Showing papers on "Added mass published in 1990"

Numerical Solutions for Large-Amplitude Ship Motions in the Time Domain

Abstract: A three-dimensional time domain approach is used to study the large-amplitude motions and loads of a ship in a seaway. In this approach, the exact body boundary condition is satisfied on the instantaneous wetted surface of the moving body while the free-surface boundary conditions are linearised. The problem is solved using a transient free-surface Green function source distribution on the submerged hull. Extensive results are presented which validate and demonstrate the efficacy of the method. These results include linear and large-amplitude motion coefficients and diffraction forces with and without forward speed, calm-water resistance and added-resistance with waves and motions, the large-amplitude motion history of a ship advancing in an irregular seaway, as well as load distributions on the changing submerged hull. Most of the large-amplitude results we obtained are new and illustrate the importance of nonlinear effects associated with the changing wetted hull. Of special significance are the dramatic changes of the added mass, the steady resistance, and sinkage and trim forces as the motion amplitudes increase.

Dynamic Analysis of Non-Linear Structures by the Method of Statistical Quadratization

Abstract: 1: Introduction.- 1.1 Introduction.- 1.2 Aim of Study.- 1.3 TLP Model.- 1.4 Environmental Loads.- 1.4.1 Methods to Compute Viscous Forces.- 1.4.2 Methods to Compute Potential Forces.- 1.5 Literature Review of TLP Analyses.- 1.6 Scope of Study.- 2: Equivalent Stochastic Quadratization for Single-Degree-of-Freedom Systems.- 2.1 Introduction.- 2.2 Analytical Method Formulation.- 2.3 Derivation of Linear and Quadratic Transfer Functions.- 2.4 Response Probability Distribution.- 2.5 Response Spectral Density.- 2.6 Solution Procedure.- 2.7 Example of Application.- 2.8 Summary and Conclusions.- 3: Equivalent Stochastic Quadratization for Multi-Degree-of-Freedom Systems.- 3.1 Introduction.- 3.2 Analytical Method Formulation.- 3.3 Derivation of Linear and Quadratic Transfer Functions.- 3.4 Response Probability Distribution.- 3.5 Response Spectral Density.- 3.6 Solution Procedure.- 3.7 Reduced Solution Analytical Method.- 3.8 Example of Application.- 3.9 Summary and Conclusions.- 4: Potential Wave Forces on a Moored Vertical Cylinder.- 4.1 Introduction.- 4.2 Volterra Series Force Description.- 4.3 Near-Field Approach for Deriving Potential Forces.- 4.3.1 Fluid Flow Boundary Value Problem.- 4.3.2 Perturbation Expansion.- 4.4 Linear Velocity Potential.- 4.5 Added Mass Force.- 4.6 Linear Force Transfer Functions.- 4.6.1 Wave Diffraction Force.- 4.6.2 Wave Diffraction Moment.- 4.6.3 Hydrodynamic Buoyancy Force.- 4.6.4 Comparison to Morison's Equation.- 4.7 Quadratic Force Transfer Functions.- 4.7.1 Wave Elevation Drift Force.- 4.7.2 Wave Elevation Drift Moment.- 4.7.3 Velocity Head Drift Force.- 4.7.4 Velocity Head Drift Moment.- 4.7.5 Body Motion Drift Forces and Moment.- 4.7.6 Numerical Examples for Fixed Vertical Cylinder.- 4.8 Transfer Functions for Tension Leg Platform.- 4.8.1 Modification of Cylinder Transfer Functions.- 4.8.2 Numerical Example for Tension Leg Platform.- 4.9 Summary and Conclusions.- 5: Equivalent Stochastic Quadratization for Tension Leg Platform Response to Viscous Drift Forces.- 5.1 Introduction.- 5.2 Formulation of TLP Model.- 5.3 Analytical Method Formulation.- 5.4 Derivation of Linear and Quadratic Transfer Functions.- 5.5 Response Probability Distribution.- 5.6 Response Spectral Density.- 5.7 Axial Tendon Force.- 5.8 Solution Procedure.- 5.9 Numerical Example.- 5.10 Summary and Conclusions.- 6: Stochastic Response of a Tension Leg Platform to Viscous and Potential Drift Forces.- 6.1 Introduction.- 6.2 Analytical Method Formulation.- 6.3 Numerical Results.- 6.3.1 Response to Quadratic Drag Force.- 6.3.2 Response to Quadratic Wave Elevation/Velocity Head Force.- 6.3.3 Response to Quadratic Body Motion Force.- 6.3.4 Response to Combined Viscous and Potential Quadratic Forces.- 6.3.5 Evaluation of Newman's Approximation.- 6.3.6 High Frequency Axial Tendon Force.- 6.4 Summary and Conclusions.- 7: Summary and Conclusions.- Appendix A: Gram-Charlier Coefficients.- A.1 Introduction.- A.2 Gram-Charlier Coefficients.- Appendix B: Evaluation of Expectations.- B.1 Introduction.- B.2 Expectations Involving Quadratic Nonlinearity.- B.3 High Order Central Moments.- Appendix C: Pierson-Moskowitz Wave Spectrum.- Appendix D: Simulation Methods.- D.1 Introduction.- D.2 Linear Wave Simulation.- D.3 Linear Wave Force Simulation.- D.4 Drag Force Simulation.- D.5 Quadratic Wave Force Simulation.- References:.

A Rankine Panel Method to Calculate Unsteady Ship Hydrodynamic Forces

Abstract: A panel method to calculate unsteady ship hydrodynamic forces is introduced. First, formulations were made for both steady and unsteady free-surface conditions under the assumption of small perturbation over the double body flow around a ship. A newly derived free-surface condition for unsteady motion makes a theoretical pair with Dawson's steady linearized free-surface condition. Next, a Rankine panel method was applied to solve the equations based on the present unsteady free-surface condition. For radiation condition of waves a numerical damping was introduced into the free-surface condition. Calculations were made of the unsteady hydrodynamic forces such as added mass, damping and wave exciting forces for a two-dimensional submerged cylinder and an ellipsoidal ship hull form. By comparing with other calculations and experiments it was shown that the present numerical method is useful for better understanding of the unsteady free-surface flow problems.

Wave‐Induced Breakout of Half‐Buried Marine Pipes

Abstract: An experimental study is conducted in order to identify the major physical processes leading to the breakout of half‐buried submarine pipelines from the seafloor under ocean‐wave action. Both the hydrodynamic loading on the exposed surface of the pipe as well as the pore‐pressure distribution on the buried surface were measured. The resulting displacement histories of the pipe were recorded and analyzed in order to identify the critical pipe‐soil‐wave conditions for the detachment of the pipe from the seabed. The paper examines the balance of the pipe under the combined lift and drag loading from the water wave. The experimental coefficients of drag, lift, and added mass have been calculated by the least squares method and compared with theoretical predictions. As for the soil response, a simple theoretical model is worked out to describe the pore‐pressure resistance force at the soil‐pipe interface. An experimental breakout force‐time power law is obtained and compared with the theoretical model.

Motion Response Simulation of Damaged Floating Platforms

Abstract: This thesis describes a computer based method and a procedure to simulate the motion response of a damaged platform under wave, wind and current effects. The aim of the study was to develop an analysis procedure which could be a useful tool to designers and certifying authorities in assessing the safety of mobile platforms in extreme environmental and damaged conditions. The thesis begins by explaining the benefits of using floating structures in developing oil fields. Basic stability requirements for floating production vessels are summarised. Recent and past damage simulation studies in the literature are reviewed. Some information about the number of accidents involving floating offshore platforms operated world-wide is presented. A few of the disasters occurring in recent years are given as examples to emphasise the importance of the subject. The Morison approach and 2D source-sink distribution technique are reviewed, and calculations of wave forces acting on a semi-submersible are carried out in order to make comparisons between the two methods. Theoretical derivations of wave forces in the frequency domain based on the Morison approach are carried out in detail for a twinhulled semi-submersible. The development of computer programs based on both methods is summarised. A general method for calculating wave forces and moments on circular cylinders of offshore structures is derived. By using the developed method one can calculate the wave loading on cylindrical members of fixed or floating offshore structures orientated randomly in waves. This method also provides a basic tool for determining the wave forces and moments that a floating structure is subjected to as it experiences large amplitude oscillations in six degrees of freedom. A general method is established in this chapter to calculate the hydrodynamic loading due to the rigid body motion of the platform. The calculation of restoring forces is discussed: a detailed description of the methods used to calculate hydrostatic forces, mooring stiffness coefficients and wind forces is given in the appendices. The calculation of inertia forces and moments defined from Newton's second law is introduced as part of a general calculation procedure. The derivation and the solution of motion equations in the time domain are presented. Details of model tests carried out to validate the non-linear large amplitude motion calculation procedures are presented. A description of a circular twin-hulled semi-submersible model and the loading conditions is given. The test setup and instrumentation are presented briefly. Test procedures for inclining, natural period and motion tests in waves are discussed. Methods of analysis of motion response measurements in six degrees of freedom in intact, transient and damaged conditions for head and beam seas are given. The results of motion response measurements are presented in time histories. In order to validate the numerical prediction procedures and the software based on these procedures, the physical test conditions are simulated numerically and a comparison of test results with numerical predictions is presented. Simulation studies based on the non-linear motion equations are presented with the aim of providing comparisons to illustrate the effects of non-linearities in wave and motion induced forces. A summary of the systematic study carried out to illustrate the effects of non-linear terms on the solution of the motion response equations is given. The results of the parametric studies to investigate the effects of flooding rate and of size of damaged compartment on motion response characteristics are also discussed. The other aspects of roll motion such as the effects of non-linear drag force, first order wave elevation, different wave heights and GM's, and non-linear added mass and damping forces on the motion behaviour and the steady tilt of semi-submersibles are investigated. The variations of GM and GZ values as a function of heel angle are also presented.

Distribution of Added Mass and Damping Along the Length of a Ship Model Moving at High Forward Speed

Abstract: A series of forced-oscillation model tests was carried out at the Delft Shiphydromechanics Laboratory. The objective was to determine the hydromechanic coefficients of a model moving at high forward speed and the distribution of the added mass and damping along the length of the model in order to compare the results obtained with values computed using the strip theory calculation method. The results of the measurements and computations are presented, and the validity of the strip theory is analyzed. The implications for the use of this theory with high forward speed are noted, and an improved method for processing experimental results to yield added mass is outlined.

Parametric study of ship-hull vibrations

Abstract: A parametric study carried out to investigate the vertical free vibrations of a ship hull is described. The analysis takes into account all the effects of the rotary inertia of mass, shear distortion, thrust force, shear lag and various damping components. The influence of these parameters on ship hull vibrations is explained. Special emphasis is placed upon a method for calculating the overall damping ratios.

Acceleration sensitivity of crystal resonators affected by the mass and location of electrodes

Abstract: Predominant thickness-shear frequencies and modes of a crystal plate with electrodes of arbitrary shape and mass distribution are obtained by a finite element method based on Mindlin's first-order equations with platings. These frequencies and modes are used in a perturbation method for computing the acceleration sensitivity of crystal resonators with electrodes. Computations are made for a square AT-cut quartz plate which is supported by a four-point mount and coated with identified square and uniform electrodes on the upper and lower faces of the plate. To study the effect of uneven distribution of electrode mass, acceleration sensitivities are calculated when a small mass is added at various locations near the edges of the square electrodes. It is found that the percent increase of the acceleration sensitivity of the resonator with a small added mass to that of the resonator without added mass ranges from 3.8% to 541.7%, depending on the location of the small mass placed at the edges of the electrodes. >

Wave radiation by truncated elliptical cylinder

Abstract: The radiation of small-amplitude water waves by an oscillating submerged elliptical cylinder is investigated analytically. The cylinder may either be totally submerged and resting on the seabed (case I) or partially immersed in the free surface (case II). The fluid domain is divided into two regions: an interior region about (Case I) or below (case II) the structure and an exterior region extending to infinity in the horizontal plane. Expressing the boundary-value problem in elliptical coordinates, analytical expressions for the velocity potentials satisfying the governing equation and boundary conditions in each region may be written in terms of infinite series involving Mathieu and modified Mathieu functions. The unknown coefficients in these series are determined by imposing continuity of mass and momentum fluxes at the fluid interface between the two regions. Utilizing this solution, numerical results are presented that illustrate the variation of the added-mass and radiation damping coefficients with oscillation frequency for several example structures.

Flow-Induced Vibration of Long-Span Gates : Verification of Added Mass and Fluid Damping

Abstract: The added mass and the fluid damping coefficient were derived theoretically in a dimensionless form in a previous study. To verify the theoretical results of the added mass and the fluid damping coefficient, the experimental results of a model test are presented in this study. A planar vertical gate undergoes free damped vibrations in air and still water. The added mass and the fluid damping coefficient are calculated from the measured frequencies and damping ratios of the damped vibrations. Consequently, it is shown that there is good agreement between the theoretical and experimental results

The Shape-Effect Of Buffer On The Longitudinal Vibration Of A Pipe-String In The Deep Sea

Abstract: In order to analyze the longitudinal vibration of the pipe-string in the deep sea, first, the drag and added mass coefficients of various buffer-models vibrating axially in water were evaluated by the method developed by the authors. Then, the forced longitudinal vibration of the pipe-string equipped with a pump-module and a buffer was analyzed theoretically by introducing the fluid forces evaluated with the above-obtained coefficients. Furthermore, the axial stress induced in the pipe-string was calculated. The results indicate that the buffer whose shape causes a higher drag force is more useful for reducing the amplitude of the vibration and the axial stress in the pipe-string, and that the highest-drag buffer used in this study causes a half amplitude of the vibration and about 63% axial stress at the first resonance as compared with those produced by the lowest-drag model.

Currents and wave forces on ships and marine structures

Abstract: Forces on a body oscillating in incoming waves and a weak current are studied. Coupling between the oscillatory wave field and the steady flow around the body is accounted for. Friction and separation effects are disregarded, and the fluid flow is modelled by potential theory. The boundary value problem for the velocity potential is transformed to an integral equation by Green's theorem, using a Green function satisfying the linear free surface condition with small forward speed. Local, small forward speed expansions for the potential and the Green function are applied in the vicinity of the body, giving two sets of integral equations for the unknown zero speed and the small forward speed potentials. There are unknowns on the wetted body surface only. The right hand side of the small forward speed integral equation involves a fast decaying integral over the free surface. There is no water line integral in the integral equations. The method is applicable to bodies of arbitrary shape. The diagonal added mass and damping coefficients are found to be functions of the current speed only through the encounter frequency. The linear exciting forces are found by generalised Haskind relations. Analytical expressions for the mean second order horizontal drift forces and the mean second order yaw moment are given, and numerical examples are presented for different body geometries. The mean drift forces are usually increased by the presence of a weak current along the incoming wave direction. For complex body geometries the wave drift damping may, however, in narrow wave number regions, become negative. The mean yaw moment may be changed by 100% by the presence of a weak current. Energy check and numerical convergence of the method are also discussed.

Hydrodynamic coefficients of a vertical circular cylinder

Abstract: The added mass and the damping coefficient of a large surface-piercing circular cylinder extending to the seabed and undergoing horizontal oscillations are described. A closed-form solution to the corresponding linear radiation problem is obtained by the use of eigenfunction expansions. Attention is given to the vertical distribution of these coefficients and to their high-frequency asymptotic behaviour. Comparisons are made with experimental measurements. The application to typical offshore structures is discussed. Key words: added mass, cylinders, damping, hydrodynamics, ocean engineering.

A boundary element method to calculate the fluid hydrodynamic mass matrix in structural analysis including free surface waves

Abstract: A boundary element method has been developed to calculate the added mass matrix of fluid coupled structures in the case when the fluid is assumed to be compressible and inviscid. The potential flow is represented by a double layer density with linear interpolation functions. A linear set of equations for the fluid motion is obtained by Galerkin's procedure. The added mass matrix is not symmetric but a symmetrization procedure is established. The method has been implemented into a computer code for two‐dimensional geometries, whose results are presented here. A comparison with the analytical results already shows excellent agreement for coarse discretizations.

Experimental study of dynamical characteristics of a long annular seal. Influence of inlet swirl on the dynamic fluid moment and force.

Abstract: The influence of inlet swirls on dynamic fluid reaction moments and forces of a long annular seal was experimentally studied. The experiment was conducted under the parameters of rotor speeds, cylindrical whirling speeds and seal inlet swirl velocities. The rotor and the outer cylinder were set in a concentric condition. The tangential and restitutional moments were derived from the measured dynamical fluid forces in order to investigate the influence of the inlet swirl. Moments and forces were expressed as stiffness, damping coefficients and added mass. As a result, it was found that the dynamic characteristics of moments and forces are affected by the inlet swirl velocity. The cross-coupling terms of moment coefficients change their sign when the inlet swirl velocity turns to the opposite direction.

Time domain simulation of slow drift motion of a moored floating structure in irregular waves including time varying slow motion hydrodynamic forces

Abstract: Time domain simulations of a slow drift motion of a moored floating structure in bichromatic or irregular waves are compared with model experiments in wave basin. The simulations include various slow motion hydrodynamic forces such as a drag coefficient depending on KC number, a time varying wave drift damping, an added mass change due to waves etc. as well as second order wave excitation. Most of them are given by slow motion forced oscillation tests in regular waves. They show excellent agreement with the experiments and determine contribution of each slow motion hydrodynamic forces.

Dynamic analysis of coupled articulated tower and floating production systems

Abstract: In this thesis, motion and structural response characteristics of coupled articulated tower and ship systems under various types of environmental loading are investigated. In Chapter 1, the main objectives of the study are explained. A discussion of the previous investigations carried out on the subject is presented briefly. The main characteristics of the existing and proposed structures, the accepted criteria for the environment in which these structures are working or are proposed to work and the assumptions underlying the theoretical analysis are summarized. The detailed literature review is left to each individual chapter. The outline of the thesis is also explained in this chapter in order to guide the reader. Chapter 2 deals with the modelling of environmental loading on coupled articulated tower and ship systems. Wave, wind and current are chosen as prime loading effects on these systems. The flow regimes of vertical surface piercing cylinders are shown. The application of Morison's equation is discussed. The Froude-Krylov forces are derived for the wave induced force calculations on the box-shaped barges which represent the storage tanker. The second order wave forces present in regular and irregular waves on the box-shaped barges are also discussed. Various formulations in defining the short crested seas, steady current as well as static and dynamic wind are given. Chapter 3 is concerned with the prediction of the motion and structural response of single articulated tower and ship systems under first and second-order wave, current, and steady and dynamic wind excitation. Chapter 4 aims to obtain the motion equations for a double articulated tower by using the Lagrange method. A double articulated tower configuration which consists of five cylindrical elements is considered. The same configuration is also used during the model tests described in Chapter 7. First order wave forces are considered as excitation forces. The shear forces and bending moments as well as the axial tension and wave induced force distribution along the tower are presented for a number of wave frequencies. The parametric studies include the sensitivity of the natural frequency of the system to the geometric changes, the effect of increasing water depth and deck weight on motion response, a comparison of the angular motion and the joint force values of the double articulated tower with the values of a geometrically similar single articulated tower. In Chapter 5 a motion response analysis of a double articulated tower and ship system in regular waves is presented. 2-DOF and 5-DOF mathematical models are considered. The results of the two mathematical models are compared with each other as well as with the experimental measurements carried out at the Hydrodynamics Laboratory. The shear force and bending moment distributions along the double articulated tower with the barge connected to it are shown. The motion and structural response values of the coupled double articulated tower and ship system are compared with the values of a geometrically similar single articulated tower and ship system. This chapter ends with some parametric studies which examine the effect of various geometrical changes on the system responses as well as on the yoke forces including the yoke length and the yoke orientation. In chapter 6 the time domain simulation procedure is applied to the motion equations to obtain motion response characteristics of three different configurations. In Chapter 7, a description of model tests carried out in regular waves is presented. These tests are: - motion response measurements with a double articulated tower over a range of wave frequencies and wave heights, - motion response and the yoke force measurements with a coupled double articulated tower and a rectangular box-shaped barge - motion response measurements for a barge model moored by means of linear springs located on the fore and aft ends of the model. In addition to the measurements listed above, the added mass, drift force coefficients and still water and wave damping coefficients of the barge model were measured. The numerical filtering procedure developed to analyse the data obtained from the free oscillation tests in waves is described in Appendix C. In the final Chapter 8, the main emphasis is placed on drawing overall conclusions and on making some recommendations for future studies on this subject.

The Concepts of Added Mass and Inertia Forces and Their Use in Structural Dynamics

Abstract: A discussion on the concepts of added mass and inertia forces is provided combined with illustrative examples. The paper relates to submerged circular cylinders - single or in groups - only, and from an assessment of measured forces and analytical developments it is advocated that the added mass values determined from potential flow theory are adequate also for real flows. A procedure for determining the added mass coefficients for single cylinders and groups of cylinders has been developed and results are given for 4 different configurations.

Method and device for stabilizing marine platform

Abstract: PURPOSE: To efficiently control the primary motion to be induced by heaving, pitching, rolling, surging, and swaying waves without fixing a floating platform to the bottom of the sea, by connecting a mass stabilizer having the sufficient added mass formed of water surrounding the stabilizer so that it may be suspended beneath the lower side of a floating platform. CONSTITUTION: An added mass stabilizer 24 is suspended beneath a strut stabilizing floating platform 22 by many tendons 22, namely, ropes or stretching materials, at a sufficient distance. A stabilizer system maintains suspending tendons 26 in the pulling state in relation to all loading state by providing the added mass stabilizer of a water weight, and the sufficient water mass (that obtained by the weight of water to be moved when the sunk weight and the stabilizer mass are moved) performs the specified operation. That is, since the mass acts as a fixing member according to external force, the floating platform can be so designed as to cope with the heave, pitch, roll, surge and sway motions as the primary motion.

Drag and added mass study on arbitrary oscillating marine bodies

Abstract: An original applied study has been developed, concerning the analysis and the prediction of the hydrodynamic forces which act upon arbitrarily oscillating bodies in the sea The Morison formulations have been applied also for the case of constant drag and mass coefficients, when the wake velocities which are produced by the body motions in all the past histories are corrected Wake velocities have also been computed on the basis of the unsteady turbulence theory, which is available from the existing literature The predicted results have been compared with experimental ones from many laboratory pendulum tests The said tests have been performed both on single and coupled cylinders, with particular care for the overall configuration cases and possibilities Starting from the 1st case of square cylinders, the study has been generalised to the case of circular cylinders

シェル形長径間ゲートの流体関連振動 : 第1報, アンダフロータイプの基本的な自励振動特性

Abstract: This study presents the fundamental characteristics for a flow-induced vibration of shell-type long-span gates which have a gate front consisting of vertical and inclined weir plates. The shell-type gates possess two freedoms to vibrate in the streamwise and vertical directions due to their bending flexibility. Both streamwise and vertical vibrations couple well with each other through hydrodynamical forces acting on the weir plates, thus resulting in a severe self-excited vibration. A two-dimensional model test for a shell-type long-span gate under small gate-openings was performed to measured the vibration frequency, the exciting ratio and the gate motion trajectories. From the obtained results, the fundamental characteristics, such as the vibration frequency ratios, a reduced fluid exciting coefficient, a reduced added mass, and a phase difference between the vertical and streamwise vibrations, were calculated. Furthermore, it was revealed from the measured gate motion trajectories that a press-shut device which causes a self-excited vibration is formed by a skillful dynamic mechanism of the coupled vibration.