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Aims to present recent activities in numerical modeling of turbulent transport processes in induction crucible furnace.

3D large eddy simulation (LES) method was applied for fluid flow modeling in a cylindrical container and transport of 30,000 particles was investigated with Lagrangian approach.

Particle accumulation near the side crucible boundary is determined mainly by the ρ_p/ρ ratio and according to the presented results. Particle settling velocity is of the same order as characteristic melt flow velocity. Particle concentration homogenization time depends on the internal flow regime. Separate particle tracks introduce very intensive mass exchange between the different parts of the melt in the whole volume of the crucible.

Transient simulation of particle transport together with LES fluid flow simulation gives the opportunity of accurate prediction of admixture concentartion distribution in the melt.

Aims to present recent activities in experimental investigations and numerical modelling of the induction cold crucible installation.

Temperature and velocity measurements using thermocouples and electromagnetic velocity probes were performed in aluminium melt which was used as a model melt. Measured temperature field and flow pattern were compared with transient 3D calculations based on large eddy simulation (LES) turbulence modelling scheme. Numerical results are in good coincidence with the experimental data.

The modelling results show that only 3D transient LES is able to model correctly these heat and mass transfer processes.

It is revealed that transient 3D modelling provides a universal tool for simulating convective heat and mass transfer processes in the entire melt influenced by large scale instabilities in the recirculating flows, which contain several main vortexes of the mean flow.

Aims to present recent activities in numerical modeling of cold crucible melting process.

3D numerical analysis was used for electromagnetic problem and 3D large eddy simulation (LES) method was applied for fluid flow modeling.

The comparative modeling shows, that higher H/D ratio of the melt is more efficient when total power consumption is considered, but this advantage is held back by higher heat losses through the crucible walls. Also, calculations reveal that lower frequencies, which are energetically less effective, provide better mixing of the melt.

3D electromagnetic model, which allows to take into account non‐symmetrical distribution of Joule heat sources, together with transient LES fluid flow simulation gives the opportunity of accurate prediction of temperature distribution in the melt.

Experimental investigations of the turbulent flow velocities measured in the melt of experimental induction furnaces show, that beside the intensive local turbulence pulsations, macroscopic low‐frequency oscillations of the recirculated toroidal main flow eddies play an important role in the heat and mass exchange processes. Traditional numerical calculations of the flow and transfer processes, based on wide spread commercial codes using various modifications of the k‐ε turbulence model show that these models do not take into account the low‐frequency oscillations of the melt flow and the calculated temperature and concentration distributions in the melt essentially differs from experimental results. Therefore, the melt flow dynamics in an induction crucible furnace was numerically simulated with help of transient three‐dimensional calculations using the large eddy simulation turbulence model. This leads to a good agreement between calculated and measured periods of low‐frequency oscillations and heat and mass transfer between the toroidal flow eddies.

Most of optimal design or control engineering problems present conflicting objectives that need to be simultaneously minimized or maximized. Often, however, it is a priori known that some functions have greater importance than other. This paper aims to present a novel multi-surrogate, multi-objective, decision-making (DM) optimization algorithm, which is suitable for time-consuming simulations. Its performances have been compared, on the one hand with a standard decision-making algorithm (iTDEA), on the other with a self-adaptive evolutionary algorithm (AMALGAM*). The comparison concerns numerical tests and an optimal control task in induction heating.

In particular, the algorithm makes use of surrogates (meta-models) to concentrate the field evaluations at the most promising areas of the design space. The effect of the decision-maker is instead to drive the search to given regions of the Pareto front. The synergy between surrogates and the decision-maker leads to a greater effectiveness of the optimization search. For the field analysis of the optimal control task, a coupled electromagnetic-thermal FEM model has been developed.

The novel algorithms outperform both iTDEA and AMALGAM* in all done tests.

The algorithm could be applied to other computationally intensive multi-objective real-life problems whenever a preference between the objectives is known.

The combination of surrogates and a decision-maker is beneficial with time-consuming multi-objective optimization problems.

The transverse flux heating (TFH) concept offers very high electrical efficiency in combination with unique technological flexibility. Numerous advantages make this method beyond competition to be applied in e.g. processing lines. However, all potential advantages of TFH can be realized in practice only by optimal design of the inductor shape using numerical modelling and optimization techniques. This paper aims to describe a hierarchical approach to the optimal design of a one-sided induction coil, which will be used for one-sided TFH of continuous moving thin metal strip to achieve a homogeneous temperature distribution along the strip width.

Depending on the design step, 2D or 3D FEM simulations using ANSYS® Mechanical including the electromagnetics package are used. The harmonic electromagnetic solution is coupled to a transient thermal model which takes the strip movement into account. All models use the symmetries of the inductor workpiece arrangement to keep the calculation times as low as possible.

Due to the geometry of a TFH coil, the models can image a quarter or half of the arrangement. Preliminary investigations of different inductor head shapes can be carried out quickly and then further improved on more complex models in combination with the use of optimization algorithms.

Using hierarchical structure for designing a one-sided TFH coil, offers an efficient and quick way to create a coil which is adapted to the application.

The one-sided inductor design is considered, and the results are generally valid.

Reliable modeling of induction hardening requires a multi-physical approach, which makes it time-consuming. In designing an induction hardening system, combining such model with an optimization technique allows managing a high number of design variables. However, this could lead to a tremendous overall computational cost. This paper aims to reduce the computational time of an optimal design problem by making use of multi-fidelity modeling and parallel computing.

In the multi-fidelity framework, the “high-fidelity” model couples the electromagnetic, thermal and metallurgical fields. It predicts the phase transformations during both the heating and cooling stages. The “low-fidelity” model is instead limited to the heating step. Its inaccuracy is counterbalanced by its cheapness, which makes it suitable for exploring the design space in optimization. Then, the use of co-Kriging allows merging information from different fidelity models and predicting good design candidates. Field evaluations of both models occur in parallel.

In the design of an induction heating system, the synergy between the “high-fidelity” and “low-fidelity” model, together with use of surrogates and parallel computing could reduce up to one order of magnitude the overall computational cost.

On one hand, multi-physical modeling of induction hardening implies a better understanding of the process, resulting in further potential process improvements. On the other hand, the optimization technique could be applied to many other computationally intensive real-life problems.

This paper highlights how parallel multi-fidelity optimization could be used in designing an induction hardening system.

The purpose of this paper is to describe main ideas and demonstrate results of the research activities carried out by the authors in the field of design concepts of induction mass heating technology based on multiple-criteria optimization. The main goal of the studies is the application of different optimization methods and numerical finite element method (FEM) codes for field analysis to solve the multi-objective optimization problem that is mathematically formulated in terms of the most important optimization criteria, for example, maximum temperature uniformity, maximum energy efficiency and minimum scale formation.

Standard genetic algorithm (GA), non-dominated sorting genetic algorithm (NSGA) and alternance method of parametric optimization based on the optimal control theory are applied as effective tools for the practice-oriented problems for multiple-criteria optimization of induction heaters’ design based on non-linear coupled electromagnetic and temperature field analysis. Different approaches are used for combining FEM codes for interconnected field analysis and optimization algorithms into the automated optimization procedure.

Optimization procedures are tested and investigated for two- and three-criteria optimization problems solution on the examples of induction heating of a graphite disk, induction heating of aluminum and steel billets prior to hot forming.

Solved problems are based on the design of practical industrial applications. The developed optimization procedures are planned to be applied to the wide range of real-life problems of the optimal design and control of different electromagnetic devices and systems.

The paper describes main ideas and results of the research activities carried out by the authors during past years in the field of multiple-criteria optimization of induction heaters’ design based on numerical coupled electromagnetic and temperature field analysis. Implementing the automated procedure that combines a numerical FEM code for coupled field analysis with an optimization algorithm and its subsequent application for designing induction heaters makes the proposed approach specific and original. The paper also demonstrates that different optimization strategies used (standard GA, NSGA-II and the alternance method of optimal control theory) are effective for real-life industrial applications for multiple-criteria optimization of induction heaters design.

This paper aims to describe main ideas and demonstrates results of the research activities carried out by the authors in the field of optimal design concepts for induction heater for surface hardening. The main goal of the research studies is the application of different optimization methods and numerical finite element method (FEM) codes for field analysis to solve the optimal design problem that is mathematically formulated in terms of the one of the most important optimization criteria for surface hardening technology, e.g. maximum temperature uniformity within the hardening surface layer.

Evolutionary algorithm based on Adaptive Gaussian Process-Assisted Differential Evolution for MEMS Design Optimization (AGDEMO) and alternance method of parametric optimization based on optimal control theory are applied as effective tools for the practice-oriented problem for optimization of induction heater design based on non-linear coupled electromagnetic and temperature field analysis. Different approaches are used for combining FEM codes for interconnected field analysis and optimization algorithms into automated optimization procedure.

Optimization procedures are tested and investigated for optimal design problem solution on the examples of induction hardening of steel cylindrical billet.

Solved problems are based on the design of practical industrial applications. The developed optimization procedures are planned to be applied to the wide range of real-life problems of the optimal design of different electromagnetic devices and systems.

This paper describes main ideas and results of the research activities carried out by the authors in the field of optimal design of induction heaters for hardening based on numerical coupled electromagnetic and temperature field analysis. The implementation of the automated procedure that combines a numerical FEM code for coupled field analysis with an optimization algorithm and its subsequent application for designing induction heaters makes the proposed approach specific and original. This paper also demonstrates that different optimization strategies used (evolutionary algorithm based on AGDEMO and alternance method of optimal control theory) are effective for real-life industrial applications for optimization of induction heaters design.

This paper aims to investigate different multi-objective optimization (MOO) approaches for design and control of electromagnetic devices. The main goal of MOO is to find the set of design variables or control parameters which will provide the best possible values of typical conflicting objective functions.

In the research studies, standard genetic algorithm (GA), non-dominated sorting GA (NSGA-II), migration NSGA algorithm and alternance method of optimal control theory are discussed and compared.

The test practical problems of multi-criteria optimization of induction heating processes with respect to chosen quality criteria confirm the effectiveness of application of considered MOO approaches both for the problems of design and control.

This paper represents and investigates different MOO approaches for design and control of electrotechnological systems.