Francis Noblesse

Hydrodynamic Optimization of Ship Hull Forms

Abstract An extremely simple CFD tool is used to compare the calm-water drags of a series of hull forms and to define ‘optimized’ monohull ships for which the total (friction+wave) calm-water drag is minimized. The friction drag is estimated using the classical ITTC formula. The wave drag is predicted using the zeroth-order slender-ship approximation. Comparisons of theoretical predictions and experimental measurements for a series of eight hull forms show that—despite the extreme simplicity of the method that is used here to estimate the friction drag and the wave drag—the method is able to rank the drags of a series of hull forms roughly in accordance with experimental measurements. Thus, the method may be used, with appropriate caution, as a practical hull form design and optimization tool. For purposes of illustration, optimized hull forms that have the same displacement and waterplane transverse moment of inertia as the classical Wigley hull, taken as initial hull in the optimization process, are determined for three speeds and for a speed range.

The Green function in the theory of radiation and diffraction of regular water waves by a body

SummaryThis study is concerned with the Green function of the theory of potential flow about a body in regular (time-harmonic) water waves in deep water, that is with the linearized velocity potential of the flow due to a source of pulsating strength at a fixed position below the free surface (or a pulsating flux across the free surface) of a quiescent infinitely deep sea. An asymptotic expansion and a convergent ascending-series expansion for the Green function are obtained from two alternative complementary ‘near-field’ and ‘far-field’ single-integral representations in terms of the exponential integral. The asymptotic expansion and the ascending series allow efficient numerical evaluation of the Green function for large and small distances, respectively, from the mirror image of the singularity (submerged source or free-surface flux) with respect to the mean sea surface.

Alternative integral representations for the Green function of the theory of ship wave resistance

SummaryThree alternative single-integral representations for the Green function of the theory of ship wave resistance are derived in a unified manner from a basic double-integral representation. These alternative single-integral representations, which essentially are modifications of well-known double-internal representations due to Michell, Havelock, and Peters, are compared and discussed. Another object of this study is to examine the field equation and the boundary condition satisfied by the Green function in the limiting case when the singular point is exactly at the free surface.

Practical evaluation of the drag of a ship for design and optimization

We consider two major components of the drag of a ship, the “friction drag” and the “wave drag”, that are related to viscous friction at the hull surface and wavemaking, and mostly depend on the Reynolds number and the Froude number, respectively. We also consider the influence of sinkage and trim, viscosity, and nonlinearities on the drag. The sum of the friction drag given by the classical ITTC friction formula and the wave drag predicted by the modification, called Neumann-Michell (NM) theory, of the classical Neumann-Kelvin theory of ship waves is found to be within about 10% of experimental drag measurements for four ship hulls for which theoretical predictions and experimental measurements are compared. The sum of the ITTC friction drag and the NM wave drag can then be expected to yield realistic practical estimates that can be useful for routine applications to design and hullform optimization of a broad range of displacement ships. Furthermore, we note several simple extensions of this highly simplified approach that can be expected to significantly improve accuracy.

Boundary between unsteady and overturning ship bow wave regimes

Measurements of the bow waves generated by a rectangular flat plate, immersed at a draught D = 0.2 m, towed at constant speed U = 1.75 m s −1 in calm water and held at a heel angle 10° and a series of nine yaw angles α = 10°, 15°, 20°, 25°, 30°, 45°, 60°, 75° and 90° are reported. The measurements show that bow wave unsteadiness is significantly larger for the flat plate towed at yaw angles 30° ≤ α ≤ 90° than at 10° ≤ α ≤ 20°, which are associated with the unsteady and overturning bow wave regimes, respectively, separated by the boundary with g ≡ acceleration of gravity. These measurements of bow wave unsteadiness provide preliminary experimental validation of the foregoing simple theoretical relation for the boundary between the unsteady and overturning bow wave regimes for non-bulbous wedge-shaped ship bows with insignificant rake and flare. Extension of this relation to more complicated ship bows, notably bows with rake and flare, is also considered.

Ship bow waves

The bow wave generated by a ship hull that advances at constant speed in calm water is considered. The bow wave only depends on the shape of the ship bow (not on the hull geometry aft of the bow wave). This basic property makes it possible to determine the bow waves generated by a canonical family of ship bows defined in terms of relatively few parameters. Fast ships with fine bows generate overturning bow waves that consist of detached thin sheets of water, which are mostly steady until they hit the main free surface and undergo turbulent breaking up and diffusion. However, slow ships with blunt bows create highly unsteady and turbulent breaking bow waves. These two alternative flow regimes are due to a nonlinear constraint related to the Bernoulli relation at the free surface. Recent results about the overturning and breaking bow wave regimes, and the boundary that divides these two basic flow regimes, are reviewed. Questions and conjectures about the energy of breaking ship bow waves, and free-surface effects on flow circulation, are also noted.

Velocity representation of free-surface flows and Fourier-Kochin representation of waves

A new fundamental mathematical representation of linear free-surface potential flows is given. The flow representation, called velocity representation, only involves first derivatives of the Green function and defines the velocity inside a flow domain in terms of source and vortex distributions given by the normal and tangential velocity components of the velocity at the boundary surface. The velocity representation yields remarkably simple analytical representations of the waves generated by an arbitrary boundary velocity distribution for time-harmonic flows, with or without forward speed, and for steady flows.

Nonlinear ship-wave theories by continuous mapping

The exact equations of steady inviscid flow past a ship hull are formulated in a reference domain, onto which the flow domain is mapped. A thin-ship perturbation analysis is performed in the reference domain, and the first- and second-order solutions are derived. The classical thin-ship theory is obtained as the consistent, mapping-independent, perturbation solution in the physical space. Guillotons method is interpreted as an inconsistent, mapping-dependent, second-order approximation. A new inconsistent approximation is obtained by exploiting the freedom in the mapping of the flow domain onto the reference domain. Further improvements are suggested.

Experimental investigation of the effects of blade geometry on pressure fluctuation and noise of tunnel thrusters

ABSTRACT Tunnel thrusters are more vulnerable to cavitation due to the tip clearance flow, blockage effect of the gearbox, and heavy blade loads as compared with open propellers, which makes the problems of structure vibration and radiated noise more serious. Unfortunately, there are few public sources of relevant experimental study. In this context, model experiments have been carried out in the cavitation tunnel of the Shanghai Jiao Tong University to investigate the effects of blade geometry on pressure fluctuation and noise. The experimental results indicate that the traditional ‘flat plate’ blade is unfavourable for vibration excitation, while unloading towards the tip can effectively reduce both the fluctuating pressure and the noise levels.

Stationary phase and practical numerical evaluation of ship waves in shallow water

A simple and highly-efficient method for numerically evaluating the waves created by a ship that travels at a constant speed in calm water, of large depth or of uniform depth, is given. The method, inspired by Kelvin’s classical stationary-phase analysis, is suited for evaluating far-field as well as near-field waves. More generally, the method can be applied to a broad class of integrals with integrands that contain a rapidly oscillatory trigonometric function with a phase function whose first derivative (and possibly also higher derivatives) vanishes at one or several points, commonly called points of stationary phase, with the range of integration.