Extensions Of The Neumann-Michell Theory

The flow around a ship hull that steadily advances in calm water of large depth is considered within the framework of a linear potential flow theory,called NeumannMichell(NM)theory,that has been widely shown to be useful for routine applications to ship design and hull-form optimization.This practical and realistic theory is expanded here to account for two important aspects of the flow around a ship hull:(i)two alternative practical methods to predict the sinkage and the trim of a freely floating ship,and the resulting increase in the drag of the ship,are given,and(ii)simple nonlinear corrections of the NM theory are given for the sinkage,the trim,the drag and wave profiles.In addition to these two extensions of the NM theory of the nearfield flow around a ship hull,a notable feature of farfield ship waves is considered;specifically,the wavelengths of the highest waves that result from constructive interferences among the divergent waves created by a fast ship are analyzed.Practical prediction of sinkage and trim effects on the drag of a ship:Two alternative practical methods,an experimental method and a numerical method,to predict the sinkage and the trim of a freely-floating ship are considered.The experimental approach,based on a detailed analysis of experimental data for 22 ship models given in the literature,yields simple analytical relations that explicitly predict(without flow computations)the sinkage and the trim of a ship in terms of the speed,the length,the beam,the draft and the block coefficient of the ship.The numerical approach only requires flow computations(based on the NM theory)for the hull surface of the ship at rest rather than for the actual mean wetted hull surface.Thus,iterative flow computations for a sequence of hull positions are not used in this numerical method.The experimentally-based analytical relations and the numerical method both yield predictions of sinkage and trim that agree well with experimental measurements for monohull ships at common Froude numbers F ? 0.45.The influence of the sinkage and trim of a freely-floating ship on the total drag(notably wave drag and viscous drag)is significant,and theoretical predictions based on the NM theory are in satisfactory agreement with experimental measurements for three ship models(Wigley,S60 and DTMB5415)at F ? 0.45.The practical method to predict the increase in the drag of a freely-floating ship due to sinkage and trim given here can be applied to ship models as well as full-scale ships with smooth or rough hull surfaces,and is well suited for early ship design and optimization.Practical nonlinear corrections to Neumann-Michell linear predictions:Nonlinear effects on the wave drag,the sinkage,the trim and the wave profile along a ship hull are investigated,via the NM linear potential flow theory,for four freely-floating ship models(Wigley,S60,DTMB5415,KCS).Nonlinear effects are shown to be relatively small.However,an important exception to this general finding is that the wave drag of a bulbous ship(DTMB5415,KCS)is greatly reduced due to the nonlinear component of the pressure in the Bernoulli relation.This important nonlinear effect is readily included in the NM theory.The nonlinear component of the pressure in the Bernoulli relation also yields a small increase of the sinkage,likewise readily included in the NM theory.Moreover,free-surface nonlinearities can have appreciable,although not large,effects on the wave profile.These nonlinear effects can also be approximately taken into account via a simple transformation of the linear wave profile.The flow computations for the four ship models considered here show that simple(post-processing)nonlinear corrections(that require no additional flow computations)of the NM theory yield numerical predictions of the wave drag,the sinkage,the trim and the wave profile that agree well with experimental measurements,and compare favorably with predictions given by more complex computational methods.Wavelengths of the highest waves created by a fast ship:Constructive interference among the divergent waves created by sources and sinks distributed over the hull surface of a ship that travels at a high speed in calm water results in highest waves along ray angles located inside the cusps of the classical Kelvin wake.These highest waves are much shorter than the waves along the cusps of the Kelvin wake and are also significantly shorter than the ship length.Simple analytical relations that determine the wavelengths of the highest waves in terms of the Froude number and,for a catamaran,the distance between the twin bows of the catamaran are given.