Numerical Study of a Slender-Ship Theory of Wave Resistance

1985 ◽  
Vol 29 (02) ◽  
pp. 81-93
Author(s):  
Francis Noblesse
Keyword(s):  
Froude Number ◽  
Numerical Study ◽  
Near Field ◽  
Field Potential ◽  
Analytical Approximation ◽  
Wave Resistance ◽  
Theoretical Predictions ◽  
Wigley Hull ◽  
The Green Function ◽  
Hull Forms

This study is a continuation of the previous numerical study by Chen and Noblesse [1]2 of the slender-ship theory of wave resistance presented in Noblesse [2]. Results of systematic calculations of wave resistance are presented for three simple sharp-and round-ended strut-like hull forms having beam/length and draft/length ratios equal to 0.15 and 0.075, respectively. Numerical results are presented for the first order slender-ship approximation and for seven closely related wave-resistance approximations. The nondimensional wave-resistance values associated with these eight approximations are plotted versus the Froude number in the range 1 ≥ F ≥ 0.18. The Kochin wave-energy function corresponding to four approximations is also depicted for three Froude-number values. The wave potential is shown to have more pronounced effects upon the wave resistance, causing large phase shifts in particular, than the nonoscillatory near-field potential. A simple analytical approximation to the near-field term in the Green function is proposed. Finally, theoretical predictions are compared with experimental data for the Sharma strut and the Wigley hull.

Comparison Between Theoretical Predictions of Wave Resistance and Experimental Data for the Wigley Hull

1983 ◽  
Vol 27 (04) ◽  
pp. 215-226
Author(s):  
C. Y. Chen ◽  
F. Noblesse
Keyword(s):  
Experimental Data ◽  
Froude Number ◽  
Resistance Coefficient ◽  
Wave Resistance ◽  
Number Range ◽  
Theoretical Predictions ◽  
Wigley Hull ◽  
Sinkage And Trim ◽  
Theoretical Results ◽  
Good Agreement

A number of theoretical predictions of the wave-resistance coefficient of the Wigley hull are compared with one another and with available experimental data, to which corrections for sinkage and trim are applied. The averages of eleven sets of experimental data (corrected for sinkage and trim) and of eleven sets of theoretical results for large values of the Froude number, specifically for F 0.266, 0.313, 0.350, 0.402, 0.452, and 0.482, are found to be in fairly good agreement, in spite of considerable scatter in both the experimental data and the numerical results. Furthermore, several sets of theoretical results are fairly close to the average experimental data and the average theoretical predictions for these large values of the Froude number. Discrepancies between theoretical predictions and experimental measurements for small values of the Froude number, specifically for F = 0.18, 0.20, 0.22, 0.24, and 0.266, generally are much larger than for the above-defined high-Froude-number range. However, a notable exception to this general finding is provided by the first-order slender-ship approximation evaluated in Chen and Noblesse [1],3 which is in fairly good agreement with the average experimental data over the entire range of values of Froude number considered in this study.

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.

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.

Potential of Michell’s Integral for Ship Wave Resistance

2014 ◽  
Author(s):  
Takashi Tsubogo
Keyword(s):  
Integral Equation ◽  
Froude Number ◽  
Computing Time ◽  
Wave Resistance ◽  
Boundary Integral ◽  
Hull Form ◽  
Number Range ◽  
Gradient Effect ◽  
Depth Direction ◽  
Wigley Hull

The Michell’s integral (Michell 1898) for the wave making resistance of a thin ship has not been used widely in practice, since its accuracy is questioned especially for a Froude number range about 0.2 to 0.35 for conventional ships. We examine calculations by Michell’s integral for some ship forms, e.g. a parabolic strut, Wigley hull and so on. As a result, one reason of the disagreement with experiments is revealed. It must be the gradient of hull form in the depth direction. Then a thin ship theory including the hull gradient effect in the depth direction is presented, which improves slightly in low Froude numbers but needs more computing time than Michell’s integral so as to solve a boundary integral equation.

Bow Flow and Added Resistance of Slender Ships at High Froude Number and Low Wave Lengths

1983 ◽  
Vol 27 (03) ◽  
pp. 160-171
Author(s):  
Odd M. Faltinsen
Keyword(s):  
Froude Number ◽  
Near Field ◽  
Wave Length ◽  
Experimental Results ◽  
Solution Technique ◽  
Complete Agreement ◽  
Sea Waves ◽  
Added Resistance ◽  
Wigley Hull ◽  
High Froude Number

Flow around a slender ship bow at high Froude number and regular incident head sea waves is analyzed by matched asymptotic expansions. The near-field solution implies solving a two-dimensional Laplace equation with complete linear free-surface conditions. A solution technique with fundamental sources and dipoles is used. The solution technique is tested with good results for transient forced heave oscillation of a circular cylinder and for steady flow around a wedge. Comparisons with other numerical and experimental results for steady bow flow around a Wigley hull and a Series 60, Cb = 0.6 model show partly satisfactory results. The theoretical model for unsteady flow around a ship bow is used to calculate added resistance on a slender ship in high Froude number and incident regular head sea waves of low wave lengths. Experimental results for added resistance at low wave length for a cargo ship with Cb = 0.61 are not in complete agreement with the theoretical predictions.

Experimental and numerical study on onset of inflow in near field of buoyant jet at low Froude number

2011 ◽  
Vol 15 (1) ◽  
pp. 67-75 ◽  
Author(s):  
T. Maeda ◽  
N. Fujisawa ◽  
T. Syuto ◽  
T. Yamagata
Keyword(s):  
Froude Number ◽  
Numerical Study ◽  
Near Field ◽  
Buoyant Jet ◽  
Low Froude Number

Numerical study on near-field characteristics of landslide-generated impulse waves in channel reservoirs

2021 ◽  
Vol 595 ◽  
pp. 126012
Author(s):  
Xiaoliang Wang ◽  
Chuanqi Shi ◽  
Qingquan Liu ◽  
Yi An
Keyword(s):  
Numerical Study ◽  
Near Field ◽  
Impulse Waves

A Two-Region Model for Gradient Modification of Salt-Gradient Solar Ponds by Radial Injection

1996 ◽  
Vol 118 (1) ◽  
pp. 37-44 ◽  
Author(s):  
G. A. Eghneim ◽  
S. J. Kleis
Keyword(s):  
Turbulence Model ◽  
Field Model ◽  
Numerical Study ◽  
Numerical Models ◽  
Domain Boundary ◽  
Near Field ◽  
Solar Ponds ◽  
Numerical Predictions ◽  
Region Model ◽  
Salt Gradient

A combined experimental and numerical study was conducted to support the development of a new gradient maintenance technique for salt-gradient solar ponds. Two numerical models were developed and verified by laboratory experiments. The first is an axisymmetric (near-field) model which determines mixing and entrainment in the near-field of the injecting diffuser by solving the conservation equations of mass, momentum, energy, and salt. The model assumes variable properties and uses a simple turbulence model based on the mixing length hypothesis to account for the turbulence effects. A series of experimental measurements were conducted in the laboratory for the initial adjustment of the turbulence model and verification of the code. The second model is a one-dimensional far-field model which determines the change of the salt distribution in the pond gradient zone as a result of injection by coupling the near-field injection conditions to the pond geometry. This is implemented by distributing the volume fluxes obtained at the domain boundary of the near-field model, to the gradient layers of the same densities. The numerical predictions obtained by the two-region model was found to be in reasonable agreement with the experimental data.

scholarly journals HARBOUR DESIGN INCLUDING SEDIMENTOLOGICAL PROBLEMS USING MAINLY NUMERICAL TECHNICS

1980 ◽  
Vol 1 (17) ◽  
pp. 132 ◽  
Author(s):  
B. Latteux
Keyword(s):  
Continuity Equation ◽  
Numerical Study ◽  
Numerical Models ◽  
Near Field ◽  
Step Method ◽  
Access Channel ◽  
Load Transport ◽  
Erosion Area ◽  
Bed Load Transport ◽  
Water Height

For most of the needed studies for the design of Calais harbour enlargement works, the "Laooratoire National d'Hydraulique" chose to use numerical models. This approach includes the determination of currents around and insiae the new outer-haroour, just as the evaluation of the project sedimentologic impact and of the long-term evolution of a bank nameo "le Riaen de ia Rade", edging the access channel. Current studies were performed using four nested bidimensionnal computer models fitted on field data and supplying in eac;i point the depth-averaged velocity and the total water height. These four models are based on an implicite finite difference fractionnal step method. Besides for the very near field model the method is especially elaborated to enable' the detailed reproduction of eddies and flow separations. The sedimentological numerical study is based upon current models results : the bed-load transport is computed from the depth-averaged velocity and the water height previously determined using an empirical formula, and tne continuity equation applied to this loaa transport gives then the bed evolution. As soon as the depth variation is significant enough to react on the flow pattern, current fielos are readjusted oy a simple metnod based on flow continuity equation. This numerical model, applied to the near fielo, has given an evaluation of the sedimentological impact of the haroour enlargement project : - strong erosion in front of the new harbour due to current strengthening ; - accretion on each side of this erosion area, especially in the channel ; - bar formation at the harbour entrance.

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