Numerical simulations of bouncing jets

Abstract

Bouncing jets are fascinating phenomenons occurring under certain conditions when a jet impinges on a free surface. This effect is observed when the fluid is Newtonian and the jet falls in a bath undergoing a solid motion. It occurs also for non-Newtonian fluids when the jets falls in a vessel at rest containing the same fluid. We investigate numerically the impact of the experimental setting and the rheological properties of the fluid on the onset of the bouncing phenomenon. Our investigations show that the occurrence of a thin lubricating layer of air separating the jet and the rest of the liquid is a key factor for the bouncing of the jet to happen. The numerical technique that is used consists of a projection method for the Navier-Stokes system coupled with a level set formulation for the representation of the interface. The space approximation is done with adaptive finite elements. Adaptive refinement is shown to be very important to capture the thin layer of air that is responsible for the bouncing.

An conservative anti-diffusion technique for the level set method

“…The level set method typically refers to the transport of a smooth distance function whose zero isosurface is the interface to be tracked. The method has been used successfully in many fluid flow applications, see e.g., Sussman et al [38], Osher and Sethian [34], Gibou et al [13], Ville et al [40], Bonito et al [2], but it can also be used in other contexts like shape optimization as in Dapogny et al [10], Yamada et al [43].…”

Iterative coupling of flow, geomechanics and adaptive phase-field fracture including level-set crack width approaches

“…Here the method is inspired by a recent idea proposed in [46] by introducing an (explicit) level-set function ϕ LS for the fracture. However, we also note that employing a level-set function to compute the normal vectors of iso-surfaces has been used for many different applications (for example, see [22,6] and references cited therein). The initial step follows a standard procedure in level-set methods.…”

Analytical and variational numerical methods for unstable miscible displacement flows in porous media

“…Here µ Stab|T denotes the piecewise-constant field of the entropy residual-based viscosity, which can be implemented implicitly or explicitly. More details are found in [295,251,174,296]. We note also that the EG method employs DG variational formulations, but with fewer degrees of freedom.…”