Bag breakup

Subjected to steady acceleration, a droplet is flattened gradually. When a critical relative velocity is reached, the flattened droplet is blown out into a hollow bag anchored to a nearly circular rim which contains at least 70% of the mass of the original droplet. Surface tension force is sufficient to allow the bag shape to develop. The bag, with a concave surface to the gas flow, is stretched and swept off in the downstream direction. The rupture of the bag produces a cloud of very fine droplets presumably via a perforation mode, and the rim breaks up into relatively larger droplets, although all droplets are at least an order of magnitude smaller than the initial droplet size. This is referred to as bag breakup (Fig. 3.10)T2861... 

Figure 3.10. Some modes of droplet breakup. Left bag breakup Right breakup.

Chou, W.-H., L.-P. Hsiang, and G. M. Faeth. 1997. Dynamics of drop deformation and formation during secondary breakup in the bag breakup regime. AIAA Paper No. 97-0797. 

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)... 

Here, WecOk->o is the critical We for O < 0.1. This equation was derived only for the transition from vibrational to bag breakup. However, in [2], the behavior for other transitional We is shown to be similar. 

In some instances, oscillation may lead to breakup into a few large fragments. This is referred to as vibrational breakup. As noted by [1], this breakup mode does not always occur, proceeds much more slowly than the other modes, and does not lead to small final fragment sizes. As a result, most authors ignore vibrational breakup and consider bag breakup to be the first mode of secondary atomizatirm. 

The goal of atomization is often to create the smallest possible fragment sizes while minimizing energy input. Bag breakup occurs at low We. Therefore, minimal energy is needed to achieve secondary atomization. For this reason, bag breakup is perhaps the most important mode, and the We marking the start of bag breakup has been termed the critical Weber number. Wee. When Oh <0., multiple smdies have shown that Wee — 11 2 [4]. 

During bag breakup, separation of the flow around the deformed drop leads to a positive pressure difference between the leading stagnation point and the wake. This tends to blow the center of the drop downstream resulting in the formation of the bag [12]. The outer edge forms a toroidal ring to which the bag is attached. 

Sheet-thinning breakup occurs at higher relative velocities (yVe) than bag breakup, and proceeds in a markedly different fashion. Following initial deformatiOTi, a sheet is formed at the periphery of the drop. The sheet evolves into ligaments that break up into a multitude of small fragments. The process continues until the drop is completely fragmented, or until it has accelerated to the point at which aerodynamic... 

To date, no definitive explanation exists for why bag breakup occurs at low levels of aerodynamic forces and sheet-thinning breakup occurs at higher levels. Some have proposed that unstable surface waves dictate the breakup modes. However, as discussed in [4], this explanation fails to fully explain aU of the modes and is not supported by recent numerical simulations. Other possibilities may include a competition between internal flow in the deforming drop and surface tension [4], or strong backflow in the wake at high We which prevents bag growth [12]. More research is warranted. 

The last piece of knowledge needed to determine drop-size distributions a priori is either MMD or D 2- In [23], a correlation was proposed based on the analysis of the physics of bag breakup ... 

W. H. Chou, G. M. Faeth Temporal Properties of Secondary Drop Breakup in the Bag Breakup Regime, Inti. J. Multi. Flow 24(6), 889-912 (1998). 

The breakup parameter, Kbu, in the bag breakup and the stripping breakup regime is proportional to the characteristic breakup frequencies suggested by [5]. The characteristic breakup frequency for the catastrophic breakup regime is derived from the study of the RT instability by Bellman and Pennington [21] as reported by Patterson and Reitz [11]. The constant k = 0.05 has been determined such that the drop radii match the phase Doppler measurements of Schneider [22], whereas the values for the constants ki and k are chosen such that Kbu is continuous at the regime-dividing Weber numbers, Web,s and Wcg c-... 

When a droplet breaks up, it results in a group of new droplets with a certain size distribution and mean diameter. The Sauter mean diameter (SMD) is computed for bag breakup and multimode breakup from the following relation ... 

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