Coupled heave and pitch motions of planing hulls at non-zero heel angle

Current paper presents a mathematical model based on 2D-asymmetric wedge water entry to model heave and pitch motions of planing hulls at non-zero heel angles. Vertical and horizontal forces as well as heeling moment due to asymmetric water entry are computed using momentum theory in conjunction with added mass of impact velocity in vertical and horizontal directions. The proposed model is able to compute sway and yaw forces, roll moment, as well as heave and pitch motions in calm water and regular waves. Validity of the proposed model is verified by comparing the results against existing experimental data in both symmetric and asymmetric conditions. Ultimately, different parametric studies are conducted to examine the effects of non-zero heel angle on dynamic vertical motions. The resulting sway and yaw forces due to asymmetric motion are also derived and effects of heel angle on these side forces are investigated.     

Second-order resonant heave,roll and pitch motions of a deep-draft semi-submersible: Theoretical and experimental results

Large volume semi-submersible units may present significant wave induced resonant motions in heave, roll and pitch. Evaluating the slow motions of such systems is important from the initial stages of their designs and therefore requires a model that is both accurate and expedite enough. In the present article, different options for modeling the second-order hydrodynamic forces and induced motions are discussed using as a case-study the PETROBRAS 52 unit—P-52. Computations of the low frequency forces are performed in the frequency domain by means of a commercial Boundary Element Method (BEM) code. Different hydrodynamic approximations are tested and evaluated by directly comparing the predicted responses with those measured in small-scale tests performed in a wave-basin. From the results obtained in theses comparisons, a methodology based on a white-noise approach of the force spectrum is proposed. The validity of such approximation is attributable to the typically low damping levels in heave, roll and pitch motions. Furthermore, results also indicate that the second order forces may be calculated disregarding the free-surface forcing components, an option that helps to reduce the computational burden even more, rendering the procedure suitable for preliminary design calculations.     

Investigation of motions of catamarans in regular waves—II

By extending the linear frequency domain theory, a quasi-non-linear time-domain technique has been developed to investigate the large amplitude motions of catamarans in regular waves. The non-linearity of hydrodynamic forces included in this practical method comes from variations of a ship's submerged portion. These forces are obtained from a database generated by the linear frequency domain method at each time step. The coupled equations, heave and pitch, are solved in the time domain by using the Runge-Kutta method with proper initial values. In order to investigate the non-linear effects of large amplitude motions of the V-1 catamaran in the head-sea condition, numerical results obtained from the linear and non-linear strip methods have been compared with those obtained from a series of experiments carried out in the towing tank of the Hydrodynamics Laboratory at the University of Glasgow. Based on the comparative studies, the numerical results obtained from the time-domain program can provide better predictions for the large amplitude motions of catamarans than the linear frequency domain method. It is concluded that the non-linear effects are significant when the model speeds and wave amplitudes increase. The peak values of large amplitude motions around the resonance frequencies, as obtained from the non-linear time-domain predictions as well as from measurements, are smaller than those obtained from the linear theory.     

扁平潜器微速操纵性研究

针对扁平潜器的特点建立了其微速操纵性运动方程,提出了忽略攻角、漂角与旋转角速度耦合影响的水动力模型,由拖曳水池模型试验确定了攻角、漂角水动力,近似估算了旋转水动力.在主辅推进器的PD控制下,数值仿真计算了水平面航向保持与改变、垂直面潜浮的微速运动控制.     

Development of an adaptive disturbance rejection system for the rapidly deployable stable platform—Part 2: Controller design and closed loop response

Currently, both military and civilian operations that require at-sea cargo transfers are severely limited by environmental conditions and loading forces that induce vessel motions. To increase the robustness of at-sea cargo transfer to these environmental conditions and loading forces, efforts have recently been made toward an actively controlled, rapidly deployable stable platform (RDSP). The purpose of the research presented here is to implement an output feedback adaptive controller and adaptive disturbance rejection scheme that will mitigate the effect of environmental conditions and reject disturbances caused by various loading situations. Because of the controller's distinct ability to adapt to various operating conditions, anticipate and reject load disturbances of unknown magnitude, and adjust to stay within input saturation constraints, the framework is a good fit for the RDSP. Three missions are considered using a previously developed 3 degree of freedom simulation of a 1/10th scale RDSP prototype. Results show successful mitigation of load disturbances and a significant reduction in pitch motions using a control command that remains within the given amplitude and rate constraints. In the case of cargo transfer operations, the adaptive control system is able to significantly increase the cargo throughput by rejecting the disturbances before they are able to cause large pitching dynamics.     

Adaptive input–output feedback linearizing yaw plane control of BAUV using dorsal fins

This paper presents the design of an adaptive input–output feedback linearizing dorsal fin control system for the yaw plane control of low-speed bio-robotic autonomous underwater vehicles (BAUVs). The control forces are generated by cambering two dorsal fins mounted in the vertical plane on either side of the vehicle. The BAUV model includes nonlinear hydrodynamics, and it is assumed that its hydrodynamic coefficients as well as the physical parameters are not known. For the purpose of design, a linear combination of the yaw angle tracking error and its derivative and integral is chosen as the controlled output variable. An adaptive input–output feedback linearizing control law is derived for the trajectory control of the yaw angle. Unlike indirect adaptive control, here the controller gains are directly tuned. The stability of the zero dynamics is examined. Simulation results are presented for tracking exponential and sinusoidal yaw angle trajectories and for turning maneuvers, and it is shown that the adaptive control system accomplishes precise yaw angle control of the BAUV using dorsal fins in spite of the nonlinearity and large uncertainties in the system parameters.     

The differences between a wing and a planing plate in two-dimensional flow

The normal force coefficient on a flat planing surface having arbitrary heave and pitch motion in two-dimensional flow is compared with the lift coefficient of a thin wing in an infinite fluid. Despite the totally different derivations, they are found to be identical (at large Froude numbers and low trim angles and allowing for the wing's interaction with twice as much fluid) at low reduced frequencies. For higher frequency motions, the wing's angle of attack induced lift and its pitch and heave damping are less than those of a planing surface, but the acceleration terms remain identical. The differences at the higher reduced frequencies are due to the fact that, in invisad irrotational flow, the planning plate cannot leave a vortex wake, whereas a wing does.It seems to follow that the “virtual mass” planing hull analysis can be applied to “quasi-static” problems involving wings and bodies in an infinite fluid without the slenderness restriction originally imposed by Jones (1946). Certainly, it is remarkable that the so called “quasi-steady” forces on a two-dimensional wing can be obtained in a few lines of elementary analysis. On the other hand, the method fails entirely when used to compute the pitching moment on a two-dimensional plate, even though it has been found to give good results for the three-dimensional case (Payne, 1981c).This work is offered as a very incomplete study of an intriguing relationship between two very different bodies of analysis. Much more work will need to be done before the relationship between the two approaches will be fully understood.     

基于UDF的水平轴潮流能水轮机被动旋转水动力性能研究

针对水平轴潮流能水轮机被动旋转问题,基于Fluent 17.0,运用UDF(User Defined Function)控制滑移网格对网格进行动态调整,仿真研究水轮机在不同安放角下被动旋转的水动力特性。通过仿真分析,结果表明:潮流能水轮机随着叶片安放角度的增加,尖速比、输出功率、捕能系数都是先增大后减小,叶片安放角为6°时,叶轮前后速度差最大,对潮流能利用充分,且各项性能均达到最佳;通过分析叶片受力,叶尖叶素在安放角为2°时阻力最大,3°时升力最大,升阻比在6°时最大,此时叶尖叶素升阻比C_L/C_D=6.27、攻角α=3.06°。由仿真结果可知水平轴潮流能叶轮的自启动过程由5个阶段组成,即加速度增大的加速运动段—加速度减小的加速运动段—加速度反向增大的减速运动段—加速度反向减小的减速运动段—稳定运行段,这对潮流能水轮机的设计具有重要的指导意义。     

Robust control for an autonomous underwater vehicle that suppresses pitch and yaw coupling

Attitude control systems for autonomous underwater vehicles are often implemented with separate controllers for pitch motion in the vertical plane and yaw motion in the horizontal plane. We propose a novel time-varying model for a streamlined autonomous underwater vehicle that explicitly displays the coupling between yaw and pitch motion due to nonzero roll angle and/or roll rate. The model facilitates the use of a multi-input multi-output H_∞ control design that is robust to yaw-pitch coupling. The efficacy of our approach is demonstrated with field trials.     

A nonlinear model of parametric rolling stabilization by anti-roll tanks

The present paper describes a mathematical model in which the fluid motion inside a U-tank is nonlinearly coupled to the heave, roll and pitch motions of the ship. The main purpose of the investigation is centred on the control of roll motion in the case of parametric resonance in longitudinal waves. A transom stern small vessel, known to be quite prone to parametric amplification, is employed in the study. Four tank designs are employed in order to study the influence of tank mass, tank natural frequency and tank internal damping on the control of parametric rolling at different head seas conditions. Additionally, the influence of the vertical position of the tank is also investigated. The main results are presented in the form of limits of stability, with encounter frequency and wave amplitudes as parameters. Distinct dynamical characteristics are discussed and conclusions are drawn on the relevant parameters for the efficient control of the roll amplifications in head seas.     

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.     

Nonlinear Coupled Motions for a Given Two-Point Tension Mooring System

—The nonlinear behaviors of plane coupled motions for a given two-point tension mooring sys-tem,are discussed in the present paper.For a cylinder moored by two taut lines under the action ofgravity,buoyance and forces due to wave-current and mooring lines,a mathematical model of motionswith three degrees of freedom is established.The steady solution and stability are analyzed.By integratingthe equations of motions,history,phase map and Poincare map are obtained.The Liapunov exponentsare also computed.The numerical results show that:the horizontal movement will increase,and stabilitywill also increase as the steady force increases.The amplitude of responses will decrease as time-dependentforces decrease.Because of the geometric nonlinearity,there exist many windows bifurcating to pseudo-pe-riodic or multi-periodic solution.The bifurcating patterns may be different.The behaviors are very com-plex.Under wave excitation alone,the motions are nonsymmetrical but still symmetrical statistically.     

An investigation on the vertical motion sickness characteristics of a high-speed catamaran ferry

Low frequent motions of vessel may cause motion sickness in rough seas. These undesirable effects induce fatigue of crews during the navigation. The motion sickness is always an important criterion for the high-speed craft design. Modern ferry designs have been marketed with a great emphasis on the seakeeping performance. This research has been carried out by investigating the results on the vertical motion sickness incidence (MSI) study for a 40 m wave-piecing catamaran at seas. The primary purpose of this research is to investigate the vertical motion sickness characteristics of a high-speed catamaran ferry. Two mathematical models, three-dimensional translating–pulsating source distribution technique and three-dimensional pulsating source distribution technique, are used for predicting the vertical acceleration responses of the wave-piecing catamaran in oblique waves. The comparison between numerical predictions and experimental data shows a good agreement except that around the pitch resonance region in FP vertical acceleration motions. Based on the experimental observation, the discrepancies may be caused by the nonlinear effects of centre bow during large pitch motions in waves. The comfort assessments are based on the ISO-2631/1997 standard with the hydrodynamic analysis for determining the acceleration levels in different locations on the vessel. The effects of seating location, wave heading and duration of motion exposure on seasickness are discussed.     

Structure and mechanics of nonpiscine control surfaces

Animals display a variety of control surfaces that can be used for propulsion and maneuvering devises. For nonpiscine vertebrates, these control surfaces are primarily evolutionary modifications of the paired appendages (i.e., legs). The diversity of control surfaces can be classified with regard to the forces used for stability and maneuverability. For animals, the pertinent forces are pressure drag, acceleration reaction, and lift. These forces can be generated actively by motion of the control surfaces or passively from flows produced by movements of the body or external flow fields. Drag-based control surfaces are associated with paddling and rowing movements, where the limbs are oriented either in the vertical parasagittal plane or horizontal plane, respectively. The paddle is unstreamlined and has a triangular design with a broad distal end, thereby affecting a large mass of water. Appendages, which are used to generate lift-based forces, are relatively stiff hydrofoils. To maximize lift, the hydrofoil should have a crescent wing-like design with high aspect ratio. This shape provides the hydrofoil with a high lift-to-drag ratio and high propulsive efficiency. The tail flukes of cetaceans are streamlined control surfaces with a wing-like design. The flukes of cetaceans function in the hydrodynamic generation of forces for thrust, stability, and maneuverability. The three-dimensional geometry of flukes is associated with the production of lift and drag. Previous studies of fluke geometry have been limited in the number of species examined and the resolution of measurements.     

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.     

A Unified Computational Method for Simulating Dynamic Behavior of Planing Vessels

High speed planing hulls have complex hydrodynamic behaviors. The trim angle and drafts are very sensitive to speed and location of the center of gravity. Therefore, motion simulation for such vessels needs a strong coupling between rigid body motions and hydrodynamic analysis. In addition, free surface should be predicted with good accuracy for each time step. In this paper, velocity and pressure fields are coupled by use of the fractional step method. On the basis of integration of the two-phase viscous flow induced stresses over the hull, acting loads (forces and moments) are calculated. With the strategy of boundary-fitted body-attached mesh and calculation of 6-DoF motions in each time step, time history of ship motions including displacements, speeds and accelerations are evaluated. For the demonstration of the software capabilities, circular cylinder slamming is simulated as a simple type of water slamming. Then, a high-speed planing catamaran is investigated in the case of steady forward motion. All of the results are in good concordance with experimental data. The present method can be widely implemented in design as well as in performance prediction of high-speed vessels.     

Two dimensional responses of fixed offshore platform in waves

Responses of a four-legged offshore platform to wave forces are analysed by taking account of one torsional motion around the vertical axis which passes the centre of gravity of the structure, and two translational motions in the horizontal plane. Applying the spring-mass system with one degree-of-freedom to each mode of motion, a calculation method for predicting resultant dynamic displacements of the topdeck is developed. Both the inline force and the transverse force are considered as external forces. The calculated results are found to agree with experiments. Furthermore, the influence of seven important factors on the dynamic response is examined by the calculations. It is shown that the combination pattern of the direction factor of the transverse force is of importance in dynamic analysis.     

畸形波作用下张力腿浮式风力机动力响应特性

针对张力腿系泊浮式风力机的基础运动,忽略柔性构件的影响,建立气动—水动—系泊非线性耦合运动方程。在运动控制方程中包含张力腿系泊系统的非线性回复刚度,桨距角控制以及浮式基础运动对空气动力载荷的影响。在波浪载荷的计算中考虑二阶波浪载荷的作用。采用随机频率相位角调制法生成畸形波波面时历,计算在畸形波作用下张力腿型浮式风力机的动力响应特性。数值模拟结果表明,在畸形波作用下,浮式基础的运动及空气动力性能均受到了显著的影响。其中浮式基础的纵荡和纵摇运动分别受二阶差频与和频波浪力的影响,而垂荡运动的增加则主要是受下沉运动的影响。在畸形波经过的时刻,风力机的功率系数迅速下降,水平方向的风载荷波动先减小,随后其数值急剧下降,而垂直方向的风载荷波动增大。     

Spar平台垂荡-纵摇耦合运动失稳机理

研究参数激励和强迫激励共同作用下Spar平台垂荡-纵摇耦合运动的失稳机理.考虑静稳性和排水体积的变化,推导平台的垂荡回复力和纵摇回复力矩表达式,建立规则波浪中平台垂荡-纵摇耦合的运动方程.以经典Spar平台为例,分析平台垂荡-纵摇耦合运动发生马休类型不稳定运动的条件以及平台运动失稳的形式,给出波高和波浪周期平面上平台因大幅运动失稳的参数域.结果表明,当波高相对较小时,波浪的临界周期接近于垂荡固有周期,平台失稳的形式为马休失稳;当波高相对较大时,波浪的临界周期远离垂荡固有周期,平台由于大幅摇摆运动而失稳.     

Multi-variable adaptive back-stepping control of submersibles using SDU decomposition

A multi-variable adaptive autopilot for the dive-plane control of submarines is designed. The vehicle is equipped with bow and stern hydroplanes for maneuvering. It is assumed that the system parameters are not known, and the disturbance force is acting on the vehicle. Based on a back-stepping design approach, an adaptive control law is derived for the trajectory control of the depth and the pitch angle. To prevent singularity in the control law, the SDU decomposition of the high-frequency gain matrix is used for the design. In the closed-loop system, asymptotic tracking of the reference depth and pitch angle trajectories is accomplished. Simulation results are presented which show that the submarine performs dive-plane maneuvers in spite of the uncertainties in the system parameters and disturbance forces.