Near Field Expression of Ship Wave Resistance by Yeung’s Method

Volume 7A: Ocean Engineering ◽

10.1115/omae2017-61199 ◽

2017 ◽

Author(s):

Takashi Tsubogo

Keyword(s):

Green Function ◽

Boundary Value Problem ◽

Water Pressure ◽

Near Field ◽

Field Method ◽

Wave Resistance ◽

Alternative Methods ◽

Far Field ◽

Ship Wave ◽

Direct Pressure

The ship wave resistance can be evaluated by two alternative methods after solving the boundary value problem. One is the far field method e.g. Havelock’s formula, and another is the near field method based on direct pressure integration over the wetted hull surface. As is well known, there exist considerable discrepancies between wave resistance results by far field method and by near field method. This paper presents a Lagally expression in consistency with Havelock’s formula. In order to derive the Lagally expression, the symmetry of Havelock’s Green function is used in the same manner as Yeung et al (2004). Another expression to examine the relation with water pressure integrations or to ensure physical consistency is also derived by slightly deforming that expression. Some numerical comparisons of wave resistance of Wigley, KCS and KVLCC2 models among by Havelock’s formula, some direct pressure integration methods and present two new near field expressions, are shown to demonstrate consistency numerically.

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

Volume 7: Ocean Engineering ◽

10.1115/omae2016-54896 ◽

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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Comparison of ultralow-sidelobe-antenna far-field patterns using the planar-near-field method and the far-field method

IEEE Antennas and Propagation Magazine ◽

10.1109/74.482028 ◽

1995 ◽

Vol 37 (6) ◽

pp. 7-15 ◽

Cited By ~ 3

Author(s):

M.H. Francis ◽

A.C. Newell ◽

K.R. Grimm ◽

J. Hoffman ◽

H.E. Schrank

Keyword(s):

Near Field ◽

Field Method ◽

Far Field ◽

Field Patterns

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Far-Field Performances Prediction of High Frequency Projectors Using Secondary Source Array Method

Journal of Computational Acoustics ◽

10.1142/s0218396x17500023 ◽

2016 ◽

Vol 25 (02) ◽

pp. 1750002 ◽

Cited By ~ 1

Author(s):

Shiquan Wang

Keyword(s):

High Frequency ◽

Near Field ◽

Directivity Pattern ◽

Field Method ◽

Voltage Response ◽

Secondary Source ◽

Far Field ◽

Comparison Of The Results ◽

Source Array ◽

Good Agreement

This paper investigates the prediction of the far-field performances of high frequency projectors using the second source array method (SSAM). The far-field parameters can be calculated accurately using the complex acoustic pressure data of two very close parallel planes which lie in the near-field region of the projector. The paper simulates the feasibility of predicting the far-field parameters such as transmitting voltage response and the far-field directivity pattern. The predicting results are compared with that calculated using boundary element method (BEM). It shows very good agreement between the two methods. A planar high frequency projector is measured using the near-field method. In order to verify the predicting results, the far-field measurement is performed for the same projector. The comparison of the results shows that the near-field method is capable to precisely predict the far-field parameters of the projector.

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Lifting three-dimensional wings in transonic flow

Journal of Fluid Mechanics ◽

10.1017/s0022112079001440 ◽

1979 ◽

Vol 95 (2) ◽

pp. 223-240 ◽

Cited By ~ 7

Author(s):

M. S. Cramer

Keyword(s):

Boundary Value Problem ◽

Asymptotic Expansions ◽

Transonic Flow ◽

Near Field ◽

Boundary Value ◽

Three Dimensional ◽

Matched Asymptotic Expansions ◽

Far Field ◽

First Order ◽

Order Contribution

The far field of a lifting three-dimensional wing in transonic flow is analysed. The boundary-value problem governing the flow far from the wing is derived by the method of matched asymptotic expansions. The main result is to show that corrections which are second order in the near field make a first-order contribution to the far field. The present study corrects and simplifies the work of Cheng & Hafez (1975) and Barnwell (1975).

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Far-field drag decomposition using hybrid formulas and vorticity based area sensors

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1177/0954410020973904 ◽

2020 ◽

pp. 095441002097390

Author(s):

L Qiao ◽

XL He ◽

Y Sun ◽

JQ Bai ◽

L Li

Keyword(s):

Flow Field ◽

Axial Velocity ◽

Near Field ◽

Three Dimensional ◽

Field Method ◽

Wave Drag ◽

Viscous Drag ◽

Far Field ◽

Velocity Defect ◽

Detection Failure

Numerical simulation of flow-field has become an indispensable tool for aerodynamic design. Usually, wall surface integration is a tool used to calculate values of pressure drag and skin friction drag, but the aerodynamic mechanism of drag production is still confusing. In present work, in order to decompose the total drag into viscous drag, wave drag, induced drag, and spurious drag, a far-field drag decomposition (FDD) method is developed. This method depends on axial velocity defect and area sensor functions. The present work proposes three hybrid formulas for velocity defect to tackle the negative square root issue by analyzing the existing axial velocity defect formulas. For dealing with the issue of detection failure for near-wall cells, a novel vorticity based viscous area sensor function is proposed. The new area sensor function is also independent of the turbulence model, which ensures easy application to general simulation methods for flow-field. Three tests cases are there to validate the proposed FDD method. The three dimensional transonic CRM test case shows that the present improvement is crucial for accurate drag decomposition. Excellent agreement between total decomposed drags and results from the near-field method or experimental data further confirms the correctness.

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

Journal of Engineering Mathematics ◽

10.1007/bf00042923 ◽

1981 ◽

Vol 15 (4) ◽

pp. 241-265 ◽

Cited By ~ 43

Author(s):

F. Noblesse

Keyword(s):

Green Function ◽

Wave Resistance ◽

Integral Representations ◽

Ship Wave ◽

The Green Function

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Local Enhancements of the Mean Drift Wave Force on a Vertical Column Shielded by an Exterior Thin Porous Shell

Journal of Marine Science and Engineering ◽

10.3390/jmse8050349 ◽

2020 ◽

Vol 8 (5) ◽

pp. 349 ◽

Cited By ~ 1

Author(s):

Peiwen Cong ◽

Yingyi Liu

Keyword(s):

Near Field ◽

Wave Interaction ◽

Wave Force ◽

Momentum Conservation ◽

Far Field ◽

Vertical Column ◽

Porous Shell ◽

Drift Wave ◽

Direct Pressure ◽

The Mean

The wave interaction with a vertical column shielded by an exterior porous shell is studied within the framework of potential flow theory. The structures are fixed rigidly at the sea bottom. The interior cylinder is impermeable, and the exterior shell is slightly porous and thin. Additionally, the exterior shell is assumed to have fine pores, and a linear pressure drop is adopted at the porous geometry. The mean drift wave force on the system is thereby formulated by two alternative ways, based respectively on the direct pressure integration, i.e., the near-field formulation, and the application of the momentum conservation theorem in the fluid domain, i.e., the far-field formulation. The consistency of the two formulations in calculating the mean drift wave force is assessed for the present problem. Numerical results illustrate that the existence of the porous shell can substantially reduce the mean drift wave force on the interior column. It also appears that the far-field formulation consists of a conventional part as well as an additional part caused by the energy dissipation through the porous geometry. The mean drift wave force on the system is dominated by the first part, which resembles that on an impermeable body. Local enhancements of the mean drift wave force are found at some specific wave frequencies at which certain propagation modes of the fluid satisfy a no-flow condition at the porous shell.

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On the theory of the Kelvin ship-wave source: the near-field convergent expansion of an integral

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1990.0023 ◽

1990 ◽

Vol 428 (1874) ◽

pp. 15-26

Keyword(s):

Velocity Potential ◽

Near Field ◽

Wave Resistance ◽

Parabolic Cylinder ◽

Wave Source ◽

Integral Term ◽

Ship Wave ◽

Convergent Expansion ◽

Parabolic Cylinder Functions ◽

Three Term Recurrence Relation

The velocity potential of the Kelvin ship-wave source is fundamental in the mathematical theory of the wave resistance of ships, but is difficult to evaluate numerically. We shall be concerned with the integral term F ( x, ρ, ∝ ) = ∫ ∞ -∞ exp {— 1/2 ρ cosh (2 u — i ∝ )} cos ( x cosh u )d u in the source potential, where x and ρ are positive and —1/2 π ≼ ∝ ≼ 1/2 π , which is difficult to evaluate when x and ρ are small. It will be shown here that F ( x, ρ, ∝ ) = 1/2ƒ( x, ρ, ∝ ) + 1/2ƒ( x, ρ, ─∝ ) + 1/2ƒ( ─x , ρ, ∝ ) + ½ƒ( ─x, ρ, ─∝ ), where ƒ( x, ρ, ∝ ) = P 0 ( x, ρ e -i ∝ ) Σ g m ( x, ρ e i ∝ ) c m ( x, ρ e -i ∝ ) + P 1 ( x, ρ e -i ∝ ) Σ g m ( x, ρ e i ∝ ) b m ( x, ρ e -i ∝ ) + Σ g m ( x, ρ e i ∝ ) a m ( x, ρ e -i ∝ ) In this expression each of the functions g m ( x, ρ e i ∝ ), a m ( x, ρ e -i ∝ ), b m ( x, ρ e -i ∝ ), c m ( x, ρ e -i ∝ ), satisfies a simple three-term recurrence relation and tends rapidly to 0 for small x and ρ when m → ∞, and the functions P 0 ( x, ρ e -i ∝ ) and P 1 ( x, ρ e i ∝ ) are simply related to the parabolic cylinder functions D v (ζ) respectively, where ζ = — i x (2 ρ ) -1/2 e 1/2 i ∝ .

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