Resistance, wave-making and wave-decay of thin ships, with emphasis on the effects of viscosity.

Abstract

Three interrelated topics in ship hydrodynamics - resistance, wave-making and wave decay - are investigated in an attempt to improve the accuracy of some simple methods used in the preliminary design of thin ships. Several published sets of data from classical and recent boundary layer experiments on flat plates are used to estimate boundary layer quantities such as thicknesses and eddy viscosities. These quantities are subsequently used to modify the hull shape and the free-surface boundary condition as a means of including viscous effects on wave-making and ship-wave decay. A recent technique is used to analyse 161 experimental flat-plate turbulent boundary layer velocity profiles, and a new skin-friction line is derived. Some practical methods are proposed for the numerical quadrature of integrals arising in thin-ship hydrodynamics. We demonstrate that for some integrals, rapid oscillation, rather than being a hindrance to accurate quadrature, can actually be beneficial if appropriate techniques are employed. We find that boundary layer displacement thickness effects on wave resistance are very small and can be safely ignored for full-size vessels. On the other hand, the idea of a detachment layer, an indication of where the boundary layer begins to thicken rapidly, is shown to have a significant effect on wave resistance. A modification to the Kelvin free-surface boundary condition is used as a means of including viscous effects on wave-making. Detailed comparisons of total resistance predictions and experiments are made for three model-size Wigley hulls. It is shown that inclusion of viscous effects smooths out the well-known humps and hollows in the wave resistance curves calculated using Michell's (inviscid) integral. Predictions of the total resistance of a model Wigley hull using Michell's integral and a simple skin-friction line are shown to be as good as those of a modern CFD computer code. Furthermore, the simple method does so in a very small time on an inexpensive computer. The effect of employing a form factor on the skin-friction is shown to improve correlations between resistance predictions and experiments. It has recently been proposed that a form factor should also be applied to the wave resistance. We show that good predictions are indeed possible, but that the use of a modified form of Michell's integral and an “appropriate" value of the eddy viscosity leads to even better agreement. Two existing wave-decay models are examined and a new formulation is suggested that combines the theoretical – 1/2 decay rate of transverse waves with the -1/3 decay rate of diverging waves. The effects of viscosity on ship-wave decay are considered. It is found that large values of the viscosity, of the order required to have a significant effect on wave resistance, lead to an over-damping of far-field waves at low Froude numbers. We show that it may be possible to get a rough estimate of the (ambient) eddy viscosity from an analysis of the decay of ship-waves with transverse distance from the sailing line, without resorting to computationally expensive Fourier transform methods. Three wave decay models are used to estimate the eddy viscosity from the behaviour of the wave decay. The model that uses the theoretical decay rates of transverse and of diverging waves is found to be slightly better at recapturing the original eddy viscosity than the other two models.