On Turbulence Modelling for Bilge Vortices: A Test of Eight Models for Three Cases

Doctoral thesis, 2001

This work is a test, in three steps, of turbulence models for the calculation of the flow field around ships. Eight models ranging from k-e and k-w models to a Reynolds-stress model (RSM) are tested. All three of the steps contain vortices: the first is the case of a vortex in a free- stream, the second is a vortex pair embedded in a turbulent boundary layer, and the third is the flow field, with vortices, around a ship hull. The first case is divided into three parts which are all vortices in a free-stream but have different axial velocities in the vortex core; this tests the capability of the models to predict the shear stress driven decay of a vortex. The second case tests the capacities to predict the decay of a vortex in a turbulent environment and to predict a boundary layer with cross-flow. The third case adds to the problem the formation of a vortex over a curved surface, a boundary layer over curved surfaces and pressure gradients. The RSM model gave the most accurate results in a majority of the cases. The simpler turbulence models turned out to be the best for one of the parts in the first case. One combination of the k-e and k-w models (SST) predicted the most accurate resistance in the third case; it also predicted the second most accurate flow field at the propeller plane. One of the algebraic stress models (CLS) had approximately the same values as the RSM in the first case. It gave results in closer agreement with the RSM model than the other models in the second case; it was also among the three best models in the third case when the overall flow field was of concern. The SST model is an alternative to the RSM model (which may be too expensive), for wall-bounded flows with adverse pressure gradients. The CLS model is an alternative for other flows containing vortices.