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Article
Publication date: 13 September 2011

Pavel Karban, František Mach, Ivo Dolezel and Jerzy Barglik

The purpose of this paper is to present a methodology of high‐precision finite element modeling of induction heating of rotating nonferromagnetic cylindrical billets in…

Abstract

Purpose

The purpose of this paper is to present a methodology of high‐precision finite element modeling of induction heating of rotating nonferromagnetic cylindrical billets in static magnetic field produced by appropriately arranged permanent magnets.

Design/methodology/approach

The mathematical model consisting of two partial differential equations describing the distribution of the magnetic and temperature fields are solved by a fully adaptive higher‐order finite element method in the monolithic formulation and selected results are validated experimentally.

Findings

The method of solution realized by own code is very fast, robust and exhibits much more powerful features when compared with classical low‐order numerical methods implemented in existing commercial codes.

Research limitations/implications

For sufficiently long arrangements the method provides good results even for 2D model. The principal limitation consists in problems with determining correct boundary conditions for the temperature field (generalized coefficient of convective heat transfer as a function of the temperature and revolutions).

Practical implications

The methodology can successfully be used for design of devices for induction heating of cylindrical nonmagnetic bodies by rotation and determination of their operation parameters.

Originality/value

The paper is a presentation of the fully adaptive higher‐order finite element and its utilization for a monolithic numerical solution of a relatively complicated coupled problem.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 5
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 4 September 2017

Matthias Jüttner, Andreas Pflug, Markus Wick and Wolfgang M. Rucker

Multiphysics problems are solved either with monolithic or segregated approaches. For accomplishing contrary discretisation requirements of the physics, disparate meshes…

Abstract

Purpose

Multiphysics problems are solved either with monolithic or segregated approaches. For accomplishing contrary discretisation requirements of the physics, disparate meshes are essential. This paper is comparing experimental results of different interpolation methods for a segregated coupling with monolithic approaches, implemented using a global and a local nearest neighbour method. The results show the significant influence of discretisation for multiphysics simulation.

Design/methodology/approach

Applying disparate meshes to the monolithic as well as the segregated calculation of finite element problems and evaluating the related numerical error is content of the contribution. This is done by an experimental evaluation of a source and a material coupling applied to a multiphysics problem. After an introduction to the topic, the evaluated multiphysics model is described based on two bidirectional coupled problems and its finite element representation. Afterwards, the considered methods for approximating the coupling are introduced. Then, the evaluated methods are described and the experimental results are discussed. A summary concludes this work.

Findings

An experimental evaluation of the numerical errors for different multiphysics coupling methods using disparate meshes is presented based on a bidirectional electro-thermal simulation. Different methods approximating the coupling values are introduced and challenges of applying these methods are given. It is also shown, that the approximation of the coupling integrals is expensive. Arguments for applying the different methods to the monolithic and the segregated solution strategies are given and applied on the example. The significant influence of the mesh density within the coupled meshes is shown. Since the projection and the interpolation methods do influence the result, a careful decision is advised.

Originality/value

In this contribution, existing coupling methods are described, applied and compared on their application for coupling disparate meshes within a multiphysics simulation. Knowing their performance is relevant when deciding for a monolithic or a segregated calculation approach with respect to physics dependent contrary discretisation requirements. To the authors’ knowledge, it is the first time these methods are compared with a focus on an application in multiphysics simulations and experimental results are discussed.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 5
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 15 August 2019

Etienne Muller, Dominique Pelletier and André Garon

This paper aims to focus on characterization of interactions between hp-adaptive time-integrators based on backward differentiation formulas (BDF) and adaptive meshing…

Abstract

Purpose

This paper aims to focus on characterization of interactions between hp-adaptive time-integrators based on backward differentiation formulas (BDF) and adaptive meshing based on Zhu and Zienkiewicz error estimation approach. If mesh adaptation only occurs at user-supplied times and results in a completely new mesh, it is necessary to stop the time-integration at these same times. In these conditions, one challenge is to find an efficient and reliable way to restart the time-integration. The authors investigate what impact grid-to-grid interpolation errors have on the relaunch of the computation.

Design/methodology/approach

Two restart strategies of the time-integrator were used: one based on resetting the time-step size h and time-integrator order p to default values (used in the initial startup phase), and another designed to restart with the time-step size h and order p used by the solver prior to remeshing. The authors also investigate the benefits of quadratically interpolate the solution on the new mesh. Both restart strategies were used to solve laminar incompressible Navier–Stokes and the Unsteady Reynolds Averaged Naviers-Stokes (URANS) equations.

Findings

The adaptive features of our time-integrators are excellent tools to quantify errors arising from the data transfer between two grids. The second restart strategy proved to be advantageous only if a quadratic grid-to-grid interpolation is used. Results for turbulent flows also proved that some precautions must be taken to ensure grid convergence at any time of the simulation. Mesh adaptation, if poorly performed, can indeed lead to losing grid convergence in critical regions of the flow.

Originality/value

This study exhibits the benefits and difficulty of assessing both spatial error estimates and local error estimates to enhance the efficiency of unsteady computations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 5 January 2010

R. Rossi and E. Oñate

The purpose of this paper is to analyse algorithms for fluid‐structure interaction (FSI) from a purely algorithmic point of view.

Abstract

Purpose

The purpose of this paper is to analyse algorithms for fluid‐structure interaction (FSI) from a purely algorithmic point of view.

Design/methodology/approach

First of all a 1D model problem is selected, for which both the fluid and structural behavior are represented through a minimum number of parameters. Different coupling algorithm and time integration schemes are then applied to the simplified model problem and their properties are discussed depending on the values assumed by the parameters. Both exact and approximate time integration schemes are considered in the same framework so to allow an assessment of the different sources of error.

Findings

The properties of staggered coupling schemes are confirmed. An insight on the convergence behavior of iterative coupling schemes is provided. A technique to improve such convergence is then discussed.

Research limitations/implications

All the results are proved for a given family of time integration schemes. The technique proposed can be applied to other families of time integration techniques, but some of the analytical results need to be reworked under this assumption.

Practical implications

The problems that are commonly encountered in FSI can be justified by simple arguments. It can also be shown that the limit at which trivial iterative schemes experience convergence difficulties is very close to that at which staggered schemes become unstable.

Originality/value

All the results shown are based on simple mathematics. The problems are presented so to be independent of the particular choice for the solution of the fluid flow.

Details

Engineering Computations, vol. 27 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 7 September 2012

Pavel Karban, František Mach and Ivo Dolezel

The purpose of this paper is to present a model of induction heating of aluminium billets rotating in a static magnetic field generated by permanent magnets. The model is…

Abstract

Purpose

The purpose of this paper is to present a model of induction heating of aluminium billets rotating in a static magnetic field generated by permanent magnets. The model is solved by the authors' own software and the results are verified experimentally.

Design/methodology/approach

The mathematical model of the problem given by two partial differential equations describing the distribution of the magnetic and temperature fields in the system is solved by a fully adaptive higher‐order finite element method in the hard‐coupled formulation. All material nonlinearities are taken into account.

Findings

The method of solution realized by the code is reliable and works faster in comparison with the existing low‐order finite element codes.

Research limitations/implications

The method works for 2D arrangements with an extremely high accuracy. Its limitations consist mainly in problems of determining the coefficients of convection and radiation for temperature field in the system (respecting both temperature and revolutions).

Practical implications

The methodology can successfully be used for design of devices for induction heating of cylindrical nonmagnetic bodies by rotation and anticipation of their operation parameters.

Originality/value

The paper presents a fully adaptive higher‐order finite element and its utilization for a hard‐coupled numerical solution of the problem of induction heating.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 31 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 24 September 2020

Fabián Castaño and Nubia Velasco

To solve the problem, a mathematical model is proposed; it relies on a directed acyclic graph (DAG), in which arcs are used to indicate whether a pair of appointments can…

Abstract

Purpose

To solve the problem, a mathematical model is proposed; it relies on a directed acyclic graph (DAG), in which arcs are used to indicate whether a pair of appointments can be assigned to the same route or not (and so to the same care worker). The proposed model aims at minimizing the personnel required to meet daily demand and balancing workloads among the workers while considering the varying traffic patterns derived from traffic congestion.

Design/methodology/approach

This paper aims at providing solution approaches for addressing the problem of assigning care workers to deliver home health-care (HHC) services, demanding different skills each. First, a capacity planning problem is considered, where it is necessary to define the number of workers required to satisfy patients' requests and then, patients are assigned to the care workers along with the sequence followed to visit them, thus solving a scheduling problem. The benefits obtained by permitting patients to propose multiple time slots where they can be served are also explored.

Findings

The results indicate that the problem can be efficiently solved for medium-sized instances, that is, up to 100 daily patient requests. It is also indicated that asking patients to propose several moments when they can receive services helps to minimize the need for care workers through more efficient route allocations without affecting significantly the balance of the workloads.

Originality/value

This article provides a new framework for modeling and solving a HHC routing problem with multiskilled personnel. The proposed model can be used to identify efficient daily plans and can handle realistic characteristics such as time-dependent travel times or be extended to other real-life applications such as maintenance scheduling problems.

Details

The International Journal of Logistics Management , vol. 32 no. 1
Type: Research Article
ISSN: 0957-4093

Keywords

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Article
Publication date: 6 March 2017

David Pánek, Václav Kotlan, Roman Hamar and Ivo Doležel

This paper aims to present a methodology of finding temperature dependencies of selected physical parameters of metals. The method is based on the combination of…

Abstract

Purpose

This paper aims to present a methodology of finding temperature dependencies of selected physical parameters of metals. The method is based on the combination of measurement of the surface temperature of material during the process of heating and subsequent solution of the inverse problem using multi-parametric optimization.

Design/methodology/approach

The methodology is based on measurements and numerical solution of the forward and inverse problem, taking into account all involved nonlinearities (saturation curve of the processed steel material and temperature dependences of its physical parameters). The inverse problem is solved by a genetic algorithm.

Findings

The suggested methodology was successfully verified on several metal materials whose temperature-dependent parameters are known. The calculated and measured results exhibit a very good accordance (the differences do not exceed about 10 per cent for room and higher temperatures).

Research limitations/implications

At this moment, the methodology successfully works when the temperature dependence of just one material parameter is to be found (which means that the temperature dependencies of other parameters are known). The accuracy of results also depends on the correctness of other input data.

Practical implications

This paper provides a relatively easy possibility of finding the temperature dependencies of thermal conductivity or heat capacity of various alloys.

Originality/value

The paper proposes a methodology of finding the temperature dependence of a given material parameter that is not known in advance (which is of great importance in case of alloys).

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 28 August 2019

Franck Mastrippolito, Stephane Aubert, Frédéric Ducros and Martin Buisson

This paper aims to improve the radial basis fuction mesh morphing method. During a shape optimization based on computational fluid dynamic (CFD) solvers, the mesh has to…

Abstract

Purpose

This paper aims to improve the radial basis fuction mesh morphing method. During a shape optimization based on computational fluid dynamic (CFD) solvers, the mesh has to be changed. Two possible strategies are re-meshing or morphing. The morphing one is advantageous because it preserves the mesh connectivity, but it must be constrained.

Design/methodology/approach

RBF mesh deformation is one of the most robust and accurate morphing method. Using a greedy algorithm, the computational cost of the method is reduced. To evaluate the morphing performances, a rib shape optimization is performed using the NSGA-II algorithm coupled to kriging metamodels based on CFD. The morphing method is then compared to a re-meshing strategy.

Findings

The authors propose a method, based on Schur complement, to speed-up the greedy process. By using the information of the previous iteration, smaller linear systems are solved and time is saved. The optimization results highlight the interest of using a morphing-based metamodel regarding the resolution time and the accuracy of the interpolated solutions.

Originality/value

A new method based on Schur complement is addressed to speed-up the greedy algorithm and successfully applied to a shape optimization.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 13 July 2010

I. Doležel, V. Kotlan, E. Krónerová and B. Ulrych

The purpose of this paper is to present a new device (thermoelastic actuator) for accurate control of position whose principle is based on thermal dilatation of its…

Abstract

Purpose

The purpose of this paper is to present a new device (thermoelastic actuator) for accurate control of position whose principle is based on thermal dilatation of its working unit brought about by induction heating.

Design/methodology/approach

The device must satisfy the prescribed operation parameters (mainly the above thermal dilatation). The task to find them is a multiply coupled problem (interaction of electromagnetic field, temperature field and field of thermoelastic displacements) that is solved by the finite element method supplemented with a number of other procedures.

Findings

The control of position based on the described thermoelastic effect is very accurate and ranges from 1×10−6 to 1×10−3 m.

Research limitations/implications

The device also contains two self‐locking friction clutches of conical shapes whose purpose is to fix the position of the plunger in the prescribed position. Further attention should be paid to their dynamic behaviour during the process of fixing.

Practical implications

The device can be used in various technical domains such as optics and laser or microscope techniques.

Originality/value

The principal part of the device contains no movable element, which is a substantial advantage in comparison to other systems based on mechanical, hydraulic or pneumatic principles working with movable elements or media.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 29 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 28 October 2014

Paolo Di Barba, Michele Forzan and Elisabetta Sieni

The purpose of this paper is to investigate a bi-objective optimization problem characterized by coupled field analysis. The optimal design of a pancake inductor for the…

Abstract

Purpose

The purpose of this paper is to investigate a bi-objective optimization problem characterized by coupled field analysis. The optimal design of a pancake inductor for the controlled heating of a graphite disk is considered as the benchmark problem. The case study is related to the design of industrial applications of the induction heating of graphite disk.

Design/methodology/approach

The expected goal of the optimization process is twofold: to improve temperature uniformity in the disk and also electrical efficiency of the inductor. The solution of the relevant bi-objective optimization problem is based on multiphysics field analysis. Specifically, the direct problem is solved as a magnetic and thermal coupled problem by means of finite elements; a mesh-inspired definition of thermal uniformity is proposed. In turn, the Pareto front trading off electrical efficiency and thermal uniformity is identified exploiting evolutionary computing.

Findings

By varying the problem targets, different Pareto fronts are identified trading off thermal uniformity and electrical efficiency of the induction-heating device.

Practical implications

These results suggest how to improve the design of this kind of device for the epitaxial growth of silicon wafer; the advantage of using a magnetic concentrator placed close to the inductor axis is pointed out.

Originality/value

The coupling of a multiphysics direct problem with a multiobjective inverse problem is presented as a benchmark problem and accordingly solved. The benchmark provides a simple analysis problem that allows testing various optimization algorithms in a comparative way.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 33 no. 6
Type: Research Article
ISSN: 0332-1649

Keywords

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