Colloquium Mathematics - H. van der Heiden

Title:
Modelling viscous effects in offshore flow problems

Abstract:
The simulation method ComFLOW, developed at the University of Groningen, is a free- surface flow solver that is traditionally used to compute wave-impact forces on offshore structures due to strongly non-linear ocean waves or due to internal sloshing. ComFLOW solves the full Navier-Stokes equations for one fluid phase subject to a free surface boundary, or for two immiscible fluid phases separated by an interface, on a Cartesian computational grid using an improved volume-of-fluid method. Additionally, ComFLOW is endowed with excellent free-surface wave generating and absorbing boundary conditions. In this talk I will outline how ComFLOW can be extended to model the more subtle viscous effects that appear in fluid flows: skin friction at fluid-wall boundaries and turbulence in the fluid. First, I will discuss how the Navier-Stokes equations can be discretised when boundary conditions are not aligned, but rather immersed in a Cartesian computational grid, using a cut-cell discretisation technique. Secondly, I will discuss how to deal with the very wide range of dynamical (turbulent) length scales that typically characterise flows in offshore applications, which is too computationally demanding to fully resolve. A large eddy simulation technique is employed, in which the larger eddies in the flow are resolved, while the interaction between resolved and unresolved scales is modelled. Several turbulence models are compared and special attention is devoted to the class of low-dissipative eddy-viscosity models. Thirdly, I will discuss how the effect of un(der)resolved turbulent boundary layers on the outer flow is modelled by a simple modification of the effective wall-shear stress. Finally, the combined methodology for modelling viscous flow effects that has been implemented in ComFLOW is validated for the sloshing motion of water columns in special ship hull openings, so-called moonpools, which are typically used to lower equipment from a vessel through the water line. The simulated free-surface motions are compared to experimental time traces.