Added mass

About: Added mass is a(n) research topic. Over the lifetime, 2849 publication(s) have been published within this topic receiving 47899 citation(s).

Added-mass effect in the design of partitioned algorithms for fluid-structure problems

Abstract: The aim of this work is to provide a mathematical contribution to explain the numerical instabilities encountered under certain combinations of physical parameters in the simulation of fluid-structure interaction (FSI) when using loosely coupled time advancing schemes. It is also shown how the same combinations of parameters lead, in the case of strongly coupled schemes, to problems that demand a greater computational effort to be solved, requiring for example a high number of subiterations. The application that we have in mind is FSI simulation for blood flow in large human arteries, but the discussion applies as well to several FSI problems in which an incompressible fluid interacts with a thin elastic structure. To carry out the mathematical analysis, we consider a simplified model representing the interaction between a potential fluid and a linear elastic thin tube. Despite its simplicity, this model reproduces propagation phenomena and takes into account the added-mass effect of the fluid on the structure, which is known to be source of numerical difficulties. This allows to draw conclusions that apply to more realistic problems, as well.

The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight.

Abstract: We used a dynamically scaled model insect to measure the rotational forces produced by a flapping insect wing. A steadily translating wing was rotated at a range of constant angular velocities, and the resulting aerodynamic forces were measured using a sensor attached to the base of the wing. These instantaneous forces were compared with quasi-steady estimates based on translational force coefficients. Because translational and rotational velocities were constant, the wing inertia was negligible, and any difference between measured forces and estimates based on translational force coefficients could be attributed to the aerodynamic effects of wing rotation. By factoring out the geometry and kinematics of the wings from the rotational forces, we determined rotational force coefficients for a range of angular velocities and different axes of rotation. The measured coefficients were compared with a mathematical model developed for two-dimensional motions in inviscid fluids, which we adapted to the three-dimensional case using blade element theory. As predicted by theory, the rotational coefficient varied linearly with the position of the rotational axis for all angular velocities measured. The coefficient also, however, varied with angular velocity, in contrast to theoretical predictions. Using the measured rotational coefficients, we modified a standard quasi-steady model of insect flight to include rotational forces, translational forces and the added mass inertia. The revised model predicts the time course of force generation for several different patterns of flapping kinematics more accurately than a model based solely on translational force coefficients. By subtracting the improved quasi-steady estimates from the measured forces, we isolated the aerodynamic forces due to wake capture.

The Aerodynamics of Hovering Insect Flight. II. Morphological Parameters

Abstract: Morphological parameters are presented for a variety of insects that have been filmed in free flight. The nature of the parameters is such that they can be divided into two distinct groups: gross parameters and shape parameters. The gross parameters provide a very crude, first-order description of the morphology of a flying animal: its mass, body length, wing length, wing area and wing mass. Another gross parameter of the wings is their virtual mass, or added mass, which is the mass of air accelerated and decelerated together with the wing at either end of the wingbeat. The wing motion during these accelerations is almost perpendicular to the wing surface, and the virtual mass is approximately given by the mass of air contained in an imaginary cylinder around the wing with the chord as its diameter. The virtual mass ranges from 0.3 to 1.3 times the actual wing mass, indicating that the total mass accelerated by the flight muscles can be more than twice the wing mass itself. Over the limited size range of insects in this study, the interspecific variation of non-dimensional forms of the gross parameters is much greater than any systematic allometric variation, and no interspecific correlations can be found. The new shape parameters provide quite a surprise, however: intraspecific coefficients of variation are very low, often only 1%, and interspecific allometric relations are extremely strong. Mechanical aspects of flight depend not only on the magnitude of gross morphological quantities, but also on their distributions. Non-dimensional radii are derived from the non-dimensional moments of the distributions; for example, the first radius of wing mass about the wing base gives the position of the centre of mass, and the second radius corresponds to the radius of gyration. The radii are called \`shape parameters' since they are functions only of the normalized shape of the distributions, and they provide a second-order description of the animal morphology. The various radii of wing area are strongly correlated, as are those of wing mass and of virtual mass: the higher radii for each quantity can all be expressed by allometric functions of the first radius. The overall shape of the distribution of a quantity can therefore be characterized by a single parameter, the position of the centroid of that quantity. The strong relations between the radii of wing area, mass and virtual mass hold for a diverse collection of insects, birds and bats. Thus flying animals adhere to \`laws of shape' regardless of biological differences. Aerodynamic and mechanical considerations are most likely to provide an understanding of these laws of shape, but an explanation has proved elusive so far. The detailed shape of a distribution can be reconstructed from the shape parameters by matching the moments of the observed distribution to those of a suitable analytical function. A Beta distribution is compared with the distribution of wing area, i.e. the shape of the wing, and a very good fit is found. With use of the laws of shape relating the higher radii to the first radius, the Beta distribution can be reduced to a function of only one parameter, thus providing a powerful tool for drawing a close approximation to the entire shape of a wing given only its centroid of area. Quite unexpectedly, the continuous spectrum of wing shapes can then be described in detail by a single parameter of shape.

Normal and torsional spring constants of atomic force microscope cantilevers

Abstract: Two methods commonly used to measure the normal spring constants of atomic force microscope cantilevers are the added mass method of Cleveland et al. [J. P. Cleveland et al., Rev. Sci. Instrum. 64, 403 (1993)], and the unloaded resonance technique of Sader et al. [J. E. Sader, J. W. M. Chon, and P. Mulvaney, Rev. Sci. Instrum. 70, 3967 (1999)]. The added mass method involves measuring the change in resonant frequency of the fundamental mode of vibration upon the addition of known masses to the free end of the cantilever. In contrast, the unloaded resonance technique requires measurement of the unloaded resonant frequency and quality factor of the fundamental mode of vibration, as well as knowledge of the plan view dimensions of the cantilever and properties of the fluid. In many applications, such as frictional force microscopy, the torsional spring constant is often required. Consequently, in this article, we extend both of these techniques to allow simultaneous calibration of both the normal and torsional spring constants. We also investigate the validity and applicability of the unloaded resonance method when a mass is attached to the free end of the cantilever due to its importance in practice.

Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows

Abstract: This note investigates the so-called arti cial added mass e ect which is responsible for devastating instabilities within sequentially staggered Fluid-Structure Interaction (FSI) simulations where incompressible fluids are considered. A discrete representation of the added mass operatorMA is given and `instability conditions' are evaluated for different temporal discretisation schemes. It is proven that for every sequentially staggered scheme and given spatial discretisation of a problem, a mass ratio between fluid and structural mass density can be found at which the coupled system becomes unstable. The analysis is quite general and does not depend upon the particular spatial discretisation schemes used. However here special attention is put on stabilised finite elements employed on the fluid partition. Numerical investigations further highlight the results.