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The paper presents a methodology in which the slotted regions of electrical machines are replaced by homogeneous regions with anisotropic magnetic permeability. The resulting FEM model is then built and solved in an easy way, because a simplified structure is analyzed, with fixed geometrical characteristics and electrical and magnetic properties depending on the original geometry. The methodology is therefore useful for estimating the machine performances as a function of slot and winding parameters and can be conveniently used at the initial step of the design to perform parametrical analyses and optimizations with uncomplicated procedures for the generation of the FEM model. In order to test the reliability of the method, the FEM results obtained with both the actual configuration and the “smoothed” one must be compared. In the example of application, the proposed methodology is applied to a linear brushless DC motor. The dependence of the accuracy and convergence speed on different “smoothing” strategies is first discussed. Then the obtained results are compared with the ones related to the original slotted configuration. Finally, the correspondence of some important electromagnetic quantities (flux lines distribution, air‐gap flux density and electromagnetic force) is analyzed.

The purpose of this paper is to develop an indigenous three‐dimensional computational code and apply it to compare flow and heat transfer characteristics for inline and staggered arrangement of circular tubes in a tube bundle.

A finite‐volume based computational code is developed to solve the momentum and energy equations for flow through a three‐dimensional rectangular channel and past built‐in tube bundles having inline and staggered arrangement. The approach is based on SIMPLE algorithm. The basic conservation equations of mass, momentum and energy are solved over a body‐fitting grid on the physical domain to obtain the flow and temperature fields.

Heat transfer and pressure drop are compared for inline and staggered tube arrangements in a tube bundle over range of Reynolds numbers 300 ≤ Re ≤ 800. Results are validated suitably against those available in literature.

Tube‐fin heat exchangers with continuous fins on a tube array are commonly used in air‐conditioning industry and in air‐cooled condensers of power plants. The flow structure within the finned tube bank is complex due to the presence of a circular tube, which causes flow acceleration over the fin surface and flow separation on the back side of the tube resulting in low velocity wake region. The present study provides a better understanding of flow behavior and heat transfer for inline and staggered arrangement of tube bundles in tube‐fin heat exchangers at different Reynolds numbers.

A numerical code based on finite volume method has been developed and used for computations to predict heat transfer and pressure drop characteristics for flow past inline and staggered arrangement of circular tubes. Predictions are made from the computed results about suitability of staggered/inline tube arrangements in a given range of Reynolds number.

This paper aims to numerically analyse natural convection of yield stress fluids in rectangular cross-sectional cylindrical annular enclosures. The laminar steady-state simulations have been conducted for a range of different values of normalised internal radius (r_i/L 1/8 to 16, where L is the difference between outer and inner radii); aspect ratio (AR = H/L from 1/8 to 8 where H is the enclosure height); and nominal Rayleigh number (Ra from 10³ to 10⁶) for a single representative value of Prandtl number (Pr is 500).

The Bingham model has been used to mimic the yield stress fluid motion, and numerical simulations have been conducted for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for the vertical side walls. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity.

It is found that the mean Nusselt number based on the inner periphery Nu¯_i increases (decreases) with an increase in Ra (Bn) due to augmented buoyancy (viscous) forces irrespective of the boundary condition. The ratio of convective to diffusive thermal transport increases with increasing r_i/L for both Newtonian (i.e. Bn = 0) and Bingham fluids regardless of the boundary condition. Moreover, the mean Nusselt number Nu¯_i normalised by the corresponding Nusselt number due to pure conductive transport (i.e. Nu¯_i/(Nu¯_i)_cond) shows a non-monotonic trend with increasing AR in the CWT configuration for a given set of values of Ra, Pr, L_i for both Newtonian (i.e. Bn = 0) and Bingham fluids, whereas Nu¯_i/(Nu¯_i)_cond increases monotonically with increasing AR in the CWHF configuration. The influences of convective thermal transport strengthen while thermal diffusive transport weakens with increasing AR, and these competing effects are responsible for the non-monotonic Nu¯_i/(Nu¯_i)_cond variation with AR in the CWT configuration.

Detailed scaling analysis is utilised to explain the observed influences of Ra, BN, r_i/L and AR, which along with the simulation data has been used to propose correlations for Nu¯_i.

This paper aims to study the relationship between leakage flux coefficient and the coreless axial magnetic field permanent magnet synchronous generator (AFPMSG) size and obtain the expressions of leakage flux coefficient.

In this paper, a magnetic circuit model of coreless AFPMSG is proposed. Four kinds of leakage permeances of permanent magnet (PM) are considered, and the expression of no-load leakage flux coefficient is obtained. Solving the integral region of leakage permeances by generator size, which improves the accuracy of the solution.

Finite element method and magnetic circuit method are used to obtain the no-load leakage flux coefficient and its variation trend charts with the change of pole arc coefficient, air gap length and PM thickness. The average errors of the two methods are 2.835%, 0.84% and 1.347%, respectively. At the same time, the results of single-phase electromotive force obtained by magnetic circuit method, three dimensional finite element method and prototype experiments are 19.36 V, 18.82 V and 19.09 V, respectively. The results show that the magnetic circuit method is correct in calculating the no-load leakage flux coefficient.

The special structure of the coreless AFPMSG is considered in the presented equivalent magnetic circuit and equations, and the equations in this paper can be applied for leakage flux evaluating purposes and initial parameter selection of the coreless AFPMSG.

The theoretical method of converting the magnetic circuit into an electric circuit is mature, but the way to determine the inductances in the electric circuit is not reliable, especially for the core working in saturation status, and it is impossible to determine the inductances by the transformer terminal measurements, as the measurement information is not enough to determine a number of inductances. This paper aims to propose an approach of calculating the reluctances.

In this paper, an approach of calculating the reluctances is proposed based on the numerical simulation of magnetic field in transformer with different values of current excitation. The reluctance of a core segment or air region as a branch of magnetic circuit is obtained by the magnetic energy and magnetic flux. By this way, all the reluctances as function of flux can be determined, and then the inductances can be determined. The reluctances and equivalent electric circuit of three-phase integrative transformer is determined, and its validation is proved in the paper.

The single phase example shows that the proposed method has a good performances on analysis of the inrush current in deep saturation. The peak value of the inrush current derived from the proposed approach matches well with the results obtained by coupled circuit-FEM analysis, and the difference is about 4.8 per cent. For studies on dual models of single phase transformers, the leakage inductances have important effects on the peak value of the inrush current. The reluctances of three-phase transformer are calculated, and the equivalent circuit simulation results are slightly smaller than the coupled circuit-FEM simulation results.

Approach of calculating the reluctances based on the numerical simulation of magnetic field in transformer is proposed. The magnetic core and air space are divided into several segments, and the reluctance for each segment is calculated based on the energy in the region and the flux of the cross-sectional area. By applying various excitation currents, all the reluctances as function of flux can be determined, and then all the non-linear inductances including the non-linear leakage inductances are obtained. The proposed approach is reliable to determine a number of inductances in the dual electric circuit, especially for deep saturation status.

The NIRVANA project is concerned with the development of a nonoscillatory, integrally reconstructed, volume‐averaged numerical advection scheme. The conservative, flux‐based finite‐volume algorithm is built on an explicit, single‐step, forward‐in‐time update of the cell‐average variable, without restrictions on the size of the time‐step. There are similarities with semi‐Lagrangian schemes; a major difference is the introduction of a discrete integral variable, guaranteeing conservation. The crucial step is the interpolation of this variable, which is used in the calculation of the fluxes; the (analytic) derivative of the interpolant then gives sub‐cell behaviour of the advected variable. In this paper, basic principles are described, using the simplest possible conditions: pure one‐dimensional advection at constant velocity on a uniform grid. Piecewise Nth‐degree polynomial interpolation of the discrete integral variable leads to an Nth‐order advection scheme, in both space and time. Nonoscillatory results correspond to convexity preservation in the integrated variable, leading naturally to a large‐Δt generalisation of the universal limited. More restrictive TVD constraints are also extended to large Δt. Automatic compressive enhancement of step‐like profiles can be achieved without exciting “stair‐casing”. One‐dimensional simulations are shown for a number of different interpolations. In particular, convexity‐limited cubic‐spline and higher‐order polynomial schemes give very sharp, nonoscillatory results at any Courant number, without clipping of extrema. Some practical generalisations are briefly discussed.

Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed performance. Notes that 18 papers from the Symposium are grouped in the area of automated optimal design. Describes the main challenges that condition computational electromagnetism’s future development. Concludes by itemizing the range of applications from small activators to optimization of induction heating systems in this third chapter.

The purpose of the present study is to investigate the flow and turbulence characteristics of a turbulent wall jet flowing over a surface inclined with the horizontal and to investigate the effect of variation of the angle of inclination of the wall on the flow structure of the wall jet.

The high Reynolds number two-equation κ− model with standard wall function is used as the turbulence model. The Reynolds number considered for the present study is 10,000. The Reynolds averaged Navier-Stokes (RANS) equations are used for predicting the turbulent flow. A staggered differencing technique employing both contravariant and Cartesian components of velocity has been applied. Results for distribution of wall static pressure and skin friction, decay of maximum streamwise velocity, streamwise variation of integral momentum and energy flux have been compared for the cases of α=0°, 5°, and 10°.

Flow field has been represented in terms of streamwise and lateral velocity contours, static pressure contour, vorticity contour and streamwise velocity and static pressure profiles at different locations along the oblique offset plate. Distribution of Reynolds stresses in terms of spanwise, lateral and turbulent shear stresses, and turbulent kinetic energy and its dissipation rate have been presented to describe the turbulent characteristics. Similarity of streamwise velocity and the velocity parallel to the oblique wall has been observed in the developed region of the wall jet flow. A decaying trend is observed in the variation of total integral momentum flux in the developed region of the wall jet which becomes more evident with increase in oblique angle. Developed flow region has indicated trend of similarity in profiles of streamwise velocity as well as velocity component parallel to the oblique wall. A depression in wall static pressure has been observed near the nozzle exit when the wall is inclined and the depression increases with increase in inclination. Effect of variation of oblique angles on skin friction coefficient has indicated that it decreases with increase in oblique angle. Growth of the outer and inner shear layers and spread of the jet shows linear variation with distance along the oblique wall. Decay of maximum streamwise velocity is found to be unaffected by variation in oblique angle except in the far downstream region. The streamwise variation of spanwise integral energy shows increase in oblique angle and decreases the magnitude of energy flux through the domain. In the developed flow region, streamwise variation of centreline turbulent intensities shows increased values with increase in oblique angle, while turbulence intensities along the jet centreline in the region X<12 remain unaffected by change in oblique angles. Normalized turbulent kinetic energy distribution highlights the difference in turbulence characteristics between the wall jet and reattached offset jet flow. Near wall velocity distribution shows that the inner region of boundary layer of the developed oblique wall jet follows a logarithmic profile, but it shows some difference from the standard logarithmic curve of turbulent boundary layers which can be attributed to an increase in skin friction coefficient and a decrease in thickness of the wall attached layer.

The study presents an in-depth investigation of the interaction between the jet and the inclined wall. It is shown that due to the Coanda effect, the jet follows the nearby wall. The findings will be useful in the study of combined flow of wall jet and offset jet and dual offset jet on oblique surfaces leading to a better design of some mechanical jet flow devices.

To study and to analyze a second order finite‐element boundary‐flux approximation using isoparametric numerical integration.

The numerical finite‐element integration is the main method used in this research. Since a domain with curved boundary is considered we apply an isoparametric approach. The lumped flux formulation is another method of approach in this paper.

This research study presents a careful analysis of the combined effect of the numerical integration and isoparametric FEM on the boundary‐flux error. Some L₂‐norm estimates are proved for the approximate solutions of the problem under consideration.

The authors offer a general study within the framework of the boundary‐flux approximation theory, which completes the results of published works in this scientific field of research.

A useful application is to employ appropriate quadrature formulae without violating the precision of the boundary‐flux FEM. The lumped mass approximation is also an important practical approach to the problem in question.

The paper presents an entire investigation in FE boundary‐flux approximation theory, in particular, elements of arbitrary degree and domains with curved boundaries. The work is addressed to the possible related fields of interest of postgraduate students and specialists in fluid mechanics and numerical analysis.

To develop a fast and accurate method of calculation of permanent magnet machines.

Presently two ways exist of modeling of synchronous machines – the classic one, when the concept of inductances L_d and L_q is used and the numerical, time‐stepping approach. The first cannot account for precisely the saturation effects, while the second one is highly time consuming. Proposed algorithm replaces inductances by the distributions of flux densities, which were used for their definition, obtained from finite element solutions. Mathematically, the analysis is converted from the space of trigonometric functions to the more general space of periodic functions.

The compact algorithm of analysis has been found, making it possible to extend its application to other types of machines.

Validation of the proposed method was done only by cross‐checking with integral parameters coming from finite element solution.

A potentially useful idea of representation of an electric machine for control purposes.

The paper presents original concept of the new approach for the representation of electric machines. Parts of that methodology were discussed among specialists during two international conferences and received positive views.