NUMERICAL STUDY OF THE PITCHING MOTIONS OF SUPERCAVITA-TING VEHICLES

The pitching motions of supercavitating vehicles could not be avoided due to the lost water buoyancy. In order to have some insight for the design of the supercavitating vehicles, the fixed frequency and free pitching motions are investigated. A numerical predicting method based on the relative motion principle and the non-inertia coordinate system is proposed to simulate the free pitching motions of supercavitating vehicles in the longitudinal plane. Homogeneous and two fluid multiphase models are used to predict the natural and the ventilated supercavitating flows. In the fixed frequency pitching motions, a variety of working conditions are considered, including the pitching angular velocities and the supercavity scales and the results are found to be consistent with the available experimental results in literature. The mesh deformation technology controlled by the moment of momentum equation is adopted to study the free pitching motions and finally to obtain the planing states proposed by Savchenko. The numerical method is validated for predicting the pitching motions of supercavitating vehicles and is found to enjoy better calculation efficiency as comparing with the mesh regeneration technology.

Numerical investigation of an advanced aircraft model during pitching motion at high incidence

An unsteady Reynolds averaged Navier–Stokes(URANS) method combined with a rigid dynamic mesh technique was developed to simulate unsteady flows around complex configurations during pitching motion. First, a test case with the NACA0012 airfoil was selected to validate the numerical methods and our in-house codes. Then, we evaluated the unsteady flows around an advanced aircraft model during harmonic pitching motion at high incidence. The effects of pitching motion on the hysteresis of aerodynamic force, the evolution of the leading-edge vortex, and the distribution of pressure on the model's surface were analyzed in detail. The roles of several significant parameters such as the reduced frequency and pitching amplitude were revealed. Several conclusions were found: pitching motion would delay the initiation of the leading-edge vortex, strengthen the vorticity, postpone the occurrence of vortex breakdown, and weaken the massively separated flows, thus causing additional aerodynamic force. Two categories of critical reduced frequency have been found, which divide the influence of reduced frequency on aerodynamic force into three stages, called the linear increasing range, slowly increasing range, and constant range. The first-order phase lag between the aerodynamic force and the incidence is a constant that is independent of the amplitude when the reduced frequency is sufficiently high. A scaled maximum value of C_L is proposed; it depends only on the reduced frequency(instead of the amplitude), and increases linearly when the reduced frequency is sufficiently low.

Effect of Rigid Pitch Motion on Flexible Vibration Characteristics of a Wind Turbine Blade

Adynamic pitch strategy is usually adopted to improve the aerodynamic performance of the blade of awind turbine.The dynamic pitch motion will affect the linear vibration characteristics of the blade.However,these influences have not been studied in previous research.In this paper,the influences of the rigid pitch motion on the linear vibration characteristics of a wind turbine blade are studied.The blade is described as a rotating cantilever beam with an inherent coupled rigid-flexible vibration,where the rigid pitch motion introduces a parametrically excited vibration to the beam.Partial differential equations governing the nonlinear coupled pitch-bend vibration are proposed using the generalized Hamiltonian principle.Natural vibration characteristics of the inherent coupled rigid-flexible system are analyzed based on the combination of the assumed modes method and the multi-scales method.Effects of static pitch angle,rotating speed,and characteristics of harmonic pitch motion on flexible natural frequencies andmode shapes are discussed.It shows that the pitch amplitude has a dramatic influence on the natural frequencies of the blade,while the effects of pitch frequency and pith phase on natural frequencies are little.

The Investigation of the Effect of Heaving and Pitching on Wave-Induced Vertical Hull Vibration of a Container Ship in Regular Waves

The aim of this paper is to investigate the effect of heaving and pitching of ship motion due to springing bending moment. The investigation was conducted both experimentally and validated theoretically. Series of experiment were carried out using a container model-ship of which length was 3 meter, and the possibility of the so-called nth resonant springing vibration is tested by taking n from n = 2 to n = 4. The bending moment due- to vibration is also measured. The following conclusions were obtained： （l） Occurance of the higher order resonant vibration between 2nd-4th is recognized experimentally; （2） The results indicated that heaving and pitching of ship motion influenced the springing bending moment accurately.

Investigation of Pitch Motion Portion in Vertical Response at Sides of a Tension-Leg Platform

Tendons vertically moor Tension-Leg Platforms （TLPs）, thus, a deep understanding of physical tendon stresses requires the determination of the total axial deformation of the tendons, which is a combination of the heave, pitch, and surging responses. The vertical motion of the lateral sides of the TLP is coupled with surge and constitutes a portion of the pitch motion. Tendons are connected to the sides of the TLP; hence, the total displacement of the lateral sides is related to the total deformation of the tendons and the total axial stress. Therefore, investigating the total vertical response at the sides of the TLP is essential. The coupling between various degrees of freedom is not considered in the Response Amplitude Operator （RAO）. Therefore, in frequency domain analysis, the estimated vertical RAO is incomplete. Also, in the time domain, only the heave motion at the center of TLP is typically studied; this problem needs to be addressed. In this paper, we investigate the portion of the pitch motion in the vertical response at the sides of the TLP in both the frequency and time domains. Numerical results demonstrate a significant effect of the pitch motion in the vertical motion of the edges of the TLP in some period ranges.

Dynamic Positioning Control of Surge−Pitch Coupled Motion for Small-Waterplane-Area Marine Structures

For general dynamic positioning systems,controllers are mainly based on the feedback of motions only in the horizontal plane.However,for marine structures with a small water plane area and low metacentric height,undesirable surge and pitch oscillations may be induced by the thruster actions.In this paper,three control laws are investigated to suppress the induced pitch motion by adding pitch rate,pitch angle or pitch acceleration into the feedback control loop.Extensive numerical simulations are conducted with a semi-submersible platform for each control law.The influences of additional terms on surge−pitch coupled motions are analyzed in both frequency and time domain.The mechanical constraints of the thrust allocation and the frequency characters of external forces are simultaneously considered.It is concluded that adding pitch angle or pitch acceleration into the feedback loop changes the natural frequency in pitch,and its performance is highly dependent on the frequency distribution of external forces,while adding pitch rate into the feedback loop is always effective in mitigating surge−pitch coupled motions.

The stability of rolling motion of hypersonic vehicles with slender configuration under pitching maneuvering

The configurations of near space hypersonic flying vehicles are considerably different from those of conventional aircrafts.Their configurations are relatively slender;hence their moment of inertia around the longitudinal axis is much smaller than those around the other two axes,resulting in strong coupling of rotations around the three axes.Thus,the stability analysis of rolling motion for such flying vehicles is more complicated than those for conventional aircrafts,and there is no available result of stability analysis which can readily be applied to such cases.This paper is mainly concerned with the stated problem.Considering the practical situation,our investigation is targeted a slightly simpler problem,namely the rolling stability of flying vehicle under known pitching motion.The stability criterion of rolling motion is obtained with and without lateral motions.We also conducted numerical simulation for the pitching-rolling coupled motions of flying vehicles by solving Navier-Stokes equations coupled with dynamic equations of flight.The results of simulation agree well with those of theoretical analysis and experiments.

Study on Gyroscopic Effect of Floating Offshore Wind Turbines

Compared with bottom-fixed wind turbines,the supporting platform of a floating offshore wind turbine has a larger range of motion,so the gyroscopic effects of the system will be more obvious.In this paper,the mathematical analytic expression of the gyroscopic moment of a floating offshore wind turbine is derived firstly.Then,FAST software is utilized to perform a numerical analysis on the model of a spar-type horizontal axis floating offshore wind turbine,OC3-Hywind,so as to verify the correctness of the theoretical analytical formula and take an investigation on the characteristics of gyroscopic effect.It is found that the gyroscopic moment of the horizontal axis floating offshore wind turbine is essentially caused by the vector change of the rotating rotor,which may be due to the pitch or yaw motion of the floating platform or the yawing motion of the nacelle.When the rotor is rotating,the pitch motion of the platform mainly excites the gyroscopic moment in the rotor’s yaw direction,and the yaw motion of the platform largely excites the rotor’s gyroscopic moment in pitch direction,accordingly.The results show that the gyroscopic moment of the FOWT is roughly linearly related to the rotor’s inertia,the rotor speed,and the angular velocity of the platform motion.

A Practical Hull Form Design of Ferry Using Hybrid Scheme Method and Performing Experiment

Prediction of ship performance in preliminary ship design is an important consideration. It could guarantee ship in safe and comfort. However, many design works did not involve simultaneously ship performances predictions in preliminary design. Moreover, ship designers sometimes modified a ship form to obtain proper design without ship performance consideration. Therefore, this study concerns on predictions of total resistance and added wave resistance of a ferry using a hybrid particle-grid method and then its motions response after modifying bow and stern parts by conducting experiment. Research results show total resistance and added wave resistance have a significant different, therefore, it would be an important consideration in determining ship powering in preliminary ship design. The non-dimensional added wave resistance increases in increasing wave length from λ/Lpp = 0.5 to 1.0 and it decreases after L/λ = 1.0. In addition, it tends to decrease caused by increasing ship speed. The comparison of averaged heave and pitch amplitudes between basic forms after modifying bow and stem parts is quiet similar. However, the rolling amplitude of the modified form is significantly higher comparing with the basic form. We conclude that a ship could be design in preliminary design take into account performances predictions by using numerical method and experimental work.

EXPERIMENTAL STUDY OF VENTILATED SUPERCAVITIES WITH A DYNAMIC PITCHING MODEL

An investigation of the ventilated supercavitation for a supercavitating vehicle pitching up and down in the supercavity was carded out in a high-speed water tunnel. The emphasis is laid on the understanding of the interaction of the vehicle aft body with the cavity boundary. The flow characteristics were measured and the stability of supercaviting flow with different pitching frequencies and amplitudes was analyzed. In particular, the objectives of this study are to understand the effect of the impact upon the cavity distortion, and to quantify the impact process by investigating the evolution of the pressure inside the cavity and then the loads on the vehicle during the pitching motion. It is also shown that the evolution of the pressure detected in different,as inside the supercavity, is coherent and uniform during the periods of the pitching motion. This study is of direct relevance to reliable and accurate prediction of hydrodynamic loads associated with the slamming and impact on supercavitating vehicles.

Experimental investigation of shock-buffet criteria on a pitching airfoil

An experimental investigation of the shock-buffet phenomenon subject to unsteady pitching supercritical airfoil around its quarter chord has been conducted in a transonic wind tunnel.The model was equipped with pressure taps connected to the fast response pressuretransducers.Measurements were conducted at different free-stream Mach number from 0.61 to0.76.The principle goal of this investigation was to experimentally discuss the shock-buffet criterion over a SC(2)-0410 supercritical pitching related to the hysteresis loops of total drag and trailing edge pressure,the behaviour of the shock wave foot location,the pressure distribution over the upper surface,and by implementing the wavelet analysis of the normal force.To ensure capturing the buffet phenomenon by utilizing these criteria,a pressure port has been drilled exactly at the trailing edge of the airfoil where its output was used to detect the buffet phenomenon for different conditions.Visual representation of the flow using the shadow graph flow visualization technique for different test cases is further used to illustrate the unsteady shock wave motion.A comparative analysis of experimental measurements shows that the conducted criteria confirm each other when the buffet phenomenon occurs at the position of the oscillating cycle.

Numerical simulations of 2-D floating body driven by regular waves

An improved meshing method based on Fluent is used to update the computational meshes in solving the Navier-Stokes （N-S） equations for viscous and incompressible free surface flows with the volume of fluid （VOF） method. To maintain the mesh quality when updating meshes for a moving structure, the computational domain is separated into several parts and each part corre- sponds to a specific type of body motion. The numerical results of the interaction between the floating body and the regular waves agree well with the experimental data. A total of eight typical motion types are simulated separately to understand the correlation between the motion types and the wave transmission as well as the forces acting on the floating body. Numerical experiments show that the wave transmission increases in the case of sway and heave motions and decreases in the case of pitch motion as compared with the stationary case. It is also found that the sway motion reduces the horizontal wave force acting on the floating body, while the heave motion enhances the vertical wave force.