Eddy Current Region Research Articles

Design of petal-shaped probe for pulse eddy current testing based on finite element simulation

Abstract This paper employs finite element simulation techniques to devise an innovative array-type petal-shaped pulsed eddy current testing probe and investigates its distinctions related to conventional cylindrical probes. Within the simulation framework, a thorough comparative analysis of the detection capabilities of the two probe types is conducted, encompassing an examination of the eddy current regions formed, the impact of lift-off effects and sensitivity to circular corrosion defects. The simulation outcomes reveal that the probe designed in this study exhibits a more extensive detection range and superior detection performance in comparison to its counterparts. This observation holds significance for defect detection in coated materials and the refinement of pulsed eddy current testing probe designs.

Treatment of Multiply Connected Domains in Time-Domain Discontinuous Galerkin $H$ –$\Phi$ Eddy Current Analysis

This paper presents a method for the treatment of multiply connected regions within the semi-explicit time-domain discontinuous Galerkin (DG) eddy current solver based on the ${H}$ – $\Phi $ field formulation. The suggested method utilizes a multivalued magnetic scalar potential over a cutting surface that divides a multiply connected domain into two simply connected regions. The multivalued magnetic scalar potential in the nonconductive domain ( $\Phi $ -domain) is regularly updated after a sequence of time steps of the explicit vector DG-finite element method solver in the electrically conductive domain ( ${H}$ -domain) yielding an accurate time-domain solution of the magnetic field in the multiply connected space surrounding the eddy current region. The efficiency and accuracy of the method are demonstrated by a 3-D example and the obtained results are verified by comparison against the corresponding frequency-domain solution.

Magnetic Detection of Steel Corrosion at a Buried Position Near the Ground Level Using a Magnetic Resistance Sensor

Magnetic Detection of Steel Corrosion at a Buried Position Near the Ground Level Using a Magnetic Resistance Sensor

Custom edge-element FEM solver and its application to eddy-current simulation of realistic 2M-element human brain phantom.

Extensive research papers of three-dimensional computational techniques are widely used for the investigation of human brain pathophysiology. Eddy current analyzing could provide an indication of conductivity change within a biological body. A significant obstacle to current trend analyses is the development of a numerically stable and efficiency-finite element scheme that performs well at low frequency and does not require a large number of degrees of freedom. Here, a custom finite element method (FEM) solver based on edge elements is proposed using the weakly coupled theory, which separates the solution into two steps. First, the background field (the magnetic vector potential on each edge) is calculated and stored. Then, the electric scalar potential on each node is obtained by FEM based on Galerkin formulations. Consequently, the electric field and eddy current distribution in the object can be obtained. This solver is more efficient than typical commercial solvers since it reduces the vector eddy current equation to a scalar one, and reduces the meshing domain to just the eddy current region. It can therefore tackle complex eddy current calculations for models with much larger numbers of elements, such as those encountered in eddy current computation in biological tissues. An example is presented with a realistic human brain mesh of 2 million elements. In addition, with this solver, the equivalent magnetic field induced from the excitation coil is applied, and therefore there is no need to mesh the excitation coil. In combination, these significantly increase the efficiency of the solver. Bioelectromagnetics. 39:604-616, 2018. © 2018 Wiley Periodicals, Inc.

Study on local resistance of non-Newtonian power law fluid in elbow pipes

This paper focuses on the flow characteristic and local resistance of non-Newtonian power law fluid in a curved 90° bend pipe with circular cross-sections, which are widely used in industrial applications. By employing numerical simulation and theoretical analysis the properties of the flow and local resistance of power law fluid under different working conditions are obtained. To explore the change rule the experiment is carried out by changing the Reynolds number, the wall roughness and different diameter ratio of elbow pipe. The variation of the local resistance coefficient with the Reynolds number, the diameter ratio and the wall roughness is presented comprehensively in the paper. The results show that the local resistance force coefficient hardly changes with Reynolds number of the power law fluid; the wall roughness has a significant impact on the local resistance coefficient. As the pipe wall roughness increasing, the coefficient of local resistance force will increase. The main reason of the influence of the roughness on the local resistance coefficient is the increase of the eddy current region in the power law fluid flow, which increases the kinetic energy dissipation of the main flow. This paper provides theoretical and numerical methods to understand the local resistance property of non-Newtonian power law fluid in elbow pipes.

Distribution of bioavailable phosphorus between overlying water and SPM under abrupt expansion condition

Experiments on Phosphorus (P) fraction characteristics in sediment resuspension were performed under adequate hydrodynamic conditions. It is found that the concentration of Suspended Particulate Matter (SPM) in the eddy current region exhibits the “Matthew effect”. Velocity is an impact factor of the Equilibrium Phosphate Concentration (EPC), which is related to other hydraulic conditions. Overall bioavailable dissolved P in the SPM causes migration to overlying water and sediment, eventually being converted into a chemical speciation of P. Conditions of resuspension promote Al-P of SPM that migrated to the sediment and water. Concentrations of Al-P in SPM are reduced. P is released from SPM to water bodies, mainly through conversion into particulate P and dissolved total P. Meanwhile, exchange between SPM and sediments occur mainly through Ca-P migration. Al-P and BD-P possess similar geochemical characteristics or source. Ca-P and Al-P exhibit a negative correlation between migration and conversion.

Discontinuous Galerkin Finite Elements in Time Domain Eddy-Current Problems

A discontinuous Galerkin finite element approach is presented to solve eddy-current problems in the time domain based on a magnetic vector potential formulation. The mass matrix in the eddy-current region is block-diagonal allowing explicit time stepping without having to solve a large algebraic system here. Traditional finite elements, leading to well conditioned system matrices, are used in the eddy-current free domain. The time steps are different in the two regions. The method is illustrated by a simple two-dimensional example.

Error Evaluation of Surface Impedance Boundary Conditions With Magnetic Vector Potential Formulation on a Cylindrical Test Problem

Surface impedance boundary conditions (SIBCs) are used for analysis of a wide range of practical applications such as micro strips, transformers or electrical machines. In this work the SIBC was implemented with classical edge elements using the magnetic vector potential. As known, the SIBC is afflicted with errors when it is being used on curved surfaces and near corners and edges. For this reason this paper investigates the error of the SIBC on curved surfaces. Therefore, simulations have been carried out for different radii and frequencies. The simulation results of the SIBC formulation have been compared with the common formulation for eddy current regions. It will be shown, that the error of the SIBC depends on the relation of the radius to the skin depth. Results are presented and discussed by means of a canonical problem.

An Automatic Hexahedral Mesh Generation to Control Shape of Elements

We have previously proposed an automatic hexahedral mesh generator [S. Nagakura et al, 2002]. The previously proposed method can generate well-shaped mesh. However, it is required to control the element size along every direction on eddy current region, air gap region and so on. On such regions, it is needed to generate flat elements on purpose. Such flat elements can't be generated by using the previously proposed method. Therefore, ellipsoidal bubble as mesh density data is introduced. By taking into account the ellipsoidal bubble, mesh size can be controlled along each direction

Modeling electromagnetic field propagation in eddy-current regions of low conductivity

We propose a finite-element scheme which involves the use of the Lagrangian interface technique to model electromagnetic signal propagation in mixed regions of very low and high conductivity. The method has relevance to modeling underground communications in oil or gas wells. There will be a significant jump in electrical conductivity especially at the interface between the iron and the nonmetallic conductive regions

Numerical Analysis of Thin Skin Depths of 3-D Eddy-Current Problems Using a Combination of Finite Element and Meshless Methods

To alleviate the difficulties encountered in the generation of meshes for the finite element method for solving thin skin depth problems involving three-dimensional (3-D) eddy-currents, particularly in cases in which the eddy-current region is only a fraction of the entire domain, a new technique based on the combination of finite element and meshless methods is proposed. The use of numerical approach to uphold the mathematical properties of the combined shape functions in terms of consistency and linear independence is also investigated. It is shown that a very coarse mesh is already sufficient to give accurate numerical results with the proposed algorithm. To validate and demonstrate the advantages of the proposed method, typical numerical results on studies of high-frequency 3-D eddy-current problems are reported.

Novel Modeling and Solution Approach for Repeated Finite-Element Analysis of Eddy-Current Systems

In this paper, we present an efficient modeling and computational scheme for a repeated solution of an eddy-current system with different values of the supply frequency as well as of the permeability and conductivity of the eddy-current region. The scheme is based on a general parametric expression obtained for the finite-element (FE) solution with the supply frequency, permeability, and conductivity as parameters. The algorithm allows for numerically efficient updating of the solution for different values of the parameters through the solution of a much smaller sparse linear system, instead of a repeated solution of the entire FE model. Moreover, if required, the solution can be computed only over a small region of interest, making the scheme ideally suited to many coupled-field problems. As an application, the scheme is applied to a typical bar-plate eddy-current system, excited by nonsinusoidal currents. The time variations of the magnetic field are computed as a superposition of responses computed for a number of harmonics. An a priori estimate for the difference between responses to two harmonics has been obtained, which can be used as a frequency-sensitivity measure to avoid computation of responses to all individual harmonics. The applicability of the approach to general transient excitations and further possible developments are identified.

Maclean's model of flux penetration: addressing stability

The engineering design of eddy current actuated systems is expensive because of the rapid changes in field quantities and the resulting need to model very accurately. Many suggestions have been made to avoid computations in eddy current regions. The best known of these is the impedance boundary condition at steel interfaces. However, the impedance boundary condition does not work for nonlinear steel because the phasor analysis on which the impedance boundary condition is based is not applicable. MacLean's model is best suited for analyzing in the nonlinear region. Reported problems with time stepping are overcome by studying various time-stepping methods and identifying a suitable numerical scheme. The identified method is shown to be convergent by using the von Neumann stability test.

Eddy currents and electrical surface charges

AbstractIn eddy current calculations, the displacement current in the non‐conducting space surrounding the eddy current region is usually neglected. This assumption enforces that the electric charge density and the accompanying normal components of the eddy current density on the surface of the eddy current region must vanish.If the field exiting source currents are not accompanied by charges this assumption may yield acceptable results for the eddy current distribution. However, if the field exiting source currents are accompanied by charges, this assumption may lead to totally wrong results for the current distribution in the eddy current region. An example is given which makes plain this point.To obtain correct results it is not necessary to employ the full set of Maxwell's equations capable to describe wave propagation phenomena also outside the eddy current region. It is shown in the paper that by replacing the displacement current density in the field describing equations by a specifically chosen current density function makes it possible to determine eddy currents and surface charges within the quasi‐stationary calculation scheme for arbitrary field exciting source currents which may or may not be accompanied by charges. The solution obtained in this way is shown to be unique. Copyright © 2003 John Wiley & Sons, Ltd.

A novel hybrid FEM-BEM method for 3D eddy current field calculation using current density J

This paper introduces a novel hybrid FEM-BEM method for calculating 3D eddy current field. In the eddy current region, the eddy current density J is solved by the finite element method (FEM) which is discretized by brick finite element mesh, while in the eddy current free region, the magnetic field intensity H is solved by the boundary element method (BEM) which is discretized by rectangular boundary element mesh. Under the boundary conditions, an algebraic equation group is obtained that only includes J by eliminating H. This method has many advantages over traditional ones, such as fewer variables, more convenient coupling between the FEM and the BEM and wider application to multiply-connected regions. The calculated values of two models are in good agreement with experimental results. This shows the validity of our method.

Eddy-current computation in the claws of a synchronous claw-pole alternator in generator mode

This paper deals with the three-dimensional finite-element (FE) calculation of eddy currents in the claws of a claw-pole alternator taking the rotational geometry movement into account. For this calculation a transient edge-based A/spl I.oarr/, A/spl I.oarr/ - T/spl I.oarr/ formulation is utilized. The generation of the FE model with a special focus on the discretization of eddy-current regions and air gap is presented. The main intention lies in determining the eddy-current losses in the rotor claws in generator mode at constant speed. Since high-speed and high material conductivity leads to divergence, under-relaxation of the material conductivity in the claws is conducted.

On the use of the new edge based A/spl I.oarr/-A/spl I.oarr/, T/spl I.oarr/ formulation for the calculation of time-harmonic, stationary and transient eddy current field problems

Most papers concerning the calculation of 3D eddy current problems are using a combination of a vector potential and a scalar potential to solve the electromagnetic field in the eddy current regions. This paper uses the A/spl I.oarr/-A/spl I.oarr/, T/spl I.oarr/ formulation with both the magnetic vector potential A/spl I.oarr/ and the electric vector potential T/spl I.oarr/ in the eddy current regions. Since nodal vector potentials with continuous normal components have accuracy problems at interfaces of regions with different permeabilities, edge elements can be used for both potentials. The formulation is applied to the calculation of stationary eddy current field problems induced by motion, time-harmonic and transient eddy current field problems.

A divided region variational principle ofA, ϕ-Ω method for 3-D eddy current problems

In this paper, a divided region variational principle to solve 3-D eddy current problems was given. It adopts the magnetic vector potential A and the electric scalar potential ϕ in the eddy current regions and the source regions, and the magnetic scalar potential Ω in the non-conducting regions (air gap). Using variation of the functional, all governing equations in various regions, the natural boundary conditions and the interface continuity conditions study which satisfy electromagnetic continuity are obtained.

A, ↑-Θ method for 3-D eddy current analysis

After the field equations and the snonuiuoc conditions between the interfaces for 3-D eddy current problems under various gauges were discussed, it was pointed out in this paper that using the magnetic vector potential A, the electric scalar potential υ and Coulomb gauge δ·A=0 in eddy current regions and using the magnetic scalar potential Ω in the non-conducting regions are more suitable All field equations, the boundary conditions, the interface continuity conditions and the corresponding variational principle of this method are also given

Two-dimensional calculation of eddy currents on external conducting walls induced by low-n external modes

The results of two-dimensional calculations of eddy currents induced on external conducting walls surrounding a tokamak are reported. The computed eddy currents are generated by low-n (n=1,2,3) external ideal-magnetohydrodynamic (MHD) instabilities. For a given toroidal mode number n the eddy current patterns are found to be very similar in a variety of plasma configurations, e.g., different edge safety factors and different plasma–wall separation distances, in high beta plasmas. This result is promising for the design of active feedback coils for the stabilization of the resistive wall mode. Also, the effects of having a partial wall that has a poloidal gap on the outboard side are considered. Using the expected gap size in the proposed Korea Superconducting Tokamak Advanced Research (KSTAR) [“The KSTAR tokmak,” in Proceedings of the 17th Symposium on Fusion Engineering, San Diego, 1997 (Institute of Electrical and Electronics Engineers, New York, in press), Paper No. O3.1], the calculation shows that active coils mounted behind the partial walls (the KSTAR passive plates) cover an adequate portion of the eddy current dominant region, enabling feedback stabilization.