Convergence of a Sequence of Slender-Ship Low-Froude-Number Wave-Resistance Approximations

1984 ◽  
Vol 28 (03) ◽  
pp. 155-162
Author(s):  
Francis Noblesse
Keyword(s):  
Froude Number ◽  
Wave Resistance ◽  
Beam Length ◽  
Remarkable Property ◽  
Ship Hulls ◽  
Low Froude Number ◽  
Vertical Cylinders ◽  
Elliptical Cylinders ◽  
Double Hull ◽  
Special Case

Convergence of the sequence of slender-ship low-Froude-number wave-resistance approximations /"/, n > 0, obtained as a particular case of the slender-ship theory of wave resistance recently proposed by the author, is proved for the special case of ship hulls in the form of vertical cylinders with elliptical waterlines. Specifically, it is shown that we have where b is the thickness (beam/length) ratio of the cubical cylinder, Fis the Froude number, and r lf(b,F) is the Guevel-Baba-Maruo-Kayo low-Froude-number wave-resistance approximation associated with the exact zero-Froude-number (double-hull) potential. Vertical elliptical cylinders thus have the remarkable property that the ratio iipj{b,F)/rpp(b,F) is independent of the Froude number, that is, depends only on the thickness ratio of the cylinder.

A Slender-Ship Theory of Wave Resistance

1983 ◽  
Vol 27 (01) ◽  
pp. 13-33
Author(s):  
Francis Noblesse
Keyword(s):  
Froude Number ◽  
Wave Resistance ◽  
Successive Approximations ◽  
Zeroth Order ◽  
Remarkable Effect ◽  
Ship Wave ◽  
First Order ◽  
Wigley Hull ◽  
Low Froude Number ◽  
The Waves

A new slender-ship theory of wave resistance is presented. Specifically, a sequence of explicit slender-ship wave-resistance approximations is obtained. These approximations are associated with successive approximations in a slender-ship iterative procedure for solving a new (nonlinear integro-differential) equation for the velocity potential of the flow caused by the ship. The zeroth, first, and second-order slender-ship approximations are given explicitly and examined in some detail. The zeroth-order slender-ship wave-resistance approximation, r(0) is obtained by simply taking the (disturbance) potential, ϕ, as the trivial zeroth-order slender-ship approximation ϕ(0) = 0 in the expression for the Kochin free-wave amplitude function; the classical wave-resistance formulas of Michell [1]2 and Hogner [2] correspond to particular cases of this simple approximation. The low-speed wave-resistance formulas proposed by Guevel [3], Baba [4], Maruo [5], and Kayo [6] are essentially equivalent (for most practical purposes) to the first-order slender-ship low-Froude-number approximation, rlF(1), which is a particular case of the first-order slender-ship approximation r(1): specifically, the first-order slender-ship wave-resistance approximation r(1) is obtained by approximating the potential ϕ in the expression for the Kochin function by the first-order slender-ship potential ϕ1 whereas the low-Froude-number approximation rlF(1) is associated with the zero-Froude-number limit ϕ0(1) of the potentialϕ(1). A major difference between the first-order slender-ship potential ϕ(1) and its zero-Froude-number limit ϕ0(1) resides in the waves that are included in the potential ϕ(1) but are ignored in the zero-Froude-number potential ϕ0(1). Results of calculations by C. Y. Chen for the Wigley hull show that the waves in the potential ϕ(1) have a remarkable effect upon the wave resistance, in particular causing a large phase shift of the wave-resistance curve toward higher values of the Froude number. As a result, the first-order slender-ship wave-resistance approximation in significantly better agreement with experimental data than the low-Froude-number approximation rlF(1) and the approximations r(0) and rM.

Preliminary Numerical Study of a New Slender-Ship Theory of Wave Resistance

1983 ◽  
Vol 27 (03) ◽  
pp. 172-186
Author(s):  
C. Y. Chen ◽  
F. Noblesse
Keyword(s):  
Experimental Data ◽  
Froude Number ◽  
Numerical Study ◽  
Wave Resistance ◽  
Remarkable Effect ◽  
First Order ◽  
Wave Potential ◽  
Wigley Hull ◽  
Low Froude Number ◽  
Large Phase

Results of various numerical calculations of wave resistance designed to evaluate the new slender-ship approximations obtained in Noblesse [1]3 are presented. Specifically, three main wave-resistance approximations are evaluated and studied. These are the zeroth-order slender-ship approximation r(0), which is compared with the classical approximations of Hogner and Michell; the first-order slender-ship low Froude-number approximation rIF(1), which is shown to be practically equivalent: to the Guevel-Baba-MaruoKayo low-Froude-number approximation rIF; and the first-order slender-ship approximation r(1), which is evaluated for the Wigley hull and compared with existing experimental data, corrected for effects of sinkage and trim, and with numerical results obtained by using the theory of Guilloton, the low-speed theory, and Dawson's numerical method. The approximations r(1) and rIF(1) are obtained by taking the velocity potential in the Kochin free-wave amplitude function as the first-order slender-ship potential Φ(1) and its zero-Froudenumber limit Φ0(1) respectively. A major difference between the potentials Φ(1) and Φ0(1) resides in the wave potential ΦW(1) that is included in Φ(1), but is ignored in the zero-Froude-number potential Φ0(1). It is shown that the wave potential ΦW(1) may not be neglected in comparison with the potential Φ0(1) and in fact has a remarkable effect upon the wave resistance. In particular, the wave potential ΦW(1) causes a very large phase shift of the wave-resistance curve, which results in greatly improved agreement with experimental data.

Further Results on Lee Vortices in Low-Froude-Number Flow

1991 ◽  
Vol 48 (19) ◽  
pp. 2204-2211 ◽  
Author(s):  
Richard Rotunno ◽  
Piotr K. Smolarkiewicz
Keyword(s):  
Froude Number ◽  
Low Froude Number ◽  
Number Flow

The Denver Cyclone. Part I: Generation in Low Froude Number Flow

1990 ◽  
Vol 47 (23) ◽  
pp. 2725-2742 ◽  
Author(s):  
N. Andrew Crook ◽  
Terry L. Clark ◽  
Mitchell W. Moncrieff
Keyword(s):  
Froude Number ◽  
Low Froude Number ◽  
Number Flow

Discussion of “Stilling Basin Design for Low Froude Number”

1976 ◽  
Vol 102 (6) ◽  
pp. 797-799
Author(s):  
Heramb D. Sharma ◽  
Dharam V. Varshney
Keyword(s):  
Froude Number ◽  
Stilling Basin ◽  
Low Froude Number

scholarly journals Nose-Angle Bridge Piers as Alternative Countermeasures for Local Scour Reduction

2018 ◽  
Vol 13 (2) ◽  
pp. 110-120 ◽  
Author(s):  
Ibtesam Abudallah Habib ◽  
Wan Hanna Melini Wan Mohtar ◽  
Atef Elsaiad ◽  
Ahmed El-Shafie
Keyword(s):  
Froude Number ◽  
Local Scour ◽  
Bridge Piers ◽  
Scour Depth ◽  
Skew Angle ◽  
Flow Angle ◽  
Sediment Size ◽  
Low Froude Number ◽  
Skew Angles ◽  
Depth Reduction

This study investigates the performance nose-angle piers as countermeasures for local scour reduction around piers. Four nose angles were studied, i.e., 90°, 70°, 60° and 45° and tested in a laboratory. The sediment size was fixed at 0.39 mm whereas the flow angle of attack (or skew angle) was varied at four angles, i.e., skew angles, i.e., 0°, 10°, 20° and 30°. Scour reduction was clear when decreasing nose angles and reached maximum when the nose angle is 45°. Increasing the flow velocity and skew angle was subsequently increasing the scour profile, both in vertical and transversal directions. However, the efficiency of nose angle piers was only high at low Froude number less than 0.40 where higher Froude number gives minimal changes in the maximum scour depth reduction. At a higher skew angle, although showed promising maximum scour depth reduction, the increasing pier projected width resulted in the increase of transversal lengths.

A Contribution to Study on the Lift of Ventilated Supercavitating Vehicle With Low Froude Number

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Yu Kaiping ◽  
Zhou Jingjun ◽  
Min Jingxin ◽  
Zhang Guang
Keyword(s):  
Numerical Simulations ◽  
Froude Number ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Gravitational Effect ◽  
Gas Leakage ◽  
Supercavitating Vehicle ◽  
Numerical Predictions ◽  
Low Froude Number

A ventilated cavity was investigated using three-dimensional numerical simulation and cavitation water tunnel experiments under the condition of low Froude number. A two-fluid multiphase flow model was adopted in numerical predictions. The drag between the different phases and gravitational effect, as well as the compressibility of gas, was considered in the numerical simulations. By comparing the ventilated coefficient computational results of three different turbulence models with the Epshtein formula, the shear-stress-transport turbulence model was finally employed. The phenomenon of double-vortex tube gas-leakage was observed in both numerical simulations and experiments. Based on the validity of the numerical method, the change law of the lift coefficient on the afterbody was given by numerical predictions and accorded well with experimental results. The cause for the appearance of an abrupt increase in lift was difficult to get from experiments for the hard measurement, whereas the numerical simulations provided some supplements to analyze the reasons. The distribution of lift coefficient on the afterbody had important significance to the design of underwater vehicles.

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