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

GONZÁLEZ-GUTIERREZ, LEO M.; GIMENEZ, JUAN M.; FERRER, ESTEBAN

Galway

Workshop; 13th SPHERIC Workshop; 2018

In this paper, a new generation of the particle method known as Particle Finite Element Method (PFEM-2), which combines convective particle movement and a fixed mesh resolution, is applied to a 2D monophasic laminar flow past a circular cylinder close to a free surface. To accomplish this task, different improved versions of discontinuous and continuous enriched basis functions for the pressure field have been developed 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 3 and 4 and for gap ratios between 0.55 and 2 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. In order to test the accuracy of the computed baseflows, a global stability analysis of a circular cylinder is performed when submerged in a two phase gravitational flow. The flow behavior is governed by both the Reynolds and the Froude number, while the depth of the cylinder has been varied to create different scenarios for the stability analysis. The base flow obtained by the Navier-Stokes equations has been analyzed, and the first bifurcation (i.e. Hopf type) has been explored for different depths, Reynolds and Froude numbers. The critical Reynolds number and the frequency of the most unstable mode have been compared to the classical solution without free surface and gravity effects. The most unstable mode is deformed and distorted according to the free surface location, while the critical Reynolds numbers and frequency are both affected by the gravity and the free surface presence. Overall, we show that an increase in depth or Froude results in an early onset of the first instability and a lower critical Reynolds number. The presence of the free surface has a stabilizing effect at low Froude numbers, suppressing the unsteadiness of the wake. This study is performed using velocity baseflows obtained with the described PFEM-2 methodology and analyzing the stability of the profile solving an eigenvalue problem and selecting the dominant modes from the computed spectrum.