Flux Vector Research Articles

Estimation of Depth Direction of Crack by measuring the Residual Magnetic Vector Flux Density around Grains

We suggests an algorithm to estimate the depth direction of fatigue cracks. This algorithm uses the distribution of residual magnetic vector flux density (RMVFD) on the specimen. Magnetic domains are the region with a magnetic moment in the same direction. A grain has several magnetic domains. Domain wall is the boundary of the magnetic domain. Magnetic energy stabilized when no external magnetic field applied. That is, the sum of the total magnetic moments is close to zero. It is because that the magnetic flux densities are canceling each other at both ends of the domain wall. The domain wall moves when an external magnetic field applied. As a result, the magnetic domain, which has the same direction with the external magnetic field, enlarged. This phenomenon is magnetization. The domain wall stops moving when it meets with factors that limit the domain wall movement (FLWM). Here FLWM are dislocations, defects, and crystal boundaries. The magnetic energy is unstable at the end of FLWM in the magnetic hysteresis phenomenon. Other end of FLWM has to have the opposite direction of RMVFD to stabilize the magnetic energy. Thus, there are opposite direction of RMVFD each other around crack or grain boundaries. Three dimensional RMVFD (3-RMVFD) can indicates crack existence and depth direction of crack. To verify this theorem, we prepared fatigue crack specimens with different depth direction. The three dimensional shapes of grains reconstructs at the crack. The RMVFD measured by scanning a 3-axis magnetic sensor. And the 3-RMVFD indicated in each grains around crack. The depth directions of crack and grains could estimated by using the 3-RMVFD.

Optimal [formula omitted](div) flux approximations from the Primal Hybrid Finite Element Method on quadrilateral meshes

In this work, we propose and analyze an element-wise H(div,Ω)-conforming computational strategy to post-process the flux vector from the approximated solution of a second-order elliptic equation, obtained by the Primal Hybrid Finite Element Method on regular meshes of convex quadrilaterals generated by bilinear isomorphisms. The recovery strategy makes use of the Arnold–Boffi–Falk (ABFt, t≥0) spaces, leading to locally conservative approximated fluxes with continuous normal components. The proposed method is proven to provide optimal order approximations in H(div,Ω), in the sense that both the flux and its divergence achieve optimal order ht+1 in the L2(Ω)-norm, on quadrilateral meshes. We also show that, within the recovery strategy, it is possible to achieve higher-order approximations for the divergence of the flux by increasing the index t of the local spaces, with almost no extra overall computational cost. Numerical results on affine and bilinear quadrilateral meshes are presented, confirming the theoretical predictions.

Optimal Design and Control of a Spoke-Type IPM Motor with Asymmetric Flux Barriers to Improve Torque Density

This paper studies the optimal design and control scheme of a spoke-type interior permanent magnet motor (SIPM). An asymmetric rotor structure with flux barriers is designed to improve the torque density of SIPM. The design method improves the torque density by approximating the maximum value of the magnetic torque and the reluctance torque, wherein the torque components are separated by the frozen permeability method (FPM) to evaluate the contribution. This scheme does not increase the amount of permanent magnets or the motor size, and reduces motor weight while increasing motor torque output. Firstly, the asymmetric flux barriers are applied in a 27/4 SIPM to illustrate the design principle. Further, by optimizing the width of flux barriers, based on finite-element analyze (FEA), a higher torque density is obtained. Compared with the basic model, the output torque and the torque density of the optimal model are both increased. Based on the optimal model, an angle scanning method is proposed to orient the flux vector and dq-axis. Then, the mathematical model of the optimal model is established, and the maximum torque per ampere (MTPA) control system is designed. Compared with the conventional control system, the proposed control system has a higher torque per ampere (TPA), which shows that the designed control system can give full play to the advantages of the high torque density.

Entropy analysis during heat dissipation via thermomagnetic convection in a ferrofluid-filled enclosure

Thermomagnetic convection and entropy analysis in a ferrofluid-filled cubical cavity, having a centrally placed cylindrical heat source is investigated numerically. The magnetic field is created by either three normal permanent magnets or two Halbach array magnets. The governing equations are solved using a finite-volume, primitive-variables method. Thermal energy interactions between the heat-generating cylindrical heat source and the fluid are visualized through magnetic field distribution, velocity contours, velocity vectors, static temperature, and heat flux vectors. Also, a volumetric entropy generation analysis has been performed for understanding the quality of heat transfer and evaluating the thermodynamic merit of the heat-dissipation system. Results indicate that there is a considerable enhancement of cooling with both the magnetic arrangements. Parametric study shows that the arrangement with a double-Halbach array yields a slightly better overall performance compared to the one with three normal permanent magnets. Although the heat transfer is found to increase with increasing magnetic field strength, strong advection leads to a higher entropy generation at a large field. An intermediate magnetic Nusselt number is found to provide the optimal cooling amongst the investigated cases.

СПОСТЕРІГАЧ ПОТОКОЗЧЕПЛЕННЯ, АДАПТИВНИЙ ДО ЗМІН АКТИВНОГО ОПОРУ РОТОРА АСИНХРОННИХ ДВИГУНІВ

A flux observer for induction motors which is adaptive to the active rotor resistance variations is presented. Due to the added fluxes overestimation in the observer structure, the global exponential stability properties of the current and flux vector components and active rotor resistance estimation are ensured under conditions of persistency of excitation. The proposed observer has a simpler structure compared to existing solutions with the global stability properties. The simulation results of the observer dynamic performance investigation confirm its effectiveness. It is shown that even if the conditions of persistency of excitation are not met, the active rotor resistance is estimated correctly; consequently, the designed observer can be implemented as an identification algorithm in self-commissioning systems of induction electric drives. References 9, figures 5.

Generation mechanism of fracture-induced electromagnetic radiation and directionality characterization in the near field

The electromagnetic radiation generated during the fracturing process is generally regarded as vector field that holds an imperative significance in rock engineering and fracture mechanics. With this motive, based on the theory of fracture mechanics and electromagnetics, the nonlinear field at the crack tip and the atomic bond breaking condition are analyzed in this study. Considering the electromagnetic field pattern generated by the oscillating dipole, the generation process of the electromagnetic radiation signal is divided into two stages namely, initiation of the forced oscillation of the dipole and the damped dipole oscillation. Followed by this, the experimental investigations on limestone and shale under the condition of Brazilian tests are performed. In the whole loading process, four sets of three-axis electromagnetic antennas are used for simultaneous measurement in different directions. The experimental and theoretical results exhibit close resemblance. The superposition effect of the electromagnetic field from microcrack initiation to macro-fracture is analyzed further. Based on the obtained results, three indicators are proposed to characterize the directionality of the electromagnetic radiation generated by the rock fracture. It is observed that the changing law of the direction angles is consistent, showing a strong correlation with the symmetrical position. The direction of the magnetic flux density vector generated by rock Brazilian tests tends to be parallel to the crack surface.

An Analytical Solution of the Hyperbolic Bioheat Model of the Cornea Subjected to Laser Irradiation

The thermal effects occurring in a cornea subjected to short-pulsed laser irradiation during laser thermokeratoplasty (LTK) are investigated. The transient bioheat transfer is described by the hyperbolic model and solved analytically using the finite Fourier transform technique and the method of variation of parameters. The computational results predicted by the hyperbolic model show that the degree of damage in the corneal tissue induced by Ho: YAG laser irradiation under LTK surgery increases linearly with time. An increase in the convection coefficient of the anterior corneal surface causes an insignificant reduction in the corneal temperature, whereas an increase in the value of phase lag in the heat flux vector causes a rise in the corneal temperature .

On the Theory of Entropy Solutions of Nonlinear Degenerate Parabolic Equations

We consider a second-order nonlinear degenerate parabolic equation in the case, where the flux vector and the nonstrictly increasing diffusion function are merely continuous. In the case of zero diffusion, this equation degenerates into a first order quasilinear equation (conservation law). It is known that in the general case under consideration an entropy solution (in the sense of Kruzhkov–Carrillo) of the Cauchy problem can be nonunique. Therefore, it is important to study special entropy solutions of the Cauchy problem and to find additional conditions on the input data of the problem that are sufficient for uniqueness. In this paper, we obtain some new results in this direction. Namely, the existence of the largest and the smallest entropy solutions of the Cauchy problem is proved. With the help of this result, the uniqueness of the entropy solution with periodic initial data is established. More generally, the comparison principle is proved for entropy sub- and supersolutions, in the case where at least one of the initial functions is periodic. The obtained results are a generalization of the results known for conservation laws to the parabolic case.

Comparison of Poynting’s vector and the power flow used in electrical engineering

This paper will analyze how the energy flux of Poynting’s vector is compared to the power flow in electrical engineering, where the power, instead, is defined by voltages and currents. There are alternatives to Poynting’s energy flux vector that agree more with circuit theory methods such that the energy flow is in the current conductor and not in the insulation surrounding it. One such basic formulation would only consist of the total current density and the voltage potential, but it would need an alternative theorem for energy transfer. Another formulation proposed by Slepian would instead still agree with Poynting’s energy transfer theorem, but it needs to add the power of alternating magnetic vector potential. The alternatives to Poynting’s vector may better illustrate the energy flow in electrical engineering, but two things could be considered in their generality. First, since they are expressed by potentials, they are gauge invariant and depend on the definition of the potentials. Second, Poynting’s vector is used to formulate the electromagnetic momentum, and any alternative energy flow vectors would not. These two notes are of minor importance in electrical engineering, and the alternatives could be used as good alternatives for describing power flow. The main purpose of this paper is to bridge the differences between the physical theory of energy flux and the methods in electrical power engineering. This could simplify the use of energy flux and Poynting’s vector in engineering problems.

14-moment maximum-entropy modeling of collisionless ions for Hall thruster discharges

Ions in Hall effect thrusters are often characterized by a low collisionality. In the presence of acceleration fields and azimuthal electric field waves, this results in strong deviations from thermodynamic equilibrium, introducing kinetic effects. This work investigates the application of the 14-moment maximum-entropy model to this problem. This method consists in a set of 14 partial differential equations (PDEs) for the density, momentum, pressure tensor components, heat flux vector, and fourth-order moment associated with the particle velocity distribution function. The model is applied to the study of collisionless ion dynamics in a Hall thruster-like configuration, and its accuracy is assessed against different models, including the Vlasov kinetic equation. Three test cases are considered: a purely axial acceleration problem, the problem of ion-wave trapping, and finally the evolution of ions in the axial-azimuthal plane. Most of this work considers ions only, and the coupling with electrons is removed by prescribing reasonable values of the electric field. This allows us to obtain a direct comparison among different ion models. However, the possibility to run self-consistent plasma simulations is also briefly discussed, considering quasi-neutral or multi-fluid models. The maximum-entropy system appears to be a robust and accurate option for the considered test cases. The accuracy is improved over the simpler pressureless gas model (cold ions) and the Euler equations for gas dynamics, while the computational cost shows to remain much lower than direct kinetic simulations.

Control Strategy of a Five-Phase Induction Machine Supplied by the Current Source Inverter With the Third Harmonic Injection

In the five-phase induction machine (IM), it is possible to better use the electromagnetic circuit than in the three-phase IM. This requires the use of an adequate converter system which will be supplied by an induction machine. The electric drive system described, in this article, includes the five-phase induction machine supplied by the current source inverter (CSI). The proposed novelty—not presented previously—is the control system structures for the five-phase IM, which is supplied by CSI. The proposed control systems allow for independent control of IM state variables in the first and the second system plane to inject the third harmonic. However, the third harmonic must be suitably associated with the fundamental harmonic. In the proposed solution, the machine vector model is not transformed into the ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d–q</i> ) coordinate system that is connected to the rotor flux vector but utilizes the stationary system ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α–β</i> ). The nonlinear model linearization is based on the demonstrated nonlinear variables transformation for i-orthogonal ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α–β</i> ) (i) planes. Voltage control is applied to the control system structure. The control variables of the five-phase IM are the voltage in the dc link and the angular speed of the output current vector. In the control strategy, the control variables are determined for both system planes. Therefore, the transformation of these control variables to the dc link of CSI is proposed. The proposed control structure allows for independent control of variables in the first and second system planes. It leads to the possibility to increase the value of electromagnetic torque up to 12% for the five-phase IM, which has not been used before in the case of the machine supplied by the CSI. All theoretical issues are confirmed by experimental tests in the 5.5 kW five-phase IM.

Thermal transport in porous graphene with coupling effect of nanopore shape and defect concentration

Thermal conductivity of porous graphene can be affected by defect concentration, nanopore shape and distribution, and it is hard to clarify the effects due to the correlation of those factors. In this work, molecular dynamics simulation is used to compare the thermal conductivity of graphene with three shapes of regularly arranged nanopores. The results prove the dominant role of defect concentration under certain circumstances in reducing thermal conductivity, while the coupling effect of nanopore shape should be noticed. When the atoms at the local phonon scattering area around each nanopore are properly removed, the abnormal increment of thermal conductivity can be detected with the increase of defect concentration. Heat flux vector angles can effectively characterize the local phonon scattering area, which can be used to describe the effect of nanopore shape. The coupling effect of defect concentration and pore shape with similar heat flux path is clarified according to this process. By adjusting vertex angle of triangle defect, there is a balanced state of the effect factors between the variation of defect concentration and the same phonon scattering area. It provides a possible way to describe the weighing factors of the coupling effect. The results suggest a feasible approach to optimize and regulate thermal properties of porous graphene in nanodevice.

Dynamic Performance Enhancement of a Direct-Driven PMSG-Based Wind Turbine Using a 12-Sectors DTC

This paper focuses on the performance analysis, modeling, and control of permanent magnet synchronous generator (PMSG)-based wind energy conversion. This work analyzes controllers for the machine-side converter (MSC) and grid-side converter (GSC) and presents a new direct torque control (DTC) scheme based on a 12-sectors polygonal DTC for variable speed control of the PMSG. The proposed method solves the drawbacks faced by conventional six-sectors DTC control. The proposed method utilizes 12 sectors of 30° each compared to 60° in the conventional 6-sectors DTC. The 12-sectors technique was applied to voltages and flux vectors to increase the degrees of freedom for the selection of optimal vectors and, thus, reduce the torque ripple. This work analyzed the aforementioned DTC methods using MATLAB/Simulink, comparing the dynamic response of the proposed 12-sectors DTC with the conventional 6-sectors DTC control, and the results verified the effectiveness of the proposed DTC control.

Advanced Speed Control Methods for Induction Motor: An Analysis

Induction motors are widely used in a wide range of industrial and domestic applications. Induction motors are a common option compared to other motors because of their low maintenance requirements, robustness, and low cost. With advancements in power electronics and speed control technology, it is now possible to precisely control the speed of an induction motor for particular industrial applications. This paper provides a comprehensive literature review of advanced 3-phase induction motor speed control techniques such as direct/indirect vector control, direct torque and flux control, adaptive and optimal control, and intelligent control. Hopefully, all of the main takeaways from this analysis will spur further research and development of advanced switching techniques and controllers for future induction motor drives. The authors are confident that this survey article would be extremely useful to researchers in locating important references in speed control 3-phase induction motors.

Extraordinary quasi-16-day wave activity from October 2013 to January 2014 with radar observations at mid-latitudes and MERRA2 reanalysis data

Combining two meteor radar observations at mid-latitudes and MERRA2 reanalysis data, we report an extraordinary quasi-16-day wave (Q16DW) activity in the mesosphere and lower thermosphere (MLT) from about October 2013 to January 2014. The Q16DW is not only active for a long period, but also unrelated to stratospheric sudden warming (SSW), while 7-year radar observations indicate that strong waves and oscillations in the MLT at mid-latitudes occur generally in winter, and are almost always associated with SSW and stratospheric final warming (SFW), except the extraordinary Q16DW. Meanwhile, during the SSW and SFW in February and March 2014, the observation and reanalysis data show that an intense Q16DW arises in the stratosphere but is not present in the MLT. The two Q16DWs are obviously distinguished from each other. The exceptional Q16DW shows a slowly downward phase progression from the MLT to the troposphere with predominant wavenumber 1, while the second Q16DW has a steeper vertical phase in the stratosphere with predominant wavenumber 2. Although the eastward winds prevail, these Q16DWs are weakened and evanescent in the region with the westward wind and negative refractive index. EP flux vector indicates that these waves originate mainly from the lower atmosphere at mid- and high-latitudes, and are intensified in the middle stratosphere. The first Q16DW may make a little contribution to polar vortex intensification due to small EP flux divergence. However, the Q16DW in the SSW has a strong negative divergence almost in the whole polar stratosphere, implying an important role in the stratospheric zonal wind reduction in the SSW.Graphical

A flux‐vector splitting scheme for the shallow water equations extended to high‐order on unstructured meshes

AbstractWe present a flux vector splitting method for the one and two‐dimensional shallow water equations following the approach first proposed by Toro and Vázquez for the compressible Euler equations. The resulting first‐order schemes turn out to be exceedingly simple, with accuracy and robustness comparable to that of the sophisticated Godunov upwind method used in conjunction with complete non‐linear Riemann solvers. The technique splits the full system into two subsystems, namely an advection system and a pressure system. The sought numerical flux results from fluxes for each of the subsystems. As to the source terms, there is potential for treating general source terms by incorporating them into either subsystem. In this article we show preliminary results for the case of a discontinuous bottom, incorporated into the pressure system. Results show that the resulting method is well balanced. The basic methodology, extended on 2D unstructured meshes, constitutes the building block for the construction of numerical schemes of very high order of accuracy following the ADER approach. The presented numerical schemes are systematically assessed on a carefully selected suite of test problems with reference solutions, in one and two space dimensions. The applicability of the schemes is illustrated through simulations of tsunami wave propagation in the Pacific Ocean.

ROTOR SPEED OBSERVER OF ASYNCHRONOUS GATE CASCADE

The vector control system of an asynchronous motor, which is closed in terms of the rotor speed, assumes the presence of a sensor on the shaft of the electric machine. However, in practice, often there are problems of regulating the speed of rotation of asynchronous electric drives, in the solution of which the use of mechanical movement coordinate sensors is technically irrational or impossible. In this case, it is necessary to use one of the sensorless vector control algorithms, which involve direct measurement of only electrical quantities. In rotor vector control systems, when the stator is connected to the network at the same time, the need to measure the angle of rotation of the rotor relative to the stator is added, which complicates the structure of the observer.&#x0D; For the synthesis of speed observers in asynchronous electric drives, the approach known in control theory is widely used, in which, based on the second Lyapunov method, an adaptation function is formed that provides asymptotic convergence of the adaptive model to the reference one.&#x0D; In this paper, the synthesis of the rotor speed observer of an asynchronous gate cascade (AGC) was carried out for its application in a sensorless relay-vector control system. Equations of electromagnetic processes in an asynchronous machine, formulas for coordinate transformations and an identifier for the position angle of the rotor AGC were used as initial mathematical models. The observer synthesis is based on the second Lyapunov method, which allows to determine the structure of the adaptation function, which adjusts the adaptive model in such a way that the difference between the outputs of the adaptive and reference models tends to zero. Thus, the adaptation function, which uses the stator flux vector, ensures the asymptotic stability of the perturbed motion. The proposed speed observer AGC differs from the known observers for stator control in that, along with the speed calculation, the trigonometric functions of the rotor rotation angle are determined, and the structure of the observer includes coordinate transducers that are absent in stator vector control systems, since they do not need to calculate the projections of the voltage vector of one part of the machine onto the orthogonal axes of its other part.

Evaluation of magnetic properties of two kinds of permendurs by vector magnetic measurement

Vector magnetic properties of various electrical steel sheets have been investigated by using a vector magnetic property measurement apparatus to select a magnetic material suitable as a motor core material. However, a magnetic material with a higher saturation magnetization than an electrical steel sheet is useful for increasing torque of a motor. Therefore, a permendur with higher saturation magnetization than an electrical steel sheet is selected as a measurement sample. It is known that a permendur does not have magnetic anisotropy. In this paper, vector magnetic properties of two kinds of permendurs made by VACUUMSCHMELZE (VAC) and Hitachi Metals are measured. Moreover, maximum magnetic field intensities and core losses of two kinds of permendurs to an inclination angle of magnetic flux density vector locus from rolling direction are evaluated for investigation of those magnetic anisotropies. As a result, differences of vector magnetic properties of two kinds of permendurs are revealed.

Generalized Fluid Models of the Braginskii Type

Several generalizations of the well-known fluid model of Braginskii (1965) are considered. We use the Landau collisional operator and the moment method of Grad. We focus on the 21-moment model that is analogous to the Braginskii model, and we also consider a 22-moment model. Both models are formulated for general multispecies plasmas with arbitrary masses and temperatures, where all of the fluid moments are described by their evolution equations. The 21-moment model contains two “heat flux vectors” (third- and fifth-order moments) and two “viscosity tensors” (second- and fourth-order moments). The Braginskii model is then obtained as a particular case of a one ion–electron plasma with similar temperatures, with decoupled heat fluxes and viscosity tensors expressed in a quasistatic approximation. We provide all of the numerical values of the Braginskii model in a fully analytic form (together with the fourth- and fifth-order moments). For multispecies plasmas, the model makes the calculation of the transport coefficients straightforward. Formulation in fluid moments (instead of Hermite moments) is also suitable for implementation into existing numerical codes. It is emphasized that it is the quasistatic approximation that makes some Braginskii coefficients divergent in a weakly collisional regime. Importantly, we show that the heat fluxes and viscosity tensors are coupled even in the linear approximation, and that the fully contracted (scalar) perturbations of the fourth-order moment, which are accounted for in the 22-moment model, modify the energy exchange rates. We also provide several appendices, which can be useful as a guide for deriving the Braginskii model with the moment method of Grad.

An Efficient Method for Litz-Wire AC Loss Computation in Transient Finite Element Analysis

An efficient method is proposed to predict eddy current loss of Litz wire coils, or completely transposed multi-strand coils, in transient finite element analysis (FEA). The method is based on analytical solutions of eddy current loss in a solid wire due to skin effects and proximity effects. The bundle of Litz or solid wires is homogenized by introducing a fill factor to describe the conducting area ratio. The analytical solutions in the frequency domain for round, square, and rectangular wires are further expanded to those in the time domain. The wire length direction in each 3-D mesh is automatically detected so that the flux density vector in each mesh can be correctly decomposed to the orthogonal and tangential components for anisotropic proximity effect loss computation. The method is applied to calculating eddy current loss of a gapped inductor in both 2-D and 3-D, and the results are compared with that using real solid wires.