Sheet Breakup

Keywords Bag breakup Breakup mode Breakup time Catastrophic breakup Fragments Fragment size distribution Initiation time Multimode breakup Newtonian drops Non-Newtonian drops Ohnesorge number (Oh) Secondary atomization Secondary breakup Sheet-thinning breakup Total breakup time Vibrational breakup Weber number (We)... 

The theory has beea exteaded to evaluate sheet breakup (19). This model (19) assumes that the fastest growing wave detaches at the leading edge ia the form of a ribboa with a width of a half-waveleagth. The ribboa ioimediately coatracts iato multiple ligaments, which subsequeatly reshape themselves iato spherical droplets. The characteristic dimension of the ligament, Dy is as foUows, where / is the sheet thickness at the breakup locatioa. 

Hollow-Cone Sprays. In swid atomizers, the Hquid emerges from the exit orifice ia the form of a cooical sheet. As the Hquid sheet spreads radially outward, aerodyaamic iastabiHty ioimediately takes place and leads to the formation of waves which subsequently disiategrate iato ligaments and droplets. Figure 3 illustrates the breakup process ia an annular Hquid sheet. 

Liquid-Sheet Breakup The basic principle of most hydraulic atomizers is to form a thin sheet that breaks via a variety of mechanisms to form ligaments of liquid which in turn yield chains of droplets. See Fig. 14-86. 

Further differences from hydraulic nozzles (controlled by sheet and ligament breakup) are the stronger increase in drop size with increasing surface tension and decreasing gas density. 

At higher vapor loads, the kinetic energy of the vapor rather than the bubble burst supphes the thrust for jets and sheets of hquid that are thrown up as well as the energy from breakup into spray. This yields much higher levels of entrainment. In distillation trays it is the most common limit to capacity. 

FIG. 27-24 Idealized process of drop formation by breakup of a liquid sheet. After Domhrowski and Johns, Chem. Eng. Sci. 18 203, 1963. )... 

Experiments in closed vessels by Abdel-Gayed and Bradley [19], left Ka.Le = 0.003 continuous laminar flame sheet, right Ka.Le = 0.238 breakup of the continuous flame sheet. (Reprinted from Lewis, B. and Von Elbe, G., Combustion, Flames and Explosions of Gases, Academic Press, New York, 1961. With permission. Figure 204, p. 401, copyright New York Academic Press (Elsevier editions).)... 

Table 3.2. Classification and Criteria of Breakup Regimes of Round Liquid Jets in Co-flowing Air as Compared to Those of Thin Liquid Sheets and Spherical Droplets in Air Stream 210 ...

Normal Pulsating Axisymmetric Rayleigh-type Sheet forms a round jet No breakup WfN <15... 

Figure 3.8. Liquid sheet/film breakup modes Successive stages in the idealized breakup of (a) a sheet with a thick rim, (b) a wavy sheet, and (c) a perforated sheet.

B) Flat Liquid Sheets into Air Streams Mechanical and Aerodynamic Disintegration. In air streams (with an air flow), a liquid sheet issuing from the 2-D nozzle will form a quasi-2-D expanding spray. The breakup modes are divided into two groups (1) mechanical mode due to the action of liquid injection pressure, and (2) aerodynamic mode due to the action of air friction. 

The mechanical breakup mode occurs around the rims of the sheet where the air-liquid relative velocity is low, forming relatively large droplets. At low relative velocities, aerodynamic forces are much smaller than surface tension and inertia forces. Thus, the breakup of the liquid rims is purely mechanical and follows the Rayleigh mechanism for liquid column/jet breakup. For the same air pressure, the droplets detached from the rims become smaller as the liquid flow rate is increased. 

The aerodynamic breakup mode occurs in the liquid sheet between the rims. In aerodynamic breakup, the perforation and wave... 

Farago and Chigier 2l() found that at similar aerodynamic Weber numbers, the disintegration modes of a thin liquid sheet in air streams are similar to those of a round liquid jet in a coaxial air stream (Table 3.2). At high aerodynamic Weber numbers, Membrane-Type or Fiber-Type breakup mode may set in. 

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 ... 

Recently, Knoll and Sojka[263] developed a semi-empirical correlation for the calculation of the Sauter mean diameter of the droplets after primary breakup of flat-sheets in twin-fluid atomization of high-viscosity liquids ... 

In practical fan sheet breakup processes, sheet thickness diminishes as the sheet expands away from the atomizer orifice, and liquid viscosity affects the breakup and the resultant droplet size. Dombrowski and Johns[238] considered these realistic factors and derived an analytical correlation for the mean droplet diameter on the basis of an analysis of the aerodynamic instability and disintegration of viscous sheets with particular reference to those generated by fan spray atomizers ... 

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