Showing papers on "Added mass published in 1988"

Viscous Flow Structure Interaction

Abstract: Considerable research activities in vibration and seismic analysis for various fluid-structure systems have been carried out in the past two decades. Most of the approaches are formulated within the framework of finite elements, and the majority of work deals with inviscid fluids. However, there has been little work done in the area of fluid-structure interaction problems accounting for flow separation and nonlinear phenomenon of steady streaming. In this paper, the Arbitrary Lagrangian Eulerian (ALE) finite element method is extended to address the flow separation and nonlinear phenomenon of steady streaming for arbitrarily shaped bodies undergoing large periodic motion in a viscous fluid. The results are designed to evaluate the fluid force acting on the body; thus, the coupled rigid body-viscous flow problem can be simplified to a standard structural problem using the concept of added mass and added damping. Formulas for these two constants are given for the particular case of a cylinder immersed in an infinite viscous fluid. The finite element modeling is based on a pressure-velocity mixed formulation and a streamline upwind Petrov/Galerkin technique. All computations are performed using a personal computer.

Restoring forces on vertical circular cylinders forced by earthquakes

Abstract: An eigenfunction solution is presented for the dynamic response of vertical circular cylinders to earthquake excitation in a compressible fluid of finite depth. This single eigenseries expansion eliminates the need for a double summation over both the eigenfunctions and the trial functions as required by Rayleigh-Ritz methods. Revised definitions for the added mass and hydrodynamic radiation damping coefficients per unit length are derived from the hydrodynamic fluid pressures. Based on comparisons between these newly defined coefficients, the compressibility of the fluid is found to be relatively more important at dimensionless frequencies greater than unity (ω > 1.0) when analysing both rigid and flexible cylinders having relatively large diameter to water depth ratios,r0/h > 0.25 (squatty type). This conclusion regarding the relative importance of the fluid compressibility is derived from a comparison between the relative magnitudes and the vertical distributions over depth of both the added mass and radiation damping coefficients per unit length for both rigid and flexible squatty cylinders. From additional comparisons with Rayleigh-Ritz solutions that require trial functions, the results for totally immersed flexible slender cylinders (r0/h 0.25) are not. The reason for this difference appears to be in the truncation of the trial function series in the Rayleigh-Ritz methods, which excludes the higher mode shapes, and in the definitions of the added mass coefficients. Comparisons with laboratory data for both rigid and flexible cylinders confirm the accuracy of the solutions obtained by the eigenseries in the limited frequency interval above the highest frequency for surface gravity waves (f > 1.0 Hz) and below the first dimensionless cut-off frequency for acoustic waves (ω< 1.0).

Particle size effects on Lagrangian turbulence

Abstract: Perturbation methods are used to show that the equations of motion for a small rigid sphere in a steady laminar flow take the form of a dynamical system in which phase volume is not conserved. In the absence of stagnation points, particle inertia and virtual mass effects destroy Lagrangian turbulence and the particles are captured by periodic or quasiperiodic orbits that are associated with the vortices of the flow. When gravitational effects are included, it is found that point particles can sediment chaotically, but that particle inertia and virtual mass effects tend to eliminate the chaotic behavior. An interesting consequence of the latter phenomenon is that finite particles which are denser than the fluid can be permanently suspended in three‐dimensional cellular flows. Numerical results are presented for the Arnold–Beltrami–Childress [C. R. Acad. Sci. Paris 261, 17 (1965)] flows.

A Hydrodynamic Study of the Oscillation Motion in Swimming

Abstract: The purpose of this study was to determine the validity of the quasi-static assumption—that fluid forces exerted under unsteady flow conditions are equal to those exerted under similar steady flow conditions—in the case of a cylindrical model oscillating in a vertical plane about a transverse axis normal to the flow. The findings indicated that the quasi-static approach is applicable only to cyclic motions with low frequencies and small accelerations. For swimming motions that involve high frequencies and high accelerations, like those that occur in competitive swimming, the vortex shedding effect and the added mass effect must be taken into account if accurate values are to be obtained for hydrodynamic forces.

Estimates for the Added Mass of a Multi-Component, Deeply Submerged Vehicle. Part 1. Theory and Program Description

Abstract: : An analytic method is presented for estimating all the added mass terms of a deeply submerged, submarine-like rigid body. This body may consist of any number of components (hull, sail, fins, etc.). Each component is represented as an ellipsoid with three independently sized principal axes; this allows the added masses to be calculated analytically. Ellipsoid geometry, orientation, and relative location are chosen so that both added masses and added moments of inertia are optimally modelled. Interference effects between the main hull component and an appendage are approximately accounted for by using the flow field around a replacement ellipsoid for the hull to modify the flow at the appendage; interference effects between appendages are neglected. The analysis uses incompressible potential flow theory. It does not account for any circulation in the flow. Calculations carried out using this method are very fast. They show that both appendage thickness and hull interference can appreciably affect those added mass coefficients which contribute to coupling. Keywords: Submarines hydrodynamics, Potential flow, Added mass, Acceleration coefficients, Dynamic derivatives, Equations of motion, Canada. (EDC)

Kinetic energy and added mass of hydrodynamically interacting gas bubbles in liquid

Abstract: By averaging the basic equations on microscale, expressions are derived for the effective added mass density and the kinetic energy density of a mixture of liquid and gas bubbles. Due to hydrodynamic interaction between the bubbles there appears to be a difference between the effective added mass density and the mass coefficient of the kinetic energy density due to relative motion of the phases. For spherical bubbles with velocities all equal, isotropic spatial distribution, gas fraction α and liquid density 1, the effective added mass density and the mass coefficient of the kinetic energy density (due to relative motion) are calculated. They are respectively 0.5α(1 + 3.324α)1 and 0.5α(1−0.676α)1 and show good agreement with results in the literature.

Influence of added mass on ice impacts

Abstract: The present paper applies potential theory to describe the variation of the added mass of an iceberg and its coupling effects on an offshore structure for various separation distances up to the point of contact. The strengths and weaknesses of the proposed model are discussed together with its practical application in ice mass impact problems. An impact model based on dynamic analysis is developed to calculate the impact force and response of a structure for head-on collisions. Both the contact-point added mass estimated in the present study and the traditionally assumed far-field added mass are used in the impact model separately. The results are compared and the crucial roles played by the ambient fluid during impact are discussed. Key words: added mass, hydrodynamics, ice impact, ocean engineering, offshore structures.

Numerical Analysis Method for Two-Dimensional Two-Fluid Model Using Control Volume Formulation

Abstract: A numerical calculation technique for the two-dimensional two-fluid model has been developed. The control volume formulation and non-staggered mesh scheme are employed in order to confirm that solutions satisfy the conservation equations of the two-fluid model. Numerical instability due to the non-staggered mesh is overcome by considering additional flows induced from a local pressure gradient on control volume boundaries. The Godunov method and SIMPLE method are used to estimate the additional flow for compressible and incompressible two-phase flows, respectively. These methods are modified to take the density difference between the phases and the added mass effect into account. The present method has been applied to analyses of two-dimensional two-phase flow discharge from a pipe and phase separation due to gravity in a horizontal circular pipe in order to investigate the capability of dealing with fundamental phenomena of two-dimensional two-phase flow. The present technique enables a small scale compu...

Forces on oscillating bodies in viscous fluid

Abstract: This paper describes a method for determining the fluid forces on oscillating bodies in viscous fluid when the corresponding flow problem has been solved using the finite element method. These forces are characterized by the concept of added mass, added damping and added force. Numerical results are obtained for several example body shapes. Comparison is made with exact analytical results and other finite element results for the limiting cases of Stoke's flow and inviscid flow, and good agreement is obtained. The results for finite values of the body amplitude parameter β show the appearance of added force from the steady streaming component of the flow for asymmetric bodies. Results are also obtained for the associated flow where the fluid remote from a fixed body is oscillating.

Viscous Forces Acting on Irregularly Oscillating Circular Cylinders and Flat Plates

Abstract: In the present paper hydrodynamic forces acting on oscillating circular cylinders as well as flat plates perpendicular to the motion in regular and irregular modes due to vortex shedding are experimentally investigated in order to clarify the memory effect or history effect on the hydrodynamic forces. The experimental results for sinusoidal motion show that the drag and added mass coefficients in steady-state condition are significantly different from those of the first swing from the start because of the existence of old vortices generated in the previous cycles around the cylinder. It is found from the experiments in irregular modes that the drag and added mass coefficients significantly vary every swing. It is confirmed that these coefficients during a swing depend on the relative amplitude or the Keulegan-Carpenter number of the previous swings as well as that of the swing under consideration.

A surface panel method for the calculation of added mass matrices for finite element models

Abstract: A method for generating the added field fluid mass matrix for use in dynamic analyses of submerged structures is presented. This method uses a distribution of panel singularities in the form of sources or dipoles on the fluid/structure interface to represent the velocity potential in the fluid surrounding the structure. Based on the results of a variety of investigations of computational performance, convergence, and dynamic response of floating cylinders, ship hulls, and propeller blades, the surface panel method is shown to provide an effective alternative to the finite element added mass matrix system.

In-line forces on oscillating bodies in a fluid flow

Abstract: An experimental investigation was performed to study the in-line forces acting on oscillating bluff bodies -a sphere, a cylinder and a disc- in a fluid flow. The energy dissipations calculated with fluid resistance were well correlated by the following correlation regardless of body shape over the whole range investigated. E2/3fv=E2/3f+E2/3vwhere Efv, Ef and Ev are energy dissipations for the oscillating body in a fluid flow, for the stationary body in a fluid flow and for the oscillating body in a liquid at rest.

The drag and added-mass coefficients of cylinders vibrating axially in water.

Abstract: Cylinders with various aspect-ratios and spheres, attached axially to a vertical spring, were vibrated longitudinally in still water by a vibrator which provided the top of the spring with a sinusoidal displacement. Then, the drag and added-mass coefficients were analysed by introducing the experimental values of amplitudes and frequency in the resonance into the solution of a spring-mass-damper system. First, to examine the validity of this method, the results on the spheres were compared with those by Sarpkaya, and both results proved to be in fairly good agreement. The results on the cylinders led to the following conclusions. There is a good correlation between those coefficients and Keulegan-Carpenter number Kc(=UmT/D). AS Kc. increases, the added-mass coefficient increases linearly and the drag coefficient decreases exponentially. When Kc exceeds about 10, the drag coefficient approaches the constant value. However, there is no clear correlation between these coefficients and Reynolds number.

Experimental study of hydrodyamic lateral force about a model ship berthing at a quay

Abstract: It is important to know the lateral added masses of ships moving laterally toward a quay or moored near a quay because the presence of the quay will alter that portion of the potential flow component of the hydrodynamic lateral force that is caused by lateral acceleration. Furthermore, the other portion of this component, which is generated by lateral velocity, depends upon the rate of change in the added mass. The remaining component in the force equation is viscous drag, which varies with velocity. Although there have been theoretical studies of the hydrodynamic lateral force in restricted waters having a side wall, few experimental studies have been carried out. The authors therefore undertook model experiments for a 225 GT fish carrier boat. These were carried out using lateral accelerating tests, and changes in the lateral added mass as affected by the quay were analyzed.

The limiting values of added masses of a partially submerged cylinder of arbitrary shape

Abstract: Using Schwarz's integral formula, new series expressions are obtained for the low- and high-frequency limiting values of the added-mass tensor of partially submerged cylinders of arbitrary shape, including non-smooth and nonsymmetric ones. These series contain the Fourier coefficients of simple geometric quantities of the body contour, and their rate of convergence is controlled by geometrical parameters reflecting the smoothness of the double-body contour. Alternative expressions of a more usual form, in terms of the conformal mapping coefficients of the body contour, are also presented. The off-diagonal elements of the limiting added-mass tensors as well as the low-frequency added moment of inertia for nonsymmetric sections are apparently given for the first time. As an application, closed-form expressions for the limiting added-mass coefficients of an extended-Lewis family of ship sections are obtained.

Three-Dimensional Effects on Added Masses of Ship-Like Forms for Higher Harmonic Modes

Abstract: Sectional added masses of an elastic beam vibrating vertically on the free surface in higher harmonic modes are evaluated. Hydrodynamic interactions between neighboring sections, which strip theory ignores, are considered for modal wave lengths of the order of magnitude of cross-sectional dimensions of the body. An approximate solution of modified Helmholtz equation which becomes a singular perturbation problem at small wave lengths is secured to get an analytic expression for added masses attending higher harmonic modes. As a bound of the present theory, the modified Helmholtz equation is solved for the long flat plate vibrating at high frequency on the water surface without any limitations on modal frequency. Finally, extensive series of numerical calculations are carried out for ship-like forms. It is found that when modal wave length is comparable to or shorter than a typical cross-sectional dimension of a body, sectional interaction effects are large which result in considerable reductions in added masses. For a fuller section, the ratio of added mass reduction is greater. In the limit of vanishing sectional area, the added masses approach to that of flat plate of equal beam. It is shown that the added mass distribution for a Legendre modal from can be determined form the present theory and that the results agree with the extensive three-dimensional determination of Vorus and Hilarides.

Hydrodynamic Inertia and Damping of Ship Hull Vibrations

Abstract: The entrained water plays an important role in ship hull vibrations. The classic Lewis method for calculation of hydrodynamic added mass has some inherent shortcomings that can result in insufficient accuracy, particularly for higher order modes. This is essentially due to the fact that the Lewis method uses a diagonal mass matrix that is dependent on the mode of vibration, while the physical reality is more accurately represented by a mode-independent, full mass matrix. Such full mass matrices can be calculated with Finite Volume or Source-Sink methods, which, however, require extensive computer calculations with detailed input data. A method is presented with which the Lewis transform can be used to determine a full mass matrix and gives very good agreement with Finite Volume calculations for a test case on a small ship. The Finite Volume calculations have also been used to study damping due to sound radiation. These calculations indicate that the hydrodynamic damping due to this mechanism contributes a significant part of the total modal damping.

Vertical Plane Oscillation Experiments on a Series of Two-Dimensional SWATH Demi-Hull Sections

Abstract: Results of vertical plane oscillation experiments carried out to determine the added mass and damping characteristics of a series of two-dimensional demi-hull sections are presented. These sections represent variants of several Small Waterplane Area Twin Hull (SWATH) ship designs currently under development by the U.S. Navy. Added mass and damping coefficients, along with radiated wave measurements, are calculated for eight models, at two drafts and at least two amplitudes of oscillation. Comparisons between models illustrate the effects of lower hull geometry, strut offset, and strut thickness.

Fluid-structure coupled vibration of cantilever plates and continuous plates

Abstract: In this paper the finite element method is used to calculate fluid-structure coupled free vibrations of rectangular vertical cantilever plates and continuous plates. The fundamental frequencies of rectangular vertical cantilever plates under different water depth are given, and the first three frequencies and corresponding modal shapes, and added mass coefficients are also given for the rectangular continuous plates with different water depth are given, and the first three frequencies and corresponding modal shapes, and added mass coefficients are also given for the rectangular continuous plates with different aspect ratios b/a and with all panel edges clamped, all panel edges simply supported. The results are compared with those obtained by Green's function method. By a series of FEM computations, the added mass coefficients of rectangular vertical cantilever plates and continuous plates are obtained and given in graphs and tables.

On the Hydrodynamic Coefficients of a 3-dimensional Body with a Forward Speed

Abstract: The three-dimensional boundary value problem for the unsteady motion of a ship which is translating and oscillating on the free surface of a deep water formulated. Under the assumption that the forward speed is small and order of , all formulations are made up to the first order of . For the numerical calculation, the three-dimensional source distribution method is applied, and the triangular elements are used to represent the hull surface. The results for the added mass and the damping coefficient for Series 60, at Fn=0 and Fn=0.2 shows good agreements with those of Inglis, Chang, and Inglis and Price.

The role of added mass in the theory of Hele-Shaw cell bubbles

Abstract: Viscous bubbles in a Hele-Shaw cell are studied by two-dimensional theory. The motion is caused by buoyancy and/or a pressure gradient driving a uniform basic flow in the surrounding fluid. A formula for the velocity of a steady bubble is derived, involving the ratio between the added mass of the bubble and the displaced fluid mass.

長径間ゲートの流体関連振動 : 第3報,付加質量と液体減衰係数の検証

Abstract: The long span gates vibrating in the streamwise direction push and draw the water in the reservoir, thus the gate is accompanied by an added mass of water. Moreover, the waves propagating in the upstream direction are formed on the free reservoir surface, thus resulting in a fluid damping effect on the vibrating gates. The added mass and fluid damping coefficient was derived theoretically in a dimensionless form in a previous study. To verify the theoretical results of the added mass and 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, respectively. The added mass and 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.

On the technique and the analysis of transient manoeuvre tests

Abstract: A new transient maneuver test designed to measure the hydrodynamic derivatives of a maneuvering ship has been developed. These tests were carried out using the planar motion mechanism. The forces acting on a model are decomposed into the added mass and the damping forces, using linear systems analysis. Experiment results are analyzed by a new method using a transfer function approximation and compared with the analysis by the Kramers-Kronig relations.