Free surface application of the PFEM (particles + finite elements) methodology to submerged cylinders

LEO M. GONZÁLEZ; ESTEBAN FERRER; JUAN M. GIMENEZ

Parma

Workshop; 10th SPHERIC International Workshop; 2015

In this paper, a new generation of the particle method known as Particle Finite Element Method (PFEM-2) cite{Idelsohn04}, which combines convective particle movement and a fixed mesh resolution, is applied to a 2D flow past a circular cylinder intersecting or close to a free surface at Reynolds 180 cite{Bouscasse14}. To accomplish this task, different improved versions of discontinuous and continuous enriched basis functions for the pressure field have been developed cite{Gimenez2015186} to capture the free surface dynamics without artificial diffusion or undesired numerical effects. The well-known numerical properties of PFEM-2 such as using larger time steps when compared to other similar numerical tools which implies shorter computational times while maintaining the accuracy of the computation will be checked in this case. In particular, for this free surface cylinder, the wake behavior for Froude numbers between 0.3 and 2.0 are examined. The PFEM-2 technique allows for a very little diffusive computation of the free surface evolution, even while breaking and fragmentation may occur. Vorticity shed by the cylinder, vortex generation due to free surface breaking, mixing processes, and drag and lift coefficients behavior are quantified. It has been found that, for small gap ratios, the classical von Karman vortex shedding from the cylinder does not take place for most of the Froude numbers considered. In turn, moderate vortex shedding occurs, departing not from the cylinder but originating from wave breaking at the free surface. This shedding takes places simultaneously with the transport of free surface fluid elements into the bulk of the fluid. In some combinations of Froude number and submergence ratio, a vorticity layer remains spatially localized between the cylinder and the free surface and a large recirculating wake area develops, which eventually gets detached after several shedding cycles, being advected downstream. In order to study the stability of these kind of complex flows and the tendency to develop absolute and convective instabilities, a Dynamic Mode Decomposition (DMD) stability analysis has been used. To the authors knowledge this has been the first time that a flow in the presence of free surface has been analyzed by this of technique. The DMD stability analysis captures perfectly either the growth or the damping tendency of the flow as well as the most relevant frequencies. This study is performed using a number of snapshots computed by the described PFEM methodology which are subsequently analyzed by a Dynamic Mode Decomposition (DMD) stability analysis.