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Graf Isolan
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Untersuchte Arbeit:
Seite: 47, Zeilen: 8-21
Quelle: Kollar et al 2005
Seite(n): 73-74, Zeilen: 73:3-4.11-18.22-24 - 74:1-2
3.3.2 Outcome of Collision

The binary droplet collision phenomenon is discussed in this section. The outcome of collisions can be described by three non-dimensional parameters: the collisional Weber number, the impact parameter, and the droplet size ratio (Orme, 1997; Post and Abraham, 2002; Ko and Ryou, 2005b).

The collisional Weber number is defined as


We_{coll}= \frac {\rho_l U_{rel}^2 d_2}{\sigma}
(3.21)

where Urel is the relative velocity of the interacting droplets and d2 is the diameter of the smaller droplet.

The dimensional impact parameter b is defined as the distance from the center of one droplet to the relative velocity vector, \vec{u}_{rel}, placed on the center of the other droplet. This definition is illustrated in Figure 3.6. The non-dimensional impact parameter is calculated as

[
B=\frac{2b}{d_1+d_2}= \sin \theta
(3.22)


where d1 is the diameter of the larger droplet and θ is the angle between the line of centers of the droplets at the moment of impact and the relative velocity vector.]


Ko, G.H. and H.S. Ryou (2005b). Modeling of droplet collision-induced breakup process. Int. J. Multiphase Flow 31, pp. 723-738.

Orme, M. (1997). Experiments on droplet collisions, bounce, coalescence and disruption. Prog. Energy Combust Sci. 23, pp. 65-79.

Post, S.L. and J. Abraham (2002). Modeling the outcome of drop-drop collisions in Diesel sprays. Int. J. Multiphase Flow 28, pp. 997-1019.

[page 73]

3. Droplet collision

The binary droplet collision phenomenon is discussed in this section. The phenomenon of droplet collision is mainly controlled by the following physical parameters: droplet velocities, droplet diameters, dimensional impact parameter, surface tension of the liquid, and the densities and viscosity coefficients of the liquid and the surrounding gas, but further components may also be important, such as the pressure, the molecular weight and the molecular structure of the gas. From these physical parameters several dimensionless quantities can be formed, namely, the Weber number, the Reynolds number, impact parameter, droplet size ratio, the ratio of densities, and the ratio of viscosity coefficients. Thus, for a fixed liquid-gas system, the outcome of collisions can be described by three non-dimensional parameters: either the Weber number or the Reynolds number, the impact parameter, and the droplet size ratio.

(i) The Weber number is the ratio of the inertial force to the surface force and is defined as follows:


We = \frac{\rho_d U_r^2 D_S}{\sigma}, 
(2)

where ρd is the droplet density, Ur is the relative velocity of the interacting droplets, DS is the diameter of the smaller droplet, and σ is the surface tension. [...]

(ii) The dimensional impact parameter b is defined as the distance from the center of one droplet to the relative velocity vector placed on the center of the other droplet. This definition is illustrated in Fig. 2. The non-dimensional impact parameter is calculated as follows:

[Page 74]


B=\frac{2b}{D_L+D_S} 
(3)

where DL is the diameter of the larger droplet.


Orme, M., 1997. Experiments on droplet collisions, bounce, coalescence and disruption. Progress. Energy Combust. Sci. 23, 65–79.

Post, S.L., Abraham, J., 2002. Modeling the outcome of drop-drop collisions in Diesel sprays. Int. J. Multiphase Flow 28, 997–1019.

Anmerkungen

Shortened severely but otherwise left intact. Again, significant details necessary for understanding the formulas have been left out. Nothing has been marked as a citation. No reference to the original author is given.

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