Bilge Keels Research Articles

Computation of springing transfer functions

Ship vibrations excited continually by regular waves are predicted by a potential method. It takes into account the interaction of the oscillatory flow with the steady flow due to the ship's forward speed, including steady ship waves and squat, but it excludes non-linear oscillatory wave forces. A three-dimensional Rankine source patch method is used both for the steady and the oscillatory flow. Vibration damping by an immersed transom, wave radiation, bilge keels, propeller, and hatch cover friction are approximated. Application to a large containership demonstrates that, in this example, damping is mostly attributable to the transom.

The roll damping assessment via decay model testing (new ideas about an old subject)

The methodology to obtain the non-linear roll damping from decay tests is very old. It has been proposed by Froude in the 19th century and used from then on. Behind it there is a quadratic model $$ [\dot \theta |\dot \theta |] $$ for the damping and a subsequent equivalent linearization. Probably all model basin in the world follows this approach to assess the damping from a decay test. This is well documented and so is the methods to get the p 1−p 2 coefficients. This is very general in the sense that in principle, it could be applied to any kind of hull. However, it has become clear that for hull with a flat bottom such as a very large crude carrier (VLCC), this approach may lead to confusing results such as negative p 2. Faced with this, the work presents a completely new idea. Avoiding the polynomial approximation, the basic attitude is to devise two regions from the decaying test response. The first, called the large amplitude response region yields a larger damping, probably due to the large bilge keel vortices that are attracted to the hull flat bottom. The second is the small amplitude response region where the vortices are not attracted to the bottom but travels approximately 45° sidewise. These observations has led to a new approach called the bi-linear approach as discussed in the work after analyzing several (many) model test results. In fact, a new modified bi-linear approach is ultimately proposed after the understanding of a transition region instead of a transition angle.

漁船の舵防食板に関する研究（第１報） ‐ 舵の抗力および揚力に及ぼす作用 ‐

price of fuel, in order to keep and improve the management of fishing. As for the balance of income from fishing, the technology of the saving energy should be achieved by low cost and it is desirable to be adopted not only new vessels but also existing vessels.There are usually anode protections on a ship hull, bilge keels and a rudder to protect them from electric reactions from a propeller and seawater. The rudder is behind the propeller, and the inflow velocity of rudder becomes large. On a rudder, small objects like anode protections would increase resistance and reduce the lift force. The authors researched the situation of anode protections on approximately twenty Japanese fishing vessels. It is clear that the arrangement is various and there is no single confirmed way though the front positions on a rudder would be effective for the prevention from electric reactions. This study reports the hydrodynamic characteristics of a rudder with anode protections and the influence to the propulsion and the maneuvering performance of a ship. And appropriate positions of anode protections on a rudder for the energy saving are considered.This first paper reports the drag and lift characteristics of a rudder with anode protections at different cord length from leading edge and at different directions against the flow having different thickness or conditions. By model experiments in the uniformed flow and in the flow behind a propeller, this paper concludes that anode protections become resistance and reduce the lift force. And the front positions, the positions against the flow and large thickness increase the drag force and reduce the lift force. In the next paper, the detail influence to the propulsion and maneuvering performance of a ship will be reported.

Roll Motion of a Ship and the Roll Stabilising Effect of Bilge Keels

The roll motion of a ship on waves is one of the six degrees of freedom and is the most difficult to predict since it deals with a motion similar to a spring-mass damper system, poorly damped by ship generated waves, in addition to the action of waves from the high seas. This problem increased from the second half of the 19th century when sailing propulsion was replaced by steam machines and iron replaced wood, which led to design modifications in ships affecting transversal stability, with the result of an increment in the ship's roll motion. As a consequence, it has been necessary to develop different systems which, on the one hand, increase the natural period of this motion in order to decrease its amplitude and reduce the risks that the wave encounter frequency would resonate with the natural frequency of the ship's motion; and on the other hand, to generate a damping effect to this motion. Bilge keels, passive stabilisers with no moving parts, form the simplest and cheapest element that may be incorporated on a ship to reduce this motion. This paper studies roll motion in general and then analyses bilge keels from different points of view.

Modeling nonlinear roll damping with a self-consistent, strongly nonlinear ship motion model

Appropriate modeling of roll damping is one of the key issues in accurately predicting ship roll motion. The difficulties in modeling roll damping arise from the nonlinear nature of the phenomena. In this study, we report a new effort in modeling the bilge keel roll damping effect based on the blocking mechanisms of an object in the potential flow. This effect can be implemented as a component of appropriate ship motion models. We used our digital, self-consistent, ship experimental laboratory (DiSSEL) ship motion model to test its effectiveness in predicting ship roll motion. Our numerical experiment demonstrated clearly that the implementation of this roll damping component improves significantly the accuracy of numerical model results (the results were compared with ship experiment data from the Naval Surface Warfare Center, Carderock Division, Maneuvering and Seakeeping Facility).

비정상 RANS 법과 중첩격자계를 이용한 횡파중 선박운동 수치해석

The present paper presents the CFD result for a beam wave test case. An ONR tumblehome ship model with bilge keels is used. The beam wave test is for zero forward speed and roll and heave 2DOF with wave slope <TEX>$a_k=0.156$</TEX> and wavelength <TEX>${\lambda}=1.12L_{PP}$</TEX>, with <TEX>$L_{PP}$</TEX> the ship length. The problems is solved numerically with an unsteady Reynolds averaged Navier-Stokes approach. The free surface flow is computed using a single-phase level-set method and the motions in each time step are integrated using a predictor-corrector iteration approach which uses dynamic overset grids moving with relative ship motion. The predicted CFD results for motions and forces are compared with experimental data, showing a reasonable agreement.

Application of a vortex tracking method to the piston-like behaviour in a semi-entrained vertical gap

Near resonance the piston mode amplitude in semi-entrained volumes of fluid such as in moonpools or in between a ship and a terminal may become large relative to the level of excitation. Linear theory is known to over-predict the fluid response in these types of systems significantly, suffering from the lack of damping whose only manifestation is radiated waves. In reality, however, viscous effects may act as damping and nonlinear effects associated with the free surface conditions may cause transfer of energy between the different modes. In the present work, which is within the framework of potential theory, a fully nonlinear numerical wavetank based on Green’s 2nd identity coupled with an inviscid vortex tracking method is applied to the moonpool problem. The paper presents a methodology for perpetual simplification of the free shear layer as the system undergoes near sinusoidal motion in order to reach steady state. This is practically impossible without such simplifications due to the otherwise exceedingly complex wake structures evolving only after the first one or two periods. Also the in- and out-flow of the boundary layers are modelled. The results are compared to experiments. In the investigated cases models of rectangular shape with sharp corners provide well-defined separation points, and such sharp corners are in practice introduced e.g. by bilge keels. It is found that: (1) The damping effect associated with the nonlinear free surface conditions are of minor importance, (2) the effect of the in- and out-flow of the boundary layer is negligible to all practical purposes, whereas (3) the flow separation explains the major part of the discrepancy between the measured response and that estimated by linear theory.

On the parametric rolling of ships using a numerical simulation method

This paper has shown a numerical motion simulation method which can be employed to study on parametric rolling of ships in a seaway. The method takes account of the main nonlinear terms in the rolling equation which stabilize parametric rolling, including the nonlinear shape of the righting arm curve, nonlinear damping and cross coupling among all 6 degrees of freedom. For the heave, pitch, sway and yaw motions, the method uses response amplitude operators determined by means of the strip method, whereas the roll and surge motions of the ship are simulated, using nonlinear motion equations coupled with the other 4 degrees of freedom. For computing righting arms in seaways, Grim's effective wave concept is used. Using these transfer functions of effective wave together with the heave and pitch transfer functions, the mean ship immersion, its trim and the effective regular wave height are computed for every time step during the simulation. The righting arm is interpolated from tables, computed before starting the simulation, depending on these three quantities and the heel angle. The nonlinear damping moment and the effect of bilge keels are also taken into account. The numerical simulation tool has shown to be able to model the basic mechanism of parametric rolling motions. Some main characteristics of parametric rolling of ships in a seaway can be good reproduced by means of the method. Comprehensive parametric analyses on parametric rolling amplitude in regular waves have been carried out, with that the complicated parametric rolling phenomena can be understood better.

Roll-damping qualities of constructive stabilizers

The paper presents the description and results of a model experiment carried out for comparison of the roll-damping qualities of continuous bilge keels and of wing ledges, installed in a staggered order, during rolling of the ship at zero forward speed. The damping qualities of constructive stabilizers were investigated also at motion of the ship ahead. The obtained data can be useful in subsequent experiments and in design of new sea vessels.

Nonlinear Rolling of a Biased Ship in a Regular Beam Wave under External and Parametric Excitations

We consider a nonlinear oscillator simultaneously excited by external and parametric functions. The oscillator has a bias parameter that breaks the symmetry of the motion. The example that we use to illustrate the problem is the rolling oscillation of a biased ship in longitudinal waves, but many mechanical systems display similar features. The analysis took into consideration linear, quadratic, cubic, quintic, and seven terms in the polynomial expansion of the relative roll angle. The damping moment consists of the linear term associated with radiation and viscous damping and a cubic term due to frictional resistance and eddies behind bilge keels and hard bilge corners. Two methods (the averaging and the multiple time scales) are used to investigate the first-order approximate analytical solution. The modulation equations of the amplitudes and phases are obtained. These equations are used to obtain the stationary state. The stability of the proposed solution is determined applying Liapunov’s first method. Effects of different parameters on the system behaviour are investigated numerically. Results are presented graphically and discussed. The results obtained by two methods are in excellent agreement.

Nonlinear analysis for a ship with a general roll-damping model

The qualitative behaviour of the response of a ship rolling in longitudinal waves whose amplitude or frequency (parameters) are slowly varied is presented. An analytical and numerical technique is used to predict the qualitative change taking place in the stable solutions of a ship model as one of the parameters is slowly changed. The analysis took into consideration linear, cubic and quantic terms in the polynomial expansion of the relative roll angle. The damping moment consists of the linear term associated with radiation and viscous damping and a cubic term due to frictional resistance and eddies behind bilge keels and hard bilge corners. Two methods (the averaging and the multiple time scales) are used to investigate a first-order approximate analytical solution. The modulation equations of the amplitudes and phases are obtained. These equations are used to determine steady state solutions. Numerical calculations are presented which illustrate the behaviour of the steady state response amplitude as a function of the detuning parameter. The stability of the proposed solution is determined applying Liapunov's first method. The effects of different parameters on the system behaviour are investigated numerically. The results obtained by the two methods are in excellent agreement.

Large parametric rolling of a large passenger ship in beam seas and the role of bilge keel in its restraint

Model experiments of a scale model of a large passenger ship without bilge keels in beam seas demonstrate that parametric roll resonance with roll amplitude can reach more than 25 degrees occurs in the range of short waves. It is identified that the change of wave height affects the change of metacentric height in waves so that it affects the occurrence of the parametric rolling in beam seas. It is experimentally confirmed that the designed bilge keels for the ship can restrain such parametric rolling. Moreover, the experiments with various sizes of bilge keels show that they can affect the occurrence of parametric rolling in beam seas.

Steady Current Forces On Tanker-based FPSOs

There is very little information available in the public domain on steady current forces on tanker-based Floating Production, Storage and Offloading systems (FPSOs). The general lack of available data and unresolved issues related to scale effects in model tests bring into question whether the level of uncertainty in modelling of current forces on FPSOs is sufficiently well understood, which has implications for the design of FPSO station-keeping systems. This paper presents the results of a test program to measure current forces on a tanker-based FPSO at various current speeds and relative current headings. While the results are in general agreement with the design curves published by OCIMF, there are some important differences associated with the effect of bilge keels and the

Unsteady RANS method for ship motions with application to roll for a surface combatant

An unsteady Reynolds-averaged Navier–Stokes method is developed to compute motions and the resulting flow and wave fields around surface ships. Although the formulation and RANS code are generalized for six-degree-of-freedom motions, the method is demonstrated here for the viscous phenomenon of roll decay motion for a surface combatant. The method is based on an extension of CFDSHIP-IOWA (a general-purpose code for computational ship hydrodynamics) to predict ship motions with larger amplitude and non-slender geometry, in comparison to traditional linearized methods. The flow solver uses higher-order upwind discretization, PISO method for pressure–velocity coupling, a blended k– ω/ k– ε two-equation turbulence model, free surface tracking approach, and structured multi-block grid systems. As an initial step, unsteady simulations of a modern surface combatant with predicted roll decay and prescribed sinusoidal roll motion are performed. Roll decay motion is simulated by releasing the model from an initial roll angular displacement and by computing the resulting roll motion. Verification of the time history of the roll motion is performed using iteration, grid, and time step studies and numerical uncertainties are shown to be less than 1%. Validation is performed by comparison with available experimental data with the predictions validated at 1.7% and 1.5% for the uncorrected and corrected solutions, respectively. For simulations with prescribed motions, the periodic response of the boundary layer to the rolling motion is described and quantified using a Fourier analysis. A spring–mass-damper system is used to compare the current non-linear predictions to traditional linear strip theory results. The method is shown to accurately predict the natural rolling frequency and roll decay rate at multiple ship speeds both without and with bilge keels, which demonstrates the ability to assess seakeeping characteristics for practical geometries.

Prediction Methods of Roll Damping of Ships and Their Application to Determine Optimum Stabilization Devices

About 25 years ago, the author developed a method for predicting the roll damping of a ship, and the method is widely used even now. The method is a component-based one, and each component is predicted by theoretical ways if possible, otherwise by empirical ways. For these 25 years, the methods have been modified to improve accuracy and to extend their applicability to other kinds of ships. In this paper the author reviews these continuing studies on the roll damping prediction of ships, and introduces the application to determine optimum size and location of bilge keels.

Loads and Hydrodynamic Coefficients of the Ship Contours for their Instant Position on Wave Surface

An approximate practical method of calculation nonlinear of the Khaskind -Newman hydrodynamic loads, acting on the ship's hull rolling on the waves with finite amplitude, is grounded. In so doing, the effects of variation of wetted part of the ship's surface and an anharmonicity of the velocity field on it are taken into account. Determination of loads is generally reduced to calculation of hydrodynamic coefficients of ship's sections in their instant positions, namely, the attached masses and damping coefficients. To determine the instant hydrodynamic coefficients in wide range of shapes of ships' sections the multiparameter conformal mapping in the parametric plane and the Ursell technique for the determination of the velocity potential in this plane are used. The parameters of conformal mapping and the amplitudes of hydrodynamic singularities are derived by the least-squares method. The results of comparative calculations for hydrodynamic coefficients of typical ship's sections, ship's sections pitched up to 40◦, sections with bilge keels and bulbous SWATH ship's sections are presented. The agreement of these results is estimated in general as satisfactory and good.

Non-Linear Features in Large Amplitude Ship Motions (1st Report)

In this study, large amplitude rolling motion of a ship without bilge keels in heavy regular beam seas is experimentally investigated, and a new non-linear feature of lateral ship motions in high waves is revealed.The experiments show that, in high beam waves, large amplitude rolling motion occurs not only in the frequency region of the roll resonance but also in the frequency region higher than the resonance frequency, and that jump phenomena of roll amplitudes appears near the heave natural frequency. These behaviors obtained by the experiments are investigated, and the reasons of these non-linear features are clarified as follows; the former is caused by changing encounter frequencies by large drifting velocity in high waves to make the roll-resonance region wide. The latter is caused by different drifting velocities for the same regular wave near at the heave natural frequency.A non-linear feature of heaving motion is also experimentally confirmed near heave natural frequency.

Analytical and numerical solutions of a non-linear ship rolling motion

The method of multiple time scales is applied to construct a second-order uniform expansion of the non-linear rolling response of a ship in regular beam seas. The analysis took into consideration linear, quadratic, cubic, quintus, and seven terms in the polynomial expansion of the relative roll angle. The damping moment consists of the linear term associated with radiation and viscous damping and a cubic term due to frictional resistance and eddies behind bilge keels and hard bilge corners. The analytical solution is conducted to construct the steady-state amplitude and phase of harmonic oscillations. The stability of the proposed solution is determined applying Liapunov's first method. Effects of the different parameters on system behavior are investigated numerically. Results are presented graphically and discussed.

Design of passive anti-roll tanks for roll stabilization in the nonlinear range

The best way of reducing roll motion is by increasing roll damping. Bilge keels are the most common devices for increasing roll damping. If more control is required, anti-roll tanks and fins are used. Tanks have the advantage of being able to function when the ship is not underway. Our objective is to develop design procedures for passive tanks for roll reduction in rough seas. This paper focuses on the design of passive U-tube tanks. The tank-liquid equation of motion is integrated simultaneously with the six-degree-of-freedom (6DOF) equations of the ship motion. The coupled set of equations is solved by using the Large Amplitude Motion Program ‘LAMP’, which is a three-dimensional time-domain simulation of the motion of ships in waves. The unstabilized and stabilized roll motions of a S60-70 ship with forward speed and beam waves have been analyzed. For high-amplitude waves, the unstabilized roll angle exhibits typical nonlinear phenomena: a shift in the resonance frequency, multi-valued responses, and jumps. The performance of a S60-70 ship with a passive tank is investigated in various sea states with different encounter wave directions. It is found that passive anti-roll tanks tuned in the linear or nonlinear ranges are very effective in reducing the roll motion in the nonlinear range. The effect of the tank damping, frequency, and mass on the tank performance is studied. Also, it is found that passive anti-roll tanks are very effective in reducing the roll motion for ships having a pitch frequency that is nearly twice the roll frequency in sea states 5 and 6.

Roll damping characteristics of a small fishing vessel with a central wing

The roll damping characteristics of three models of a 3-ton class fishing vessel representing the bare hull, hull with bilge keels, and hull with bilge keels and a central wing are investigated by the free roll decay tests in calm water and also in uniform head waves in a towing tank. Speed and roll initial angle and OG (distance between the centers of gravity and roll) are varied to check their dependence on roll damping. The experimental results are compared with the numerical results of mathematical modeling by the energy method and the energy dissipation patterns are also compared for these three models. The bilge keel contributes significantly to the increment of the roll damping for zero speed but as speed increases, the lift generated by the central wing contributes significantly to the roll damping increase. In addition, it is shown that the roll damping is more or less influenced by the regular head waves.