Showing papers on "Added mass published in 2000"

A finite element solution of an added mass formulation for coupled fluid-solid vibrations

Abstract: A finite element method to approximate the vibration modes of a structure in contact with an incompressible fluid is analyzed in this paper. The effect of the fluid is taken into account by means of an added mass formulation, which is one of the most usual procedures in engineering practice. Gravity waves on the free surface of the liquid are also considered in the model. Piecewise linear continuous elements are used to discretize the solid displacements, the variables to compute the added mass terms and the vertical displacement of the free surface, yielding a non conforming method for the spectral coupled problem. Error estimates are settled for approximate eigenfunctions and eigenfrequencies. Implementation issues are discussed and numerical experiments are reported. In particular the method is compared with other numerical scheme, based on a pure displacement formulation, which has been recently analyzed.

A time-domain mode-expansion method for calculating transient elastic responses of a pontoon-type VLFS

Abstract: A time-domain calculation method is described for elastic responses to arbitrary time-dependent external loads, on the basis of a general differential equation of second order including the convolution integral related to memory effects in the hydrodynamic forces. The time-dependent elastic deflection of a structure is represented by a superposition of mathematical modal functions, and a Galerkin scheme is employed to obtain a linear system of simultaneous differential equations for the amplitude of modal functions assumed. Special care is paid to numerical accuracy in computing the memory-effect function and the added mass at infinite frequency. The validity of the numerical results was confirmed through a comparison with time histories of the vertical deflection measured in an impulsive weight-drop test conducted at the Ship Research Institute and a comparison with existing numerical results for the same problem. To check the necessity of memory-effect terms, computations using a constant value for the hydrodynamic damping coefficient were also performed, and practical measures for reducing the computation time are discussed.

Three-dimensional water-wave scattering in two-layer fluids

Abstract: We consider, using linear water-wave theory, three-dimensional problems concerning the interaction of waves with structures in a fluid which contains a layer of finite depth bounded above by a free surface and below by an infinite layer of fluid of greater density. For such a situation time-harmonic waves can propagate with two different wavenumbers K and k. In a single-layer fluid there are a number of reciprocity relations that exist connecting the various hydrodynamic quantities that arise, and these relations are systematically extended to the two-fluid case. The particular problems of wave radiation and scattering by a submerged sphere in either the upper or lower layer are then solved using multipole expansions.

Flutter Limits and Behavior of a Flexible Thin Sheet in High-Speed Flow— II: Experimental Results and Predicted Behaviors for Low Mass Ratios

Abstract: Flutter phenomena of flexible thin sheets such as paper swept by wind are studied for a wide range of mass ratios by an analytical method developed by the authors. The analytical results explain well the tendencies found in the experimental data. Furthermore, the flutter behaviors for very low mass ratios are predicted to tend to deviate far from those for ordinarily stiff materials, which are attributed to the effects of both the fluid friction and the added mass effect by surrounding fluid in addition to the ordinary governing effects for higher mass ratios, i.e., elasticity, inertia force, and fluid pressure.

A robust neural controller for underwater robot manipulators

Abstract: Presents a robust control scheme using a multilayer neural network with the error backpropagation learning algorithm. The multilayer neural network acts as a compensator of the conventional sliding mode controller to improve the control performance when initial assumptions of uncertainty bounds of system parameters are not valid. The proposed controller is applied to control a robot manipulator operating under the sea which has large uncertainties such as the buoyancy, the drag force, wave effects, currents, and the added mass/moment of inertia. Computer simulation results show that the proposed control scheme gives an effective path way to cope with those unexpected large uncertainties.

Experimental studies of forces on piles

Abstract: In the design of a pile structure exposed to surface waves of a given height and period, some of the factors involved in the problem and studied herein are the size, shape and spacing of the piles and the moment distribution on uniform and non-uniform piles. Theoretical and experimental investigations have shown that the force exerted by surface waves on a pile consists of two components — a drag force and an inertia force. The drag force is proportional to the fluid density, the projected area and the square of the fluid particle velocity. The inertia force, including the virtual mass, is proportional to the fluid density, the volume of the object and the fluid particle acceleration. The virtual mass is the apparent increase of the displaced mass of fluid necessary to account for the increase in force resulting from the acceleration of the fluid relative to the object. This factor is included in the coefficient of mass term in the force calculations.

Vibration-Based Techniques for Measuring the Elastic Properties of Ropes and the Added Mass of Submerged Objects

Abstract: The magnitude of peak tensions during the deployment of subsurface moorings is dependent on the elastic stretch of the mooring line and the added masses of the mooring buoyancy and instruments. Measured transient tensions, which are twice the mooring anchor weight, highlight the importance of being able to quantify these critical parameters so that these dynamic tensions can be predicted. In this paper, the theory of the mass-spring oscillator is applied in two simple experiments to demonstrate practical techniques for measuring the elastic properties of ropes and the added mass of submerged objects. In the first procedure, a known mass is suspended from a rope, and the tension is monitored when the “mass-spring” system is set into free longitudinal oscillation. The spring constant is calculated from the measured frequency of this oscillation. Trials with ¼" diameter synthetic and wire ropes demonstrate that satisfactory results are attainable with rope lengths of less than 2 m. Results using dif...

The use of impulse response functions for evaluation of added mass and damping coefficient of a circular cylinder oscillating in linearly stratified fluid

Abstract: The damped horizontal oscillations of a circular cylinder in linearly stratified fluid are studied experimentally. The cylinder is fixed to the lower end of a physical pendulum with variable restoring moment. The impulse response function of the pendulum in time domain is recorded and converted to the frequency response function using Fourier transform. The density stratification is shown to have a strong effect on frequency-dependent hydrodynamic coefficients (added mass and damping). The data obtained are compared with available theoretical predictions. The applicability of a simplicistic method implying approximation of impulse response functions by analytical functions is discussed.

A boundary element method and spectral analysis model for small‐amplitude viscous fluid sloshing in couple with structural vibrations

Abstract: A boundary element method (BEM) is presented for the coupled motion analysis of structural vibrations with small-amplitude fluid sloshing in two-dimensional space. The linearized Navier-Stokes equations are considered in the frequency domain and transformed into a Laplace equation and a Helmholtz equation with pure imaginary constant. An appropriate fundamental solution for the Helmholtz equation is provided. The conditions of zero stress are imposed on the free surface, and non-slip conditions of fluid particles are imposed on the walls of the container. For rigid motion models, the expressions for added mass and added damping to the structural motion equations are obtained. Numerical examples are presented

Numerical studies of the motion of particles in current-carrying liquid metals flowing in a circular pipe

Abstract: A mathematical model has been developed to describe the motion of particles in current-carrying liquid metals flowing through a cylindrical pipe. The fluid velocity field was obtained by solving the Navier-Stokes equations, and the trajectories of particles were calculated using equations of motion for particles. These incorporate the drag, added mass, history, electromagnetic, and fluid acceleration forces. The results show that particle trajectories are affected by the magnetic pressure number RH, the Reynolds number Re, the blockage ratio k, and the particle-fluid density ratio γ according to the relative importance of associated force terms. In the axial direction, the particles follow the fluid velocity closely and will move further axially before reaching the wall as the fluid velocity (Re) increases. In the radial direction, the outwardly directed electromagnetic force on the particle increases with radial distance from the axis, with increasing electric current (RH), and increasing size (k) of particle. The competition between the electromagnetic force and the radial fluid acceleration force in the entrance region results in particle movement toward the central axis before moving toward the wall for small electric current (low RH) and directly toward the wall for large current (high RH). The low inertia (γ) bubbles move faster toward the wall than heavier particles do. The radial velocity of the particle movement as it approaches the wall is predicted to decrease due to wall effects. This model has been applied to the movement of inclusions within the electric sensing zone (ESZ) of the liquid metal cleanliness analyzer (LiMCA) system in molten aluminum, and it was proved that LiMCA system could be used in aluminum industries.

Computational modeling of a dilute turbulent liquid‐solid flow using a Eulerian‐Lagrangian approach

Abstract: Numerical results are reported for a dilute turbulent liquid‐solid flow in an axisymmetric sudden‐expansion pipe with an expansion ratio 2:1. The two‐phase flow has a mass‐loading ratio low enough for particle collision to be negligible. The numerical predictions for the dilute two‐phase flow are based on a hybrid Eulerian‐Lagrangian model. A nonlinear k‐e model is used for the fluid flow to account for the turbulence anisotropy and an improved eddy‐interaction model is used for the particulate flow to account for the effects of turbulence anisotropy, turbulence inhomogeneity, particle drift, and particle inertia on particle dispersion. The effects of the coupling sources, the added mass, the lift force and the shear stress on two‐phase flow predictions are separately studied. The numerical predictions obtained with the improved and conventional particle dispersion models are compared with experimental measurements for the mean and fluctuating velocities at the different measured planes.

Hydrodynamic influence on ship-hull vibration close to water bottom

Abstract: The problem of a uniform ship-hull girder vibrating vertically close to water bottom is studied. A simple formula for the added mass is found by use of the method of matched asymptotic expansions. Results obtained from the present method and BEM are compared. They are in good agreement in the range considered here. The obtained added mass is used to predict the natural vibrations of a uniform beam vibrating close to water bottom. Numerical values show that the effects of shallow water are significant. The first- and second-order frequencies of the ship hull studied in this paper in deep water are about 1·4–3 times higher than those in shallow water.

Numerical studies of the motion of spheroidal particles flowing with liquid metals through an electric sensing zone

Abstract: A mathematical model has been developed to describe the motion of variously shaped and oriented spheroids entrained in liquid metals passing through a cylindrical electric sensing zone (ESZ) developed for liquid metals cleanliness analyzer (LiMCA) systems. The fluid velocity field within the ESZ was obtained by solving the Navier-Stokes equations, while the trajectories of particles within the ESZ were calculated using the equations of motion for particles. These incorporate forces resulting from drag, added mass, history, and electromagnetic and fluid acceleration balanced against the time rate of changes in a particle momentum. The effects of particle or inclusion shape and orientation were taken into account by including correction factors for drag (RD), added mass (MA), history (B), and electromagnetic force (EM). The numerical results show that particle trajectories are affected by the magnetic pressure number (RH), the Reynolds number (Re), the blockage ratio (k), and the particle-fluid density ratio (γ). In the axial direction, spheroidal particles travel further axially before hitting the wall as the fluid velocity (Re) increases. In the radial direction, the outwardly directed electromagnetic force on nonconducting spheroids increases with radial distance from the axis, with increasing electric current (RH) and with increasing size (k) of the particle. At low electric currents (low RH), the competition between the electromagnetic force and the radial fluid acceleration force in the entrance region is predicted to result in particle movements first toward the central axis, before outward motion toward the wall, but directly toward the wall at large currents (high RH). Spheroidal particles with symmetric axes perpendicular to the transverse axis of the ESZ move faster toward the sidewall as the particle aspect ratio (E) increases. The dominating increase in the added mass force over the increase in the electromagnetic force with decreasing E makes this effect much stronger for oblates (E 1). The stronger drag force on a prolate with its symmetric axis parallel to the axis of the ESZ makes it move slower toward the wall than a prolate with its axis of symmetry perpendicular to the axis of the ESZ. Low-inertia (low-γ) spheroidal particles move faster toward the sidewall than do heavier particles. This effect of γ is stronger for prolates than for oblates traversing with their symmetric axes perpendicular to the axis of the ESZ, owing to the decreased added mass effect as E increases, while the effect of γ becomes much stronger for a prolate traversing with its symmetric axis perpendicular rather than parallel to the axis of the ESZ, owing to its smaller added mass. The radial particle velocity when approaching the wall is predicted to decrease due to the wall effects. This model has been applied to the movement of spheroidal inclusions within the ESZ of a LiMCA system in molten aluminum, and it was proven from the theoretical point of view that LiMCA systems could be used in aluminum industries.

Analysis of Fluid-Structure-Coupled Vertical Vibration for High-Speed Ships

Abstract: A practical method of vertical vibration analysis for high-speed ships based on two-dimensional finite element model is proposed in this paper.The method employed for evaluating hydrodynamic added mass is two-dimensional boundary element method in which two different free surface conditions (linearized or high frequency limit simplified free surface condition) are discussed respectively. The modified determinant search method and alternate iteration method are applied to solve the coupled fluid-structure vibration.The comparison of computation results with experiment results indicates that the program developed in this paper is reliable and practical for the design of high-speed ships.

Fundamental Vibration Modes of Stiffened Tank Plate in Contac with Fluid

Abstract: Vibration design of stiffened plates of tank wall is usually carried out in such way that the natural frequencies of both panel vibration and stiffened plate vibration should exceed the exciting frequencies to avoid the resonance. However, panel and stiffener coupling mode of vibration would appear in tank wall adjoining fluid as fundamental vibration mode due to the configuration of tank. If such vibration mode occure, it may cause vibration problem because the natural frequency of this coupling mode vibration is lower than the above two frequencies.In this paper, vibration mode of tank wall filled with fluid is investigated by analytical approach in terms of added mass effect of fluid and the followings are clarified : 1) The natural frequency of panel and stiffener coupling vibration mode “sp” is always lower than that of stiffened plate vibration mode “s”, although it never happens without fluid interaction. The reduction of this natural frequency is caused by the coupling with stiffened plate and small panels due to added mass effect.2) The natural frequency of panel and stiffener coupling vibration mode “sp” becomes lower than that of panel vibration mode “p” in case that the configuration of the tank satisfies, roughly saying, B/L≤0.3 or H/L≥0.5Therefore, in designing the tank structure, it is important to consider the natural frequency of panel and stiffener coupling mode to prevent vibration problem according to the tank dimension.

ALE Finite Volume Computations of Fluid-Structure Interaction Problems

Abstract: A computational procedure is develop ed to analyze the fluid-structure interaction problems The Navier-Stokes equati ons and the equation of the motion of the structure are coupled and solved by a predictor-corrector method The Newmark scheme is employed to solve the equ ation of structure The spatial discretization of the N-S equation is achieved by the finite volume method using non-staggered grid in a curvilinear coordina te system, while the time derivatives are approached by a second-order backward scheme The Arbitrary-Lagangian-Eulerian method is employed to incorporate th e interface conditions between the structure and fluid Extensive studies are ca rried out with the present method to analyze the vibrations of a single circular cylinder in a viscous fluid filling a circular domain Four different types of fluid, including air, water, mineral oil and silicon oil,are selected as the flu id media in the computation The added mass and damping coefficients obtained fr om time history of displacement are compared with the analytical solutions Good agreement shows that the fluid forces acting on the cylinder are accurately pre dicted Furthermore, the present method can be also used to explore the similar problem with large vibrating amplitude and eccentric cylinder, of which the anal ytical solutions are unavailable

Hydrodynamics of moving structures during a static solidification process

Abstract: The solutal / thermal convection phenomena which occur during a solidification process, are strongly coupled with the growth of the microstructure. The microstructure can be divided in two types: the columnar corresponding to a fixed structure and the equiaxed corresponding to a fixed or a moving structure. Our interest in this paper is focussed on the mechanical coupling between a swarm of growing grains of variable concentration and the conveying fluid phase. We build a numerical tool with the aim of well identify all the relevant physical phenomena which occur during the motion of the grains, from the hydrodynamic interactions point of view. We decide on a purely Lagrangian formulation which allows us to follow the motion of each grain and thus to well appreciate the relative contribution of each term used in the model. A Beckermann like growth model is coupled with the mechanical model, so the volume and the density of each grain is a function of the relative velocity and of the thermal conditions of the regions they are crossing. It's showed that, in many situations, the Stokes number is close to unity, so side effects like added mass, local pressure gradient, have significant influence on the history of the particle. We compare motion patterns provided by common models with the patterns calculated with our model, and draw conclusions concerning final distribution of solid structures.

A Method for Computation of Added-Mass Coefficients of Two-Dimensional Bodies by a Discrete Singularity Method.

Abstract: In this study, we propose a novel method to specify the added-mass coefficients of arbitrary two-dimensional bodies in an incompressible viscous fluid. This method is based on a discrete singularity method in which a fundamental solution of the Brinkman's equation is employed as a singularity. For computational examples, the following bodies are chosen : a circular cylinder in an infinite flow field and in cylindrical containers, an elliptic cylinder in an infinite flow field and a square-section cylinder in an infinite flow field. As a result, the effectivity of this method is confirmed.

Analysis of Fluid-Structure-Coupled Vertical Vibration for High-Speed Ships

Abstract: It is essential for the designer of the high speed ship to develop a relatively simple, accurate and practical calculation model. A practical method of vertical vibration analysis for high speed ships based on two dimensional finite element model was proposed. The method employed for evaluating hydrodynamic added mass is two dimensional boundary element method in which two different free surface conditions (linearized or high frequency limit simplified free surface condition) are discussed respectively. The modified determinant search method and alternate iteration method were applied to solve the coupled fluid structure vibration. The comparison of computation results with the experiment results indicates that the developed program is reliable and practical at the design of high speed ships.