Simplified CFD modeling for bilge keel force and hull pressure distribution on a rotating cylinder

A horizontal, circular cylinder fitted with one bilge keel is forced to rotate harmonically around its axis. The bilge keel load and hull pressure distribution are investigated. A fully submerged condition (infinite fluid), and three partly-submerged conditions are considered. A two-dimensional numerical study is performed, and the results are validated against recently published experimental data by van’t Veer et al. [30]. In addition, comparisons for mass and drag coefficients are also made with experimental data for plate in infinite fluid (Keulegan and Carpenter [8]), and wall-mounted plate (Sarpkaya and O’Keefe [9]) in oscillatory flow.A Navier–Stokes solver based on the Finite Volume Method is adopted for solving laminar flow of incompressible water. The free-surface condition is linearized by neglecting the nonlinear free-surface terms and the influence of viscous stresses in the free surface zone, while the body-boundary condition is exact. This simplified modeling of the problem required the mesh to be fine only around the bilge keels, leading to a total number of cells around N ≃ 1 ×10⁴, which reduced computational cost significantly.The influence of draft and amplitude of oscillations on the bilge keel force and hull pressure distribution are considered. The bilge keel force is presented in terms of non-dimensional drag and mass coefficients including higher harmonic components. The numerical results are also compared with the industry standard empirical method for calculation of roll damping proposed by Ikeda et al. [4]. In general, a good agreement between the results of the present numerical method and the experimental data is obtained and the differences with those predicted by the empirical method are addressed.     

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.     

CFD approach to roll damping of ship with bilge keel with experimental validation

The most common method of reducing roll motion of ship-shaped floating systems is the use of bilge keel which act as damping elements. The estimation of the damping introduced by bilge keel is still largely based on empirical methods. The present work adopts the CFD approach to the estimation of roll damping, both without and with bilge keel and validates the results with experiments conducted in a wave flume. Specifically, free oscillation tests are conducted at model scale to obtain roll damping, both by experiments and CFD simulation and reasonably good comparisons are obtained. The experiments also include PIV study of the flow field and attempt has been made to correlate the measured flow field with that obtained by CFD. The CFD methodology has the potential to determine rationally the size and orientation of bilge keels in design with reasonably accurate estimate of the additional roll damping that it provides to ship's roll motion.     

Effects of side keels on patrol vessel safety in astern waves

Planing hull vessel is well-known to have the problem of low damping and susceptible to large roll angles when encountering beam seas especially when stopped or operated at low speed. One approach to reduce this problem is to incorporate a pair of side keels. The effects of the side keels on both roll damping and resistance of a planing hull patrol vessel were experimentally evaluated by varying length, breadth and the position of the side keels. Tests data of the side keels have been presented on the roll damping coefficients and the resistance forces of the vessel. Next, the roll damping coefficients were utilised in time domain simulation program based on a six-degree-of-freedom mathematical model to predict the roll response and assess the vessel safety in astern waves for the case with and without the side keels. The results from the time domain simulation program have indicated that the effects of a pair of side keels can improve the vessel safety.     

Theoretical prediction of running attitude of a semi-displacement round bilge vessel at high speed

Running attitudes of semi-displacement vessels are significantly changed at high speed and thus have an effect on resistance performance and stability of the vessel. There have been many theoretical approaches about the prediction of running attitudes of high-speed vessels in calm water. Most of them proposed theoretical formulations for the prismatic hard-chine planing hull. In this paper, running attitudes of a semi-displacement round bilge vessel are theoretically predicted and verified by high-speed model tests. Previous calculation methods for hard-chine planing vessels are extended to be applied to semi-displacement round bilge vessels. Force and moment components acting on the vessel are estimated in the present iteration program. Hydrodynamic forces are calculated by ‘added mass planing theory’, and near-transom correction function is modified to be suitable to a semi-displacement vessel. Next, ‘plate pressure distribution method’ is proposed as a new hydrodynamic force calculation method. Theoretical pressure model of the 2-dimensional flat plate is distributed on the instantaneous waterplane corresponding to the attitude of the vessel, and hydrodynamic force and moment are estimated by integration of those pressures. Calculations by two methods show good agreements with experimental results.     

A study of the angle dependence of roll damping moment

The angle dependence of the roll damping moment is investigated by analysing experimentally obtained free roll decay records. Two ship models were used with and without bilge keels, also results with forward speed were obtained. The analysis indicate strong angle dependence and explains why the quadratic and cubic velocity dependent damping moments are successful in many cases.     

Vortex Patterns and Roll Damping on Various Cross Sections of Ships

A numerical study is presented on roll damping of ships by solving Navier-Stokes equation.Two-Dimensional unsteady incompressible viscous flow around the rolling cylinders of various ship-likecross sections are numerically simulated by use of the computational scheme previously developed by theauthors.The numerical results show that the location of the vortices is very similar to the existing experi-mental result.For comparison of vortex patterns and roll damping on various ship-like cross sections,vari-ous distributions of shear stress and pressure on the rolling ship hull surface are presented in this paper.Itis found that there are two vortices around the midship-like section and there is one vortex around the foreor stern section.Based on these simulation results.the roll damping of a ship including viscous effects iscalculated.The contribution of pressure to the roll moment is larger than the contribution of frictionalshear stress.     

Effects of the asymmetric riser and bilge keel arrangements on FPSO green water assessment

This article aims to report important findings on how the asymmetric riser and bilge keel arrangements affect the motion response and green water assessment by using a real FPSO conversion project. Recently, the authors have proposed a practical approach for short-term and long-term green water prediction. In this paper, the method has been further extended to include the effect of truncated bilge keel by using Morrison elements. Numerical studies are conducted focusing on the effect induced by asymmetric riser arrangement and truncated bilge keels. Comparisons of short-term and long-term results between different models indicate that the FPSO’s motion is significantly affected by asymmetrically arranged appendages and attachments in a complicated way. The relative wave elevation is also affected by appendages and attachments, but not the same trend as the motion response. The effect of the asymmetric arrangement of risers and bilge keel on long-term relative wave elevation response has been captured by both traditional contour line approach and response-based analysis, but some discrepancy identified between the results from the two methods indicates the limitation of the traditional contour line approach.     

Forces on partly buried, tandem twin cylinders in waves at low Keulegan-Carpenter numbers

This study deals with the forces on the circular cylinder, laid on, or partly buried in the bed with a parallel twin dummy cylinder nearby and without it. They were determined by measuring the pressure distribution on the cylinder in the case of wave at low KC numbers. The forces on the cylinder were calculated by the integration of the measured pressures determined by pressure transducers on the surface of the cylinder. Force coefficients were obtained for the low KC numbers (KC<5), for the burial-depth-to-the diameter ratio = 0-0.7. The distance between axis of the measurement and dummy cylinders to diameter ratio (x/D) was 2, 1.5 and 1. The dummy cylinder was replaced downstream and upstream of the measurement cylinder.     

Numerical Simulation of Viscous Flow Around a Rolling Cylinder with Ship-Like Section

Two-dimensional unsteady incompressible viscous flow around a rolling cylinder with ship-like section is numerically simulated by employing the computational scheme previously developed by the authors, in which the continuity and momentum equations are satisfied simultaneously at each time step for oscillating flow. The numerical results show that the motion of vortices around a rolling ship hull is cyclical. It is found that the location of the vortices is very similar to the existing experimental result. Using these simulation results, we can calculate the roll damping of ships including viscous effects.     

Design pressure distributions on the hull of the FLOW wave energy converter

This paper presents a procedure to calculate the design pressure distributions on the hull of a wave energy converter (WEC). Design pressures are the maximum pressure values that the device is expected to experience during its operational life time. The procedure is applied to the prototype under development by Martifer Energy (FLOW—Future Life in Ocean Waves).A boundary integral method is used to solve the hydrodynamic problem. The hydrodynamic pressures are combined with the hydrostatic ones and the internal pressures of the large ballast tanks. The first step consists of validating the numerical results of motions by comparison with measured experimental data obtained with a scaled model of the WEC. The numerical model is tuned by adjusting the damping of the device rotational motions and the equivalent damping and stiffness of the power take-off system. The pressure distributions are calculated for all irregular sea states representative of the Portuguese Pilot Zone where the prototype will be installed and a long term distribution method is used to calculate the expected maximum pressures on the hull corresponding to the 100-year return period.     

Roll stabilization by anti-roll passive tanks

Since the most severe roll motion occurs at resonance (known as synchronous rolling), the best way of reducing it is to increase the damping. The most common means of doing so is by the installation of bilge keels. If more control is required, both anti-roll tanks and fins are used. Tanks have the advantage of being able to function when the ship is not underway. The use of tanks with liquid free surfaces for reducing roll motion of ships is an old idea. Many researchers have studied the design of anti-roll tanks. However, most of the past effort has concentrated on studying the performance of anti-roll tanks in damping the roll motion of the ship. Little attention has been paid to the fluid motion inside the tank itself. Another important issue is the tank tuning. Proper tuning of the anti-roll tank, to match the ship's natural frequency, is very important in reducing the roll motion. This paper concentrates on the most familiar type, which is the U-tube passive tank as a mechanical absorber of roll motion. A detailed study, covering tank damping, mass, location relative to the ship CG, and tuning, is presented. New suggestions and observations are stated concerning tank damping and tuning.     

Internal Resonances for Heave, Roll and Pitch Modes of A Spar Platform Considering Wave and Vortex-Induced Loads in the Main Roll Resonance

We present a study of the nonlinear coupling internal resonance for the heave roll and pitch performance of a spar platform under the wave and vortex-induced loads when the ratio of the frequencies of heave, roll and pitch are approximately 2:1:1. In consideration of varying wet surface, the three DOFs nonlinear coupled equations are established for the spar platform under the effect of the first-order wave loads in the heave and pitch, and vortex-induced loads in the roll. By utilizing the method of multi-scales when the vortex-induced frequency is close to the natural roll frequency, the first-order perturbation solution is obtained analytically and further validated by the numerical integration. Sensitivity analysis is performed to understand the influence of the damping and the internal detuning parameter. Two cases with internal resonance are shown. The first case is that no saturation phenomenon exists under small vortex-induced loads. The first order perturbation solution illustrates that only the vortex-induced frequency motion in roll and the super-harmonic frequency motion in heave are excited. The second case is that the vortex-induced loads are large enough to excite the pitch and a saturation phenomenon in the heave mode follows. The results show that there is no steady response occurrence for some cases. For these cases chaos occurs and large amplitudes response can be induced by the vortex-induced excitation.     

Internal Resonances for Heave,Roll and Pitch Modes of A Spar Platform Considering Wave and Vortex-Induced Loads in the Main Roll Resonance

We present a study of the nonlinear coupling internal resonance for the heave roll and pitch performance of a spar platform under the wave and vortex-induced loads when the ratio of the frequencies of heave, roll and pitch are approximately 2:1:1. In consideration of varying wet surface, the three DOFs nonlinear coupled equations are established for the spar platform under the effect of the first-order wave loads in the heave and pitch, and vortexinduced loads in the roll. By utilizing the method of multi-scales when the vortex-induced frequency is close to the natural roll frequency, the first-order perturbation solution is obtained analytically and further validated by the numerical integration. Sensitivity analysis is performed to understand the influence of the damping and the internal detuning parameter. Two cases with internal resonance are shown. The first case is that no saturation phenomenon exists under small vortex-induced loads. The first order perturbation solution illustrates that only the vortex-induced frequency motion in roll and the super-harmonic frequency motion in heave are excited. The second case is that the vortex-induced loads are large enough to excite the pitch and a saturation phenomenon in the heave mode follows.The results show that there is no steady response occurrence for some cases. For these cases chaos occurs and large amplitudes response can be induced by the vortex-induced excitation.     

Head-wave parametric rolling of a surface combatant

Complementary CFD, towing tank EFD, and nonlinear dynamics approach study of parametric roll for the ONR Tumblehome surface combatant both with and without bilge keels is presented. The investigations without bilge keels include a wide range of conditions. CFD closely agrees with EFD for resistance, sinkage, and trim except for Fr>0.5 which may be due to free surface and/or turbulence modeling. CFD shows fairly close agreement with EFD for forward-speed roll decay in calm water, although damping is over/under predicted for largest/smaller GM. Most importantly CFD shows remarkably close agreement with EFD for forward-speed parametric roll in head waves for GM=0.038 and 0.033 m, although CFD predicts larger instability zones at high and low Fr, respectively. The CFD and EFD results are analyzed with consideration ship motion theory and compared with Mathieu equation and nonlinear dynamics approaches. Nonlinear dynamics approaches are in qualitative agreement with CFD and EFD. The CFD and nonlinear dynamics approach results were blind in that the actual EFD radius of gyration k_xx was not known a priori.     

Directional ocean wave spectra using buoy azimuth, pitch, and rollderived from magnetic field components

Buoy azimuth, pitch, and roll, when used with measurements of buoy vertical acceleration, can provide directional wave spectra. Earlier work, which considered effects of buoy hull magnetism, showed that azimuth can be determined from magnetic field measurements (K.E. Steele and J.C. Lau, 1986). This work is extended to show that buoy pitch and roll, and thus buoy slopes, can also be determined from the same measurements. These slopes can be determined from measurements of the magnetic field components inside the hull along two orthogonal axes parallel to the deck of a buoy. Algorithms are developed for estimation of azimuth, pitch, and roll angles using these measurements. The algorithms account for residual and induced hull magnetism. Azimuth, pitch, roll, and estimates of directional wave spectra are determined both from the magnetic field measurements and from a conventional wave measurement system on the same buoy. Comparisons show that estimates of directional spectra based on magnetometer-derived pitch and roll agree well     

The effect on resistance of displacement hull forms due to fore-to-aft pressure re-distribution

The results of an experimental study of the resistance reduction from modification of the pressure field around displacement hulls creating fore-aft pressure re-distribution are presented. The fore-aft pressure re-distribution is achieved by hull surface porosity created by orifices through the hull which are connected to each other by fore-aft ducting. This affects the fore-aft pressure gradient when moving. Tests were completed with Model A, which has parabolic shaped waterlines, wall sides, a flat bottom and no parallel midbody. Resistance and surface pressure measurements were obtained with and without the pressure re-distribution orifices. The extent of pressure re-distribution was varied by using three ducting sizes. The resistance measurements and surface pressure data show that in some cases there is a large fore-aft surface pressure gradient and the fore-aft pressure re-distribution results in a significant reduction in the vessel resistance. The test results suggest that fore-aft pressure re-distribution may have benefit in reducing displacement hull and/or SWATH strut resistance.     

冰脊形成过程的离散元模拟及影响因素分析

冰脊对极地船舶及海洋工程结构的冰载荷设计及冰区安全运行具有重要的影响,其几何形态是重要的考虑因素。为研究冰脊的几何形态,本文基于Voronoi切割算法构造扩展多面体海冰单元,并使其相互冻结形成平整冰;采用离散单元法模拟海冰在相对运动时挤压形成冰脊的动力过程,统计分析脊帆高度、龙骨宽度、龙骨深度、龙骨水平倾角等主要几何参数,并确定这些几何参数间的对应关系。将离散元模拟结果同冰脊现场观测资料对比分析以验证扩展多面体离散元方法模拟冰脊形成过程的可行性。在此基础上讨论冰厚、冰速、海冰强度等因素对冰脊形态的影响。本文采用离散元方法对冰脊形成过程及几何特性的数值分析可为深入开展冰脊的形成机理及其对船舶、海洋工程结构物的冰载荷分析提供参考依据。     

Oscillating inviscid flow over elliptic cylinders with flat plates and circular cylinders as special cases

The problem of oscillating inviscid flow over an elliptic cylinder is studied for various angles of attack. The flow is incompressible and two-dimensional and the oscillations are harmonic. The flow direction is always normal to the cylinder axis and oscillations are only allowed in the magnitude of the free stream velocity. The study focuses on the hydrodynamic forces acting on the cylinder as well as the surface pressure distribution and their time variation. The parameters involved are the cylinder axis ratio, the angle of attack and the Strouhal number. The variables are normalized in such a way that the solutions for the problems of oscillating flow over flat plates and circular cylinders can be easily obtained as special cases. Analytical expressions are given for the drag coefficient, the lift coefficient, and the surface pressure distribution and their variation with time. Similar analytical expressions are given for the special cases of circular cylinders and inclined flat plates in oscillating inviscid flows.     

A model equation for the transverse forces on cylinders in oscillatory flows

A quasi-steady model is presented to predict the transverse force on cylinders in waves and oscillating flows. The model assumes that the Strouhal number, based on the instantaneous flow velocity, is constant, taking a value of 0.2. It is also assumed that the lift coefficient, based on the instantaneous dynamic pressure of the flow, is constant over a half cycle of the flow. The predictions of the model are compared with measurements taken on a circular cylinder in planar oscillatory flow over the Keulegan Carpenter number, KC, range from 5 to 53. The agreement between predicted and measured transverse forces is good at high KC but deteriorates at low KC. For high KC, it is shown that the model can be further improved if additional variables are introduced into the model equation.