SPH modelling of viscous flow past a circular cylinder interacting with a free surface

Single-phase two-dimensional flow past a circular cylinder intersecting, or close to, a free surface at a Reynolds number of 180 is numerically investigated in this paper series using the Smoothed Particle Hydrodynamics (SPH) method. The wake behavior for Froude numbers between 0.3 and 2.0, based on the diameter, and for submergence-diameter ratios between -0.5 and 2.5 is examined. This range significantly extends existing literature on the topic. Vorticity shed by the cylinder, vortex generation due to free-surface breaking, and mixing processes are discussed. Regarding the submergence dependence, it has been found that for small gap ratios, the classical von Kármán vortex shedding from the cylinder does not take place. In turn, vortex shedding originates from wave-breaking at the free surface, occurring simultaneously with the transport of free-surface fluid elements into the bulk of the fluid. It has been also found that for even smaller depth ratios, a vorticity layer remains spatially localized between the cylinder and the free surface, and a large stagnation recirculating area develops behind the cylinder. In some of these cases, the whole mass of fluid in that area eventually gets detached after several shedding cycles and it is advected downstream. According to the authors' knowledge, this is a previously unreported form of wake instability. It has been also found that as the Froude number is increased, the classical von Kármán vortex street shed from the cylinder is blocked only to be recovered at very high Froude numbers, in agreement with linear stability predictions. Regarding the challenging and not previously investigated half-submerged configuration, flows in which the cylinder acts as a barrier, flows with alternation of dry and wet cylinder top surface, and flows with cavities have been described.