Interactions between a heavy particle, air, and a layer of liquid

Abstract

As an aircraft flies through cloud at temperatures below freezing, it encounters ice particles and supercooled droplets, which results in the accretion of ice onto its surfaces and hence deformation of its aerodynamic shape. This can, in worst cases, cause series accidents. Here, we focus on tackling the common situation where there is a thin layer of water on the aircraft surface and the particles are similarly thin such as to be able to interact with the water layer. Three-way interaction occurs between air, water, and body motion: under suitable assumptions (including that the Reynolds and Froude numbers are large, and that the body is much denser than the air), the model allows the shape of the layer interface and pressure profile beneath the body to be calculated for a given body position. Simultaneously, this in turn allows the forces on the body to be calculated and hence the motion of the particle to be computed in full. The result is a wide range of possible motions of the particle, including both “sink” cases (the particle enters the water and becomes submerged) and “skim” cases (where the particle is launched back off the surface of the water following contact). The latter cases have analogy with traditional “stone skimming/skipping” games. Repeated skims and significant wakes are accommodated rationally.