Showing papers on "Added mass published in 2016"

Molecular Hydrodynamics from Memory Kernels.

Abstract: The memory kernel for a tagged particle in a fluid, computed from molecular dynamics simulations, decays algebraically as t^{-3/2}. We show how the hydrodynamic Basset-Boussinesq force naturally emerges from this long-time tail and generalize the concept of hydrodynamic added mass. This mass term is negative in the present case of a molecular solute, which is at odds with incompressible hydrodynamics predictions. Lastly, we discuss the various contributions to the friction, the associated time scales, and the crossover between the molecular and hydrodynamic regimes upon increasing the solute radius.

Nanobeam sensor for measuring a zeptogram mass

Abstract: Single-walled carbon nanotubes (SWCNTs) have attracted intense interest in recent years due to their suitability for a wide range of applications, such as nano-sensors and nano-actuators. The primary objective of this paper is presenting a simplified nonlocal finite element model to investigate the potential application of CNTs as a nanomechanical mass sensor. Nonlocal differential elasticity of Eringen is exploited to reveal the long-range interactions between atoms. The CNT resonator is proposed as a bridge Euler–Bernoulli nanobeam with attached mass. An efficient finite element model is developed to discretize the nanobeam domain and solve the equation of motion numerically. The effect of nonlocal parameter on vibration characteristics is discussed and compared with published works. The effects of added mass on the nonlocal frequency shift percentage and higher vibrational modes are discussed in details. Numerical results show that the mass sensitivity of the nanotube sensor is in the zeptogram range.

Numerical and experimental investigation of natural flow-induced vibrations of flexible hydrofoils

Abstract: The objective of this work is to present combined numerical and experimental studies of natural flow-induced vibrations of flexible hydrofoils. The focus is on identifying the dependence of the foil’s vibration frequencies and damping characteristics on the inflow velocity, angle of attack, and solid-to-fluid added mass ratio. Experimental results are shown for a cantilevered polyacetate (POM) hydrofoil tested in the cavitation tunnel at the French Naval Academy Research Institute (IRENav). The foil is observed to primarily behave as a chordwise rigid body and undergoes spanwise bending and twisting deformations, and the flow is observed to be effectively two-dimensional (2D) because of the strong lift retention at the free tip caused by a small gap with a thickness less than the wall boundary layer. Hence, the viscous fluid-structure interaction (FSI) model is formulated by coupling a 2D unsteady Reynolds-averaged Navier-Stokes (URANS) model with a two degree-of-freedom (2-DOF) model representing the spanwise tip bending and twisting deformations. Good agreements were observed between viscous FSI predictions and experimental measurements of natural flow-induced vibrations in fully turbulent and attached flow conditions. The foil vibrations were found to be dominated by the natural frequencies in absence of large scale vortex shedding due to flow separation. The natural frequencies and fluid damping coefficients were found to vary with velocity, angle of attack, and solid-to-fluid added mass ratio. In addition, the numerical results showed that the in-water to in-air natural frequency ratios decreased rapidly, and the fluid damping coefficients increased rapidly, as the solid-to-fluid added mass ratio decreases. Uncoupled mode (UM) linear potential theory was found to significantly over-predict the fluid damping for cases of lightweight flexible hydrofoils, and this over-prediction increased with higher velocity and lower solid-to-fluid added mass ratio.

The impact and bounce of air bubbles at a flat fluid interface

Abstract: The rise and impact of bubbles at an initially flat but deformable liquid-air interface in ultraclean liquid systems are modelled by taking into account the buoyancy force, hydrodynamic drag, inertial added mass effect and drainage of the thin film between the bubble and the interface. The bubble-surface interaction is analyzed using lubrication theory that allows for both bubble and surface deformation under a balance of normal stresses and surface tension as well as the long-range nature of deformation along the interface. The quantitative result for collision and bounce is sensitive to the impact velocity of the rising bubble. This velocity is controlled by the combined effects of interfacial tension via the Young-Laplace equation and hydrodynamic stress on the surface, which determine the deformation of the bubble. The drag force that arises from the hydrodynamic stress in turn depends on the hydrodynamic boundary conditions on the bubble surface and its shape. These interrelated factors are accounted for in a consistent manner. The model can predict the rise velocity and shape of millimeter-size bubbles in ultra-clean water, in two silicone oils of different densities and viscosities and in ethanol without any adjustable parameters. The collision and bounce of such bubbles with a flat water/air, silicone oil/air and ethanol/air interface can then be predicted with excellent agreement when compared to experimental observations.

Frequency Shifts of Micro and Nano Cantilever Beam Resonators Due to Added Masses

Abstract: We present analytical and numerical techniques to accurately calculate the shifts in the natural frequencies of electrically actuated micro and nano (carbon nanotubes (CNTs)) cantilever beams implemented as resonant sensors for mass detection of biological entities, particularly Escherichia coli (E. coli) and prostate specific antigen (PSA) cells. The beams are modeled as Euler–Bernoulli beams, including the nonlinear electrostatic forces and the added biological cells, which are modeled as discrete point masses. The frequency shifts due to the added masses of the cells are calculated for the fundamental and higher-order modes of vibrations. Analytical expressions of the natural frequency shifts under a direct current (DC) voltage and an added mass have been developed using perturbation techniques and the Galerkin approximation. Numerical techniques are also used to calculate the frequency shifts and compared with the analytical technique. We found that a hybrid approach that relies on the analytical perturbation expression and the Galerkin procedure for calculating accurately the static behavior presents the most computationally efficient approach. We found that using higher-order modes of vibration of micro-electro-mechanical-system (MEMS) beams or miniaturizing the sizes of the beams to nanoscale leads to significant improved frequency shifts, and thus increased sensitivities.

Vibrations of Axially Moving Vertical Rectangular Plates in Contact with Fluid

Abstract: The vibration characteristics of an axially moving vertical plate immersed in fluid and subjected to a pretension are investigated, with a special consideration to natural frequencies, complex mode functions and critical speeds of the system. The classical thin plate theory is adopted for the formulation of the governing equation of motion of the vibrating plates. The effects of free surface waves, compressibility and viscidity of the fluid are neglected in the analysis. The velocity potential and Bernoulli’s equation are used to describe the fluid pressure acting on the moving plate. The effect of fluid on the vibrations of the plate may be regarded as equivalent to an added mass on the plate. The formulation of added mass is obtained from kinematic boundary conditions of the plate–fluid interfaces. The effects of some system parameters such as the moving speed, stiffness ratios, location and aspect ratios of the plate and the fluid-plate density ratios on the above-mentioned vibration characteristics of the plate–fluid system are investigated in detail. Various different boundary conditions are considered in the study.

On the dynamics of floating structures

Abstract: This paper addresses the floating body problem which consists in studying the interaction of surface water waves with a floating body. We propose a new formulation of the water waves problem that can easily be generalized in order to take into account the presence of a floating body. The resulting equations have a compressible-incompressible structure in which the interior pressure exerted by the fluid on the floating body is a Lagrange multiplier that can be determined through the resolution of a $d$-dimensional elliptic equation, where $d$ is the horizontal dimension. In the case where the object is freely floating, we decompose the hydrodynamic force and torque exerted by the fluid on the solid in order to exhibit an added mass effect; in the one dimensional case $d=1$, the computations can be carried out explicitly. We also show that this approach in which the interior pressure appears as a Lagrange multiplier can be implemented on reduced asymptotic models such as the nonlinear shallow water equations and the Boussinesq equations; we also show that it can be transposed to the discrete version of these reduced models and propose simple numerical schemes in the one dimensional case. We finally present several numerical computations based on these numerical schemes; in order to validate these computations we exhibit explicit solutions in some particular configurations such as the return to equilibrium problem in which an object is dropped from a non-equilibrium position in a fluid which is initially at rest.

Mass and position determination in MEMS mass sensors: a theoretical and an experimental investigation

Abstract: We present a method to determine accurately the position and mass of an entity attached to the surface of an electrostatically actuated clamped–clamped microbeam implemented as a mass sensor. In the theoretical investigation, the microbeam is modeled as a nonlinear Euler–Bernoulli beam and a perturbation technique is used to develop a closed-form expression for the frequency shift due to an added mass at a specific location on the microbeam surface. The experimental investigation was conducted on a microbeam made of Polyimide with a special lower electrode to excite both of the first and second modes of vibration. Using an ink-jet printer, we deposited droplets of polymers with a defined mass and position on the surface of the microbeam and we measured the shifts in its resonance frequencies. The theoretical predictions of the mass and position of the deposited droplets match well with the experimental measurements.

Determination of Hydrodynamic Parameters for Remotely Operated Vehicles

Abstract: In this paper the hydrodynamic parameters that characterize the behavior of a typical unmanned underwater vehicle are evaluated. A complete method for identifying these parameters is described. The method is developed to give a brief and accurate estimate of these parameters in all six degrees of freedom using basic properties of the vehicle such as dimensions, mass and shape. The method is based on both empirical and analytical results for typical reference geometries (ellipsoids, cubes, etc.). The method is developed to be applicable for a wide variety of UUV designs as these typically varies substantially. The method is then applied to a small observation class ROV. The results are first verified using an experimental method in which the full scale ROV is towed using a planar motion mechanism. An additional verification is performed with numerical simulations using Computational Fluid Dynamics and a radiation/diffraction program. The method shows promising results for both damping and added mass for the tested case. The translational degrees of freedom are more accurate than the rotational degrees of freedom which are expected as most empirical and analytical data are for translational degrees of freedom. The case study also reveals that the relative difference between the numerical simulations and the experimental results are similar to the relative difference between the proposed method and the experiment.Copyright © 2016 by ASME

Drag cancellation by added-mass pumping

Abstract: A submerged body subject to a sudden shape-change experiences large forces due to the variation of added-mass energy. While this phenomenon has been studied for single actuation events, application to sustained propulsion requires studying \textit{periodic} shape-change. We do so in this work by investigating a spring-mass oscillator submerged in quiescent fluid subject to periodic changes in its volume. We develop an analytical model to investigate the relationship between added-mass variation and viscous damping and demonstrate its range of application with fully coupled fluid-solid Navier-Stokes simulations at large Stokes number. Our results demonstrate that the recovery of added-mass kinetic energy can be used to completely cancel the viscous damping of the fluid, driving the onset of sustained oscillations with amplitudes as large as four times the average body radius $r_0$. A quasi-linear relationship is found to link the terminal amplitude of the oscillations $X$, to the extent of size change $a$, with $X/a$ peaking at values from 4 to 4.75 depending on the details of the shape-change kinematics. In addition, it is found that pumping in the frequency range of $1-\frac{a}{2r_0}<\omega^2/\omega_n^2<1+\frac{a}{2r_0}$ is required for sustained oscillations. These results on the unsteady fluid forces produced by shape-changing bodies provide a foundation for the design and control of soft-bodied underwater vehicles.

Wave excited motion of a body floating on water confined between two semi-infinite ice sheets

Abstract: The wave excited motion of a body floating on water confined between two semi-infinite ice sheets is investigated. The ice sheet is treated as an elastic thin plate and water is treated as an ideal and incompressible fluid. The linearized velocity potential theory is adopted in the frequency domain and problems are solved by the method of matched eigenfunctions expansion. The fluid domain is divided into sub-regions and in each sub-region the velocity potential is expanded into a series of eigenfunctions satisfying the governing equation and the boundary conditions on horizontal planes including the free surface and ice sheets. Matching is conducted at the interfaces of two neighbouring regions to ensure the continuity of the pressure and velocity, and the unknown coefficients in the expressions are obtained as a result. The behaviour of the added mass and damping coefficients of the floating body with the effect of the ice sheets and the excitation force are analysed. They are found to vary oscillatorily with the wave number, which is different from that for a floating body in the open sea. The motion of the body confined between ice sheets is investigated, in particular its resonant behaviour with extremely large motion found to be possible under certain conditions. Standing waves within the polynya are also observed.

Hydrodynamic analysis and shape optimization for vertical axisymmetric wave energy converters

Abstract: The absorber is known to be vertical axisymmetric for a single-point wave energy converter (WEC). The shape of the wetted surface usually has a great influence on the absorber’s hydrodynamic characteristics which are closely linked with the wave power conversion ability. For complex wetted surface, the hydrodynamic coefficients have been predicted traditionally by hydrodynamic software based on the BEM. However, for a systematic study of various parameters and geometries, they are too multifarious to generate so many models and data grids. This paper examines a semi-analytical method of decomposing the complex axisymmetric boundary into several ring-shaped and stepped surfaces based on the boundary discretization method (BDM) which overcomes the previous difficulties. In such case, by using the linear wave theory based on eigenfunction expansion matching method, the expressions of velocity potential in each domain, the added mass, radiation damping and wave excitation forces of the oscillating absorbers are obtained. The good astringency of the hydrodynamic coefficients and wave forces are obtained for various geometries when the discrete number reaches a certain value. The captured wave power for a same given draught and displacement for various geometries are calculated and compared. Numerical results show that the geometrical shape has great effect on the wave conversion performance of the absorber. For absorbers with the same outer radius and draught or displacement, the cylindrical type shows fantastic wave energy conversion ability at some given frequencies, while in the random sea wave, the parabolic and conical ones have better stabilization and applicability in wave power conversion.

Fixed and moored bodies in steep and breaking waves using SPH with the Froude–Krylov approximation

Abstract: Force prediction on fixed and moored bodies in steep, asymmetric and breaking waves remains a problem of great practical importance. For floating bodies snatch loads on mooring lines are of particular significance. In this paper we present an approximate approach where waves are modelled using incompressible smoothed particle hydrodynamics (SPH) which is well suited for breaking as well as non-breaking waves. For bodies of small size relative to wave length, the total force is assumed to be due to the Froude–Krylov force due to the undisturbed pressure field with additional added mass effects—in effect the Morison assumption. For a fixed vertical column in regular waves on a small slope, breaking wave force magnification is consistent with experiment and for focussed waves peak forces due to initial interaction are in good agreement with experiment; wave asymmetry is the dominant influence on overall force rather than local roller/jet breaker impact. For a taut moored hemispherical buoy in steep focussed waves the loads and motion without snatching are almost independent of added mass coefficient between zero and unity. Without breaking when snatching occurs the motion and loads measured experimentally are well predicted with zero added mass. This close agreement breaks down with wave breaking and the initial snatch load is overestimated by around 30 %. This approach is a fast alternative to fully 3-D simulations which are computationally demanding. Variation of, for example, mooring line properties and buoy position may be efficiently analysed using the same wave field and, as such, the approach has potential to be a useful design tool with further validation.

Wave diffraction and radiation by multiple rectangular floaters

Abstract: In this paper, the diffraction and radiation problem of multiple two-dimensional rectangular bodies floating on a layer of water of finite depth with waves is studied. An analytical model for the analysis of wave excitation forces and added mass and damping coefficients is proposed, based on a linearized velocity potential theory. Expressions for velocity potentials are obtained by the method of separation of variables, in which unknown coefficients are determined by utilizing the eigen-function expansion matching method. The model is validated by a comparison of the simulation results with the available data. The validated model is then utilized to examine the effect of the structure width, structure draft, spacing between adjacent structures, and structure numbers on wave transmission coefficient of floating structures.

Effect of fluid inertia on the motion of a collinear swimmer.

Abstract: The swimming of a two-sphere system and of a three-sphere chain in an incompressible viscous fluid is studied on the basis of simplified equations of motion which take account of both Stokes friction and added mass effects. The analysis is based on an explicit expression for the asymptotic periodic swimming velocity and a corresponding evaluation of the mean rate of dissipation. The mean swimming velocity of the two-sphere system is found to be nonvanishing provided that the two spheres are not identical. The swimming of a comparable chain of three identical spheres is much more efficient.

Determination of Added Mass and Inertia Moment of Marine Ships Moving in 6 Degrees of Freedom

Abstract: When a ship moves in water with acceleration or deceleration, quantities of fluid moving around the hull creating additional hydrodynamic forces acting on the hull. It is imagined as the added mass which increases the total system mass and inertia moment. In order to establish the mathematical model for ship motion, the added components need to be determined. For a particular ship, these hydrodynamic components can be obtained by experiment. However, for ship simulation especially at the initial design stage it is necessary to calculate and estimate by theoretical method. This study aims to find out a general method to calculate all components of added mass and inertia moment in 6 degrees of freedom for simulating ship movement.

Convergence acceleration for partitioned simulations of the fluid-structure interaction in arteries

Abstract: We present a partitioned approach to fluid-structure interaction problems arising in analyses of blood flow in arteries. Several strategies to accelerate the convergence of the fixed-point iteration resulting from the coupling of the fluid and the structural sub-problem are investigated. The Aitken relaxation and variants of the interface quasi-Newton -least-squares method are applied to different test cases. A hybrid variant of two well-known variants of the interface quasi-Newton-least-squares method is found to perform best. The test cases cover the typical boundary value problem faced when simulating the fluid-structure interaction in arteries, including a strong added mass effect and a wet surface which accounts for a large part of the overall surface of each sub-problem. A rubber-like Neo Hookean material model and a soft-tissue-like Holzapfel-Gasser-Ogden material model are used to describe the artery wall and are compared in terms of stability and computational expenses. To avoid any kind of locking, high-order finite elements are used to discretize the structural sub-problem. The finite volume method is employed to discretize the fluid sub-problem. We investigate the influence of mass-proportional damping and the material model chosen for the artery on the performance and stability of the acceleration strategies as well as on the simulation results. To show the applicability of the partitioned approach to clinical relevant studies, the hemodynamics in a pathologically deformed artery are investigated, taking the findings of the test case simulations into account.

Natural vibration analysis of vertical rectangular plates and stiffened panels in contact with fluid on one side

Abstract: This article presents a simple and efficient procedure for the natural vibration analysis of rectangular plates and stiffened panels in contact with fluid on one side. The assumed mode method is applied, where the natural frequencies and mode shapes are obtained by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange’s equation of motion. The Mindlin thick plate theory is applied for a plate, and in the case of stiffened panels, the effect of framing is taken into account by adding its strain and kinetic energies to the corresponding plate energies. Potential flow theory assumptions are adopted for the fluid, and free surface waves are ignored. The fluid velocity potential is derived from the boundary conditions for the fluid and structure and is utilized for the calculation of added mass using the assumed modes. The applicability and accuracy of the developed procedure are illustrated with several numerical examples using a developed in-house code. A...

On the Capability of Structural–Acoustical Fluid–Structure Interaction Simulations to Predict Natural Frequencies of Rotating Disklike Structures Submerged in a Heavy Fluid

Abstract: Predicting natural frequencies of rotating disklike structures submerged in water is of paramount importance in the field of hydraulic machinery, since the dynamic response of disks presents similarities to the dynamic response of pump-turbine runners. Well-known computational methods, such as structural-acoustical fluid–structure interaction (FSI) simulations, are perfectly capable to predict the added mass effects of standing submerged disks. However, the capability of these simulations to predict the effect of rotation in the natural frequencies of submerged disks has not been investigated. To obtain adequate results, the relationship between the disk rotation and the fluid rotation has to be introduced in the simulation model to consider the effects of the surrounding flow and the transmission within rotating and stationary frame. This procedure is explained and discussed in this technical brief comparing analytical, numerical, and experimental results.