scholarly journals Electrodynamics of a magnet moving through a conducting pipe

2006 ◽  
Vol 84 (4) ◽  
pp. 253-271 ◽  
Author(s):  
M Hossein Partovi ◽  
Eliza J Morris
Keyword(s):  
Drag Force ◽  
Eddy Currents ◽  
Numerical Study ◽  
Full Range ◽  
Magnetic Behavior ◽  
Integral Form ◽  
Asymptotic Formulas ◽  
Pipe Material ◽  
Point Dipole ◽  
Axially Symmetric

The popular demonstration involving a permanent magnet falling through a conducting pipe is treated as an axially symmetric boundary-value problem. Specifically, Maxwell's equations are solved for an axially symmetric magnet moving coaxially inside an infinitely long, conducting cylindrical shell of arbitrary thickness at nonrelativistic speeds. Analytic solutions for the fields are developed and used to derive the resulting drag force acting on the magnet in integral form. This treatment represents a significant improvement over existing models, which idealize the problem as a point dipole moving slowly inside a pipe of negligible thickness. It also provides a rigorous study of eddy currents under a broad range of conditions, and can be used for magnetic braking applications. The case of a uniformly magnetized cylindrical magnet is considered in detail, and a comprehensive analytical and numerical study of the properties of the drag force is presented for this geometry. Various limiting cases of interest involving the shape and speed of the magnet and the full range of conductivity and magnetic behavior of the pipe material are investigated and corresponding asymptotic formulas are developed.PACS Nos.: 81.70.Ex, 41.20.–q, 41.20.Gz

Analysis and Experiments of Eddy Current Brakes with Moving Magnets

2008 ◽  
Vol 575-578 ◽  
pp. 1299-1304 ◽  
Author(s):  
Jaw Kuen Shiau ◽  
Der Ming Ma ◽  
Min Jou
Keyword(s):  
Drag Force ◽  
Relative Motion ◽  
Eddy Current ◽  
Eddy Currents ◽  
Test System ◽  
Image Method ◽  
Electromagnetic Interactions ◽  
Finite Dimensional ◽  
Conducting Plate ◽  
Lorentz Force Law

This paper discusses the magnetic drag force resulting from the relative motion of a permanent magnet moving along a finite dimensional conducting plate. The image method with imaginary eddy currents is investigated. Boundary conditions are established to ensure that the eddy currents vanished at the boundaries of the conducting plate. Magnetic drag force is computed based on the eddy current distributions using Lorentz force law. A test system is built to demonstrate the magnetic brakes arose from the electromagnetic interactions.

The numerical study of viscous drag force influence on low-frequency surge motion of a semi-submersible in storm sea states

2020 ◽  
Vol 213 ◽  
pp. 107511 ◽  
Author(s):  
Shan Ma ◽  
De-kang Xu ◽  
Wen-yang Duan ◽  
Ji-kang Chen ◽  
Kang-ping Liao ◽  
...  
Keyword(s):  
Drag Force ◽  
Numerical Study ◽  
Low Frequency ◽  
Viscous Drag ◽  
Viscous Drag Force

scholarly journals A rigorous mathematical treatment of the shape of a dissipative rope fountain

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190612
Author(s):  
Jonathan J. Bevan ◽  
Jonathan H. B. Deane
Keyword(s):  
Energy Conservation ◽  
Drag Force ◽  
Numerical Study ◽  
Analytical Description ◽  
Mathematical Treatment ◽  
Numerical Treatment ◽  
Constant Tension ◽  
Free Case ◽  
Parameter Values

This is a theoretical and numerical study of a model of a rope fountain subject to a drag force that depends linearly on the rope velocity. A precise, analytical description of the long-term shape adopted by the rope is given, and various consequences are derived from it. Using parameters that naturally appear in the model, we distinguish between cases wherein energy is conserved by means of a constant tension far from the rope source (the ‘free’ case) and where energy conservation is a consequence of a non-constant tension (the ‘braked’ case). The model is used, among other things, to generate rope fountain shapes based on approximate experimental estimates of the parameter values and a careful numerical treatment.

Numerical Study on Film Foam Flow Characteristics in a Straight Duct

2013 ◽  
Vol 561 ◽  
pp. 472-477 ◽  
Author(s):  
Dong Xing Du ◽  
Fa Hu Zhang ◽  
Dian Cai Geng ◽  
Ying Ge Li
Keyword(s):  
Drag Force ◽  
Pressure Difference ◽  
Numerical Study ◽  
Flow Behavior ◽  
Petroleum Industry ◽  
Flow Characteristics ◽  
Viscous Force ◽  
Ideal Condition ◽  
Surface Evolver ◽  
The Mathematical Model

Straight ducts capture some essential features of the motion of foam in porous media in petroleum industry. In this paper, Surface Evolver was employed to build the mathematical model to study the flow behavior of lamellas in the duct with different models. Numerical results show good agreement with experiments and some important features of lamella flow behavior in straight ducts are obtained. It is concluded that, the physical model with viscous force can adequately describe the flow characteristics of reality foam in the experiment. The actual pressure difference consists of the pressure difference caused by the curvature of the lamellas and the drag force on the boundary wall. Under the ideal condition of without drag force along the wall, the pressure drop for lamella flow in the duct is zero, and the shape and the velocity of the lamellas will maintain constant.

scholarly journals A Numerical Study of Axisymmetric Wave Propagation in Buried Fluid-Filled Pipes for Optimizing the Vibro-Acoustic Technique when Locating Gas Pipelines

Energies ◽  
2019 ◽  
Vol 12 (19) ◽  
pp. 3707 ◽  
Author(s):  
Liu ◽  
Habibi ◽  
Chai ◽  
Wang ◽  
Chen
Keyword(s):  
Wave Motion ◽  
Numerical Study ◽  
Acoustic Method ◽  
Vital Role ◽  
Pipe Material ◽  
Water Pipes ◽  
Axisymmetric Wave ◽  
Pipeline Systems ◽  
Buried Gas Pipeline ◽  
Effective Radiation

Buried pipeline systems play a vital role in energy storage and transportation, especially for fluid energies like water and gas. The ability to locate buried pipes is of great importance since it is fundamental for leakage detection, pipeline maintenance, and pipeline repair. The vibro-acoustic locating method, as one of the most effective detection technologies, has been studied by many researchers. However, previous studies have mainly focused on vibro-acoustic propagation in buried water pipes. Limited research has been conducted on buried gas pipes. In this paper, the behavior of gas-dominated wave motion will be investigated and compared against water-dominated wave motion by adapting an established analytical model of axisymmetric wave motion in buried fluid-filled pipes. Furthermore, displacement profiles in spatial domain resulting from gas-dominated wave in buried gas pipeline systems will be analyzed, and the effects of pipe material, soil property, as well as mode wave type will be discussed in detail. An effective radiation coefficient (ERC) is proposed to measure the effective radiation ability of gas-dominated wave and water-dominated wave. It is observed that the gas-dominated wave in gas pipes cannot radiate into surrounded soil as effectively as water-dominated wave in water pipes because of the weak coupling between gas and pipe-soil. In this case, gas-dominated wave may not be the best choice as the target wave for locating buried gas pipes. Therefore, the soil displacements result from the shell-dominated wave are also investigated and compared with those from gas-dominated wave. The results show that for buried gas pipes, the soil displacements due to radiation of shell-dominated wave are stronger than gas-dominated wave, which differs from buried water pipe. Hence, an effectively exciting shell-dominated wave is beneficial for generating stronger vibration signals and obtaining the location information. The findings of this study provide theoretical insight for optimizing the current vibro-acoustic method when locating buried gas pipes.

scholarly journals Hydrodynamic Effects Produced by Submerged Breakwaters in a Coastal Area with a Curvilinear Shoreline

2019 ◽  
Vol 7 (10) ◽  
pp. 337 ◽  
Author(s):  
Francesco Gallerano ◽  
Giovanni Cannata ◽  
Federica Palleschi
Keyword(s):  
Coastal Area ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Integral Form ◽  
Navier Stokes ◽  
Hydrodynamic Effect ◽  
Riemann Solver ◽  
Three Dimensional Model ◽  
Navier Stokes Equations

A three-dimensional numerical study of the hydrodynamic effect produced by a system of submerged breakwaters in a coastal area with a curvilinear shoreline is proposed. The three-dimensional model is based on an integral contravariant formulation of the Navier-Stokes equations in a time-dependent curvilinear coordinate system. The integral form of the contravariant Navier-Stokes equations is numerically integrated by a finite-volume shock-capturing scheme which uses Monotonic Upwind Scheme for Conservation Laws Total Variation Diminishing (MUSCL-TVD) reconstructions and an Harten Lax van Leer Riemann solver (HLL Riemann solver). The numerical model is used to verify whether the presence of a submerged coastal defence structure, in the coastal area with a curvilinear shoreline, is able to modify the wave induced circulation pattern and the hydrodynamic conditions from erosive to accretive.

scholarly journals A Numerical Study of Metachronal Propulsion at Low to Intermediate Reynolds Numbers

Fluids ◽  
2020 ◽  
Vol 5 (2) ◽  
pp. 86 ◽  
Author(s):  
Shawtaroh Granzier-Nakajima ◽  
Robert D. Guy ◽  
Calvin Zhang-Molina
Keyword(s):  
Phase Difference ◽  
Nearest Neighbor ◽  
Numerical Study ◽  
Full Range ◽  
Reynolds Numbers ◽  
Maximum Efficiency ◽  
Immersed Boundary ◽  
Dynamics Model ◽  
Underwater Propulsion ◽  
Average Flux

Inspired by the forward swimming of long-tailed crustaceans, we study an underwater propulsion mechanism for a swimming body with multiple rigid paddles attached underneath undergoing cycles of power and return strokes with a constant phase-difference between neighboring paddles, a phenomenon known as metachronal propulsion. To study how inter-paddle phase-difference affects flux production, we develop a computational fluid dynamics model and a numerical algorithm based on the immersed boundary method, which allows us to simulate metachronal propulsion at Reynolds numbers (RE) ranging from close to 0 to about 100. Our main finding is that the highest average flux is generated when nearest-neighbor paddles maintain an approximate 20%–25% phase-difference with the more posterior paddle leading the cycle; this result is independent of stroke frequency across the full range of RE considered here. We also find that the optimal paddle spacing and the number of paddles depend on RE; we see a qualitative transition in the dynamics of flow generated by metachronal propulsion as RE rises above 80. Roughly speaking, in terms of average flux generation, a tight paddle spacing is preferred when RE is less than 10, but a wider spacing becomes clearly favored when RE is close to or above 100. In terms of efficiency of flux generation, at RE 0.1 the maximum efficiency occurs at two paddles, and the efficiency decreases as the number of paddles increases. At RE 100 the efficiency increases as the number of paddles increases, and it appears to saturate by eight paddles, whereas using four paddles is a good tradeoff for both low and intermediate RE.

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