Lattice Boltzmann simulation of water droplet impact and freezing on inclined supercooled surfaces with different roughnesses and wettabilities

Water droplet's impact and subsequent freezing on inclined supercooled surfaces, having micro-pillar structures with three different types of wettabilities (hydrophilic, neutral, or hydrophobic) are investigated numerically by a three-dimensional, multi-relaxation time, pseudo-potential liquid-vapor phase-change lattice Boltzmann method. Effects of volume expansion of water at 0 degrees C as well as the advancing contact angle of the droplet on real rough surfaces are considered in this model. Temporal variations of droplet morphological changes after impact and subsequent freezing on the supercooled inclined surfaces under various wall temperatures are illustrated. Simulation results indicate that after impacting on the supercooled rough inclined surfaces at a given Weber number, a water droplet can form fully penetrated elliptical ice morphologies and stretched stream-like ice morphologies attached on the supercooled surface, or partially and fully rebounding from the supercooled surface depending on the wettability of the surface, the surface inclination, and the degree of supercooling. It is shown that elliptical ice patterns are formed on hydrophilic substrates where droplets do not recoil after spreading, while stream-like ice patterns are mostly formed on neutral substrates where droplets are gradually stretched due to the gravity because droplets are attached on the inclined surface. On the other hand, partial and full rebounds of droplets occur on hydrophobic surfaces having high inclination angle where droplets undergo strong recoiling and rebounding after spreading on rough surfaces. At low degrees of supercooling (i.e., higher substrate temperatures), partial rebounds occur because a portion of the water droplet freezes on the substrate during contact with the supercooled substrate; otherwise, fully rebounding occurs. These results elucidate the effects of wettability, roughness, temperature and inclined angle of the wall on ice morphologies. Additionally, effects of Stefan number (substrate temperature) on the four different ice morphologies of a water droplet (D0 = 100 and Pr = 13.5) after its impact on supercooled inclined rough surfaces at a Weber number of We = 112 (Reynolds number of Re = 164.9) are illustrated.