Topic
Inertia
About: Inertia is a research topic. Over the lifetime, 12006 publications have been published within this topic receiving 164291 citations.
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TL;DR: In this article, the authors investigate the origin of deviations from the classical Darcy law by numerical simulation of the Navier-Stokes equations in two-dimensional disordered porous media and find that such a transition can be understood and statistically characterized in terms of the spatial distribution of kinetic energy in the system.
Abstract: We investigate the origin of the deviations from the classical Darcy law by numerical simulation of the Navier-Stokes equations in two-dimensional disordered porous media. We apply the Forchheimer equation as a phenomenological model to correlate the variations of the friction factor for different porosities and flow conditions. At sufficiently high Reynolds numbers, when inertia becomes relevant, we observe a transition from linear to nonlinear behavior which is typical of experiments. We find that such a transition can be understood and statistically characterized in terms of the spatial distribution of kinetic energy in the system. [S0031-9007(99)09541-1]
244 citations
TL;DR: This paper reviews the inertia concept in terms of values and their evolution in the last decades, as well as the damping factor values.
Abstract: Traditionally, inertia in power systems has been determined by considering all the rotating masses directly connected to the grid. During the last decade, the integration of renewable energy sources, mainly photovoltaic installations and wind power plants, has led to a significant dynamic characteristic change in power systems. This change is mainly due to the fact that most renewables have power electronics at the grid interface. The overall impact on stability and reliability analysis of power systems is very significant. The power systems become more dynamic and require a new set of strategies modifying traditional generation control algorithms. Indeed, renewable generation units are decoupled from the grid by electronic converters, decreasing the overall inertia of the grid. ‘Hidden inertia’, ‘synthetic inertia’ or ‘virtual inertia’ are terms currently used to represent artificial inertia created by converter control of the renewable sources. Alternative spinning reserves are then needed in the new power system with high penetration renewables, where the lack of rotating masses directly connected to the grid must be emulated to maintain an acceptable power system reliability. This paper reviews the inertia concept in terms of values and their evolution in the last decades, as well as the damping factor values. A comparison of the rotational grid inertia for traditional and current averaged generation mix scenarios is also carried out. In addition, an extensive discussion on wind and photovoltaic power plants and their contributions to inertia in terms of frequency control strategies is included in the paper.
241 citations
TL;DR: In this article, the authors considered the case of spheroidal particles immersed in a very viscous fluid which is moving parallel to a plane with a uniform shearing motion and showed that the motion depends on the initial conditions of release of the Particle.
Abstract: In a recent paper* Dr. G. B. Jeffery has discussed the equations of motion of ellipsoidal particles immersed in a moving viscous fluid. He has solved the problem completely in The case of spheroidal particles immersed in a very viscous fluid which is moving parallel to a plane with a uniform shearing motion. his so1ution shows that the motion depends on the initial conditions of release of the Particle. The motion is periodic, and there appears to be no tendency for a particle to set itself so that its axis 1ies in any Particular direction. The Particle, in fact, takes up the rotation of the fluid, and its axis of symmetry describes a kind of elliptic cone round the direction of the vortex filaments, that is, round the direction which is perpendicular to the plane in which the motion of the fluid takes places. Though the ana1ysis, which neglects the inertia terms in the equations of motion, gives no indication of any tendency for the axis to set itself in any particular direction, Dr. Jeffery considers that ultimate1y the axis would probably adopt some special position, and he puts forward a " minimum energy ” hypothesis, which leads to the following definite, though unproved and unverified, results:— 1. A prolate spheroid, subject to the restriction imposed by this hypothesis, would set itself so that its long axis was Parallel to the vortex lines, and therefore perpendicular to the plane in which this undisturbed motion of the fluid takes places. It would then rotate with the fluid, which would move in steady motion relative to it.
237 citations
TL;DR: In this article, the authors presented the results of the first comprehensive two-dimensional numerical analysis of the split Hopkinson pressure bar and quantitatively described the effects of realistic friction and of variations in both the specimen geometry and the imposed strain-rate on the validity of the assumptions used in analyzing experimental data.
Abstract: T he split Hopkinson pressure bar is widely used to measure the dynamic properties of solid materials. This paper presents the results of the first comprehensive two-dimensional numerical analysis of the technique, and quantitatively describes the effects of realistic friction and of variations in both the specimen geometry and the imposed strain-rate on the validity of the assumptions used in analyzing experimental data. A two-dimensional axisymmetric numerical analysis is used to compute all components of the stress, strain and strain-rate tensors at each mesh point within the specimen and the elastic bars. The calculated response of the pressure bars is used to reconstruct the stress-strain behavior of the specimen and this is compared to both the input stress-strain curve and the actual calculated stress-strain states in the specimen. Thus, the validity of the assumptions and the corrections used in the analysis of the data is determined. Inertia and friction between the specimen and the elastic bars affect the response of the specimen differently for different length-to-diameter ratios. Inertia effects produce stress waves propagating radially and axially in the specimen and may result in an oscillating reconstructed stress-strain curve. If the ends of the specimen are well lubricated and care is taken to minimize the effects of inertia, the reconstructed stress-strain curve agrees with the input. However, serious stress and strain nonuniformity exists when the ends are not lubricated and this results in a reconstructed stress-strain curve where, for any given strain, the stress magnitude is larger than the correct value. A comparison of the calculations with experiment shows excellent agreement for various interface conditions. Finally, the inertia correction of E.D.H. Davies and S.C. Hunter (1963) is found to be reasonable.
234 citations
TL;DR: In this paper, a fully developed forced convection in a porous channel bounded by parallel plates is considered based on the general flow model, and exact solutions are obtained and presented for both the velocity and the temperature fields.
Abstract: In this paper fully developed forced convection in a porous channel bounded by parallel plates is considered based on the general flow model. Exact solutions are obtained and presented for both the velocity and the temperature fields. From these results the Nusselt number can be expressed in terms of the Darcy number and the inertia parameter. Finally, comparisons are made with the limiting case of no inertia and/or boundary effects. These results provide an in-depth insight into the underlying relationships between all of the pertinent variables. Furthermore, they can be used as strong candidates for bench marking of many numerical schemes.
232 citations