The Wave and Induced Drag of a Hydrofoil of Finite Span in Water of Limited Depth

1961 ◽  
Vol 5 (03) ◽  
pp. 15-21
Author(s):  
J. P. Breslin
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Finite Depth ◽  
Wave Resistance ◽  
Finite Span ◽  
Induced Drag ◽  
Special Cases ◽  
The Waves ◽  
Limited Depth ◽  
Good Agreement

The wave resistance and the induced drag of a simple hydrofoil of finite span moving at a fixed submergence in water of finite depth are derived from a knowledge of the shallow water potential of a source. From this the waves produced by the semi-infinite doublet sheet which represents the undisturbed mathematical model of the hydrofoil are computed and the wave resistance is then inferred from the formula for the waves. Special cases which have been published previously are recaptured from the formulas. The induced drag is computed from a knowledge of the nature of the potential functions needed to satisfy the boundary conditions on the bottom and free surface. A comparison with one set of experimental data shows the theory to underestimate the experimentally determined lift-dependent drag curve at low Froude numbers F and to agree very well as high F. It is conjectured that the lack of good agreement at low F is due to the neglect of the influence of the free surface on the lift which has been omitted in this analysis.

Application of Ship-Wave Theory to the Hydrofoil of Finite Span

1957 ◽  
Vol 1 (02) ◽  
pp. 27-55
Author(s):  
John P. Breslin
Keyword(s):  
Wave Theory ◽  
Wave Pattern ◽  
Wave Drag ◽  
Test Results ◽  
Dimensional Theory ◽  
Ship Hydrodynamics ◽  
Finite Span ◽  
Induced Drag ◽  
Load Distributions ◽  
The Waves

It is demonstrated in this paper2 that the deepwater wave drag of a hydrofoil of finite span can be found directly from the theory developed largely for ship hydrodynamics by Havelock and others. The wave drag is then studied at high Froude numbers and from the observed behavior the induced drag of the hydrofoil can be deduced from existing aerodynamic formulas. Evaluation of the resulting formulas is effected for two arbitrary load distributions and a comparison with some model test results is made. A practical approximation which gives the influence of gravity over a range of high Froude numbers is found and from this one can deduce a Froude number beyond which the effects of gravity may be ignored. It is also shown that an expression for the waves at some distance aft of the hydrofoil can be deduced from the general formulas developed for ship hydrodynamics. A discussion of the wave pattern is given with particular emphasis on the centerline profile at high Froude numbers and a contrast is pointed out in regard to the results of the two-dimensional theory for the hydrofoil waves and wave resistance.

The translation of two bodies under the free surface of a heavy fluid

1950 ◽  
Vol 46 (3) ◽  
pp. 453-468 ◽  
Author(s):  
A. Coombs
Keyword(s):  
Free Surface ◽  
Large Range ◽  
Three Dimensional ◽  
Finite Depth ◽  
Arbitrary Cross Section ◽  
Wave Resistance ◽  
Vertical Force ◽  
First Approximation ◽  
Special Case ◽  
Two Bodies

1. Many investigations have been made to determine the wave resistance acting on a body moving horizontally and uniformly in a heavy, perfect fluid. Lamb obtained a first approximation for the wave resistance on a long circular cylinder, and this was later confirmed to be quite sufficient over a large range. In 1926 and 1928, Havelock (4, 5) obtained a second approximation for the wave resistance and a first approximation for the vertical force or lift. Later, in 1936(6), he gave a complete analytical solution to this problem, in which the forces were expressed in the form of infinite series in powers of the ratio of the radius of the cylinder to the depth of the centre below the free surface of the fluid. General expressions for the wave resistance and lift of a cylinder of arbitrary cross-section were found by Kotchin (7) using integral equations, and the special case of a flat plate was evaluated. He continued with a discussion of the motion of a three-dimensional body. More recently, Haskind (3) has examined the same problem when the stream has a finite depth.

On the swimming of a flexible plate of arbitrary finite thickness

1964 ◽  
Vol 20 (1) ◽  
pp. 1-33 ◽  
Author(s):  
J. P. Uldrick ◽  
J. Siekmann
Keyword(s):  
Experimental Data ◽  
Finite Thickness ◽  
Numerical Calculations ◽  
Flexible Plate ◽  
Two Dimensional ◽  
Present Contribution ◽  
Fish Propulsion ◽  
Special Cases ◽  
Good Agreement

This paper studies the effect of profile thickness on the propulsive forces generated by the swimming of a two-dimensional fish. Comparison of numerical calculations with reported experimental data shows good agreement and demonstrates a decrease of thrust with increasing thickness. Previous two-dimensional linearized theories on fish propulsion dealing with the motion of an infinitesimally thin hydrofoil are included in the present contribution as special cases.

Stress-Strain Relation in Rubber Blocks under Compression. I

1959 ◽  
Vol 32 (2) ◽  
pp. 409-419
Author(s):  
Géza Schay ◽  
Péter Ször
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Cross Section ◽  
Experimental Error ◽  
Stress Strain ◽  
General Applicability ◽  
Empirical Constant ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Good Agreement

Abstract For the stress-strain relation of differently shaped rubber blocks submitted to compression, an equation of general applicability is deduced, starting from the idea that compression work must be done also against the tension arising through the increase of the free surface. In this equation the stress is not a function of the compression ratio only, but of the ratio of the fixed to the free surface as well. Besides the shear modulus of the block's substance, this equation involves a single empirical constant which changes only slightly with the shape of the block's cross section. The validity of the equation obtained was tested by measurements performed by the authors on cylinders as well as by data on quadratic prisms published in previous literature. The calculated values are in good agreement with the experimental data within the limits of experimental error.

Blockage with a Free Surface

1976 ◽  
Vol 20 (04) ◽  
pp. 199-203
Author(s):  
J. N. Newman
Keyword(s):  
Free Surface ◽  
Velocity Potential ◽  
Finite Depth ◽  
Wave Resistance ◽  
Steady Flows ◽  
Two Dimensional ◽  
Present Context ◽  
Two Dimensional Flow ◽  
Field Radiation ◽  
Radiation Conditions

The occurrence of blockage, or a jump in the velocity potential between the upstream and downstream infinities, is well known for steady two-dimensional flow past a body in a rigid channel. This paper considers the analogous situation where there is a free surface, as in the wave resistance problem for submerged two-dimensional bodies in a fluid of finite depth. It is shown that blockage occurs in spite of the free surface, taking values which depend not only on the dipole moment but also upon the Froude number based on depth. The occurrence of blockage, in the present context, has a bearing primarily upon the correct formulation of far-field radiation conditions for steady flows with finite depth.

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.

Determination of nonlinear forces of the second order arising from the interaction of waves and certain types of ship’s motions

2021 ◽  
pp. 21-30
Author(s):  
В.Ю. Семенова ◽  
Д.А. Альбаев
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Second Order ◽  
Complete Agreement ◽  
Interaction Of Waves ◽  
Diffracted Waves ◽  
Definition Of ◽  
Limited Depth ◽  
Good Agreement

В статье рассматривается определение нелинейных сил второго порядка, обусловленных взаимодействием набегающего, дифрагированного волнения и волнения, обусловленного различными видами колебаний на основании применения трехмерной потенциальной теории. Для их определения необходимо вычисление потенциалов второго порядка малости. Представленное решение в отечественной практике является новым. Решение задачи осуществляется на основании методов малого параметра и интегральных уравнений с учетом нелинейного граничного условия на свободной поверхностью жидкости. В работе расчет интегралов по свободной поверхности проводится напрямую за счет их сходимости на бесконечном удалении от судна. Нелинейные силы и моменты определяются в работе с использованием различных функций Грина: для бесконечно-глубокой жидкости и жидкости ограниченной глубины, когда . Полученные результаты практически полностью согласуются между собой. Приводятся результаты расчетов нелинейных сил и моментов для разных судов. Расчеты представлены в сравнении с расчетами по двумерной теории, выполненными также для случая бесконечно глубокой жидкости и жидкости ограниченной глубины при больших значениях отношения глубины к осадке H/T. Показано хорошее согласование результатов между собой в большинстве случаев. Показана возможность расчета нелинейных сил, возникающих при взаимодействии волнения и отдельных видов качки на произвольных курсовых углах. The article considers the definition of nonlinear second-order forces caused by the interaction of incoming, diffracted waves and waves caused by various types of motions based on the application of three-dimensional potential theory. To determine them, it is necessary to calculate the potentials of the second order of smallness. The presented solution is new in domestic practice. The problem is solved on the basis of small parameter methods and integral equations taking into account the nonlinear boundary condition on the free surface of the liquid. The paper shows the possibility of calculating the integrals over the free surface directly due to their convergence at an infinite distance from the ship. Nonlinear forces and moments are determined in the work using various Green's functions: for an infinitely deep fluid and a fluid of limited depth when H → ∞. The results obtained are in almost complete agreement with each other. The results of calculations of nonlinear forces and moments for different ships are presented. The calculations are presented in comparison with the calculations according to the two-dimensional theory, performed also for the case of an infinitely deep liquid and a liquid of limited depth at large values of ratio H / T. A good agreement of the results is shown among themselves in most cases. The possibility of calculating nonlinear forces arising from the interaction of waves and certain types of motions at arbitrary course angles is shown.

scholarly journals Pulsation of Ventilated Cavities

1962 ◽  
Vol 6 (01) ◽  
pp. 8-20 ◽  
Author(s):  
C. S. Song
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Artificial Ventilation ◽  
Liquid System ◽  
Resonance Problem ◽  
Two Dimensional ◽  
Substantial Portion ◽  
Open Sea ◽  
Good Agreement ◽  
Undetermined Constant

The problem of pulsating supercavities under artificial ventilation is analytically treated as a resonance problem of a two-dimensional gas-liquid system using a linearized method. A simple kinematical consideration and a dynamical model of the flow lead to solutions for frequency and amplitude of pulsations. The criteria of pulsation are given in terms of a formula relating σv. and σ Maximum air-carrying capacities of pulsating cavities are also estimated. Most of the formulas involve an undetermined constant which must be estimated by using experimental data. The analytical results are compared with the experimental data obtained at the St. Anthony Falls Hydraulic Laboratory, and, in general, good agreement is obtained. It is found that pulsation is possible only for a two-dimensional cavity or a cavity in which a substantial portion of the span can be regarded as two-dimensional. The existence of a free surface is also essential to pulsation. The strong effect of the free surface suggests that pulsation may become an important problem in the open sea only when submergence is relatively small.

scholarly journals The Determination of nonlinear second-order diffraction forces acting on a ship based on three-dimensional theory

2021 ◽  
pp. 20-27
Author(s):  
В.Ю. Семенова ◽  
Д.А. Альбаев
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Second Order ◽  
Complete Agreement ◽  
Dimensional Theory ◽  
Nonlinear Diffraction ◽  
Definition Of ◽  
Limited Depth ◽  
Good Agreement

В статье рассматривается определение нелинейных дифракционных сил второго порядка, на основании применения трехмерной потенциальной теории. Для их определения необходимо вычисление потенциалов второго порядка малости. Представленное решение в отечественной практике является новым. Решение задачи осуществляется на основании методов малого параметра и интегральных уравнений с учетом нелинейного граничного условия на свободной поверхностью жидкости. В работе показана возможность расчета интегралов по свободной поверхности напрямую за счет их сходимости на бесконечном удалении от судна. Нелинейные дифракционные силы и моменты определяются в работе с использованием различных функций Грина: для бесконечно-глубокой жидкости и жидкости ограниченной глубины, когда H→∞. Полученные результаты практически полностью согласуются между собой. Приводятся результаты расчетов дифракционных сил и моментов для четырех разных судов. Расчеты представлены в сравнении с расчетами по двумерной теории, выполненными также для случая бесконечно глубокой жидкости и жидкости ограниченной глубины при больших значениях отношения глубины к осадке H/T. Показано хорошее согласование результатов между собой. Показана возможность расчета нелинейных дифракционных сил на произвольных курсовых углах. The article discusses the definition of nonlinear diffraction forces of the second order, based on the application of three-dimensional potential theory. To determine them, it is necessary to calculate the potentials of the second order of smallness. The presented solution is new in domestic practice. The problem is solved on the basis of small parameter methods and integral equations taking into account the nonlinear boundary condition on the free surface of the liquid. The paper shows the possibility of calculating the integrals over the free surface directly due to their convergence at an infinite distance from the ship. Nonlinear diffraction forces and moments are determined in the work using various Green's functions: for an infinitely deep fluid and a fluid of limited depth when H → ∞. The results obtained are in almost complete agreement with each other. The results of calculations of diffraction forces and moments for four different ships are presented. The calculations are presented in comparison with the calculations according to the two-dimensional theory, performed also for the case of an infinitely deep liquid and a liquid of limited depth at large values of ratio H / T. Good agreement of the results with each other is shown. The possibility of calculating nonlinear diffraction forces at arbitrary heading angles is shown.

Spilling breakers in shallow water: applications to Favre waves and to the shoaling and breaking of solitary waves

2016 ◽  
Vol 808 ◽  
pp. 441-468 ◽  
Author(s):  
S. L. Gavrilyuk ◽  
V. Yu. Liapidevskii ◽  
A. A. Chesnokov
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Shallow Water ◽  
Froude Number ◽  
Fluid Velocity ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Undular Bore ◽  
Characteristic Wavelength ◽  
Good Agreement

A two-layer long-wave approximation of the homogeneous Euler equations for a free-surface flow evolving over mild slopes is derived. The upper layer is turbulent and is described by depth-averaged equations for the layer thickness, average fluid velocity and fluid turbulent energy. The lower layer is almost potential and can be described by Serre–Su–Gardner–Green–Naghdi equations (a second-order shallow water approximation with respect to the parameter $H/L$, where $H$ is a characteristic water depth and $L$ is a characteristic wavelength). A simple model for vertical turbulent mixing is proposed governing the interaction between these layers. Stationary supercritical solutions to this model are first constructed, containing, in particular, a local turbulent subcritical zone at the forward slope of the wave. The non-stationary model was then numerically solved and compared with experimental data for the following two problems. The first one is the study of surface waves resulting from the interaction of a uniform free-surface flow with an immobile wall (the water hammer problem with a free surface). These waves are sometimes called ‘Favre waves’ in homage to Henry Favre and his contribution to the study of this phenomenon. When the Froude number is between 1 and approximately 1.3, an undular bore appears. The characteristics of the leading wave in an undular bore are in good agreement with experimental data by Favre (Ondes de Translation dans les Canaux Découverts, 1935, Dunod) and Treske (J. Hydraul Res., vol. 32 (3), 1994, pp. 355–370). When the Froude number is between 1.3 and 1.4, the transition from an undular bore to a breaking (monotone) bore occurs. The shoaling and breaking of a solitary wave propagating in a long channel (300 m) of mild slope (1/60) was then studied. Good agreement with experimental data by Hsiao et al. (Coast. Engng, vol. 55, 2008, pp. 975–988) for the wave profile evolution was found.

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