Cavitation and Multiphase Flow Laboratory at the University of Michigan

Abstract

Series 60 CB= 0.6 represents an important class of ships for which vast amount of experimental data is available. Thus, it represents an ideal test bed for validating Computational Fluid Dynamics (CFO) codes. The code UNCLE incorporates the recently introduced algorithm for tracking incorporates the recently introduced algorithm for tracking unsteady free surface flows in a time accurate manner. In this algorithm, to facilitate the tracking of the free surface, a background grid is employed. Using the background grid the free surface grid points are forced to move along predetermined paths in order to simplify the grid regeneration process at the new time level. Newton's method is used to find the intersection of the background grid lines with the free surface. This allows to preserve the shape of the free surface during various grid operations at a given time level. The governing equations of the flow field are cast with respect to an unsteady Eulerian coordinate system and solved using the modified artificial compressibility method. The resulting numerical algorithm is implicit and time accurate and is formulated based on a finite volume approach. Roe's formulation is used for obtaining the first order inviscid numerical fluxes and van Leer's MUSCL approach is used for obtaining higher order (third) corrections. Central differencing is used for the viscous terms and a two point backward Euler formula is used for the time derivative. The same algorithm is also used for implicitly solving the free surface kinematic condition which is cast with respect to surface curvilinear coordinates. The numerical results are compared with the experimental results. The flow conditions are Fr= 0.316 and Re= 4,020,000. The results are quite encouraging.