Weber number droplet

Both effects can produce coarser atomization. However, the influence of Hquid viscosity on atomization appears to diminish for high Reynolds or Weber numbers. Liquid surface tension appears to be the only parameter independent of the mode of atomization. Mean droplet size increases with increasing surface tension in twin-fluid atomizers (34). is proportional to CJ, where the exponent n varies between 0.25 and 0.5. At high values of Weber number, however, drop size is nearly proportional to surface tension. 

The emulsification process in principle consists of the break-up of large droplets into smaller ones due to shear forces (10). The simplest form of shear is experienced in lamellar flow, and the droplet break-up may be visualized according to Figure 4. The phenomenon is governed by two forces, ie, the Laplace pressure, which preserves the droplet, and the stress from the velocity gradient, which causes the deformation. The ratio between the two is called the Weber number. We, where Tj is the viscosity of the continuous phase, G the velocity gradient, r the droplet radius, and y the interfacial tension. 

As an approximate rule, break-up of droplets occurs for a Weber number in excess of one, a rule of thumb that is actually valid for the range of viscosity ratios of the dispersed phase to the continuous phase of less than approximately five. Higher viscosities of the disperse phase lead to serious difficulties with emulsification because the shear energy is then dispersed in rotation of the droplets. 

Concerning a liquid droplet deformation and drop breakup in a two-phase model flow, in particular the Newtonian drop development in Newtonian median, results of most investigations [16,21,22] may be generalized in a plot of the Weber number W,. against the vi.scos-ity ratio 8 (Fig. 9). For a simple shear flow (rotational shear flow), a U-shaped curve with a minimum corresponding to 6 = 1 is found, and for an uniaxial exten-tional flow (irrotational shear flow), a slightly decreased curve below the U-shaped curve appears. In the following text, the U-shaped curve will be called the Taylor-limit [16]. 

The purpose of our calculation was to quantitatively evaluate the deformational behavior of the TLCP droplets and their fibrillation under the processing conditions, and finally, to establish a relationship among the calculated Weber number, the viscosity ratio, and the measured aspect ratio of the fibers. Figure 13 illustrates this procedure. All calculated results were plotted as... 

Weber number Pe L We = -s a inertial force surface-tension force 8 10-2 2 10-2 Relevant for bubble (droplet) flows. Length scale bubble diameter... 

Droplet delivery from an airblast nebulizer is governed by the surface tension, density and viscosity of the fluid, and the applied pressure, which can be passive or forced. Droplet breakup is illustrated in Fig. 6. Droplets form during this breakup at a critical Weber number (We) ... 

To validate the model developed in the present study, the simulations are first conducted and compared with the experimental results of Wachters and Westerling (1966). In their experiments, water droplets impact in the normal direction onto a hot polished gold surface with an initial temperature of 400 °C. Different impact velocities were applied in the experiment to test the effect of the We number on the hydrodynamics of the impact. The simulation of this study is conducted for cases with different Weber numbers, which represent distinct dynamic regimes. 

The simulation shown in Fig. 10 is an impact of a saturated water droplet of 2.3 mm in diameter onto a surface of 400°C with an impact velocity of 65 cm/s, corresponding to a Weber number of 15. This simulation and all others presented in this study are conducted on uniform meshes (Ax — Ay — Az = A). The mesh resolution of the simulation shown in Fig. 10 was 0.08 mm in grid size, although different resolutions are also tested and the results are compared in Figs. 11 and 12. The average time-step in this case is around 5 ps. It takes 4000 iterations to simulate a real time of 20 ms of the impact process. The simulation... 

Fig. 14 shows the comparison of the photographs from Chandra and Avedisian (1991) with simulated images of this study for a subcooled 1.5 mm n-heptane droplet impact onto a stainless-steel surface of 200 °C. The impact velocity is 93 cm/s, which gives a Weber number of 43 and a Reynolds number of 2300. The initial temperature of the droplet is room temperature (20 °C). In Fig. 14, it can be seen that the evolution of droplet shapes are well simulated by the computation. In the first 2.5 ms of the impact (frames 1-2), the droplet spreads out right after the impact, and a disk-like shape liquid film is formed on the surface. After the droplet reaches the maximum diameter at about 2.1ms, the liquid film starts to retreat back to its center (frame 2 and 3) due to the surface-tension force induced from the periphery of the droplet. Beyond 6.0 ms, the droplet continues to recoil and forms an upward flow in the center of the... 

The impact process of a 3.8 mm water droplet under the conditions experimentally studied by Chen and Hsu (1995) is simulated and the simulation results are shown in Figs. 16 and 17. Their experiments involve water-droplet impact on a heated Inconel plate with Ni coating. The surface temperature in this simulation is set as 400 °C with the initial temperature of the droplet given as 20 °C. The impact velocity is lOOcm/s, which gives a Weber number of 54. Fig. 16 shows the calculated temperature distributions within the droplet and within the solid surface. The isotherm corresponding to 21 °C is plotted inside the droplet to represent the extent of the thermal boundary layer of the droplet that is affected by the heating of the solid surface. It can be seen that, in the droplet spreading process (0-7.0 ms), the bulk of the liquid droplet remains at its initial temperature and the thermal boundary layer is very thin. As the liquid film spreads on the solid surface, the heat-transfer rate on the liquid side of the droplet-vapor interface can be evaluated by... 

Table 12.1 gives a summary of the dimensionless variables. Two additional groups have been added, the Weber number, We, to account for droplet formation and the Nusselt number, Nu = hj/k, to account for gas phase convection. A corresponding Nusselt... 

For liquids of higher viscosities, the influence of liquid viscosity on droplet breakup needs to be considered. According to Hinze,[270] the critical Weber number may be modified to the following expression to account for the effect of liquid viscosity ... 

In some practical processes, a high relative velocity may not exist and effects of turbulence on droplet breakup may become dominant. In such situations Kolmogorov, 280 and Hinze[27°l hypothesized that the turbulent fluctuations are responsible for droplet breakup, and the dynamic pressure forces of the turbulent motion determine the maximum stable droplet size. Using Clay s data, 2811 and assuming isotropic turbulence, an expression was derived for the critical Weber number 270 ... 

Figure 3.18. Spreading behavior of a single droplet impinging on flat (eID0=0) and non-flat (eID0=0.33, WD0 = 2.8) surfaces at different Weber numbers (Re = 3000) (Reprinted from Ref. 389, 1995, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.)...

F), in addition to the Reynolds and Weber numbers, to fully describe a droplet spreading and solidification process upon impact on a substrate. They introduced two new dimensionless numbers, defined as ... 

Senda et al)335 415 also derived equations describing the thickness and diameter of the radial film formed on a hot surface as a function of the Weber number, and correlated the mean diameter of droplets resulted from the breakup of the radial film with the thickness of the radial film and the Weber number. 

Generally, the occurrence of a specific mode is determined by droplet impact properties (size, velocity, temperature), surface properties (temperature, roughness, wetting), and their thermophysical properties (thermal conductivity, thermal capacity, density, surface tension, droplet viscosity). It appeared that the surface temperature and the impact Weber number are the most critical factors governing both the droplet breakup behavior and ensuing heat transfer. I335 412 415]... 

To determine if a droplet experiences spreading or splashing when it impinges onto a liquid film on a solid surface, the correlation between the Weber number and Ohnesorge number derived by Walzel[398] may be used ... 

Various correlations for mean droplet size generated using pressure-swirl and fan spray atomizers are summarized in Tables 4.4 and 4.5, respectively. In the correlations for pressure-swirl data, FN is the Flow number defined as FN = ml/APlpl) )5, l0 and d0 are the length and diameter of final orifice, respectively, ls and ds are the length and diameter of swirl chamber, respectively, Ap is the total inlet ports area, /yds the film thickness in final orifice, 6 is the half of spray cone angle, and Weyis the Weber number estimated with film... 

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