account of the very small size and rapidly changing features of disintegrating Hquid jets or films. 

Quantitative correlations for jet breakup length have been proposed by many investigators based on experiments. I381141 ] 122°]l247 I248]... 

They also proposed an empirical correlation for laminar jet breakup length ... 

To overcome the discrepancies between the predictions of Weber s correlations and subsequent experiments, Mahoney and Sterling 248] modified Weber s theory, and derived a universal equation for the breakup length of laminar Newtonian jets ... 

Arai and Hashimoto[2611 studied disintegration of a thin liquid sheet in a co-flowing air stream. For a constant sheet thickness, an empirical correlation was derived for the sheet breakup length as ... 

As ambient air pressure is increased, the mean droplet size increases 455 " 458] up to a maximum and then turns to decline with further increase in ambient air pressure. ] The initial rise in the mean droplet size with ambient pressure is attributed to the reduction of sheet breakup length and spray cone angle. The former leads to droplet formation from a thicker liquid sheet, and the latter results in an increase in the opportunity for droplet coalescence and a decrease in the relative velocity between droplets and ambient air due to rapid acceleration. At low pressures, these effects prevail. Since the mean droplet size is proportional to the square root of liquid sheet thickness and inversely proportional to the relative velocity, the initial rise in the mean droplet size can be readily explained. With increasing ambient pressure, its effect on spray cone angle diminishes, allowing disintegration forces become dominant. Consequently, the mean droplet size turns to decline. Since ambient air pressure is directly related to air density, most correlations include air density as a variable to facilitate applications. Some experiments 452] revealed that ambient air temperature has essentially no effect on the mean droplet size. 

Linear stability theories have also been applied to analyses of liquid sheet breakup processes. The capillary instability of thin liquid sheets was first studied by Squire[258] who showed that instability and breakup of a liquid sheet are caused by the growth of sinuous waves, i.e., sideways deflections of the sheet centerline. For a low viscosity liquid sheet, Fraser et al.[73] derived an expression for the wavelength of the dominant unstable wave. A similar formulation was derived by Li[539] who considered both sinuous and varicose instabilities. Clark and DombrowskF540 and Reitz and Diwakar13161 formulated equations for liquid sheet breakup length. 

Although these results apply to the instability of a stationary jet, they can be used to estimate the length at which a circular jet of uniform initial velocity L/y will break up. We estimate the breakup length as... 

For a 5-mm-diameter water jet the characteristic capillary time (pa Ia) is 4.14 X 10 s, so we may expect such a slow-moving jet to break up very quickly, in distances on the order of a centimeter for speeds approximately 0.1 ms The jet breakup length is predicted remarkably well by Rayleigh s linear result over a wide range of disturbance amplitudes even though the breakup process may be strongly nonlinear. 

Spray Applications. In sprays, atomization of the fluid is generally the desired goal. The critical breakup length of the filament was described over a decade ago by equation 1 in terms of a dimensionless breakup length (28), L/2fl, for HPAM-thickened fluids. 

Figure 1.5 shows the growth rate of the capillary instability for different liquid viscosities. Viscosity dampens the instability with a damping coefficient of hpl lp and shifts the fastest growing perturbations toward longer waves. For p = 0, Rayleigh solution is obtained, whereas for very viscous jets with (3pk /2p) al2pa , a> = a/ pd) — k a ). The breakup length for a viscous jet is found as ...

The hnear theories provide a growth rate for the unstable waves. These growth rates are useful in estimating the breakup length and time. According to the linear... 

The breakup length of jets in the case of the aerodynamically-driven bending instability is determined by the following expression [1,6]... 

The linear theory does not provide a means for the liquid sheet to breakup, because during the sinuous mode of instability, the distance between the two sides of the sheet remains a constant value. Therefore, it is not possible to predict the breakup length of a sheet... 

Jazayeri and Li [41] developed up to the third order nonlinear analysis of a liquid sheet to determine the breakup length of the sheet A typical result of their solution for the surface deformation as a function of distance is shown in Fig. 3.9. This case is for the initial disturbance amplitude of 0.1, the Weber number of 40 and the gas-to-liquid density ratio of 10, which approximates the situation of liquid water in ambient air. The wave number of 0.02 is almost equal to the dominant wave number for the sinuous disturbance of the linear theory. It is seen that the surface wave grows in time, and maintains its sinuous character for the majority of its growth... 

Movassat M, Maftoon N, Dolatabadi A, A three-dimensional numerical study of the breakup length of liquid sheets, Proceedings of 21th Annual Conference on Liquid Atomization and Spray Systems, Orlando, FL, May 2008. 

Droplets are initialized with a negative deformation velocity in order to avoid the almost immediate breakup of highly tmstable initial ligaments, and to extend their lifetime to levels comparable with experimentally observed jet breakup lengths [8]. 

The primary breakup of these highly unstable initial drops is modeled by artificially prolonging their lifetime such that they agree with experimentally observed breakup lengths. More precisely, the value for the breakup time, is obtained from the experimental jet breakup length correlation of Levich [23]... 

The breakup length of a liquid sheet is defined as the total length of the liquid sheet from the edge a.t = 0°, and the maximum width of the sheet is referred to as breakup width. Combining (30.16) and (30.17) gives an equation describing the shape of the sheet in polar coordinates (r, 0) ... 

Figure 30.9 presents the theoretical (30.19 and 30.21) and experimental results of sheet breakup length and width versus We [23]. The three vertical dotted lines are the demarcation lines between the closed-rim sheet and open-rim sheet. The open-rim sheet is measured mily for the case of 0 = 120. A favorable agreement can be seen in Fig. 30.9 for liquid sheets with closed rims, which shows that the breakup width is linearly proportional to We. The slope of the linear relatimi is determined by the impinging angle. Figure 30.10 also shows that the breakup width increases... 

Fig. 30.10 Breakup length and width versus impinging angle [23] (Courtesy of the American Institute of Physics)...

Abstract Prediction of droplet size and velocity distribution produced by splash plate requires information on the liquid sheet characteristics and its breakup process. This chapter focuses on the sheet produced by splash plate nozzles and their characteristics such as sheet breakup length and produced droplet size. It explains different flow regimes occurring in splash plate nozzles as well as various breakup lengths provided by different researchers. Sheet formation phenomenon is explained theoretically and at the end correlations for droplet size prediction are provided. 

Keywords Breakup length Droplet size distribution perforation Splash plate nozzle Stability Thickness... 

Arai and Hashimoto [19] reported the following correlation for the sheet breakup length of a viscous sheet ... 

Ahmad et al. [24] provided two correlations for the breakup length. One for increasing breakup length with flow rate, and the other one for decreasing breakup length with flow. For increasing breakup length they provided ... 

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