Eddy Force Research Articles

On the Choice of Training Data for Machine Learning of Geostrophic Mesoscale Turbulence

AbstractData plays a central role in data‐driven methods, but is not often the subject of focus in investigations of machine learning algorithms as applied to Earth System Modeling related problems. Here we consider the problem of eddy‐mean interaction in rotating stratified turbulence in the presence of lateral boundaries, where it is known that rotational components of the eddy flux plays no direct role in the sub‐grid forcing onto the mean state variables, and its presence is expected to affect the performance of the trained machine learning models. While an often utilized choice in the literature is to train a model from the divergence of the eddy fluxes, here we provide theoretical arguments and numerical evidence that learning from the eddy fluxes with the rotational component appropriately filtered out, achieved in this work by means of an object called the eddy force function, results in models with comparable or better skill, but substantially reduced sensitivity to the presence of small‐scale features. We argue that while the choice of data choice and/or quality may not be critical if we simply want a model to have predictive skill, it is highly desirable and perhaps even necessary if we want to leverage data‐driven methods to aid in discovering unknown or hidden physical processes within the data itself.

Post-tensioning tendon force estimation using eddy currents at various temperature conditions

This study proposes an eddy current-based tensile force estimation technique for a post-tensioning (PT) tendon under varying temperature conditions. The tensile force in the internal PT tendon is inferred by measuring the compressive stress on the external anchor head. A dual-coil probe consisting of two identical eddy current coils with orthogonal orientations measures the unidirectional loading level based on the piezoresistive effect. The temperature effect is eliminated using identical eddy current signal alternations in the coils under temperature variation. The performance of the proposed technique was evaluated by estimating the tensile force of a PT tendon under various loading and temperature conditions. The uniqueness of this study lies in the (1) design and fabrication of a dual-coil probe for unidirectional loading level estimation, (2) elimination of the effect of temperature on tensile force estimation, and (3) experimental validation under various loading and temperature conditions.

Research on eddy current and force of non-ferrous metal in eddy current separator

For compensating the gap of present investigations, which did not consider the effect of skin depth before, a novel method is also proposed to obtain the eddy current force. At the beginning, the separating principle of eddy current separator (ECS) is given. Then, based on boundary conditions and the eddy current equations, the internal magnetic flux density, eddy current density and eddy current force density of non-ferrous metal are deduced. By calculating the double integral of eddy current density, the internal eddy current of non-ferrous metal is achieved. The theoretical calculation method (TCM) for solving the eddy current force in the process of non-ferrous metal sorting is proposed. Moreover, to verify the correctness of TCM, taking 24-pole and 30-pole magnetic roller as examples, the finite element models of static and transient magnetic field are established respectively. Additionally, the correctness of TCM is proven by finite element method (FEM) when the x-axis and y-axis component of eddy current force is calculated. At the end, by the theoretical analysis and derivation derived in this paper, based on the relationship between the relative position of N and S poles of the magnetic roller and non-ferrous metal, the internal eddy current force are analyzed by the consistency between the direction of the internal magnetic flux density and the eddy current of non-ferrous metal. The influence of the size relationship between the non-ferrous metal and a single magnetic pole on the separation effect is discussed.

Influence of multiple islands on the hysteresis and dynamics of a western boundary current perturbed by a mesoscale eddy at a gap

The hysteresis of a western boundary current (WBC) flowing across a gap and the dynamics of the mesoscale eddy–WBC interaction with the presence of two islands in the gap are studied using a 1.5-layer ocean model. The hysteresis of the WBC suggests that the two islands in the gap facilitate the WBC to intrude into the western basin by shedding eddies compared with the no-island case, but they promote the WBC to leap across the gap compared with the one-island case. The mesoscale eddies from the east of the gap can induce the critical-state WBC shifting from penetration to leap and vice versa. The dynamics revealed by the vorticity balance analysis shows that the increased (decreased) meridional advection of the WBC perturbed by the eddy forces the WBC to leap across (intrude into the western basin through) the gap. We also present the parameter space of the critical strength of the eddy with variable north–south locations inducing the critical WBC transition. For the WBC critical from the eddy-shedding to leaping regime, the regime shift is most sensitive to the anticyclonic eddy from the gap center and to the cyclonic eddy from the southern gap. It is least sensitive to the eddy downstream of the WBC. For the WBC critical from the leaping to eddy-shedding regime, the regime shift is most sensitive to the anticyclonic eddy upstream of the WBC and to the cyclonic eddy from the southern gap. The least sensitive eddy is from the northern gap.

Interaction forces and suspension characteristics in an oscillatory membrane photocatalytic reactor

The effects of the interaction between the hydrodynamic and colloidal forces on the suspension and performance characteristics of a slurry photocatalytic reactor equipped with oscillatory membrane and lateral turbulence promoters are investigated. Aggregation of catalyst particles is influenced by the magnitude of colloidal forces between the particles in relation to the hydrodynamic stresses acting on the aggregate. The interaction of the axial oscillatory shear with the transverse motion of the turbulence promoters (TP) results in generation of vortices and eddies that extended further away from the membrane surface leading to reducing particle aggregation. For the range of oscillatory conditions investigated, the aggregate size remained in the viscous subrange and decreased with increasing the oscillation intensity where an almost three folds decrease in aggregate size was achieved at high oscillation intensities. This resulted in reducing particles settling and deposition on the membrane surface which increased the catalyst specific area and volume fraction in suspension and enhanced both membrane flux and reaction rates. Improvement of the latter is also achieved by the microscale eddies attenuation of the concentration boundary layer surrounding the catalyst particles which results in better mass transfer. Using methylene blue dye (MB) degradation with ZnO photocatalyst under UV illumination as a model photocatalytic reaction, the investigation showed that increasing the oscillation intensity resulted in higher membrane flux and reaction rates that asymptotically approached maximum corresponding to near maximum catalyst suspension. This was estimated based on the magnitude of the eddy forces in the suspension in relation to the sedimentation and permeate drag forces acting on the catalyst particles. Comparison between the results of the present investigation and data from the literature showed satisfactory agreement.

СТРУМИ ТА ЕЛЕКТРОМАГНІТНІ ЗУСИЛЛЯ В СИСТЕМАХ МАГНІТНО-ІМПУЛЬСНОЇ ОБРОБКИ З ФЕРОМАГНІТНОЮ ПЛАТФОРМОЮ

The action of high-density pulsed currents (109 A/m2) leads to the appearance of the electro-plastic effect in metal products. It is proposed to use magnetic pulse treatment of nonmagnetic plates by electromagnetic inductors with a U-shaped magnetic circuit for local flow pulsed currents in the nonmagnetic plates. The work aims to establish an influence of a ferromagnetic platform with nonlinear magnetic permeability on pulsed eddy currents and magnetic pressure of nonmagnetic metal plates with different electrical conductivity in modeling magnetic pulse treatment of welded joints to achieve the electro-plastic effect. Numerical simulation of pulsed electromagnetic fields by the finite element method is used. The current calculation in the inductor's winding is performed by solving the equations of the magnetic field and the electric circuit equations for a discrete-time interval. A power source is a capacitor that is charged to a specific voltage. To study the effect of the ferromagnetic platform on eddy currents and forces in a nonmagnetic plate with its different electrical conductivity, the same pulsed current in the inductor's winding is used. The dependence of amplitude values of eddy current density and magnetic pressure on the surfaces of nonmagnetic plates of different electrical conductivity is investigated. The influence of the presence and absence of a ferromagnetic platform and its electrical conductivity and magnetic permeability on the values ​​of eddy currents and magnetic pressure in the nonmagnetic plate have been studied. Ref. 13, fig. 7, table.

Design and Analysis of a Generalized High-Order Disturbance Observer for PMSMs With a Fuzy-PI Speed Controller

This paper proposes a generalized high-order observer for estimating total disturbance of permanent magnet synchronous motors (PMSMs). This total disturbance is dominated by load torque but also includes many other terms such as frictions, viscous force, Eddy and flux pulling forces, and noises. Comprehensive experimental results and analyses under various scenarios will be presented to find the appropriate order of the observer. We will compare the performance of zero-order observer (ZDO), first-order observer (FDO), and second-order observer (SDO) under three different scenarios of load torque. Additionally, the results of an state observer (ESO) under the same conditions are also presented. The experimental results show that FDO and SDO achieve similar performance and both of them are notably better than the ZDO and ESO. However, during the severe conditions of load torque, the SDO-based controller can achieve better performance compared to that of FDO-based controller. Moreover, fuzzy algorithm is applied to online tune the PI gains in the speed loop. The results also show that the SDO-based fuzzy-PI control scheme is effective in disturbance rejection and high-performance speed tracking. All of the experiments are carried out on a 300-W PMSM testbed with a digital signal processor (DSP).

One dimensional analytical model considering end effects for analysis of electromagnetic pressure characteristics of annular linear induction electromagnetic pump

A one-dimensional analytical model with the finite magnetic core length and conductive duct wall thickness of annular linear induction electromagnetic pump (ALIP) is established in this paper. Based on this model considering both the end effects and the conductive duct wall effect, the explicit analytical expressions of the electromagnetic and force fields are deduced. At the same time, the influence of end effects and the conductive duct wall effect on electromagnetic field and force field is analyzed and the components of magnetic field, induced eddy current and force field which are produced because of the existence of end effects are separated. Then, the explicit analytical expression of the developed pressure is obtained with the introduced fluid loss. Finally, to verify the feasibility and accuracy of the analytical model, the performance of a small three-phase ALIP under different frequency and current conditions are calculated analytically and the calculated results are verified by experiments data from the experimental test loop.

Study on Electrodynamic Suspension System with High-Temperature Superconducting Magnets for a High-Speed Maglev Train

For the electrodynamic suspension (EDS) system in the high-speed magnetic levitation (Maglev) train, high-temperature superconducting (HTS) coils made of ReBCO-coated conductors can be used as levitation magnets. In this paper, a three-dimensional (3-D) model of the HTS EDS system is built for the design of the suspension system of a full-scale high-speed Maglev train. Subsequently, the levitation and drag forces are analyzed using finite-element method (FEM), and the force performances of different operating currents, reaction board thicknesses, and air gap lengths are investigated. And the distribution of the eddy current on the reaction board induced by the moving HTS magnets is obtained. Moreover, according to the eddy current distribution and force analysis results, a mirror image method is proposed to simplify the calculation and accelerate the estimation of the saturated levitation force of an HTS EDS system. The calculation results of the model are verified by the FEM model with an error less than 8%. Finally, the model is expanded to a full-scale HTS EDS system, which validates the feasibility of applying to the high-speed Maglev train.

2-D Semi-Analytical Modeling of Eddy Currents in Multiple Non-Connected Conducting Elements

This paper concerns the semi-analytical modeling of parasitic eddy current distributions and forces in electromagnetic devices. The harmonic, Fourier-based, model is extended to incorporate a position-dependent conductivity, and restrictions on the induced current density are added to model eddy currents in non-connected conducting elements. To model time-dependent behavior of eddy currents, multiple time harmonics can be incorporated in the solutions. The developed method is verified using the finite-element method for a wide range of frequencies. The model is applied to a coreless linear motor with electrically conducting cooling plates, and the parasitic force is analyzed.

A Thickness-Weighted Average Perspective of Force Balance in an Idealized Circumpolar Current

AbstractThe exact, three-dimensional, thickness-weighted averaged (TWA) Boussinesq equations are used to diagnose eddy–mean flow interaction in an idealized circumpolar current (ICC). The force exerted by mesoscale eddies on the TWA velocity is expressed as the divergence of the Eliassen–Palm flux tensor. Consistent with previous findings, the analysis indicates that the dynamically relevant definition of the ocean surface layer is composed of the set of buoyancy coordinates that ever reside at the ocean surface at a given horizontal position. The surface layer is found to be a physically distinct object with a diabatic and force balance that is largely isolated from the underlying adiabatic region in the interior. Within the ICC surface layer, the TWA meridional velocity is southward/northward in the top/bottom half and has a value near zero at the bottom. In the top half of the surface layer, the zonal forces due to wind stress and meridional advection of potential vorticity act to accelerate the TWA zonal velocity; equilibrium is obtained by eddies decelerating the zonal flow via a downward flux of eastward momentum that increases with depth. In the bottom half of the surface layer, the accelerating force of the wind stress is balanced by the eddy force and meridional advection of potential vorticity. The bottom of the surface layer coincides with the location where the zonal eddy force, meridional advection of potential vorticity, and zonal wind stress force are all zero. The net meridional transport Sf within the surface layer is a small residual of its southward and northward TWA meridional flows. The mean meridional gradient of the surface layer buoyancy is advected by Sf to balance the surface buoyancy flux.

Coupling Characteristics Research on the Subsections of Submersible Motor

The physics field coupling problem of submersible motor is studied in the paper. The influence of the magnetic isolated segment on the performance of the motor is fully considered, and the Electromagnetism-Temperature-Force coupling model is established; combined with different materials, the rated parameters of the Electromagnetism-Temperature-Force can be solved. The accuracy of the method is verified by experiment. The influence law of magnetic isolated segment size on eddy loss, temperature distribution, and force can be summarized. The results have a significant meaning for studying the high-performance submersible motors.

A new gauge-invariant method for diagnosing eddy diffusivities

Coarse resolution numerical ocean models must typically include a parameterisation for mesoscale turbulence. A common recipe for such parameterisations is to invoke mixing of some tracer quantity, such as potential vorticity or buoyancy. However, it is well known that eddy fluxes include large rotational components which necessarily do not lead to any mixing; eddy diffusivities diagnosed from unfiltered fluxes are thus contaminated by the presence of these rotational components. Here a new methodology is applied whereby eddy diffusivities are diagnosed directly from the eddy force function. The eddy force function depends only upon flux divergences, is independent of any rotational flux components, and is inherently non-local and smooth. A one-shot inversion procedure is applied, minimising the mis-match between parameterised force functions and force functions derived from eddy resolving calculations. This enables diffusivities associated with the eddy potential vorticity and Gent–McWilliams coefficients associated with eddy buoyancy fluxes to be diagnosed. This methodology is applied to multi-layer quasi-geostrophic ocean gyre simulations. It is found that: (i) a strictly down-gradient scheme for mixing potential vorticity and quasi-geostrophic buoyancy has limited success in reducing the mis-match compared to one with no sign constraint on the eddy diffusivity or Gent--McWilliams coefficient, with prevalent negative signals around the time-mean jet; (ii) the diagnostic is successful away from the jet region and wind-forced top layer; (iii) the locations of closed mean stream lines correlate with signals of positive eddy potential vorticity diffusivity; (iv) there is indication that the magnitude of the eddy potential vorticity diffusivity correlates well with the eddy energy. Implications for parameterisation are discussed in light of these diagnostic results.

An eddy current-induced magnetic plucking for piezoelectric energy harvesting

Frequency up-conversion is a very efficient method of energy harvesting in order to overcome low, non-periodic, or altered ambient vibration. In order to perform frequency up-conversion and transference of mechanical energy without contact, an eddy current-induced magnetic drag force is used. In this paper, we present a novel configuration of eddy current-induced magnetic plucking for piezoelectric energy harvesting. Our method consists of two permanent magnets, a piezoelectric beam, and a copper disk piece. We design our harvesting method to achieve loading, sudden release, and free vibration using the actuation of the piezoelectric beam through the magnetic mutual coupling between the magnet and copper disk piece. We present the principle of magnetic drag force-generation, characterize the energy harvesting performance of our harvesting method, and demonstrate our harvesting method’s capability of frequency up-conversion and transference of mechanical energy without contact under low, non-periodic, or altered ambient vibration. To that end, we describe the calculation of magnetic drag force with various geometric dimensions and material properties, model of the piezoelectric cantilever beam, comparison between estimation response and measured experiment response, and the measured voltage and power responses.

Automated Green Sorting Device for Ferrous and Non-Ferrous Material Wastes Using Eddy Current Technique

This project is to design an automated green sorting device that can be used to recognize, differentiate and separate between ferrous and non-ferrous materials, as well as to perform transferring of the mentioned materials. In particular, the technique of separation is using magnetic and Eddy-current concept. Eddy-current is generated on a conductor when the conductor is placed in a magnetic field. These Eddy-currents circulate such a way that they induce their own magnetic field and causing a repulsive force (Eddy force). The analysis done is to analyzed the maximum Eddy force generated to the non-ferrous materials when the materials coming close to the Eddy-current roller. The focused parameters in this analysis are a gap distance between magnet to magnet and a gap distance between magnet to material. The results show this sorting device is completely sort the mix materials (ferrous and non-ferrous materials) up to 90% of consistency.

Piezoelectric response of a PZT thin film to magnetic fields from permanent magnet and coil combination

In this study, we report the magnetically induced electric field E3 in Pb(Zr0.57Ti0.43)O3 (PZT) thin films, when they are subjected to both dynamic magnetic induction (magnitude Bac at 45 kHz) and static magnetic induction (Bdc) generated by a coil and a single permanent magnet, respectively. It is found that highest sensitivity to Bdc—\( {{\Delta \left| {E_{3} } \right|} \mathord{\left/ {\vphantom {{\Delta \left| {E_{3} } \right|} {\Delta B_{\text{dc}} }}} \right. \kern-0pt} {\Delta B_{\text{dc}} }} \)—is achieved for the thin film with largest effective electrode. This magnetoelectric (ME) effect is interpreted in terms of coupling between eddy current-induced Lorentz forces (stress) in the electrodes of PZT and piezoelectricity. Such coupling was evidenced by convenient modelling of experimental variations of electric field magnitude with both Bac and Bdc induction magnitudes, providing imperfect open circuit condition was considered. Phase angle of E3 versus Bdc could also be modelled. At last, the results show that similar to multilayered piezoelectric-magnetostrictive composite film, a PZT thin film made with a simple manufacturing process can behave as a static or dynamic magnetic field sensor. In this latter case, a large ME voltage coefficient of \( \alpha = {{\left| {E_{3} } \right|} \mathord{\left/ {\vphantom {{\left| {E_{3} } \right|} {B_{\text{ac}} }}} \right. \kern-0pt} {B_{\text{ac}} }} = 3.55\,{\text{V}}/{\text{cm}}\,{\text{Oe}} \) under Bdc = 0.3 T was found. All these results may provide promising low-cost magnetic energy harvesting applications with microsized systems.

Simulation of Electromagnetic Transients in ITER Thermal Shield Manifolds

A study of eddy currents and forces associated with electromagnetic (EM) transients for the event of current quench in the ITER thermal shield manifolds is presented. EM response of the tokamak passive structures with respect to their inductive coupling has been estimated using the shell approximation. The external field obtained within the model, assuming their 40-degree symmetry, has been applied to the local model of the thermal shield (TS) manifolds covering the 360-degree domain. Fields sources are modeled accurately to the input data description. At this stage of the study related to first estimates of EM loads, acting on the TS manifolds, the electric contact between the cooling tubes and adjacent TS plates was neglected. The current flow is restricted between the neighboring panels. Such simplification uncouples galvanically the manifold tubes from other TS conducting shells, which makes possible a local simulation of eddy currents and EM loads on the manifolds. Two design options with/without electrical breaks in outlet manifolds have been considered. Detailed temporal and spatial distributions of eddy currents and EM forces were obtained. The simulated results were validated in a comparison with a lumped equivalent circuit. Maximal EM loads per unit length were evaluated and found to be low.

Analysis of the eddy force disturbance on foil-wound coils in magnetic levitated planar motion

Analysis of the eddy force disturbance on foil-wound coils in magnetic levitated planar motion

A 3-D analytic eddy current model for a finite width conductive plate

Purpose – A 3-D analytic modeling technique for calculating the eddy current distribution, force and power loss in a conductive plate of finite width and thickness is presented. The derived equations are expressed in a general form so that any magnetic source can be utilized. The model assumes the length of the conductive plate is large and the thickness of the plate is thin but not negligible. The paper aims to discuss these issues. Design/methodology/approach – The conducting and non-conducting regions are formulated in terms of decoupled magnetic vector potential components. In order to accurately compute the eddy current fields and forces the source field only needs to be applied on the surface of the conducting plate. The primary focus is on reducing the eddy current computational time. Findings – The accuracy of the presented approach is verified by utilizing a magnetic rotor that has both a rotational and translational motion. The proposed method is computationally efficient and its accuracy is validated using the finite element method. Research limitations/implications – The conducting plate thickness is assumed to be thin (but not negligible), and this enables the field interaction through the edge of the plate to be neglected. The lateral force is not calculated in the proposed approach. Practical implications – The calculation procedure presented is computationally fast and therefore this can enable the 3-D eddy current forces to be computed in near real-time. Originality/value – This paper presents a fully 3-D analytic based eddy current formlation for computing the eddy current fields and forces in a conducting plate of finite thickness and finite width. The modeling approach is shown to be computationally accurate and relatively fast.

Finite-Element Modeling of Eddy Current and Force Distribution for Induction Dampers

The eddy current and force distribution on the plunger of a single-stage induction damper is analyzed for the numerical investigation and design improvement of induction dampers. A 3-D finite-element method is applied to the eddy current analysis of the magnetic field, and the Lorentz force on the plunger is calculated using the nodal force method. The simulation results show that the Lorentz force on the plunger can be increased by installing a ferromagnetic enclosure around the coil. Furthermore, an induction damper model is proposed considering the skin effect of eddy current on the plunger. The results show that the flux interlinking the plunger is increased by reducing the thickness of the plunger. Finally, the dynamic simulation is carried out to verify the design and investigate the dynamic characteristics of the induction damper. The damper with a ferromagnetic groove enclosing the coil is proven to be more effective.