Numerical analysis of a propeller during heave motion in cavitating flow

In practical maritime conditions, ship hulls experience heave motion due to the action of waves, which can further drive the ship’s propellers to oscillate relative to the surrounding water. In order to investigate the motion of a propeller working behind a surface vessel sailing in waves, a numerical simulation is conducted on a propeller impacted by heave motion in cavitating flow using the Reynolds-averaged Navier-Stokes (RANS) method. The coupling of the propeller’s rotation and translation is fulfilled using equations of motion defined for this purpose. The heave motion is simplified as a periodic motion based on a sinusoidal function. The numerical transmission of information from the unsteady flow field is achieved using the overset grid approach. In this manner, the unsteady thrust coefficient and torque coefficient of propellers in different periods of heave motion are analyzed. A comparative study is implemented on the unsteady cavitation performance and wake characteristics of propeller. With the propeller’s heave motion, the flow field non-uniformity constantly changes the load on the propeller during each revolution period and each heaving period, the propeller load and the wake field are closely related to the variation of heave motion period. The results obtained from the numerical simulation are expected to serve as a useful theoretical reference for the numerical analysis of a propeller in a heave motion.     

Theoretical and experimental study on dynamic behavior of a damaged ship in waves

Most of the large scaled casualties are caused by loss of structural strength and stability due to the progressive flooding and the effect of waves and wind. To prevent foundering and structural failure, it is necessary to predict the motion of the damaged ship in waves.This paper describes the motion of damaged ship in waves resulting from a theoretical and experimental study. A time domain theoretical model, which can be applied to any type of ship or arrangement, for the prediction of damaged ship motion and accidental flooding has been developed considering the effects of flooding of compartments. To evaluate the accuracy of the model, model tests are carried out in ship motion basin for three different damaged conditions: engine room bottom damage, side shell damage and bow visor damage of Ro–Ro ship in regular and irregular waves with different wave heights and directions.     

Unsteady hydromechanics of a steering podded propeller unit

Unsteady forces, torques and bending moments were predicted for a model podded propulsor unit at various azimuth angles. Predictions in time history include propeller shaft thrust, propulsor unit thrust, normal forces to the propeller shaft bearing, total forces acting on the propulsor unit, propeller shaft torque, blade spindle torque, in-plane and out-of-plane bending moments, and propulsor unit stock shaft torque and bending moments. Analysis was performed for averaged forces and their fluctuations as well. A time-domain unsteady multi-body panel method code, PROPELLA, was further developed for this prediction work. Predictions were compared with a set of time averaged in-house experimental data for a puller-type podded propulsor configuration in the first quadrant operation. Unsteady fluctuations of forces were predicted numerically. Analysis was made for the bending moment on propeller blades, shaft and the propulsor unit stock shaft for azimuth angles from 0° to 45°. It indicates that the magnitude and fluctuation of the forces are significant and they are essential for structural strength and design optimization. The predicted bending moment and global forces on the propulsor unit provide some useful data for ship maneuvering motion and simulation in off-design conditions.     

Numerical analysis on ship maneuvering coupled with ship motion in waves

This paper considers a numerical analysis of ship maneuvering performance in the presence of incident waves and resultant ship motion responses. To this end, a time-domain ship motion program is developed to solve the wave–body interaction problem with the ship slip speed and rotation, and it is coupled with a modular-type 4-DOF maneuvering problem. In this coupled problem, the second-order mean drift force, which can play an important role in the ship maneuvering trajectory, is estimated by using a direct pressure integration method. The developed method is validated by observing the second-order mean drift force, and planar trajectories in maneuvering tests with and without the presence of incident waves. The comparisons are made for two ship models, Series 60 with block coefficient 0.7 and the S-175 containership, with existing experimental data. The maneuvering tests observed in this study include a zig-zag test in calm water, and turning tests in calm water and in regular waves. The present results show a fair agreement of overall tendency in maneuvering trajectories.     

深远海养殖工船最小推进功率研究

针对十万吨级深远海养殖工船在波浪中的阻力和运动响应开展了船模试验与模拟计算,并对其最小推进功率进行了校核。以试验流体力学（EFD）模型试验与模型尺度计算流体力学（CFD）模拟计算的结果进行对比作为方法验证,将实尺度CFD模拟计算的结果直接用于最小推进功率的校核。结果显示,EFD模型试验结果与模型尺度CFD计算结果误差在10%左右,计算精度满足工程要求。在规定的恶劣海况下该船型波浪增阻占总阻力的比例最高可达56.3%,螺旋桨转矩可达最大转矩的63.9%。等级2简化评估法得到的最小推进功率为等级1线评估法给出的最小功率线值的58.9%。研究表明实尺度CFD模拟计算可直接用于船舶最小推进功率的校核,此深远海养殖工船使用等级2简化评估方法进行校核更容易满足规范要求,其最小推进功率应不小于6 833 kW。     

Effect of waves on cavitation and pressure pulses of a tanker with twin podded propulsion

There is increasing interest in optimizing ships for the actual operating condition rather than just for calm water. In order to optimize the propeller designs for operations in waves, it is essential to study how the propeller performance is affected by operation in waves. The effect of various factors that influence the propeller is quantified in this paper using a 8000 dwt chemical tanker equipped with twin-podded propulsion as a case vessel. Propeller performance in waves in terms of cavitation, pressure pulses, and efficiency is compared with the performance in calm water. The influence of wake variation, ship motions, RPM fluctuations and speed loss is studied. Substantial increase in cavitation and pressure pulses due to wake variation in the presence of waves is found. It is found that the effect of other factors is relatively small and easier to take into account as compared to wake variation. Therefore, considering the wake variation at least in the critical wave condition (where the wavelength is close to ship length) in addition to calm water wake is recommended in order to ensure that the optimized propeller performs well both in calm water and in waves.     

Computations of self-propulsion free to sink and trim and of motions in head waves of the KRISO Container Ship (KCS) model

Two computations of the KCS model with motions are presented. Self-propulsion in model scale free to sink and trim are studied with the rotating discretized propeller from the Hamburg Model Basin (HSVA) at Fr = 0.26. This case is particularly complex to simulate due to the close proximity of the propeller to the rudder. The second case involves pitch and heave in regular head waves. Computations were performed with CFDShip-Iowa version 4.5, a RANS/DES CFD code designed for ship hydrodynamics. The self-propulsion computations were carried out following the procedure described in Carrica et al. [1], in which a speed controller is used to find the propeller rotational speed that results in the specified ship velocity. The rate of revolutions n, sinkage, trim, thrust and torque coefficients K_T, K_Q and resistance coefficient CT_(SP) are thus obtained. Comparisons between CFD and EFD show that the rate of revolutions n, thrust and torque coefficients K_T and K_Q have higher prediction accuracies than sinkage and trim. For the simulation of pitch and heave in head waves, the geometry includes KCS hull and rudder under three conditions with two Froude numbers and three wave length and amplitude combinations. 0th and 1st harmonic amplitudes and 1st harmonic phase are computed for total resistance coefficient C_T, heave motion z and pitch angle θ. Comparisons between CFD and EFD show that pitch and heave are much better predicted than the resistance. In both cases comparisons with simulations by other authors presented at the G2010 CFD Workshop [2] using different CFD methodologies are included.     

Numerical investigation on the hydrodynamic characteristics of a marine propeller operating in oblique inflow

The hydrodynamic characteristics of a marine propeller operating in oblique inflow are investigated by using CFD method. Two propellers with different geometries are selected as the study subjects. RANS simulation is carried out for the propellers working at a wide range of advance coefficients and incidence angles. The effects of axial inflow and lateral inflow are demonstrated with the hydrodynamic force on the propeller under different working conditions. Based on the obtained flow field details, the hydrodynamic mechanism of propeller operating in oblique inflow is analyzed further. The trailing vortex wake of propeller is highly affected by the lateral inflow, resulting in the deflected development path and the circumferentially non-uniform structure, as well as the enhanced axial velocity in slipstream. Different flow patterns are observed on the propeller blade with the variation of circumferential position. Combined with the computed hydrodynamic forces and pressure distribution on propeller, the mechanism resulting in the increase of propulsive loads and the generation of propeller side force is explored. Finally, a systematic analysis is carried out for the propulsive loads and propeller side force as a function of axial and lateral advance coefficients. The major terms that play a dominant role in the modeling of propulsive loads and propeller side force are determined through the sensitivity analysis. This study provides a deeper insight into the hydrodynamic characteristics of propeller operating in oblique inflow, which is useful to the investigation of propeller performance during ship maneuvers.     

A note on the horizontal momentum exchange in combined waves and current

The horizontal exchange of momentum due to the organized motion in combined waves and current has been analyzed. The combination of the vertical orbital wave motion and the mean current gives a periodic variation in the horizontal velocity in addition to the wave orbital motion. This periodic variation, combined with the wave orbital motion, gives a significant contribution to the momentum exchange. Two examples are considered, the interaction of a pure wave motion and a current normal to the direction of wave propagation, and a wave driven longshore current with an undertow velocity profile. It is demonstrated that the new contribution changes the resulting momentum exchange considerably.     

Time-domain numerical and segmented ship model experimental analyses of hydroelastic responses of a large container ship in oblique regular waves

Real sea conditions are characterized by multidirectional sea waves. However, the prediction of hull load responses in oblique waves is a difficult problem due to numeral divergence. This paper focuses on the investigation of numerical and experimental methods of load responses of ultra-large vessels in oblique regular waves. A three dimensional nonlinear hydroelastic method is proposed. In order to numerically solve the divergence problem of time-domain motion equations in oblique waves, a proportional, integral and derivative (PID) autopilot model is applied. A tank model measurement methodology is used to conduct experiments for hydroelastic responses of a large container ship in oblique regular waves. To implement the tests, a segmented ship model and oblique wave testing system are designed and assembled. Then a series of tests corresponding to various wave headings are carried out to investigate the vibrational characteristics of the model. Finally, time-domain numerical simulations of the ship are carried out. The numerical analysis results by the presented method show good agreement with experimental results.     

Numerical simulation of viscous cavitating flow around a ship propeller

In the present study, cavitation and a ship propeller wake are reported by computed fluid dynamics based on viscous multiphase flow theory. Some recent validation results with a hybrid grid based on unsteady Navier-Stokes (N-S) and bubble dynamics equations are presented to predict velocity, pressure and vapor volume fraction in propeller wake in a uniform inflow. Numerical predictions of sheet cavitation, tip vortex cavitation and hub vortex cavitation are in agreement with the experimental data, same as numerical predictions of longitudinal and transversal evolution of the axial velocity. Blade and shaft rate frequency of propeller is well predicted by the computed results of pressure, and tip vortex is the most important to generate the pressure field within the near wake. The overall results indicate that the present approach is reliable for prediction of cavitation and propeller wake on the condition of uniform inflow.     

Numerical study of propagation of ship waves on a sloping coast

The aim of this paper is to investigate the propagation of ship waves on a sloping coast on the basis of results simulated by a 2D model. The governing equations used for the present model are the improved Boussinesq-type equations. The wave breaking process is parameterized by adding a dissipation term to the depth-integrated momentum equation. To give the boundary conditions at the ship location, the slender-ship approximation is used. It was verified that, although ship waves are essentially transient, the Snell's law can be applied to predict crest orientation of the wake system on a sloping coast. Based on simulated results, an applicable empirical formula to predict the maximum wave height on the slope is introduced. The maximum wave height estimated by the proposed method agrees well with numerical simulation results.     

考虑诱导速度的螺旋桨敞水性能CFD模拟

螺旋桨工作时在其周围形成诱导速度场,诱导速度随到桨叶距离的增大而衰减。采用CFD方法模拟螺旋桨敞水性能时,只能截取有限尺度的流域进行计算,此时计算域边界上诱导速度并不为零,将进口速度设为进速是近似的。一般采用足够大的计算域,使螺旋桨前方及侧面边界尽量远离桨叶。为了在较小的计算域中实现螺旋桨敞水性能的准确预报,提出在设定进口速度时计入螺旋桨诱导速度的CFD模拟方法。应用升力面方法计算诱导速度,将进口速度设为进速与诱导速度之和。逐步减小计算域尺度,考察敞水性能及压力分布计算结果的变化情况及精度。算例比较表明:通过考虑诱导速度,可以大幅度减小进口与螺旋桨的距离而不降低计算精度。     

PIV measurements of hull wake behind a container ship model with varying loading condition

Flow characteristics of the hull wake behind a container ship model were investigated under different loading conditions (design and ballast loadings) by employing the particle image velocimetry (PIV) technique. Measurements were made at four transverse locations and two longitudinal planes for three Reynolds numbers (Re) (=U₀Lpp/ν, where U₀ is the freestream velocity, Lpp is the length between two perpendiculars of the ship model and ν is the kinematic viscosity) of 5.08×10⁵, 7.60×10⁵, and 1.01×10⁶. It was observed that symmetric, large-scale, longitudinal counter-rotating vortices (with respect to centerline) of nearly the same strength were formed in the near wake. For the ballast-loading condition, the vortices appear at propeller plane below the propeller-boss. The vortex center exhibits a significant upward shift near the propeller-boss as the Reynolds number increase, and as the flow moves downstream. Under the design-loading condition, the vortices first appear at a further downstream location than that for the ballast-loading condition above the propeller-boss. This difference in the flow structure can significantly change the inflow conditions to the propeller blades, such as the streamwise mean velocity profiles and turbulence intensity distributions at the propeller plane. In particular, under the ballast-loading condition, asymmetric inflow may weaken the propulsion and cavitation performance of the marine propeller.     

Sediment concentration measurement by transverse suction

A simple and inexpensive method is proposed to measure time-averaged concentrations under waves. Basically, it is defined by sucking samples in a direction normal to the ambient water motion at an intake velocity which exceeds the ambient flow velocity more than three times. Under two-dimensional wave conditions (laboratory wave flume) the direction of suction should be normal to the (vertical) plane of the orbital motion. Tests in the prototype-surfzone indicate that the method is applicable under three-dimensional conditions as well. It is tentatively concluded that a downward suction nozzle is preferable for such conditions.     

涌浪作用下港内大型集装箱船运动特性数值研究

随着船舶大型化和港口建设深水化发展,外海不同周期波浪作用下大型系泊船泊稳问题与小型系泊船相比出现了新的特点。为此,利用数值模型方法研究了在不同入射角度和周期的涌浪作用下港内大型系泊船的水动力响应,针对系泊船的泊稳情况探讨了船舶的运动规律和运动特性。研究发现,在涌浪周期较大的情况下,限定波高的泊稳标准不足以用来确定系泊船的正常作业条件,港内泊船的水平运动（纵荡、横荡和艏摇）极易超出运动标准值并影响装卸作业效率,并且船舶的水平运动表现出主要由次重力波主导的低频运动特性,而垂直运动（垂荡、横摇和纵摇）表现出主要由短波主导的波频运动特性。     

Generation and propagation of transient nonlinear waves in a wave flume

A semi-analytical nonlinear wavemaker model is derived to predict the generation and propagation of transient nonlinear waves in a wave flume. The solution is very efficient and is achieved by applying eigenfunction expansions and FFT. The model is applied to study the effect of the wavemaker and its motion on the generation and propagation of nonlinear waves. The results indicate that the linear wavemaker theory may be applied to predict only the generation of waves of low steepness for which the nonlinear terms in the kinematic wavemaker boundary condition and free-surface boundary conditions are of secondary importance. For waves of moderate steepness and steep waves these nonlinear terms have substantial effects on wave profile and wave spectrum just after the wavemaker. A wave spectrum corresponding to a sinusoidally moving wavemaker possesses a multi-peak form with substantial nonlinear components, which disturbs or may even exclude physical modeling in wave flumes. The analysis shows that the widely recognized weakly nonlinear wavemaker theory may only be applied to describe the generation and propagation of waves of low steepness. This is subject to further restrictions in shallow and deep waters because the kinematic wavemaker boundary condition as well as the nonlinear interaction of wave components and the evolution of wave energy spectrum is not properly described by weakly nonlinear wavemaker theory. Laboratory experiments were conducted in a wave flume to verify the nonlinear wavemaker model. The comparisons show a reasonable agreement between predicted and measured free-surface elevation and the corresponding amplitudes of Fourier series. A reasonable agreement between theoretical results and experimental data is observed even for fairly steep waves.     

Experimental investigation on a cabin-suspended catamaran in terms of motion reduction and wave energy harvesting by means of a semi-active motion control system

A novel concept catamaran equipped with a suspended cabin, named Wave Harmonizer Type 4 (WHzer-4), is proposed and evaluated. The mass-spring-mass system is constructed by mounting four sets of suspensions in-between the cabin and the twin-hull. Two sets of dual motor/generators (M/Gs) are attached on the center beam of the cabin's deck fore and aft. Each shaft-end of the dual M/Gs is connected to the twin-hull through a rack-pinion gear unit. In this way the vertical relative motion between the cabin and the twin-hull can be transferred into the rotational motion of the M/Gs, and vice versa. A semi-active motion control system, which contains a proportional-integral (PI) controller, is designed and applied to each of the dual M/Gs for the aim of absorbing wave energy under the condition of suppressing the local vertical velocity of the cabin as much as possible. A 1/5 scale model ship with a length of 1.6 m is built, and a forced-oscillation bench test is implemented to validate the performance of the control system. Then, a series of towing tank tests is carried out in regular head waves. The heave and pitch responses of the cabin, those of the twin-hull and the corresponding wave energy capture width ratio (CWR) at five control scenarios and two reference scenarios are investigated. Discussion on the results of the tank test shows that the motion reduction of the cabin and the wave energy harvesting can be achieved simultaneously at a few wave conditions. However, at other conditions, although noticeable amount of wave energy is harvested, motion reduction of the heave and pitch of the cabin could not be obtained at the same time. It is suggested that varying the gain settings of the PI controllers according to the location of the controllers may improve the effectiveness of the proposed control system.     

Nonlinear wave effect on the slow drift motion of a floating body

The slow drift motion of a floating body in a two-dimensional wave field has been investigated using a time-domain, fully nonlinear numerical model with non-reflective open boundaries. Preliminary computations were conducted for incident bichromatic waves, in which wave theories with different orders were applied in generating the waves required. The results show that the use of low-order theories generates undesirable free waves, and that fourth-order terms contribute markedly to low-frequency input. The motion of a rectangular floating body in response to nonlinear bichromatic waves was computed. The numerical results for small-amplitude incident waves agree reasonably well with the second-order approximation for both the steady and difference-frequency (Δσ) components in the body's motion. For relatively large waves, however, the 2Δσ component becomes predominant compared with the Δσ component. The motion of the body in irregular waves with different wave parameters has also been presented in order to discuss the validity range of a second-order approximation.