Numerical Simulation of Three-dimensional Viscous Flow around Marine Structures

Abstract

The first part of the thesis covers the theoretical background for computational fluid dynamics; specifically, the incompressible Navier-Stokes equations. Some general solution methods are reviewed, as well as the most common discretization techniques, which form the basis of modern CFD codes.

The second part is a report of a series of numerical experiments, including a short description of the computational method applied in the Navier-Stokes solver. The following flow cases are computed:

• Laminar flow around a fixed, three-dimensional circular cylinder at a Reynold number Re=u∞d/u = 265. Different cylinder lengths are tested. The onset of three-dimensionality in the wake flow is given particular attention. The sensitivity to time step and grid refinement is investigated.

• Subcritical turbulent flow around a cylinder at Re = 3900. The turbulence is modeled using large-eddy simulations (LES). The effects of using the wall damping and different time integration schemes are investigated.

• Turbulent flow around two fixed circular cylinders arranged in tandem at Re = 21600. This test is a model problem for flow around marine risers. Drag and lift of the two cylinders are compared with experimental data; both mean values and standard deviation.

Laminar cross flow around a 6:1 ellipsoid at Re = 100. An initial calculation is performed.

The three first cases can be seen as steps towards the VIV problem, taking a bottom-up approach. A logical next step could be, for example, adding forced motion to the downstream cylinder in the tandem case. In all the flow simulations performed in this thesis work, we have aimed for high fidelity, obtaining a higher level of accuracy than in most engineering calculations. Computational tools currently under development at SINTEF Applied Mathematics in collaboration with NTNU have been used.