Showing papers on "Added mass published in 2006"

Hydrodynamic loading of microcantilevers vibrating in viscous fluids

Abstract: The hydrodynamic loading of elastic microcantilevers vibrating in viscous fluids is analyzed computationally using a three-dimensional, finite element fluid-structure interaction model. The quality factors and added mass coefficients of several modes are computed accurately from the transient oscillations of the microcantilever in the fluid. The effects of microcantilever geometry, operation in higher bending modes, and orientation and proximity to a surface are analyzed in detail. The results indicate that in an infinite medium, microcantilever damping arises from localized fluid shear near the edges of the microcantilever. Closer to the surface, however, the damping arises due to a combination of squeeze film effects and viscous shear near the edges. The dependence of these mechanisms on microcantilever geometry and orientation in the proximity of a surface are discussed. The results provide a comprehensive understanding of the hydrodynamic loading of microcantilevers in viscous fluids and are expected to be of immediate interest in atomic force microscopy and microcantilever biosensors.

Note on the induced Lagrangian drift and added-mass of a vortex

Abstract: Darwin (1953) introduced a simple heuristic that relates the Lagrangian fluid drift induced by a solid body propagating in irrotational flow to its virtual- or added-mass. The force required to accelerate the solid body must also overcome this added-mass. An extension of Darwin's (1953) method to the case of vortices propagating in a real fluid is described here. Experiments are conducted to demonstrate the existence of an added-mass effect during uni-directional vortex motion, which is analogous to the effect of solid bodies in potential flow. The definition of the vortex added-mass coefficient is modified from the solid body case to account for entrainment of ambient fluid by the vortex. This modified coefficient for propagating vortices is shown to be equal in magnitude to the classical coefficient for a solid body of equivalent boundary geometry. An implication of these results is that the vortex added-mass concept can be used as a surrogate for the velocity potential, in order to facilitate calculations of the pressure contribution to forces required to set fluid into unsteady vortical motion. Application of these results to unsteady wake analyses and fluid–structure interactions such as vortex-induced vibrations is suggested.

The unsteady drag force on a cylinder immersed in a dilute granular flow

Abstract: This paper presents results from hard-particle discrete element simulations of a two-dimensional dilute stream of particles accelerating past an immersed fixed cylinder. Simulation measurements of the drag force Fd are expressed in terms of a dimensionless drag coefficient, Cd=Fd∕[12ρνU2(D+d)], where ρ is the particle density, ν is the upstream solid fraction, U is the upstream instantaneous velocity, and D and d are the cylinder and particle diameters, respectively. Measurements indicate that the cylinder’s unsteady drag coefficient does not vary significantly from its steady (nonaccelerating) drag coefficient for both frictionless and frictional particles implying that the added mass for the flow is negligible. However, the drag coefficient is larger than its nominal value during an initial transient stage, during which a shock wave develops in front of the cylinder. Once the shock has developed, the drag coefficient remains constant despite the stream’s acceleration. The duration of the shock developme...

Rotordynamic coefficients measurements versus predictions for a high-speed flexure-pivot tilting-pad bearing (load-between-pad configuration)

Abstract: Experimental dynamic force coefficients are presented for a four pad flexure-pivot tilting-pad bearing in load-between-pad configuration for a range of rotor speeds and bearing unit loadings. Measured dynamic coefficients have been compared to theoretical predictions using an isothermal analysis for a bulk-flow Navier-Stokes (NS) model. Predictions from two models-the Reynolds equation and a bulk-flow NS equation models are compared to experimental, complex dynamic stiffness coefficients (direct and cross-coupled) and show the following results: (i) The real part of the direct dynamic-stiffness coefficients is strongly frequency dependent because of pad inertia, support flexibility, and the effect of fluid inertia. This frequency dependency can be accurately modeled for by adding a direct added-mass term to the conventional stiffness/damping matrix model. (ii) Both models underpredict the identified added-mass coefficient (∼32 kg), but the bulk' flow NS equation predictions are modestly closer. (iii) The imaginary part of the direct dynamic-stiffness coefficient (leading to direct damping) is a largely linear function of excitation frequency, leading to a constant (frequency-independent) direct damping model. (iv) The real part of the cross-coupled dynamic-stiffness coefficients shows larger destabilizing forces than predicted by either model. The frequency dependency that is accounted for by the added mass coefficient is predicted by the models and arises (in the models) primarily because of the reduction in degrees of freedom from the initial 12 degrees (four pads times three degrees of freedom) to the two-rotor degrees of freedom. For the bearing and condition tested, pad and fluid inertia are secondary considerations out to running speed. The direct stiffness and damping coefficients increase with load, while increasing and decreasing with rotor speed, respectively. As expected, a small whirl frequency ratio (WFR) was found of about 0.15, and it decreases with increasing load and increases with increasing speed. The two model predictions for WFR are comparable and both underpredict the measured WFR values. Rotors supported by either conventional tilting-pad bearings or flexure-pivot tilting-pad (FPTP) bearings are customarily modeled by frequency-dependent stiffness and damping matrices, necessitating an iterative calculation for rotordynamic stability. For the bearing tested and the load conditions examined, the present results show that adding a constant mass matrix to the FPTP bearing model produces an accurate frequency-independent model that eliminates the need for iterative rotordynamic stability calculations. Different results may be obtained for conventional tilting-pad bearings (or this bearing at higher load conditions).

Vehicle loading based vehicle dynamic and safety related characteristic adjusting system

Abstract: A method of controlling a controllable chassis system or a safety system (44) for a vehicle (10) includes determining an added mass placed on the vehicle and relative to a known vehicle mass. A vehicle characteristic is adjusted in response to the added mass. A control system (18) for an automotive vehicle (10) includes a sensor (20, 28-42) that generates a signal. A controller (26) determines added mass on the vehicle (10) in response to the signal and adjusts a vehicle characteristic in response to the added mass.

The principle of a MEMS circular diaphragm mass sensor

Abstract: The paper presents the design principles of a degenerate mode resonant mass sensor in which the unloaded sensor takes the form of a cyclically symmetric structure. The simplest structure with these features is a circular diaphragm and its properties are exploited in this paper. Such structures support pairs of independent modes of vibration which share a common natural frequency and these are referred to as degenerate modes. If extra mass is added to the structure over predefined regions, then the degeneracy can be broken and this produces a separation of the previously identical frequencies. This frequency split is the output of the sensor and is proportional to the added mass. Such a sensor is self-compensating, and ambient effects which equally influence both modes, such as temperature and in-plane stress, do not add to the frequency split. A Lagrangian approach is used to derive the relationship between added mass and frequency split.

The artificial added mass effect in sequential staggered fluid-structure interaction algorithms

Abstract: The artificial added mass effect inherent in sequentially staggered coupling schemes is investigated by means of a fluid-structure interaction problem. A discrete representation of a simplified added mass operator in terms of the participating coefficient matrices is given and instability conditions are evaluated for different temporal discretisation schemes. With respect to the time discretisation two different cases are distinguished. Discretisation schemes with stationary characteristics might allow for stable computations when good natured problems are considered. Such schemes yield a constant instability limit. Temporal discretisation schemes which exhibit recursive characteristics however yield an instability condition which is increasingly restrictive with every further step. Such schemes will therefore definitively fail in long time simulations irrespective of the problem parameters. It is also shown that for any sequentially staggered scheme and given spatial discretisation of a problem, a mass ratio between fluid and structural mass density exists at which the coupled system becomes unstable. Numerical observations confirm the theoretical results.

Ship Motion Computations Using a High Froude Number Time Domain Strip Theory

Abstract: High-speed strip theories are discussed, and a time domain formulation making use of a fixed reference frame for the two-dimensional fluid motion is described in detail. This, and classical (low-speed) strip theory, are compared with the experimental results of Wellicome et al. (1995) up to a Froude number of 0.8, as well as with our own test data for a semi-SWATH, demonstrating the marked improvement of the predictions of the former at high speeds, while the need to account for modest viscous effects at these speeds is also argued. A significant contribution to time domain computations is a method of stabilizing the integration of the ship's equations of motion, which are inherently unstable due to feedback from implicit added mass components of the hydrodynamic force. The time domain high-speed theory is recommended as a practical alternative to three-dimensional methods. It also facilitates the investigation of large-amplitude motions with stern or bow emergence and forms a simulation base for the investigation of ride control systems and local or global loads.

The principle of a MEMS circular diaphragm mass sensor

Abstract: The paper presents the design principles of a degenerate mode resonant mass sensor in which the unloaded sensor takes the form of a cyclically symmetric structure. The simplest structure with these features is a circular diaphragm and its properties are exploited in this paper. Such structures support pairs of independent modes of vibration which share a common natural frequency and these are referred to as degenerate modes. If extra mass is added to the structure over predefined regions, then the degeneracy can be broken and this produces a separation of the previously identical frequencies. This frequency split is the output of the sensor and is proportional to the added mass. Such a sensor is self compensating and ambient effects which equally influence both modes, such as temperature and in-plane stress, do not add to the frequency split. A Lagrangian approach is used to derive the relationship between added mass and frequency split.

Non-Contact Eddy Current Excitation Method for Vibration Testing

Abstract: When a conductive material is subjected to a time changing magnetic field, eddy currents are induced in that structure. The eddy currents circulate inside the conductor resulting in a magnetic field that interacts with the applied field. The eddy current field is such that it opposes the change in flux resulting in a force between the source and conductor. The time changing magnetic field necessary to induce an electrometric force in the materials can be generated through a variety of different ways. In the present study, a permanent magnet will be mounted to the tip of an electromagnetic shaker such that the motion of the magnet relative to the structure will cause a time changing field and the formation of eddy currents. The actuator will be demonstrated to be beneficial due to its ability to apply actuation forces without contacting the structure. This study will show that the non-contact nature of the system eliminates mass loading and added stiffness which are downfalls of traditional excitation techniques. Additionally, it will be shown that the use of a non-contact device preserves the mode shapes of the structure, whereas a stinger results in distortions due to the added constraint. Using this concept, a model of the actuation system will be developed, allowing the beams response to be simulated. The actuation system will then be used to excite a cantilever beam to obtain the modal parameters without contacting the structure. The novel non-contact actuation system developed in this paper provides a new method performing vibration testing of on lightweight or flexible structures while preserving their dynamics.

Dynamic Analysis of a Flexible Hanging Riser in the Time and Frequency Domain

Abstract: This paper outlines the dynamic analysis of flexible risers in the time and frequency domain using lumped mass discretization, where tension and bending are modeled with extensional and rotational springs respectively. For the time domain analysis, integration is carried out using the Wilson-theta implicit scheme, which allows the use of relatively large time steps without compromising stability. This increases computational efficiency and automatically filters the high frequency axial responses. The time domain code is validated with the commercial software Orcaflex, which employs an explicit scheme, and results are found to match for the same number of elements. The relative merits of implicit and explicit integration schemes are discussed. For the frequency domain analysis, the added mass, damping, axial/bending stiffness matrices are formulated in global coordinates. The nonlinear drag force is linearized iteratively for both regular and random waves. The range of accuracy for the linearized frequency domain simulations is assessed by methodical comparisons with the nonlinear time domain results for varying loading amplitudes. One problem encountered during the early development of an analytical tool is the lack of published results for validation, especially where access to commercial packages and test facilities is unavailable or limited. Hence, the simulation results presented herein are for a flexible hanging riser with simple boundary conditions and load cases to facilitate benchmarking.Copyright © 2006 by ASME

Interaction Law for a Collision Between Two Solid Particles in a Viscous Liquid

Abstract: This thesis addresses the problem of inter-particle collisions in a viscous liquid. Experimental measurements were made on normal and oblique collisions between identical and dissimilar pairs of solid spheres. The experimental evidence supports the hypothesis that the normal and the tangential component of motions are decoupled during a rapid collision. The relative particle motion in the normal direction is crucial to an immersed collision process and can be characterized by an effective coefficient of restitution and a binary Stokes number. The effective coefficient of restitution monotonically decreases with a diminishing binary Stokes number, indicating a particle motion with less inertia and higher hindering fluid forces. The correlation between the two parameters exhibits a similar trend to what is observed in a sphere-wall collision, which motivates a theoretical modeling. The collision model developed in the current work includes a flow model and a revised rebound scheme. The flow model considers the steady viscous drag, the added mass force, and the history force. How the presence of a second nearby solid boundary affects these forces is investigated. A flow model is proposed with wall-correction terms and is used to predict an immersed pendulum motion toward a solid wall. General agreement with the available experimental data validates the model. The rebound scheme considers the magnitude of the surface roughness and the minimum distance of approach resuling from an elastohydrodynamic contact. The performance of the collision model in predicting the effective coefficient of restitution is evaluated through comparisons with experimental measurements and an existing elastohydrodynamic collision model that the current work is based on. Based on the current experimental findings, the tangential component of motion can be described by a dry collision model, provided that the material parameters are properly modified for the interstitial liquid. Two pertinent parameters are the normal effective coefficient of restitution and an effective friction coefficient.