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.

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.

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.

scholarly journals Influence of the transom immersion to ship resistance components at low and medium speeds

2020 ◽  
Vol 17 (2) ◽  
pp. 165-182
Author(s):  
I. Z. Mustaffa Kamal ◽  
A. Imran Ismail ◽  
M. Naim Abdullah ◽  
Y. Adnan Ahmed
Keyword(s):  
Froude Number ◽  
Wave Resistance ◽  
Hull Form ◽  
Ship Resistance ◽  
Resistance Components ◽  
Ranse Solver

The transom stern offered some advantages over the traditional rounded cruiser stern reducing the resistance of a ship. This can only be achieved if the transom stern is carefully designed with suitable transom immersion ratio. In this study, the influence of different transom area immersion ratios on the resistance components was investigated for a semi-displacement hull and a full displacement hull.  The base hull was based on NPL hull form and KCS hull form for a semi-displacement and full-displacement hull respectively. The transom immersion ratios for the NPL hull were varied at a ratio of 0.5, 0.7, 0.8 and 1.0.  The resistance of each of the NPL hull form was simulated at Froude number 0.3 up to 0.6. The transom immersion ratios for the KCS hull were varied at a ratio of 0.05, 0.1, 0.15 and 0.3. The resistance of each of the KCS hull form was simulated at Froude number 0.195, 0.23, 0.26 and 0.28.  The transoms of both hulls were modified or varied systematically to study the influence of the transom shape or immersion on the total and wave resistance components. The investigation was carried out using a CFD software named SHIPFLOW 6.3 based on RANSE solver. These results on the NPL hull shows that the larger the transom immersion, the higher the resistance will be for a semi-displacement vessel. The increased resistance is contributed by additional frictional and wave resistance components. The results for the KCS hull seems to contradict with the results obtained from the NPL hull. The larger and deeper transom for the case of KCS hull form sometimes can be beneficial at higher Froude number.

Reduction of Wave Resistance of Displacement Vessels by Waterline Parabolization

2009 ◽  
Author(s):  
S. M. Çalisal ◽  
D. B. Danisman ◽  
Ö. Gören ◽  
K. Gould ◽  
P. Maurice ◽  
...  
Keyword(s):  
Froude Number ◽  
Optimization Algorithm ◽  
Optimization Technique ◽  
Wave Resistance ◽  
Optimum Shape ◽  
Total Resistance ◽  
Hull Form ◽  
University Of British Columbia ◽  
Constant Displacement ◽  
The University

Waterline parabolization is a method to reduce the wave resistance of a displacement type hull with a parallel mid-body by adding amidships bulbs to the hull. Tow tank tests of the optimized bulbs at ITU confirmed that significant reductions in total resistance were obtained. This paper describes the use of a nonlinear optimization technique developed at the University of British Columbia (UBC) and tank testing at Istanbul Technical University (ITU) to find the optimum shape and location of midship bulbs as well as midship bulbs and a bow bulb together. Tow-tank tests at UBC and ITU have shown that mid-ship bulbs can provide significant reductions in total resistance. The study validated the use of the technique both constraining the displacement and when only constraining the draft (retrofit). The optimization algorithm considers only wave resistance which is calculated with a Dawson's method type program; TRAWSON. In this study a RO/RO ferry hull is used as the baseline hull form. The tank tests revealed that the bulb location and geometry identified as the optimum, at Froude number Fn = 0.33, by the optimization program achieved a reduction in total resistance of 15 percent at constant displacement and retrofit applications.

Computation of Wave-Body Interactions Using the Panel-Free Method and Exact Geometry

2006 ◽  
Vol 128 (1) ◽  
pp. 31-38 ◽  
Author(s):  
W. Qiu ◽  
H. Peng ◽  
J. M. Chuang
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Body Surface ◽  
Analytical Description ◽  
Finite Depth ◽  
Boundary Integral ◽  
The Body ◽  
Floating Bodies ◽  
Wigley Hull ◽  
The Time Domain

A panel-free method was developed earlier to solve the radiation and the diffraction problems of floating bodies in waves in the time domain. This method has been extended to compute wave interactions with bodies in water of infinite depth and finite depth in the frequency domain. After removing the singularities in the boundary integral equation and representing the body surface exactly by either analytical description or NURBS surfaces, the boundary integral equation can be discretized over the exact body surface by Gaussian quadratures. Accuracy of the method is demonstrated by its application to the radiation and the diffraction problems of a floating hemisphere, a vertically floating axisymmetric cylinder, and a Wigley hull. Computed added-mass, damping coefficients, and wave exciting forces agree well with published results.

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.

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.

Near Field Expression of Ship Wave Resistance by Green’s Theorem

2016 ◽  
Author(s):  
Takashi Tsubogo
Keyword(s):  
Integral Equation ◽  
Near Field ◽  
Field Method ◽  
Momentum Conservation ◽  
Wave Resistance ◽  
Boundary Integral ◽  
Far Field ◽  
Ship Wave ◽  
Direct Pressure ◽  
Run Up

The ship wave resistance can be estimated by two alternative methods after solving the boundary integral equation. One is the far field method e.g. Havelock’s formula based on momentum conservation in fluid domain, and another is the near field method based on direct pressure integration over the wetted body surface. Nakos and Sclavounos (1994) had shown a new near field expression of ship wave resistance from the momentum conservation law in the fluid domain with linearized free surface condition. Their new expression differs slightly from the traditional near field form. This problem of near field expression is reconsidered in terms of Green’s second identity. After linearization of the free suface condition and some transformation of equations, the present paper will agree with the Nakos and Sclavounos’ near field expression for the ship wave resistance. Some numerical calculations of wave resistance from the far field method and from the near field method are shown using the classical Kelvin sources distributed on the centerplane of thin ship but solving the different boundary integral equation. Numerical results suggest that the problematic run-up square integration along the waterline is to be omitted as a higher order small quantity. If this run-up term is omitted in each method except for far field, the traditional direct pressure integrtaion is equal to the Nakos and Sclavounos’ near field expression.

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