15.6 Wall-Jet Model Theory

The direction and velocity of the droplet particles are given by the resulting momentum flux, which is a function of the impingement angle, $\phi$, and Weber number. See Figure  15.6.1.

Figure 15.6.1: "Wall Jet'' Boundary Condition for the Discrete Phase

The wall-jet type boundary condition assumes an analogy with an inviscid jet impacting a solid wall. Equation  15.6-1 shows the analytical solution for an axisymmetric impingement assuming an empirical function for the sheet height ( $H$) as a function of the angle that the drop leaves the impingement ( $\Psi$).

where $H_{\pi}$ is the sheet height at $\Psi=\pi$ and $\beta$ is a constant determined from conservation of mass and momentum. The probability that a drop leaves the impingement point at an angle between $\Psi$ and $\Psi+\delta\Psi$ is given by integrating the expression for $H(\Psi)$

where $P$ is a random number between 0 and 1. The expression for $\beta$ is given in Naber and Reitz [ 244] as