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 Autor László E. Kollár, Masoud Farzaneh, Anatolij R. Karev Titel Modeling droplet collision and coalescence in an icing wind tunnel and the influence of these processes on droplet size distribution Zeitschrift International Journal of Multiphase Flow Datum January 2005 Jahrgang 31 Nummer 1 Seiten 69-92 DOI 10.1016/j.ijmultiphaseflow.2004.08.007 Literaturverz. no Fußnoten no Fragmente 4

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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. Sichter (Graf Isolan)

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[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.

[Figure 3.6: Illustration of the definition of geometric parameters of the droplet collision.]

The droplet size ratio is given by

$\gamma = \frac{d_1}{d_2}\quad$ (3.23)

The possible outcomes of collisions are illustrated in Figure 3.7. Droplet bounce will occur if there is not enough time for the gas trapped between the droplets to escape and the surfaces of the droplets do not make contact due to the intervening gas film. When the relative velocity of the droplets is higher and the collisional kinetic energy is sufficient to expel [the intervening layer of gas, the droplets will coalesce.]

[page 73]

The non-dimensional impact parameter is calculated as follows:

[Fig. 2. Illustration of the definition of impact parameter b.]

[Page 74]

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

where DL is the diameter of the larger droplet.

(iii) The droplet size ratio is given by

$\Delta = \frac{D_S}{D_L}. \quad$ (4)

It should be clear that $\Delta \le 1,$ although some authors prefer to use the reciprocal $\gamma = \frac{1}{\Delta}.$

[...]

When two droplets interact during flight, five distinct regimes of outcomes may occur, as listed in Section 1, and depicted in Fig. 3 in the B–We plane for four different values of Δ. [...] If the relative velocity of the droplets is higher, there is not enough time for the gas to escape and the surfaces of the droplets do not make contact due to the intervening gas film, so the droplets become deformed and bounce apart. The corresponding domain in Fig. 3 is regime II. When the relative velocity is even higher and the collisional kinetic energy is sufficient to expel the intervening layer of gas, the droplets will coalesce after substantial deformation.

 Anmerkungen Continued from the previous page. The formulas and the figure are slightly adapted. The comments are taken verbatim without any reference given. Sichter (Graf Isolan)

 Zuletzt bearbeitet: 2014-06-27 23:03:47 Graf Isolan

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[When the relative velocity of the droplets is higher and the collisional kinetic energy is sufficient to expel] the intervening layer of gas, the droplets will coalesce. If the collisional energy exceeds the value for permanent coalescence, then temporary coalescence occurs. Temporary coalescence may result in either disruption or fragmentation. In disruption, the collision product separates into the same number of droplets which existed prior to the collision. In fragmentation, the coalesced droplet breaks up into numerous satellite droplets (Orme, 1997).

Bounce affects droplet trajectory, but it does not modify droplet size. Coalescence followed by disruption does not have any significant influence on droplet size. Even if some mass transfer occurs, the droplet diameters are not changed in any observable way. However, other types of collision outcomes may influence the DSD, because the sizes of post-collision droplets are different from those of the pre-collision droplets. During fragmentation, a number of small satellite droplets are formed with the accompanying decrease in size. Fragmentation occurs when the relative velocity of colliding droplets is high.

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

When the relative velocity is even higher and the collisional kinetic energy is sufficient to expel the intervening layer of gas, the droplets will coalesce after substantial deformation. [...] If the collisional kinetic energy exceeds the value for permanent coalescence, then the temporarily coalesced droplets separate into two or more droplets. [...] Temporary coalescence (regimes IV and V) may result in either disruption or fragmentation. In disruption, the collision product separates into the same number of droplets which existed prior to the collision. In fragmentation, the coalesced droplet breaks up into numerous satellite droplets (Orme, 1997).

It is clear that bounce affects droplet trajectory, but it does not modify the droplet size. Coalescence followed by disruption does not have any significant influence on droplet size. Even if some mass transfer occurs, the droplet diameters are not usually changed in any observable way. Other regions of collision outcomes, however, may influence DSD, because the sizes of post-collision droplets are different from those of the pre-collision droplets. During fragmentation, a number of small satellite droplets is formed with the accompanying decrease in droplet size. Fragmentation occurs when the relative velocity of colliding droplets is high, and since low velocity flows are under examination here, the phenomenon almost never occurs in this investigation.

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

 Anmerkungen Shortened but nonetheless the pieces taken are verbatim. Nothing has been marked as a citation. Sichter (Graf Isolan)

Fakten zu „Jem/Kollar et al 2005RDF-Feed
 Bearbeiter Graf Isolan QAutor László E. Kollár, Masoud Farzaneh, Anatolij R. Karev QFragmente 4 + QHrsg - QISBN - QInFN no QInLit no QJahr 2.005 + QOrt - QReihe - QSammlung - QSeiten 69-92 QTitel Modeling droplet collision and coalescence in an icing wind tunnel and the influence of these processes on droplet size distribution QVerlag - Sichter (Graf Isolan)