Weber number impact

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... 

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 ... 

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]... 

Andreani and Yadigaraoglul309 indicated that if the impact Weber number is smaller than 30, practically no breakup occurs ... 

For droplets of high surface tension, the droplet flattening process may be governed by the transformation of impact kinetic energy to surface energy. In case that this mechanism dominates, the flattening ratio becomes only dependent on the Weber number, as derived by Madej ski by fitting the numerical results of the full analytical model ... 

Fig. 1. The impact of a water droplet with an initial diameter of 85 /j.m, a velocity of 5.1 m/s and a Weber number of 30. The contact angle formed by water with the substrate was 35 . The delay between each picture is 3 /j,s, with whole sequence taking 135 /rs. (From Ref. 2 2004 American Institute of Physics.)...

Although they used droplets with diameters of 2 mm and more, the work of Park et alP is interesting on account of the fact that they used four different substrates and four different hquids. They observed the impact of droplets of distilled water, n-Octane, n-Tetradecane or n-Hexadecane onto glass slides, sihcon wafers, HMDS (Hexamethyl dishazane) coated sihcon wafers or Teflon, for Reynolds numbers from 180 to 5513 and Weber numbers from 0.2 to 176. A model was constructed to predict the maximum spreading ratio, which is the ratio of the maximum spreading diameter to the initial droplet s diameter, for low impact velocities. 

Fig. 3.2. Typical droplet-droplet collision outcome map with four regimes [88] Bouncing (Bo), Coalescence (Co), Stretching Separation (Ss), and Reflexive Separation (Rs). X denotes the impact factor, and TVe is the Weber number.

A semiempirical analysis of heat transfer to impacting sprays has been developed by considering the major components of spray heat transfer to consist of (1) contact heat transfer to impacting droplets, (2) convective heat transfer to gas, and (3) thermal radiation heat transfer [142], The model further assumes that the droplet interference is negligible (i.e., dilute sprays), and the three heat transfer components are independent of each other. The heat transfer data to a single impacting droplet have been correlated by the Weber number, surface temperature superheat, and thermophysical properties. 

Abstract We put together the state of knowledge on binary colUsional interactions of droplets in a gaseous environment. Phenomena observed experimentally after drop collisions, such as coalescence, bouncing, reflexive separation and stretching separation, are discussed. Collisions of drops of the same liquid and of different -miscible or immiscible - liquids, as well as collisions of drops of equal and different size are addressed. Collisions of drops of immiscible liquids may lead to an unstable interaction which is not observed with drops of equal or miscible liquids. Regimes characterized by the various phenomena are depicted in nomograms of the Weber number and the non-dimensional impact parameter. The state-of-the-art in the simulation of binary droplet collisions is reviewed. Overall three different methods are represented in the literature on these simulations. We discuss models derived from numerical simulations and from experiments, which are presently in use for simulations of spray flows to account for the influence of coUisional interactions of the spray droplets on the drop size spectrum of the spray. 

In collisions at Weber numbers greater than, say, 10, we observe that, for moderate non-dimensional impact parameter, the droplets merge and form one common drop (Figs. 7.4e and f, regime III in Fig. 7.3). The newly formed drop... 

What was said about the state of knowledge on collisions of different miscible liquid drops applies to the case of immiscible liquids also. We find the work by Chen and Chen [49], who investigated the collision of equal-sized droplets of water and Diesel oil. The dynamic viscosities and surface tensions of the two liquids against air at the temperature of the experiments are different by a factor of 3.1 and 2.6, respectively. Drop sizes, produced with the same piezoelectric droplet generators as in Gao et al. [45], ranged between 700 and 800 pm. The result of an experimental survey of the outcome fi om the collisions for varying impact Weber number and non-dimensional impact parameter is a flow chart similar to that in Fig. 7.5a, where the Weber number is defined with the relative velocity of the colliding drops and the liquid properties of Diesel oU. The boundaries between the... 

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