2.5. Eulerian Wall Film Model

When droplets impinge on the wall, four different mechanisms are possible depending on the droplet impact energy and wall temperature. Figure 3b schematically shows these mechanisms: stick, splash, evaporate, and spread [49]. In this study, droplet evaporation was neglected considering that the body temperature is much lower than the boiling temperature of the sprays (~100 °C).

After droplets are collected on the wall surface, a liquid thin film forms and will move/spread depending on the net forces acting on it. The Eulerian wall film model considers four major processes for the droplet-wall interactions: interaction during the initial impact with a wall boundary, subsequent tracking of the air–liquid interface, calculation of film variables, and coupling to the gas phase and solid wall. The governing equations for the mass and momentum conservation of the wall-film are the following:

In Equation (1), h is the film height, ∇s is the surface gradient operator, V⇀l is the mean film velocity, ρ_l is the liquid density, and m˙s is the mass source due to droplet collection, film separation, and film stripping. In the right-hand side of Equation (2), the first term represents the loading in the normal direction, the second-to-fourth terms represent the loading in the tangential direction, while the last term is the momentum gain or loss due to droplet collection or separation. Specifically, Pg is the air pressure, Ph=−ρhn⇀×g⇀ is liquid-film-induced pressure normal to the film (spreading), and Pσ=−σ∇s×∇shis the pressure caused by surface tension. The second term (g⇀τh) is the gravitational effect tangential to the film, the third term (3τ⇀fs/2ρl) is the viscous shear force at the air–film interface, and the fourth term (3ϑlV⇀/h) is the viscous force at the film–wall interface. The last term q˙ is the momentum source term, with q˙=m˙sV⇀p−V⇀l and V⇀p, V⇀lbeing the droplet and liquid film velocities, respectively. To calculate the viscous force, the film velocity is assumed to have a parabolic profile.