Showing papers on "Added mass published in 1996"

Hydroelastic vibration of rectangular plates

Abstract: This paper is concerned with the virtual mass effect on the natural frequencies and mode shapes of rectangular plates due to the presence of the water on one side of the plate. The approximate formula, which mainly depends on the so-called nondimensionalized added virtual mass incremental factor, can be used to estimate natural frequencies in water from natural frequencies in vacuo. However, the approximate formula is valid only when the wet mode shapes are almost the same as the one in vacuo. Moreover, the nondimensionalized added virtual mass incremental factor is in general a function of geometry, material properties of the plate and mostly boundary conditions of the plate and water domain. In this paper, the added virtual mass incremental factors for rectangular plates are obtained using the Rayleigh-Ritz method combined with the Green function method. Two cases of interfacing boundary conditions, which are free-surface and rigid-wall conditions, and two cases of plate boundary conditions, simply supported and clamped cases, are considered in this paper. It is found that the theoretical results match the experimental results. To investigate the validity of the approximate formula, the exact natural frequencies and mode shapes in water are calculated by means of the virtual added mass matrix. It is found that the approximate formula predicts lower natural frequencies in water with a very good accuracy.

A simple and accurate added mass model for hydrodynamic fluid—Structure interaction analysis

Abstract: A theoretical model of an added mass representation for a flexible cylinder vibrating in a fluid medium is presented. To accomplish this, the fluid-structure interaction problem under the influence of harmonic ground and inertia dominated hydrodynamic loading, is first studied by solving the coupled differential equations exactly. Explicit expressions for computing the hydrodynamic interaction pressure and eigenquantities like natural frequencies and mode shapes are given here. However, this analytical model, as in many other mathematical models, suffers from a severe handicap; its expressions are too complicated and require the use of a computer program to generate the results. One solution which is of particular interest, is the computation of natural frequencies. Using the added mass representation, a simple formula for evaluating the natural frequency is proposed. The formula is very simple to use, requiring only a minimal computational effort on a standard calculator. Comparison with the analytical solutions shows that the formula is extremely accurate, with errors under 0.5% or less, in nearly all the cases tested. Also, more importantly, this accuracy does not appear to deteriorate in the computation of higher natural frequencies, and thus should be very useful for designers working in the dynamics of submerged structures, taking into account their hydrodynamic interactions.

Dynamics and energetics of scallop locomotion

Abstract: A dynamic model for a swimming scallop was developed which integrates the mechanical properties of the hinge ligaments, valve inertia, the external fluid-flow reaction, the fluid pressure in the mantle cavity and the muscle contraction. Kinematic data were recorded for a swimming Placopecten magellanicus from high-speed film analysis. Dynamic loading experiments were performed to provide the required mechanical properties of the hinge for the same species. The swimming dynamics and energetics based on data from a 0.065 m long Placopecten magellanicus at 10 °C were analyzed. The main conclusions are as follows. 1. The mean period of a clapping cycle during swimming is about 0.28 s, which can be roughly divided into three equal intervals: closing, gliding and opening. The maximum angular velocity and acceleration of the valve movements are about 182 degrees s-1 and 1370 degrees s-2, respectively. 2. The hysteresis loop of the hinge was found to be close to an ellipse. This may be represented as a simple Voigt body consisting of a spring and dashpot in parallel, with a rotational stiffness of 0.0497 N m and viscosity coefficient of 0.00109 kg m2 s-1 for the 0.065 m long Placopecten magellanicus. 3. The external fluid reaction has three components, of which the added mass is about 10 times higher than the mass of a single valve, and the flow-induced pseudo-viscosity compensates for nearly half of the hinge viscosity for the 0.065 m long Placopecten magellanicus. 4. The locomotor system powered by the muscle can be divided into two subsystems: a pressure pump for jet production and a shell-hinge/outer-fluid oscillator which drives the pumping cycle. The dynamics of the oscillator is determined predominantly by the interaction of the external fluid reaction and the hinge properties, and its resonant frequency was found to be close to the swimming frequencies. 5. The momentum and energy required to run the oscillator are negligibly small (about 1 % for the 0.065 m long Placopecten magellanicus) compared with that for the jet. Almost all the mechanical energy from muscle contraction is used to perform hydrodynamic work for jet production. Thus, the Froude efficiency of propulsion in scallops is nearly the same as the entire mechanical efficiency of the locomotor system. This could be a fundamental advantage of jet propulsion, at least for a scallop. 6. The estimated maximum muscle stress is about 1.06x10(5) N m-2, the cyclic work is 0.065 J and power output is 1.3 W. Using an estimate of the mass of an adductor muscle, the work done by the muscle per unit mass is 9.0 J kg-1 and the peak power per unit mass is 185 W kg-1. 7. The time course of the force generation of the contracting adductor muscle is basically the same as that of the hydrodynamic propulsive force.

Simulation of the Zero-Gravity Environment for Dynamic Testing of Structures

Abstract: : Simulation of unconstrained (free-free) boundary conditions is a longstanding problem in ground vibration testing of spacecraft. The test article weight must be supported without introducing constraining forces due to stiffness, inertia, or friction from the suspension system. High-fidelity simulation of the space environment requires that such constraint forces be kept small compared to forces inherent in the experiment. A multipoint, six degree of freedom suspension system for dynamic testing is described. Intended primarily for highly flexible space structures, it uses a combination of passive pneumatic and active electromagnetic subsystems. The suspension offers a wide payload range, near-zero stiffness, zero static deflection, small added mass, and zero friction. The electromagnetic system can also provide active cancellation of added mass, accurate ride-height control, and integrated disturbance input. Several versions of the system are described, aimed at test articles ranging from very flexible solar arrays to a 7000-lb simulated optical truss. The concept and hardware are described, test results are given, and applications experience from several industry, government, and university installations is discussed.

Roughness Influence on Turbulent Flow Through Annular Seals Including Inertia Effects

Abstract: An analysis is developed to calculate the static and dynamic characteristics for a rough seal that includes inertia effects. The method is detailed for a seal made up of a rough stator and a smooth rotor, a configuration which presents some peculiarities modifying the pattern of the model of turbulence where roughness effects and flow equations are included. A geometry with two identically roughened surfaces can be considered as a special case of the first one. In an earlier study, we developed a model of turbulence built from Prandtl's relation and Van Driest's mixing length method including roughness effects. This model is used to calculate the zeroth-order coefficients of turbulence k X , k z , the Couette velocity u cr for a roughened stator as well as the inertia coefficients. These coefficients derive from the numerical solution of the Generalized Couette Flow. The effects of inertia forces in the film are taken into account in an integrated way according to the film height and are expressed versus the mean velocity. Flow equations are derived from Navier-Stokes' equations and from the continuity equation for incompressible flows. An analytical perturbation of the flow parameters leads to a set of zeroth-order and first-order equations. The integration of nonlinear zeroth-order equations leads to the steady state solution which permits the calculation of the seal leakage and static load. Dynamic stiffness, damping and added mass coefficients are obtained from the integration of the linear first-order equations. Comparisons are made with the results of the Bulk-flow theory applied to rough seals.

Force Acting on a Spherical Bubble Rising through a Quiescent Liquid.

Abstract: The direct numerical simulation is performed on the spherical bubble unsteadily rising through a quiescent liquid. The method is based on a finite-volume solution of the equations on an orthogonal curvilinear coordinate system. The calculations are performed for a bubble rising through a clean liquid and contaminated one. Following the former experimental results, the tangential stress free condition is given for a clean bubble, and no-slip condition for contaminated one. The numerical results are compared with those of the model equation of the translational motion of the bubble, which is often used in numerical models of a bubbly flow. The steady drag, added mass and history terms are checked up by the comparison. It is revealed that the history force effect is negligible for a bubble rising through the clean liquid beyond Re=O (50). From the numerical point of view, the fact that the history force is negligible is quite important, because it reduces the calculation time and memory for a bubbly flow model. For a contaminated bubble, history force effect is not negligible even though the Reynolds number is high enough. It is found that the expression of the history force by Basset kernel gives an over-estimation of the history force for the bubble rising at moderate Reynolds number. This error becomes larger with increasing Reynolds number and it reduces the accuracy to calculate the bubble motion by the model equation.

Stability of Vertical Fluid-Conveying Pipes Having the Lower End Immersed in Fluid

Abstract: This paper concerns a beam-type flutter of vertical pipes containing a flowing fluid and having the lower end immersed in fluid. The effect of surrounding fluid on motions of the pipe is assumed as a mass added to the immersed part of the pipe. The equivalent added mass is estimated using Morison's formula. The effects of the immersed length of the pipe on the critical flutter velocity are investigated. It is predicted theoretically that the lower end immersed in fluid may exert a considerable destabilizing effect, except in the case where the lower end is only slightly immersed in fluid and the mass ratio is as high as 0.75. Experiments with silicone-rubber tubes conveying water were conducted to check the theoretical predictions. It was confirmed that for sufficiently high flow velocities the tube was subject to violent flutter, and that the critical flutter velocity decreased with increasing immersed length of the lower end.

Axial Vibrations of Fluid-Filled Bellows Expansion Joints

Abstract: This paper presents the results of a project undertaken to study the axisymmetric natural vibrations and fluid-added mass of fluid-filled bellows expansion joints. The bellows were modeled using axisymmetric shell finite elements, while the fluid region was discretized using axisymmetric triangular elements. The in-vacuo bellows modes were used as boundary conditions on the potential flow model for the fluid and the added mass determined for each bellows mode. This added mass was then used to determine the in-fluid bellows natural frequencies. Experiments were conducted to verify the theoretical model and agreement was found to be very good. The results were also compared with the frequency predictions of previously developed relatively simple theoretical models.

Hydrodynamics of a body moving over a mud layer-Part II: Added-mass and damping coefficients

Abstract: A ship cross section undergoes periodic oscillations in a finite water layer, overlaying a mud layer The upper fluid is considered to be inviscid, and the mud is modelled as a Newtonian liquid The section contour is replaced by a distribution of wave sources with unknown strength, satisfying a corresponding boundary integral equation Its kernel is expressed through a newly derived Green function The numerical solution of the integral equation allows evaluation of the added-mass and damping coefficients Specific computations pertaining to Lewis forms show a drastic dependence of the added-mass and damping coefficients on the mud thickness and density

Modeling of robot manipulators working under the sea and the design of a robust controller

Abstract: This paper presents a study of the dynamics of undersea robot manipulators in an unstructured sea water environment and a control scheme appropriate for manipulating them. Under the sea, the buoyancy and the added mass should be considered in modeling the dynamics of the robot manipulators. However, due to the complexity of the modeling of the added mass, the dynamics of the robot manipulators are treated as an unmodeled dynamics in this paper. In addition to the buoyancy and added mass/moment of inertia, disturbing forces due to drag, and current affecting the dynamics of the robot manipulators should be considered. In this paper, the forces due to the drag are defined as disturbance forces in addition to the frictional force of manipulator joints. In order to control the manipulator, a robust control scheme is devised to achieve trajectory tracking while regulating disturbance forces. A numerical example is shown.

Solutions for the Combined Motion of Finite Length Squeeze Film Dampers Around the Bearing Center

Abstract: Analytical expressions for the hydrodynamic forces, and four related dynamic coefficients, are presented for finite length squeeze film dampers (SFDs) executing combined radial and tangential motion around the bearing center, with small amplitude. Previous analyses by Mulcahy (1980) and San Andres and Vance (1987) are shown to be particular cases of the present treatment. The influence of combined motion on the coefficients is found to differ, in several respects, from that which can be deduced from results for one dimensional radial motion and circular centred orbital motion. The effects of combined motion on the mean flow velocity and the wall stress are also studied. The study provides further insight into the validity of bulk flow assumptions, often used when dealing with lubrication problems where fluid inertia effects are significant.

Fluid-solid interaction in a rectangular container

Abstract: An analytical study of the interaction of a liquid with the elastic side wall of a rectangular container with a free surface is considered, where the effects of gravity are taken into account. The elastic side wall of the container is assumed as being either a vertical beam or a mass-spring system. In each case, the coupled natural frequencies and modes of the system are obtained. Examples are presented to show the typical behaviour in this kind of problem; two types of coupled modes are observed for the beam type side wall case. The added mass of fluid on the structure is found to be zero, positive or negative in the case of a mass-spring type side wall. The results given here may be extended to the interaction problem in a rectangular container with elastic side and bottom walls.

Large amplitude ship motions and bow flare slamming pressures in regular head seas

Abstract: In this paper, the motion equations incorporating nonlinear terms due to large amplitude motions and bow flare slamming pressures are described in regular head seas. Numerical predictions of ship motions based on a small amplitude linear theory and large amplitude nonlinear method and experimental data are compared with each other in the frequency and time domain. The nonlinear restoring force, nonlinear damping force and nonlinear fluid momentum force are considered in predicting ship motions. The frequency dependent added mass and damping coefficient are computed at the instantaneous submerged sections of the ship. The momentum slamming theory and Wagner theory are used to predict the bow flare slamming pressure. The total impact pressure is expressed as the sum of water immersion impact pressure and wave striking impact pressure. There is a satisfactory agreement between theoretical predictions and model test measurements.

The added mass of a deformable cylinder moving in a liquid

Abstract: Let an infinitely long cylinder move perpendicular to its length in an infinite mass of liquid which is at rest at infinity. If the cylinder is rigid, the whole effect of the presence of the liquid may be represented by adding to the inertia per unit length of the solid cylinder the mass per unit length of the displaced fluid. If, however, the cylinder is elastically deformable, the mass of the moving fluid depends on the change in shape of the, initially circular, cross-sections of the cylinder. Thus the added mass is no longer a constant, but a function of the pressure exerted by the fluid on the solid cylinder.

Air loads on solar panels during launch

Abstract: The dynamical behaviour of solar panels during launch is significantly affected by the thin layers of air trapped between the panels. For narrow gaps the air manifests itself not only as a considerable added mass, but its viscosity can result in a substantial amount of damping. A model has been developed which describes the pressure distribution in the gap. The model includes the effects of inertia, viscosity, compressibility and thermal conductivity. The model is written in terms of dimensionless parameters which govern the motion of the air in the gap For rigid panels, suspended in springs, located parallel to a fixed surface and performing translational or rotational oscillations, analytical solutions are presented. The results from specially designed experiments show good agreement with the analytical results. A large shift in eigenfrequency is observed and an increase in damping to almost critical values for narrow gaps. On the basis of the theory, a new acoustic finite element has been developed for the calculation of acousto-elastic interaction. Numerical results are shown for a flexible panel located parallel to a fixed surface.

A study on the hydroelastic response of a plate under impulsive pressures due to breaking waves

Abstract: In this paper, breaking waves are generated in a 2-D wave tank and simulated by using a higher-order boundary element method. A piston-type wavemaker is operated by signals composed of elementary waves. The phase of elementary waves is determined by the linear theory such that they are focused to a prescribed position. Calculated plunging waves coincide well with experiment. A steel box with different plate thicknesses is installed at a predetermined position in the tank. Measured impulsive pressures due to breaking waves are found to be 0.8-1.2C2, where corresponds to water density and C to wave celerity. The transverse displacement of the plate is described in terms of modal eigenfunctions. The natural frequencies measured by impact tests in air for thin plate coincide with the computational and theoretical values. The radiationpotential due to plate vibration is derived and the radiation force is expressed in terms of hydroelastic added mass and damping forces. Comparison of natural frequencies of plate in water proves that hydroelastic added mass and damping are properly considered. The measured strain due to regular waves supports the calculated one, but there are apparent discrepancies between theory and experiment in the impulsive case.

A Study on the Hydroelastic Response of a Plate Under Impulsive Pressures Due to Breaking Waves

Abstract: In this paper, breaking waves are generated in a 2-D wave tank and simulated by using a higher-order boundary element method. A piston-type wavemaker is operated by signals composed of elementary waves. The phase of elementary waves is determined by the linear theory such that they are focused to a prescribed position. Calculated plunging waves coincide well with experiment. A steel box with different plate thicknesses is installed at a predetermined position in the tank. Measured impulsive pressures due to breaking waves are found to be 0.8-1.2C2, where corresponds to water density and C to wave celerity. The transverse displacement of the plate is described in terms of modal eigenfunctions. The natural frequencies measured by impact tests in air for thin plate coincide with the computational and theoretical values. The radiationpotential due to plate vibration is derived and the radiation force is expressed in terms of hydroelastic added mass and damping forces. Comparison of natural frequencies of plate in water proves that hydroelastic added mass and damping are properly considered. The measured strain due to regular waves supports the calculated one, but there are apparent discrepancies between theory and experiment in the impulsive case.

Added Mass And Damping On An Oscillating Surface-Piercing Column With A Horizontal Cylinder: Square Cross Sections

Abstract: Added mass and damping on a long horizontal cylinder of a square cross section (Model A) and a vertical surface-piercing square cylinder or column with a long horizontal cylinder of a square cross section (Model B) oscillating in water of finite and infinite depths, are measured using a planar motion mechanism. The width of both the vertical and horizontal cylinders is 22.86 cm. The horizontal cylinder comprises a test section of 91.44 cm in length at the center and two 91.44-cm dummy sections on each end of the test section. The model was forced to sway and heave sinusoidally with small amplitudes for several submergences below a free surface. The added-mass and wave-damping coefficients are shown to be influenced strongly by the free-surface effect and are presented as a function of water depth, frequency and direction of oscillation and of depth of submergence from the free surface. There clearly exists a critical nondimensional frequency near ora/g = 0.3 for the heave oscillations near the free surface, as was measured previously but not predicted by a potential theory for a long, 2D horizontal cylinder in infinite depth (Chung, 1977). Also, negative added mass is measured at ofa/g = 0.4~0.8 for the shallow subergence, and it was cinfirmed by the present computation. The general trend of the added mass curve shows a behavior similar to the results of the previous 2-D horizontal cylinder except for the differences in their values. The added mass coefficients are larger for finite depth, while a limited number of sub mergences was tested. The experimental values are generally larger than theoretical predictions. As the model is placed closer to the bottom, the discrepancy becomes larger. 90.17 em 2r = 22.86cm -..j t2a = 22.86cm ~8~ ---1:; a ...L T I91.44cm + 91,44cm + 91,44cm -l H -II0.889 mm h Gap Detail F~ j --=.w~ 635 ;nm, , , , , I I , I , , , , I , , , , Fig. 1b Schematic of Model B: Model A is identical to Model B with column removed. the 2-D horizontal cylinder in infinite depth influenced by the free-surface effect as calculated using potential theories (e.g., Frank, 1967) were previously compared with the experimental data in Chung (1977). Members of many floating ocean structures can be approximated as two-dimensional except for those parts close to the joints of the members. Recently three-dimensional (3-D) potential theories and computational methods have made much progress in contributing to the 3-D theoretical prediction of hydrodynamic forces and motions of floating structures. However, the accuracy of theoretical predictions needs to be confirmed by experimental results. The added mass and wave damping computation by 3-D potential theory for the computation of motions of the floating structures Dummy Section ~ Dummy Section Gap Gap

Fluid-elastic force measurements acting on a tube bundle in two-phase cross flow

Abstract: Fluid-elastic force acting on a square tube bundle of P/D = 1.47 in air-water two-phase cross flow was measured to investigate the characteristics and to clarify whether the fluid elastic vibration characteristics could be expressed using two-phase mixture characteristics. Measured fluid elastic forces were separated into fluid-elastic force coefficients such as added mass, added stiffness, and added damping coefficient. The added damping coefficient was separated into a two-phase damping and a flow-dependent component as in previous research (Carlucci, 1981 and 1983; Pettigrew, 1994). These coefficients were nondimensionalized with two-phase mixture characteristics such as void fraction, mixture density and mixture velocity, which were obtained using the drift-flux model with consideration given to the model. The result was compared with the result obtained with the homogeneous model. It was found that fluid-elastic force coefficients could be expressed with two-phase flow mixture characteristics very well in the experimental result, and that better result can be derived using the slip model as compared to the homogeneous model. Added two-phase flow, which could be expressed as a function of void fraction, where two-phase damping was nondimensionalized with the relative velocity between the gas and liquid phases used as a reference velocity. Using these, the addedmore » stiffness coefficient and flow-dependent component of damping could be expressed very well as a function of nondimensional mixture velocity.« less

Added mass effects in two-phase solid/liquid media

Abstract: The results of a series of studies are reported in which the added mass experienced by a 25 mm sphere oscillating in two-phase systems consisting of bonded spheres in various liquid media is measured in a variety of configurations using a remote drive vibrating reed technique.The arrangements considered investigate the effects of surface roughness and bed voidage together with variations in fluid density and viscosity expressed in terms of the Stokes number in the range of 4.5-110. The results are then correlated in terms of simple mathematical expressions for the subsequent prediction of added mass as a function of the above parameters.

Axial vibrations of fluid-filled bellows expansion joints

Abstract: This paper presents the results of a project undertaken to study the axisymmetric natural vibrations and fluid-added mass of fluid-filled bellows expansion joints. The bellows were modeled using axisymmetric shell finite elements, while the fluid region was discretized using axisymmetric triangular elements. The in-vacuo bellows modes were used as boundary conditions on the potential flow model for the fluid and the added mass determined for each bellows mode. This added mass was then used to determine the in-fluid bellows natural frequencies. Experiments were conducted to verify the theoretical model and agreement was found to be very good. The results were also compared with the frequency predictions of previously developed relatively simple theoretical models.