Sinusoidal Flux Research Articles

Analytical expressions of the dynamic magnetic power loss under alternating or rotating magnetic field

Analytical methods are recommended for rapid predictions of the magnetic core loss as they require less computational resources and offer straightforward sensitivity analysis. This paper proposes analytical expressions of the dynamic magnetic power loss under an alternating or rotating magnetic field. The formulations rely on fractional derivative analytical expressions of trigonometric functions. The simulation method is validated on extensive experimental data obtained from state-of-the-art setups and gathered in the scientific literature. Five materials are tested for up to at least 1 kHz in both alternating and rotating conditions. The relative Euclidean distance between the simulated and experimentally measured power loss is lower than 5 % for most tested materials and always lower than 10 %. In standard characterization conditions, i.e., sinusoidal flux density, the dynamic power loss contribution under a rotating magnetic field is shown to be precisely two times higher than an alternating one. The knowledge of electrical conductivity reduces the dynamic magnetic power loss contribution to a single parameter (the fractional order). This parameter has the same value for a given material's rotational and alternating contribution. This study confirms the viscoelastic behavior of the magnetization process in ferromagnetic materials and, consequently, the relevance of the fractional derivative operators for their simulation.

Frequency domain‐based analytical solutions for one‐dimensional soil water flow in layered soils

AbstractSolutions of the linearized Richardson–Richards Equation (RRE) for one‐dimensional soil water flow in layered soils with sinusoidal flux in the frequency domain are derived. We evaluate the accuracy of our analytical and other analytical solutions by comparing them with results from a standard numerical model. Our analytical solution agrees with the numerical solution under multi‐layered heterogeneous soil, while others disagree. We also demonstrate the capability of the proposed solution to simulate soil moisture dynamics under a realistic, multi‐frequency flux case. The procedure described in the paper is valid for any series of arbitrary periodic flux superpositions for layered heterogeneous . Moreover, our solution is efficient in the calculation compared with numerical solutions, especially when dealing with long‐time series soil moisture, which can provide a validation of numerical models.

Numerical and experimental analysis of the sinusoidal heat flux source of heat transfer in laminar flow in a tube for single phase flow

Numerical and experimental analysis of the sinusoidal heat flux source of heat transfer in laminar flow in a tube for single phase flow

Methodology for determining the degree of magnetic induction of transformers with a sinusoidal magnetic flux

The research presented in the article is aimed at reducing losses in the magnetic circuits of electrical machines. These losses amount to up to 5 % of the generated electricity, do not depend on the load and can increase over the life of the equipment. To effectively design and construct transformers with low no-load losses, total losses in steel are minimized by optimizing the crystal grain size and thickness of core sheets, improving the steel texture and magnetic circuit design, etc. However, the hysteresis, classical eddy current and anomalous eddy current components of losses in steel react in different directions to these measures, which does not effectively minimize total losses. To determine the three components of losses, a modernized method of three frequencies is proposed, which takes into account the dependence of the hysteresis loss coefficient on frequency. A formula for correcting this coefficient is derived. It is shown that the indicator of the degree of magnetic induction given in most modern scientific sources in the expression for eddy current anomalous losses has become irrelevant. A method for calculating this indicator for the core of a specific transformer is presented, which uses the loss components and total losses in steel found by the method of three frequencies and the total losses in steel at a reduced primary voltage. For the transformer under study, the degree of magnetic induction in anomalous losses was 1.88. The results obtained can be used in the design of dry and oil transformers of different powers operating with a sinusoidal magnetic flux.

Study of melting behavior of phase change material in a square enclosure with constant and variable heat flux at different wall heating conditions: A numerical approach

Latent heat thermal energy storage system offers the most promising cost-effective solution in thermal energy storage applications like solar water heaters to building air conditioning, textile industries, pharmaceutical industries, etc. In this article, the melting process of phase change material (PCM) in a square enclosure with constant, linearly increasing, linearly decreasing and sinusoidal heat flux on different sides of the wall is studied. The result shows that double-wall heating has the highest melting rate followed by side-wall heating and bottom-wall heating. This happens because double-wall heating increases the heat transfer area. Between side-wall heating and bottom-wall heating with uniform heat flux, side-wall heating gives a higher melting rate due to the higher length of solid–liquid interface promoting the heat transfer to solid PCM, thus increasing the melting rate. Again, for different heat distributions of side-wall heating the linearly decreasing heat flux provides the highest melting rate. This type of heat distribution actually transfers more heat to the lower part of the container, which counters the effect of convection, resulting in an enhanced melting process. On the other hand, in the case of distributions at bottom-wall heating, linearly increasing heat flux shows the highest melting rate. In addition, for linearly increasing heat flux, the shape of the liquid cavity is triangular, which gives more space and thereby intense natural convective circulation. This enhanced convection heat transfer leads to a higher melting rate.

Time-periodic natural convection in a pentagonal house with pitched roof during one day

A numerical investigation of unsteady natural convective flow and heat transfer in a pentagonal house is performed. We set a sinusoidal periodic heat flux boundary condition for the pitched roof. Local radial basis function method and Fourier spectral method are adopted to solve the governing equations. The Rayleigh number varies from 103 to 105, the period of the roof heat flux ranges from 10 to 1,000, and the amplitude is set as 0.1, 0.3, and 0.5, respectively. It is found that all the control parameters significantly impact the fluid flow and heat transfer. The temperature and flow fields exhibit periodic behavior due to the sinusoidal heat source. The increasing Rayleigh number leads to a larger periodic average Nusselt number of the top and right walls and a smaller value of the bottom wall. Moreover, an obvious hysteresis phenomenon of heat transfer occurs especially for high Rayleigh number and large period.

Inefficiencies in Unbalanced Three-Phase Power Systems. Relationship Between System Asymmetry and Instantaneous Power Waves.

This work analyzes the energy phenomena occurring in linear power systems characterized by the presence of load unbalances, using the principles of the Unifying General Theory of Electric Power. The energy fluxes characterize each phenomenon in the power system, especially the energy associated with the asymmetry phenomenon; thus it is possible to quantify the asymmetry phenomenon from the instantaneous power shapes, manifested by three unbalanced sinusoidal fluxes, whose resultant is a sinusoidal wave. In addition, this work presents the relationship between the quantification of the phenomenon and the amplitudes of the power fluxes.

Multiscale homogenization of aluminum honeycomb structures: Thermal analysis with orthotropic representative volume element and finite element method

This study develops a thermal homogenization model for an aluminum honeycomb panel using the representative volume element (RVE) concept, considering the orthotropic nature of the structure. The RVE thermal homogenization method is a numerical approach for analyzing heterogeneous materials. It employs a constitutive model based on RVE performance to represent thermal behavior. Effective parameters are determined through averaging techniques, and the finite element method solves the thermal problem, accounting for structure topology and material behavior. The resulting heat conduction problem is solved using the finite element method (FEM) to evaluate the effective thermal characteristics. A 3D RVE is generated based on the honeycomb panel's geometry, evaluating thermal conductivity tensor and describing the medium's thermal performance. Numerical tests validate the model by comparing it with the real honeycomb structure under sinusoidal heat flux. Results show good correlation, with maximum temperatures of 1101.9 °C in the real structure and 1096.4 °C in the medium. The homogeneous medium is further used to investigate thermal performance under convective conditions with varying panel thicknesses, achieving over 77 °C temperature reduction with the thickest panel. Natural vibration behavior is considered, demonstrating strong correlation between modal responses and natural frequencies. This modeling approach efficiently analyzes thermal behavior in large honeycomb structures, reducing computational time significantly.

Implicit Finite Difference Simulation of Hybrid Nanofluid along a Vertical Thin Cylinder with Sinusoidal Wall Heat Flux under the Effects of Magnetic Field

A numerical analysis of magnetohydrodynamic natural convection along a thin vertical cylinder with a sinusoidal heat flux at the wall immersed in copper (Cu) and aluminum-oxide (Al2O3) hybrid nanofluids has been studied. A 2D vertical thin cylinder shape geometry has been considered with a radius of R. The fluid flow is considered laminar and incompressible with the Prandtl number of Pr = 6.2 and 10% concentration of hybrid nanoparticles. The nondimensional governing equations have been solved numerically by using the implicit finite difference method. An in-house FORTRAN 90 code is used for solving this problem and the code is validated with the available benchmark results. Numerical simulations have been performed for a wide range of governing parameters, Hartmann number from Ha = 0 to Ha = 4, nanoparticles volume fractions ϕ = 0.0 to ϕ = 0.1, and the amplitude of the wall heat flux ε = 0.0–0.3. The findings have been illustrated in terms of streamlines, isotherms, local skin friction coefficients, local Nusselt numbers, velocity, and temperature distributions. The flow field and temperature distribution within the boundary layer are deceased by the effects of the wall heat flux amplitudes. It is also noted that the rate of heat transfer increases with particle volume fraction and the amplitude of the wall heat flux. According to the findings, Nu increases by 24.72% as ϕ increases from 0 to 0.1 while ε = 0.3, and 27.66% while ε increases from 0.0 to 0.3 at 5% hybrid nanoparticles. The local skin frictions and Nusselt number diminish with the increment of the Hartman number due to the effects of the Lorenz force. The findings of this study can lead to a better understanding of the fundamental principles regarding the behavior of hybrid nanofluids under complex conditions, such as a vertical thin cylinder with a sinusoidal wall heat flux. Understanding the behavior of hybrid nanofluids in the presence of a magnetic field and a nonuniform wall heat flow can also lead to the development of innovative heat transfer enhancement strategies.

Complex analytical transducer model of a permanent magnet synchronous motor for vibroacoustic applications

This paper presents the complex analytical transducer model of a Permanent Magnet Synchronous Motor (PMSM) for vibroacoustic applications, meaning when the motor actually does not rotate but only the rotor oscillates with low amplitude around an equilibrium position relative to the stator. Using only two assumptions – sinusoidal air-gap flux density and evenly distributed winding – the single phase transducer model is introduced, which is then extended to cover motors with any number of phases. The article proposes adequate transducer symbols and transmission equations as well. In order to enhance the practical relevance of the proposed approach, it is shown that using complex amplitudes and appropriate phase shift vectors in the transducer equations, a complex parameter transducer model can be obtained for sinusoidal signals.

Modelling and simulation for defect detection in hydroelectric penstock using infrared thermography

Modelling and simulation have now become a standard method that serves to cut the economic costs of R&D of novel advanced systems. This paper introduces the study on modelling and simulation of infrared thermography process to detect the defects in the hydroelectric penstock. A 3-D penstock model was built in ANSYS version 19.2.0. Flat bottom holes of different sizes and depths were created on the inner surface of the model as an optimal scenario to represent the subsurface defect in the penstock. The FEM was applied to mimic the heat transfer in the proposed model. The model outer surface was excited at multiple excitation frequencies by a sinusoidal heat flux and the thermal response of the model was presented in the form of thermal images to show the temperature contrast due to the presence of defects. Harmonic approximation method was applied to calculate the phase angle and its relationship with respect to defect depth and defect size was also studied. The results confirmed that the FEM model has led to a better understanding of lock-in infrared thermography and can be used to detect the subsurface defects in the hydroelectric penstock.

An estimation of temperature in living tissue using a fractional model with sinusoidal heat flux conditions on the skin surface

An accurate and quantitative description of the thermal responses of skin tissue under sinusoidal heat flux conditions on the skin surface is provided in this study using a fractional model of the bioheat transfer equation. The governing fractional one-dimensional bio-heat transfer equation was transformed into a dimensionless form to get closed solution by the Caputo-Fabrizio time-fractional derivative technique. The proposed technique, with the aid of symbolic computation, provides an impressive solution for the bioheat transfer equation. Numerical simulations were performed with the aid of Mathcad software to study the behavior of temperature transients on the skin surface exposed to instantaneous surface heating. To investigate the thermal impacts of various control factors on tissue temperature, sensitivity analysis is carried out. We found that the effects of the fractional derivative and the moving heat source velocity on the temperature of the tissue and thermal injuries are enormous, and are shown graphically for an explicit and detail discussion. Observations from the graphical representation of results, show clearly that increasing pressure term leads to increase in velocity distribution of temperature and the effect is maximum towards the center in most cases. The study reveals that bio-thermal research can help with skin burn evaluation, clinical thermal treatment equipment design, and thermal protection from various risks of skin heat injuries. In conclusion, the results of this investigation will be very helpful and useful to both clinical-therapeutic applications and medical sciences.

Design and Performance Analysis of 25 kW Class HTS Induction/Synchronous Motor With Self-Organizing Method for Transportation Applications

We proposed a non-empirical self-organizing design method to obtain a unique stator structure for a high-temperature superconducting induction/synchronous machine. The method starts from a line current model with an approximately ideal sinusoidal distribution of the air-gap magnetic field. It keeps increasing the cross-sectional area of the windings under appropriate constraints to achieve a model with realistic current density. In this work, we applied this method to design a 25 kW-class high-temperature superconducting induction/synchronous motor. In the model, each slot has three-phase windings with different areas representing different numbers of turns. The width and height of the two slots are different for each pole and phase. The results demonstrated that the self-organizing design method significantly suppressed the torque ripple of the motor and reduced the high-order harmonics. The self-organizing windings are equivalent to a short-pitching configuration, which produce a more sinusoidal air-gap flux density than windings in general design. Reducing torque ripple to the lowest possible level facilitates the practical use of superconducting machines for transportation applications.

Numerical simulation of burn injuries with temperature-dependent thermal conductivity and metabolism under different surface heat sources

In the present paper, the phenomena of heat transport inside human forearm tissue are studied through a one-dimensional nonlinear bioheat transfer model under the influence of various boundary and interface conditions. In this study, we considered temperature-dependent thermal conductivity and metabolic heat to predict temperature distribution inside the forearm tissue. We have studied the temperature distribution inside inner tissue and bone because it has been found that burn injuries are mostly affected by layer thickness. The temperature distribution inside human forearm tissue is analyzed using the finite difference and bvp4c numerical techniques. To examine the accuracy of present numerical code, we compare the obtained numerical result with the exact analytical result in a specific case and find an excellent agreement with the exact results. We also validated our present numerical code with a hybrid scheme based on Runge-Kutta (4,5) and finite difference technique and found it in good compliance. From the obtained results, we observed that the homogeneous heat flux has a greater impact on the temperature at the outer surface of the skin, but the sinusoidal heat flux has a greater impact on the temperature of the subcutaneous layer and inner tissue. It is found that there is no burn injury in the first type of heat source (Tw=44°C), but it may occur in the second and third types of heat sources. It has been observed that by raising the blood perfusion rate and reducing the values of reference metabolic heat, coefficient of thermal conductivity, and heat fluxes, we can manage and reduce burn injuries and achieve hyperthermia temperature.

Mixed Convection in a Square Cavity Filled with Porous Medium with Bottom Wall Periodic Boundary Condition

Transient mixed convection heat transfer in a confined porous medium heated at periodic sinusoidal heat flux is investigated numerically in the present paper. The Poisson-type pressure equation, resulted from the substituting of the momentum Darcy equation in the continuity equation, was discretized by using finite volume technique. The energy equation was solved by a fully implicit control volume-based finite difference formulation for the diffusion terms with the use of the quadratic upstream interpolation for convective kinetics scheme to discretize the convective terms and the temperature values at the control volume faces. The numerical study covers a range of the hydrostatic pressure sinusoidal amplitude range and time period values of . Numerical results show that the pressure contours lines are influenced by hydrostatic head variation and not affected with the sinusoidal amplitude and time period variation. It is found that the average Nusselt number decreases with time and pressure head increasing and decreases periodically with time and amplitude increasing. The time averaged Nusselt number decreases with imposed sinusoidal amplitude and cycle time period increasing.

Continuous Rotor Position Estimation for Flux Modulated Doubly Salient Reluctance Motor Drives Based on Back EMF Harmonics

DC-biased sinusoidal current excited flux modulated doubly-salient reluctance motor (FMDRM) drives are developed to reduce the torque ripple and vibration of doubly-salient reluctance motors (DRMs). Conventionally, because of the discontinuous quasi-square current excitation, the rotor position of DRMs is estimated by the combination of piecewise estimation of phase angle information for each phase, where the continuous position estimation for the novel FMDRM drives cannot be realized. To solve this issue, this paper proposes a continuous rotor position estimation strategy for FMDRM drives based on back electromotive force (back-EMF) harmonic characteristics. Firstly, the back-EMF harmonics caused by the rotor saliency and their relationship with the rotor position are analyzed in detail. Then, the corresponding harmonic current regulator and quadrature signal generator are investigated to achieve harmonic current suppression and obtain the quadrature harmonic back-EMF components in the rotating reference frame for rotor position estimation simultaneously. Furthermore, a virtual-inductance-based method is developed to calibrate the phase angle offset between the estimated and actual rotor positions. With the proposed scheme, accurate continuous rotor position estimation can be achieved without any additional hardware. Experimental validations are presented on a three-phase 12/8 FMDRM prototype to verify the accuracy of the proposed rotor position estimation scheme.

Experimental investigation on heat transfer of supercritical water flowing in a horizontal tube with axially non-uniform heating

For a heat exchanger, the heat flux is usually non-uniform in the axial direction, and the knowledge about heat transfer of supercritical water with axially non-uniform heating is scarce. To fill the gap, experiments were conducted in a horizontal tube to study the heat transfer characteristics of supercritical water with axially sinusoidal heating. The pressures varied from 23.5 to 26.5 MPa, mass fluxes 200 to 400 kg·m−2·s−1 and average heat fluxes 50 to 150 kW·m−2. Compared with uniform heat flux, the temperature difference between the top and bottom wall is larger than that of the axially sinusoidal heat flux. The inner-wall heat flux is non-uniform along the circumference due to the temperature difference, being higher at the side wall and lower at the top wall. A relative heat flux parameter is defined to describe the relative magnitude of the local heat flux. The relative heat flux parameter of the top generatrix, which is inversely proportional to the average heat flux, decreases linearly with the increase of the temperature difference between the top and side generatrix. The non-uniform degree of heat flux along the circumference is positively correlated with the average heat flux. Additionally, the local heat transfer characteristics should be considered in horizontal tubes. On the one hand, the heat transfer deterioration may occur when the fluid temperature near the top wall is higher than the pseudo-critical temperature and it can be suppressed with increasing Reynolds number. On the other hand, the local heat transfer can be enhanced if the side and bottom wall temperatures exceed the pseudo-critical temperature.

Design and analysis of in-wheel motor with sinusoidal permanent magnet shape for electrical vehicles

This paper deals with the design and analysis of a surface-mounted outer rotor in-wheel motor (IWM) with the aim of reducing cogging torque and torque ripple for electric vehicles. The proposed IWM is equipped with axial sinusoidal surface-mounted permanent magnets (PMs), with the purpose of producing sinusoidal air gap flux density distribution, thus to realize sinusoidal back electromotive force (EMF) and smooth electromagnetic torque. To highlight the advantage of the proposed IWM, the conventional IWM with tile-shaped PMs and the IWM with stepwise-shaped PMs are also studied for comparison. The finite element method in the commercial software package is utilized to analyze the performance of the three motors, including the radial flux density of air gap, back EMF, cogging torque, and electromagnetic torque. Through the quantitative comparison, it is found that the proposed IWM greatly reduces the cogging torque, highly improves the sinusoidality of back EMF, and nearly eliminates the torque ripple.

Machine learning model for transient exergy performance of a phase change material integrated-concentrated solar thermoelectric generator

Despite the merits of incorporating phase change materials in concentrating solar thermoelectric generating systems, the following research gaps still need to be filled to make the technology viable. Past research efforts focused on pulsed rectangular and sinusoidal heat flux forms which differ from actual transient weather data obtainable under field exposure. Additionally, a comprehensive exergy performance modeling of the system is yet to be presented in the literature, hence, there is no known thermodynamic implication of incorporating phase change materials in thermoelectric systems from a first and second law perspective. Finally, optimization insights obtained for designing these systems are based on inefficient, computationally expensive, and time-consuming numerical solvers or experimental methods which significantly hinder the ease at which useful design insights are obtained. This work aims to fill in these gaps by presenting the first-ever exergy performance investigation of a paraffin wax integrated thermoelectric generating system using data-driven surrogate machine learning models trained with numerically generated data computed from actual 12 h transient timeseries weather data collected every minute and averaged for a 10-year period (2010–2020). Results show that for an optical concentration of 10, the incorporated system with phase change material provides a 25%, 57%, 25%, and 56% improvement in the thermoelectric temperature difference, power generation, exergy efficiency, and thermodynamic irreversibility of the stand-alone system, respectively, without phase change material. Furthermore, the incorporated system generates electricity for 2 more hours into the night when solar irradiance is unavailable. Finally, the cheap surrogate machine learning model accurately predicts the thermodynamic performance of the stand-alone and incorporated systems with an almost zero error and almost unity coefficient of determination in just 5 s after the numerical method has taken 24 h to generate the data, indicating a 17,280-computation time saving.

A Parameter-Free Method for Estimating the Stator Resistance of a Wound Rotor Synchronous Machine

This paper presents a new online method based on low frequency signal injection to estimate the stator resistance of a Wound Rotor Synchronous Machine (WRSM). The proposed estimator provides a parameter-free method for estimating the stator resistance, in which there is no need to know the values of the parameters of the machine model, such as the stator and rotor inductances or the rotor flux linkage. In this method, a low frequency sinusoidal current is injected in the d axis of the stator current to produce a sinusoidal flux in the stator. In this paper, it is shown that the phase difference between the generated sinusoidal flux and the injected sinusoidal current is related to the stator resistance mismatch. Using this phase difference, the stator resistance is estimated. To validate the proposed model-free estimator, simulations were performed with Matlab Simulink and the results were compared with the extended Kalman filter observer. Finally, experimental tests, under different conditions, were performed to estimate the stator resistance of a WRSM.