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22.4.2 Interaction During Impact with a Boundary

The wall interaction is based on the work of Stanton [ 354] and O'Rourke [ 272], where the regimes are calculated for a drop-wall interaction based on local information. The four regimes, stick, rebound, spread, and splash are based on the impact energy and wall temperature. The following chart is helpful in showing the cutoffs.

Figure 22.4.2: Simplified Decision Chart for Wall Interaction Criterion.
\begin{figure}\begin{center} \begin{picture}(300,150)(10,10) \put(0,20){\vecto... ... \put(150,135){\makebox(0,0){\em Splash}} \end{picture} \end{center}\end{figure}

Below the boiling temperature of the liquid, the impinging droplet can either stick, spread or splash, while above the boiling temperature, the particle can either rebound or splash.

The criteria by which the regimes are partitioned are based on the impact energy and the boiling temperature of the liquid. The impact energy is defined by

 E^2 = \frac{\rho V_r^2 D}{\sigma} \left( \frac{1}{\min\left( h_0/D,1 \right) + \delta_{bl}/D} \right) (22.4-1)

where $\rho$ is the liquid density, $V_r$ is the relative velocity of the particle in the frame of the wall (i.e. $V_r^2 = (V_p - V_w)^2$), $D$ is the diameter of the droplet, and $\sigma$ is the surface tension of the liquid. Here, $\delta_{bl}$ is a boundary layer thickness, defined by
 \delta_{bl} = \frac{D}{\sqrt{\mbox{Re}}} (22.4-2)

where the Reynolds number is defined as $Re = \rho V_r D / \mu$. By defining the energy as in Equation  22.4-1, the presence of the film on the wall suppresses the splash, but does not give unphysical results when the film height approaches zero.

The sticking regime is applied when the dimensionless energy $E$ is less than 16, and the particle velocity is set equal to the wall velocity. In the spreading regime, the initial direction and velocity of the particle are set using the wall-jet model, where the probability of the drop having a particular direction along the surface is given by an analogy of an inviscid liquid jet with an empirically defined radial dependence for the momentum flux.

If the wall temperature is above the boiling temperature of the liquid, impingement events below a critical impact energy ( $E$) results in the particles rebounding from the wall. For the rebound regime, the particle rebounds with the following coefficient of restitution:

 e = 0.993 - 1.76 \Theta_I + 1.56 \Theta_I^2 - 0.49 \Theta_I^3 (22.4-3)

where $\Theta_I$ is the impingement angle as measured from the wall surface.

Splashing occurs when the impingement energy is above a critical energy threshold, defined as $E_{cr} = 57.7$. The number of splashed droplet parcels is set in the Boundary Conditions panel with a default number of 4, however, the user can select numbers between zero and ten. The splashing algorithm follows that described by Stanton [ 354] and is detailed in Section  22.4.3.

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