This paper presents, mathematical model of induction heating process by using analytical and numerical
methods. In analytical method, series equivalent circuit (SEC) is used to represent induction coil and work
piece. Induction coil and workpiece parameters (resistance and reactance) are calculated by standard
formulas along with Nagaoka correction factors and Bessel functions. In Numerical method, magnetic
vector potential formulation is done and finite element method (FEM) is used to solve the field equations.
Analytically and numerically computed parameters such as equivalent coil resistance, reactance, coil
voltage, work piece power are compared and found that they are in good agreement. Analytically and
numerically obtained coil voltages at different frequencies are validated by experimental results. This
mathematical model is useful for coil design and optimization of induction heating process.
Transient Numerical Analysis of Induction Heating of Graphite Cruciable at Di...ijeljournal
Mathematical modeling of Induction heating process is done by using 2D axisymmetric geometry.
Induction heating is coupled field problem that includes electromagnetism and heat transfer. Mathematical
modeling of electromagnetism and heat transfer is done by using maxwell equations and classical heat
transfer equation respectively. Temperature dependent material properties are used for this analysis. This
analysis includes coil voltage distribution, crucible electromagnetic power, and coil equivalent impedance
at different frequency. Induction coil geometry effect on supply voltage is also analyzed. This analysis is
useful for designing of induction coil for melting of nonferrous metal such as gold, silver, uranium etc.
Transient Numerical Analysis of Induction Heating of Graphite Cruciable at Di...ijeljournal
Mathematical modeling of Induction heating process is done by using 2D axisymmetric geometry.
Induction heating is coupled field problem that includes electromagnetism and heat transfer. Mathematical
modeling of electromagnetism and heat transfer is done by using maxwell equations and classical heat
transfer equation respectively. Temperature dependent material properties are used for this analysis. This
analysis includes coil voltage distribution, crucible electromagnetic power, and coil equivalent impedance
at different frequency. Induction coil geometry effect on supply voltage is also analyzed. This analysis is
useful for designing of induction coil for melting of nonferrous metal such as gold, silver, uranium etc.
Transient numerical analysis of induction heating of graphite cruciable at di...ijeljournal
Mathematical modeling of Induction heating process is done by using 2D axisymmetric geometry. Induction heating is coupled field problem that includes electromagnetism and heat transfer. Mathematical
modeling of electromagnetism and heat transfer is done by using maxwell equations and classical heat
transfer equation respectively. Temperature dependent material properties are used for this analysis. This
analysis includes coil voltage distribution, crucible electromagnetic power, and coil equivalent impedance
at different frequency. Induction coil geometry effect on supply voltage is also analyzed. This analysis is useful for designing of induction coil for melting of nonferrous metal such as gold, silver, uranium etc.
In developing electric motors in general and induction motors in particular
temperature limit is a key factor affecting the efficiency of the overall design. Since
conventional loading of induction motors is often expensive, the estimation of temperature
rise by tools of mathematical modeling becomes increasingly important. Excepting for
providing a more accurate representation of the problem, the proposed model can also
reduce computing costs. The paper develops a three-dimensional transient thermal model in
polar co-ordinates using finite element formulation and arch shaped elements. A
temperature-time method is employed to evaluate the distribution of loss in various parts of
the machine. Using these loss distributions as an input for finite element analysis, more
accurate temperature distributions can be obtained. The model is applied to predict the
temperature rise in the stator of a squirrel cage 7.5 kW totally enclosed fan-cooled induction
motor. The temperature distribution has been determined considering convection from the
back of core surface, outer air gap surface and annular end surface of a totally enclosed
structure.
MODELING AND OPTIMIZATION OF PIEZOELECTRIC ENERGY HARVESTING adeij1
In this paper, the modeling, optimization and simulation results of the piezoelectric energy harvesting using bond graph approach are presented. Firstly, a lightweight equivalent model derived from the bond graph is proposed. It’s a comprehensive model, which is suitable for piezoelectric seismic energy harvester investigation and power optimization. The optimal charge impedance for both the resistive load and complex load are given and analysed. Finally a bond graph approach is proposed to allow optimization of the extracted energy while keeping simplicity and standalone capability. The proposed model does not rely on any inductor and is constructed with a simple switch. The power harvested is more than twice the conventional technique one on a wide band of resistive load. The bond graph model is valid close to the analysed mode centre frequency and delivers results compared to experimental and analytical data. Furthermore, we also show that the harvester can be electrically tuned to match the excitation frequency. This makes it possible to maximize the power output for both linear and non-linear loads.
Analysis of Reactivity Accident for Control Rods Withdrawal at the Thermal Re...ijrap
In the present work, the point kinetics equations are solved numerically using the stiffness confinement
method (SCM). The solution is applied to the kinetics equations in the presence of different types of
reactivities, and is compared with other methods. This method is, also used to analyze reactivity accidents
in thermal reactor at start-up, and full power conditions for control rods withdrawal. Thermal reactor
(HTR-M) is fuelled by uranium-235. This analysis presents the effect of negative temperature feedback, and
the positive reactivity of control rods withdrawal. Power, temperature pulse, and reactivity following the
reactivity accidents are calculated using programming language (FORTRAN), and (MATLAB) Codes. The
results are compared with previous works and satisfactory agreement is found.
Transient Numerical Analysis of Induction Heating of Graphite Cruciable at Di...ijeljournal
Mathematical modeling of Induction heating process is done by using 2D axisymmetric geometry.
Induction heating is coupled field problem that includes electromagnetism and heat transfer. Mathematical
modeling of electromagnetism and heat transfer is done by using maxwell equations and classical heat
transfer equation respectively. Temperature dependent material properties are used for this analysis. This
analysis includes coil voltage distribution, crucible electromagnetic power, and coil equivalent impedance
at different frequency. Induction coil geometry effect on supply voltage is also analyzed. This analysis is
useful for designing of induction coil for melting of nonferrous metal such as gold, silver, uranium etc.
Transient Numerical Analysis of Induction Heating of Graphite Cruciable at Di...ijeljournal
Mathematical modeling of Induction heating process is done by using 2D axisymmetric geometry.
Induction heating is coupled field problem that includes electromagnetism and heat transfer. Mathematical
modeling of electromagnetism and heat transfer is done by using maxwell equations and classical heat
transfer equation respectively. Temperature dependent material properties are used for this analysis. This
analysis includes coil voltage distribution, crucible electromagnetic power, and coil equivalent impedance
at different frequency. Induction coil geometry effect on supply voltage is also analyzed. This analysis is
useful for designing of induction coil for melting of nonferrous metal such as gold, silver, uranium etc.
Transient numerical analysis of induction heating of graphite cruciable at di...ijeljournal
Mathematical modeling of Induction heating process is done by using 2D axisymmetric geometry. Induction heating is coupled field problem that includes electromagnetism and heat transfer. Mathematical
modeling of electromagnetism and heat transfer is done by using maxwell equations and classical heat
transfer equation respectively. Temperature dependent material properties are used for this analysis. This
analysis includes coil voltage distribution, crucible electromagnetic power, and coil equivalent impedance
at different frequency. Induction coil geometry effect on supply voltage is also analyzed. This analysis is useful for designing of induction coil for melting of nonferrous metal such as gold, silver, uranium etc.
In developing electric motors in general and induction motors in particular
temperature limit is a key factor affecting the efficiency of the overall design. Since
conventional loading of induction motors is often expensive, the estimation of temperature
rise by tools of mathematical modeling becomes increasingly important. Excepting for
providing a more accurate representation of the problem, the proposed model can also
reduce computing costs. The paper develops a three-dimensional transient thermal model in
polar co-ordinates using finite element formulation and arch shaped elements. A
temperature-time method is employed to evaluate the distribution of loss in various parts of
the machine. Using these loss distributions as an input for finite element analysis, more
accurate temperature distributions can be obtained. The model is applied to predict the
temperature rise in the stator of a squirrel cage 7.5 kW totally enclosed fan-cooled induction
motor. The temperature distribution has been determined considering convection from the
back of core surface, outer air gap surface and annular end surface of a totally enclosed
structure.
MODELING AND OPTIMIZATION OF PIEZOELECTRIC ENERGY HARVESTING adeij1
In this paper, the modeling, optimization and simulation results of the piezoelectric energy harvesting using bond graph approach are presented. Firstly, a lightweight equivalent model derived from the bond graph is proposed. It’s a comprehensive model, which is suitable for piezoelectric seismic energy harvester investigation and power optimization. The optimal charge impedance for both the resistive load and complex load are given and analysed. Finally a bond graph approach is proposed to allow optimization of the extracted energy while keeping simplicity and standalone capability. The proposed model does not rely on any inductor and is constructed with a simple switch. The power harvested is more than twice the conventional technique one on a wide band of resistive load. The bond graph model is valid close to the analysed mode centre frequency and delivers results compared to experimental and analytical data. Furthermore, we also show that the harvester can be electrically tuned to match the excitation frequency. This makes it possible to maximize the power output for both linear and non-linear loads.
Analysis of Reactivity Accident for Control Rods Withdrawal at the Thermal Re...ijrap
In the present work, the point kinetics equations are solved numerically using the stiffness confinement
method (SCM). The solution is applied to the kinetics equations in the presence of different types of
reactivities, and is compared with other methods. This method is, also used to analyze reactivity accidents
in thermal reactor at start-up, and full power conditions for control rods withdrawal. Thermal reactor
(HTR-M) is fuelled by uranium-235. This analysis presents the effect of negative temperature feedback, and
the positive reactivity of control rods withdrawal. Power, temperature pulse, and reactivity following the
reactivity accidents are calculated using programming language (FORTRAN), and (MATLAB) Codes. The
results are compared with previous works and satisfactory agreement is found.
Analysis of Reactivity Accident for Control Rods Withdrawal at the Thermal Re...ijrap
In the present work, the point kinetics equations are solved numerically using the stiffness confinement
method (SCM). The solution is applied to the kinetics equations in the presence of different types of
reactivities, and is compared with other methods. This method is, also used to analyze reactivity accidents
in thermal reactor at start-up, and full power conditions for control rods withdrawal. Thermal reactor
(HTR-M) is fuelled by uranium-235. This analysis presents the effect of negative temperature feedback, and
the positive reactivity of control rods withdrawal. Power, temperature pulse, and reactivity following the
reactivity accidents are calculated using programming language (FORTRAN), and (MATLAB) Codes. The
results are compared with previous works and satisfactory agreement is found.
Solar Module Modeling, Simulation And Validation Under Matlab / SimulinkIJERA Editor
Solar modules are systems which convert sunlight into electricity using the physics of semiconductors. Mathematical modeling of these systems uses weather data such as irradiance and temperature as inputs. It provides the current, voltage or power as outputs, which allows plot the characteristic giving the intensity I as a function of voltage V for photovoltaic cells. In this work, we have developed a model for a diode of a Photovoltaic module under the Matlab / Simulink environment. From this model, we have plotted the characteristic curves I-V and P-V of solar cell for different values of temperature and sunlight. The validation has been done by comparing the experimental curve with power from a solar panel HORONYA 20W type with that obtained by the model.
Radiation patterns account of a circular microstrip antenna loaded two annularwailGodaymi1
In this paper, theoretical study of circular microstrip antenna loaded two annular (CMSAL2AR) and calculation
of the radiation pattern using principle equivalence with moment of method formulation of electromagnetic
radiation in this these based on the bodies of revolution (BoR), which are generated by revolution a planar curve
about an axis called axis of symmetry to solving the electric fields integral equation (EFIE) and magnetic field
integral equation (MFIE). To find an unknown electric current density on the conductor surface ,and both
unknowns electric and magnetic density current on the dielectric surface which are responsible for the
generation of far fields radiation in the space for the components (Eθ ,Eφ) ,the surface currents was represented
by a set of basis functions that give the Fourier series because the body has a circular symmetry property and
then select a set of weighted functions to find a linear system by using Galerkin method which requires that the
weighted functions are equal to the complex conjugate of the current ( ) * W = J .from radiation pattern
calculated the Directive gain can be utilized to the directive gain increased to (G= 21.30 dB) when
( 0.015λ 1 = g R ) for the ratio of (Rab= 5.5), and bandwidth has been better (BW%= 19.9%) when
( 0.01λ 1 = g R ) for the ratio (Rab= 6.5) .
STUDY OF THE EQUIVALENT CIRCUIT OF A DYESENSITIZED SOLAR CELLSAEIJjournal2
The dye-sensitized solar cells (DSSC) have gained the last decades an important place among photovoltaic
technologies due to their low-cost of implementation and their performance, which becomes more efficient.
The experimental data for this type of cells are enriched and accumulated quickly, given the enthusiasm for
this new technology. The present work treats the equivalent circuit of a dye-sensitized solar cell (DSSC) for
a model in an exponential, and by using the results of some works, we shall make a simulation by the
software Scilab to obtain the characteristics (I-V), then we will study the influence of every parameter on
the curve.
STUDY OF THE EQUIVALENT CIRCUIT OF A DYESENSITIZED SOLAR CELLSAEIJjournal2
The dye-sensitized solar cells (DSSC) have gained the last decades an important place among photovoltaic technologies due to their low-cost of implementation and their performance, which becomes more efficient. The experimental data for this type of cells are enriched and accumulated quickly, given the enthusiasm for this new technology. The present work treats the equivalent circuit of a dye-sensitized solar cell (DSSC) for a model in an exponential, and by using the results of some works, we shall make a simulation by the software Scilab to obtain the characteristics (I-V), then we will study the influence of every parameter on the curve.
ANALYSIS OF LIGHTNING STRIKE WITH CORONA ON OHTL NEAR THE SUBSTATION BY EMTP ADEIJ Journal
Lightning protection and insulation coordination of transmission lines and substations require an accurate
knowledge of the magnitudes and waveforms of lightning overvoltage. To simulate the lightning
overvoltage precisely near the substation, this study has shown how to consider the lightning impulse
corona for distortion effect of this overvoltage.
Determination of transient thermal characteristics for thermal electric behav...journalBEEI
In the current study, it was tried to describe a method for determining thermal characteristics of integrated micro-circuits to identify thermal parameters of multidisciplinary (thermal-electric) behavioral models. The problem is solved on the example of high-frequency pulse voltage converters. A solution was proposed to refine the minimum structure of the thermoelectric model based on an iterative least squares method using the Levenberg-Marquardt algorithm, as well as a graph of the spectral den-sity of time constants. This made it possible to reduce the influence of the filtering factor in the deconvolution operation when building a thermal model using the structural function of the thermal characteristic transition. Also, the results obtained can be used to build integrated circuits (IC) behavioral models, taking into account the thermal processes occurring in them.
EFFECTIVE PEEC MODELING OF TRANSMISSION LINES STRUCTURES USING A SELECTIVE ME...EEIJ journal
The transmission lines structures are quite common in the system of electromagnetic compatibility (EMC)
analysis. The increasing complexities of physical structures make electromagnetic modeling an
increasingly tough task, and computational efficiency is desirable. In this paper, a novel selective mesh
approach is presented for partial element equivalent circuit (PEEC) modeling where intense coupling parts
are meshed while the remaining parts are eliminated. With the proposed approach, the meshed ground
plane is dependent on the length and height of the above transmission lines. Relevant compact formulae for
determining mesh boundaries are deduced, and a procedure of general mesh generation is also given. A
numerical example is presented, and a validation check is accomplished, showing that the approach leads
to a significant reduction in unknowns and thus computation time and consumed memories, while
preserving the sufficient precision. This approach is especially useful for modeling the electromagnetic
coupling of transmission lines and reference ground, and it may also be beneficial for other equivalent
circuit modeling techniques.
Research on Transformer Core Vibration under DC Bias Based on Multi-field Cou...inventionjournals
The Mathematical models for DC bias vibration analysis of the transformer core are developed in this paper. The model is combined into multi-physical field coupling modeling for vibration analysis of the transformer. By applying the primary voltage as excitation and under different DC bias, vibrations of the transformer core is simulated and analyzed.
RESEARCH ON INDUCTION HEATING - A REVIEWEditor IJCATR
This paper presents results of finite element analysis of induction heating problems considering temperature dependence of
material characteristics. In this analysis, we have used the three-dimensional finite element method in order to correctly express
induction heating coil’s shapes and to make clear its effects on temperature distributions. The heat-conducting problem and the eddy
current problem are coupled, and solved by using the step-by-step calculations.
Effect of mesh grid structure in reducing hot carrier effect of nmos device s...ijcsa
This paper presents the critical effect of mesh grid that should be considered during process and device
simulation using modern TCAD tools in order to develop and optimize their accurate electrical
characteristics. Here, the computational modelling process of developing the NMOS device structure is
performed in Athena and Atlas. The effect of Mesh grid on net doping profile, n++, and LDD sheet
resistance that could link to unwanted “Hot Carrier Effect” were investigated by varying the device grid
resolution in both directions. It is found that y-grid give more profound effect in the doping concentration,
the junction depth formation and the value of threshold voltage during simulation. Optimized mesh grid is
obtained and tested for more accurate and faster simulation. Process parameter (such as oxide thicknesses
and Sheet resistance) as well as Device Parameter (such as linear gain “beta” and SPICE level 3 mobility
roll-off parameter “ Theta”) are extracted and investigated for further different applications.
Model to Evaluate the Performance of Building Integrated Photovoltaic Systems...IJECEIAES
This article describes a mathematical model implemented in Matlab/Simulink to evaluate the performance of building integrated photovoltaic systems (BIPVS). The proposed methodology allows to model independently the solar panel, the photovoltaic (pv) generator, inverter and the grid to integrate them into a single model in Simulink in order to evaluate the performance of the complete system. The validation of the model was made on a BIPV system of 6 kWp installed in a building at the Universidad de Bogotá Jorge Tadeo Lozano in Bogota, Colombia. The results indicate that there is a correlation greater than 0.9 between DC and AC power generated by the BIPV system and calculated by the model proposed for any weather condition.
Design and Simulation of Array of Rectangular Micro Cantilevers Piezoelectric...IJERA Editor
This paper presents the design, analysis and simulation of MEMS based array of bimorph rectangular microcantilever piezoelectric energy harvester structure with and without tip mass, to analyze their sensitivity. The microcantilever beams are made up of piezoelectric material and Aluminium as a substrate material. The analytical simulation of design is done by FEM (COMSOL Multiphysics). The simulation results of bimorph cantilever structure, applied force of 0.1 N and obtained end displacement and electric potential developed are given. The analytical model of the cantilever beam will be analyzed and the process of its construction will be discussed. The changes in the sensitivity of a cantilever beam with respect to change in its shape for the same applied force of 0.1N are denoted.
Analysis of Reactivity Accident for Control Rods Withdrawal at the Thermal Re...ijrap
In the present work, the point kinetics equations are solved numerically using the stiffness confinement
method (SCM). The solution is applied to the kinetics equations in the presence of different types of
reactivities, and is compared with other methods. This method is, also used to analyze reactivity accidents
in thermal reactor at start-up, and full power conditions for control rods withdrawal. Thermal reactor
(HTR-M) is fuelled by uranium-235. This analysis presents the effect of negative temperature feedback, and
the positive reactivity of control rods withdrawal. Power, temperature pulse, and reactivity following the
reactivity accidents are calculated using programming language (FORTRAN), and (MATLAB) Codes. The
results are compared with previous works and satisfactory agreement is found.
Solar Module Modeling, Simulation And Validation Under Matlab / SimulinkIJERA Editor
Solar modules are systems which convert sunlight into electricity using the physics of semiconductors. Mathematical modeling of these systems uses weather data such as irradiance and temperature as inputs. It provides the current, voltage or power as outputs, which allows plot the characteristic giving the intensity I as a function of voltage V for photovoltaic cells. In this work, we have developed a model for a diode of a Photovoltaic module under the Matlab / Simulink environment. From this model, we have plotted the characteristic curves I-V and P-V of solar cell for different values of temperature and sunlight. The validation has been done by comparing the experimental curve with power from a solar panel HORONYA 20W type with that obtained by the model.
Radiation patterns account of a circular microstrip antenna loaded two annularwailGodaymi1
In this paper, theoretical study of circular microstrip antenna loaded two annular (CMSAL2AR) and calculation
of the radiation pattern using principle equivalence with moment of method formulation of electromagnetic
radiation in this these based on the bodies of revolution (BoR), which are generated by revolution a planar curve
about an axis called axis of symmetry to solving the electric fields integral equation (EFIE) and magnetic field
integral equation (MFIE). To find an unknown electric current density on the conductor surface ,and both
unknowns electric and magnetic density current on the dielectric surface which are responsible for the
generation of far fields radiation in the space for the components (Eθ ,Eφ) ,the surface currents was represented
by a set of basis functions that give the Fourier series because the body has a circular symmetry property and
then select a set of weighted functions to find a linear system by using Galerkin method which requires that the
weighted functions are equal to the complex conjugate of the current ( ) * W = J .from radiation pattern
calculated the Directive gain can be utilized to the directive gain increased to (G= 21.30 dB) when
( 0.015λ 1 = g R ) for the ratio of (Rab= 5.5), and bandwidth has been better (BW%= 19.9%) when
( 0.01λ 1 = g R ) for the ratio (Rab= 6.5) .
STUDY OF THE EQUIVALENT CIRCUIT OF A DYESENSITIZED SOLAR CELLSAEIJjournal2
The dye-sensitized solar cells (DSSC) have gained the last decades an important place among photovoltaic
technologies due to their low-cost of implementation and their performance, which becomes more efficient.
The experimental data for this type of cells are enriched and accumulated quickly, given the enthusiasm for
this new technology. The present work treats the equivalent circuit of a dye-sensitized solar cell (DSSC) for
a model in an exponential, and by using the results of some works, we shall make a simulation by the
software Scilab to obtain the characteristics (I-V), then we will study the influence of every parameter on
the curve.
STUDY OF THE EQUIVALENT CIRCUIT OF A DYESENSITIZED SOLAR CELLSAEIJjournal2
The dye-sensitized solar cells (DSSC) have gained the last decades an important place among photovoltaic technologies due to their low-cost of implementation and their performance, which becomes more efficient. The experimental data for this type of cells are enriched and accumulated quickly, given the enthusiasm for this new technology. The present work treats the equivalent circuit of a dye-sensitized solar cell (DSSC) for a model in an exponential, and by using the results of some works, we shall make a simulation by the software Scilab to obtain the characteristics (I-V), then we will study the influence of every parameter on the curve.
ANALYSIS OF LIGHTNING STRIKE WITH CORONA ON OHTL NEAR THE SUBSTATION BY EMTP ADEIJ Journal
Lightning protection and insulation coordination of transmission lines and substations require an accurate
knowledge of the magnitudes and waveforms of lightning overvoltage. To simulate the lightning
overvoltage precisely near the substation, this study has shown how to consider the lightning impulse
corona for distortion effect of this overvoltage.
Determination of transient thermal characteristics for thermal electric behav...journalBEEI
In the current study, it was tried to describe a method for determining thermal characteristics of integrated micro-circuits to identify thermal parameters of multidisciplinary (thermal-electric) behavioral models. The problem is solved on the example of high-frequency pulse voltage converters. A solution was proposed to refine the minimum structure of the thermoelectric model based on an iterative least squares method using the Levenberg-Marquardt algorithm, as well as a graph of the spectral den-sity of time constants. This made it possible to reduce the influence of the filtering factor in the deconvolution operation when building a thermal model using the structural function of the thermal characteristic transition. Also, the results obtained can be used to build integrated circuits (IC) behavioral models, taking into account the thermal processes occurring in them.
EFFECTIVE PEEC MODELING OF TRANSMISSION LINES STRUCTURES USING A SELECTIVE ME...EEIJ journal
The transmission lines structures are quite common in the system of electromagnetic compatibility (EMC)
analysis. The increasing complexities of physical structures make electromagnetic modeling an
increasingly tough task, and computational efficiency is desirable. In this paper, a novel selective mesh
approach is presented for partial element equivalent circuit (PEEC) modeling where intense coupling parts
are meshed while the remaining parts are eliminated. With the proposed approach, the meshed ground
plane is dependent on the length and height of the above transmission lines. Relevant compact formulae for
determining mesh boundaries are deduced, and a procedure of general mesh generation is also given. A
numerical example is presented, and a validation check is accomplished, showing that the approach leads
to a significant reduction in unknowns and thus computation time and consumed memories, while
preserving the sufficient precision. This approach is especially useful for modeling the electromagnetic
coupling of transmission lines and reference ground, and it may also be beneficial for other equivalent
circuit modeling techniques.
Research on Transformer Core Vibration under DC Bias Based on Multi-field Cou...inventionjournals
The Mathematical models for DC bias vibration analysis of the transformer core are developed in this paper. The model is combined into multi-physical field coupling modeling for vibration analysis of the transformer. By applying the primary voltage as excitation and under different DC bias, vibrations of the transformer core is simulated and analyzed.
RESEARCH ON INDUCTION HEATING - A REVIEWEditor IJCATR
This paper presents results of finite element analysis of induction heating problems considering temperature dependence of
material characteristics. In this analysis, we have used the three-dimensional finite element method in order to correctly express
induction heating coil’s shapes and to make clear its effects on temperature distributions. The heat-conducting problem and the eddy
current problem are coupled, and solved by using the step-by-step calculations.
Effect of mesh grid structure in reducing hot carrier effect of nmos device s...ijcsa
This paper presents the critical effect of mesh grid that should be considered during process and device
simulation using modern TCAD tools in order to develop and optimize their accurate electrical
characteristics. Here, the computational modelling process of developing the NMOS device structure is
performed in Athena and Atlas. The effect of Mesh grid on net doping profile, n++, and LDD sheet
resistance that could link to unwanted “Hot Carrier Effect” were investigated by varying the device grid
resolution in both directions. It is found that y-grid give more profound effect in the doping concentration,
the junction depth formation and the value of threshold voltage during simulation. Optimized mesh grid is
obtained and tested for more accurate and faster simulation. Process parameter (such as oxide thicknesses
and Sheet resistance) as well as Device Parameter (such as linear gain “beta” and SPICE level 3 mobility
roll-off parameter “ Theta”) are extracted and investigated for further different applications.
Model to Evaluate the Performance of Building Integrated Photovoltaic Systems...IJECEIAES
This article describes a mathematical model implemented in Matlab/Simulink to evaluate the performance of building integrated photovoltaic systems (BIPVS). The proposed methodology allows to model independently the solar panel, the photovoltaic (pv) generator, inverter and the grid to integrate them into a single model in Simulink in order to evaluate the performance of the complete system. The validation of the model was made on a BIPV system of 6 kWp installed in a building at the Universidad de Bogotá Jorge Tadeo Lozano in Bogota, Colombia. The results indicate that there is a correlation greater than 0.9 between DC and AC power generated by the BIPV system and calculated by the model proposed for any weather condition.
Design and Simulation of Array of Rectangular Micro Cantilevers Piezoelectric...IJERA Editor
This paper presents the design, analysis and simulation of MEMS based array of bimorph rectangular microcantilever piezoelectric energy harvester structure with and without tip mass, to analyze their sensitivity. The microcantilever beams are made up of piezoelectric material and Aluminium as a substrate material. The analytical simulation of design is done by FEM (COMSOL Multiphysics). The simulation results of bimorph cantilever structure, applied force of 0.1 N and obtained end displacement and electric potential developed are given. The analytical model of the cantilever beam will be analyzed and the process of its construction will be discussed. The changes in the sensitivity of a cantilever beam with respect to change in its shape for the same applied force of 0.1N are denoted.
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ANALYTICAL, NUMERICAL AND EXPERIMENTAL VALIDATION OF COIL VOLTAGE IN INDUCTION MELTING PROCESS
1. International Journal of Electromagnetics ( IJEL ), Vol 1, No 1, August 2016
21
ANALYTICAL, NUMERICAL AND
EXPERIMENTAL VALIDATION OF COIL
VOLTAGE IN INDUCTION MELTING PROCESS
B Patidar, M.T.Saify, M.M.Hussain, S.K.Jha, and A.P.Tiwari
Bhabha Atomic Research Centre, Mumbai
ABSTRACT
This paper presents, mathematical model of induction heating process by using analytical and numerical
methods. In analytical method, series equivalent circuit (SEC) is used to represent induction coil and work
piece. Induction coil and workpiece parameters (resistance and reactance) are calculated by standard
formulas along with Nagaoka correction factors and Bessel functions. In Numerical method, magnetic
vector potential formulation is done and finite element method (FEM) is used to solve the field equations.
Analytically and numerically computed parameters such as equivalent coil resistance, reactance, coil
voltage, work piece power are compared and found that they are in good agreement. Analytically and
numerically obtained coil voltages at different frequencies are validated by experimental results. This
mathematical model is useful for coil design and optimization of induction heating process.
KEYWORDS: -
Electromagnetic, FEM, induction coil parameter, induction heating
1. INTRODUCTION
Induction heating is widely utilized in different industrial applications such as melting, forging,
welding, hardening etc [1, 2]. It is based on electromagnetic induction phenomenon, which is
very complex and results completely depend upon various design and process parameters [3].
Often, many experiments need to be conducted to optimize the melting process, which is
expensive and time consuming. Mathematical modeling and simulation of induction melting
process not only helps to avoid tedious experiments, it also helps to understand the process in
depth.
Most of literature on induction heating system design and optimization are based on
mathematical modeling and simulation [4]-[8]. Only few articles [9][10][11] are available, in
which analytical methods are used to explain the induction heating process. In this paper,
Analytical and numerical methods are used to calculate the coil voltages at different frequencies
and validated it with experimental results.
In Analytical method, Nagaoka short coil correction factor is used to account the end effect and
flux density outside the coil. Nagaoka modified correction factor is included in formulation to
account presence of work piece inside the coil [6]. Lead resistance and inductance are significant,
therefore they are also included in computation. Work piece resistance and power are calculated
by using Bessel function, because it gives more accurate values compared to generalized formulas
2. International Journal of Electromagnetics ( IJEL ), Vol 1, No 1, August 2016
22
[6]. Coil equivalent inductance is used to select proper values of capacitors for coil tuning with
power source [1]. Analytical methods are generally applicable to simple geometries.
In Numerical method, magnetic vector potential formulation is used for computation of different
design parameters. Magnetic vector potential formulation requires less computation compared to
magnetic field formulation. Finite element method (FEM) based multiphysics software is used to
solve the field equations and compute various parameters such as coil impedance, voltage and
work piece power at different frequencies. Numerical methods can be applied to complicated
geometry, but it requires detailed understanding of coding language. Numerical methods are
iteration based and require lot of computation resources and time to solve the problem.
This paper is organized as follows: After introduction in section I, section II includes analytical
formulation which is used to calculate various parameters such as coil equivalent resistance,
reactance, coil voltage, work piece power, and coil efficiency. Mathematical model, numerical
method, simulation procedure and experimental set up details are also explained in section II. In
section III, all results computed from analytical and numerical method are displayed, analyzed
and validated with experimental results.
2. METHODS
2.1 Analytical formulation
2-D Axisymmetric geometry of induction melting process is shown in figure1 (a). Here, graphite
crucible is placed inside the multi turn copper induction coil. Graphite is used as a susceptor and
it heats up the charge by radiation and conduction. In induction melting process, Induction coil
and workpiece can be represented by using series equivalent circuit (SEC) as shown in figure
1(b).
Dc
dc
Sc
Dw
lc
lw
Refractory
Copper
Induction coil
Graphite
Crucible
Charge
z
r
1 (a)
3. International Journal of Electromagnetics ( IJEL ), Vol 1, No 1, August 2016
23
R'w
Xg
Xc X'w
VL
R
IC
L
R
IC
L
R
IC
L Rc
XL
1(b)
Figure 1(a) 2-D geometry of induction coil and workpiece. 1(b). Series equivalent circuit of Coil
and workpiece (Graphite crucible)
In Series equivalent circuit, VL is the coil voltage (V), Ic is the coil current (A), Rc is the coil
resistance (Ω), Xc is the coil reactance (Ω), Rw is the work piece resistance (Ω), Xw is the work
piece reactance (Ω), XL is the lead reactance (Ω), RL is the lead resistance (Ω), R’
W is the work
piece resistance refereed to coil side (Ω), Xg is air gap reactance (Ω), X’W is work piece reactance
refereed to coil side (Ω).
Coil equivalent impedance (Zeq) and coil voltage (VL) are expressed by eq (1.1) and eq (1.2)
respectively,
= ( + + ′ ) + ( + + ′ + ) (1.1)
= (1.2)
Coil and workpiece parameters are calculated [9], [11] by using following formulas,
Coil resistance =
( )
(2.1)
Space factor ! = (2.2)
Coil skin depth " = #$# %
(2.3)
In these equations, Nc is the no of turns, lc is the coil height (m), ' is the coil diameter(m), ρc is
the copper resistivity (Ω-m) at 393 0
K, µ0 is the permeability of free space i.e. 4πX10 (-7)
, µr is the
relative permeability (µr=1 for copper, graphite),f is the power source frequency(Hz).
Coil reactance for (tc>2δc) Xc = Rc (3)
In this equation, tc is coil tube thickness (m)
Air gap reactance = (
∗ #$ %( * +)
(4.1)
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24
,
∗
= , -1 − 0 +* +
( )
1 2 + 0 +* +
( )
1 (4.2)
, =
3
[3
$.67$ (8 9: )
;
]
(4.3)
In these equations, Dw is the workpiece diameter (m), δw is the workpiece skin depth (m), ,
∗
is the
modified Nagaoka correction factor, , is the short coil correction factor.
Workpiece resistance and reactance are calculated by using workpiece active and reactive power
respectively.
Workpiece active and reactive power is calculated by,
= = (>?@A@!)B - +
2 C D (5)
E = (>?@A@!)B - +
2C F (6)
Here, lH= Workpiece length (m)
p, q= Workpiece power loss constant, this parameters are find out using equations given in [2],
H= Magnetic field intensity (A/m)
Magnetic field intensity is calculated by,
C = (
∗ I
(7)
Lead resistance is calculated by standard ohms law considering the skin effect and proximity
effect. Lead reactance is calculated by using parallel transmission line formula.
2.2 Mathematical modeling
Induction heating is multiphysics process i.e combination of Electromagnetic field and heat
transfer. Electromagnetic field produced by induction coil is represented by maxwell equations
[4]-[8], [15], [16],[17] as shown below,
∇ × C
L
LM = NO
LM + PQ
LLLM (8.1)
∇ × O
LM = −
RS
LM
RT
(8.2)
∇. U
LM = 0 (8.3)
Constitutive equations,
U
LM = @A@!C
L
LM (8.4)
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25
W
M = NO
LM (8.5)
In these equations, H is the Magnetic field strength (A/m), E is the Electric field strength (V/m),
σ is the Electrical conductivity (S/m), js
is the source current density (A/m2
), B is the Magnetic
flux density (T). From eq (8.3), magnetic vector potential is defined as,
U
LLLM= X × Y
M (9)
eq (8.4), eq (9) put into eq (8.1) gives,
X × X × Y
M = @A@!ZNO
LM + PQ
LLLM[ (10)
From eq (8.2), eq (9) and by applying vector identity, eq (10) can be written as,
∇ Y = @A@!(N
R
M
RT
− PQ
LLLM) (11.1)
Induction coil carries sinusoidal current, Hence eq(11.1) can be written as,
∇ Y = @A@!(N]Y
LLLLLLM − PQ
LLLM) (11.2)
For 2-D axisymmetric geometry shown in figure 2(a) and using cylindrical coordinates, eq (11.2)
can be written as,
In induction coil
R ^
R!
+
3
!
R^
R!
+
R ^
R_
−
^
!
= `]@A@!NYa − @A@!PQ
LLLM (12.1)
In Workpiece
R ^
R!
+
3
!
R^
R!
+
R ^
R_
−
^
!
= `]@A@!NYa (12.2)
In vacuum/air
R ^
R!
+
3
!
R^
R!
+
R ^
R_
−
^
!
= 0 (12.3)
In these equations, θ, z, r are the Cylindrical coordinates, Aθ is the θ Component of the magnetic
vector potential (V.sec/m), ω is the Angular frequency of coil current (rad/sec).
2.3 Numerical analysis
Finite Element Method (FEM) is used to solve the eq (12.1), (12.2) & (12.3) in geometry given in
figure 2(a). In this method, Solution domain is discretized into number of discrete sub domain or
elements. After discretization, integral formulation is obtained by using Galerkin technique,
which is known as weak form. After that, algebraic equations for each element are obtained in
matrix form. Assembling of all element equations gives the global matrices [18] as shown below
[b]cYd + [C]cYd = cWd (13)
In this equation, [K] is the stiffness matrix, [H] is the Mass matrix,
6. International Journal of Electromagnetics ( IJEL ), Vol 1, No 1, August 2016
26
{A} is the Magnetic vector Potential, {J} is the Electrical current density.
Eq (13) is solved by using suitable boundary conditions and forcing function. Once, magnetic
vector potential is determined, then other quantities like, coil resistance, reactance, voltage, and
work piece power are computed.
2.4 Simulation
Simulation is done in three steps i.e. preprocessing, processing & post processing [1], [19], .In
preprocessing, 2-D axisymmetric geometry shown in figure 2(a) is used for simulation. Materials
and their properties given in table-I and table –II are assigned to different domains. Boundary
conditions are specified as per table -III. Current is used as forcing function. Triangular elements
are used for domain discretization. Mesh is refined on the surface of induction coil and workpiece
as shown in the figure 2(b) [19]. Induction coil carries sinusoidal current, therefore frequency
domain study is done for this analysis [16]. In processing step, magnetic vector potential is
computed in different domains as shown in figure 2(c). In post processing step, other process
related quantities like Magnetic flux density, Coil resistance, reactance, voltage and workpiece
power are computed.
Table-I. Workpiece dimension and properties
Table-II Induction coil dimensions and properties
Table-III Boundary condition and forcing function
Sr. No. Work Piece Description
1. Material Graphite
2. Outer Diameter 160 mm
3. Inner Diameter 117.5 mm
4. Height 180 mm
5. Electrical Conductivity at 2730
K 1.42653X105
S/m
6. Electric permittivity 1
7. Magnetic permeability 1
Sr.No. Induction coil Description
1. Material Copper
2. Inside diameter 215mm
3. Outside diameter 247mm
4. Height 200mm
5. Coil tube diameter 16mm
6. Coil tube thickness 2mm
7. No. of turn 9
8. Electrical conductivity at 2730
K 5.998X107
S/m
9. Electric permittivity 1
10. Magnetic permeability 1
Sr.No. Boundary condition Description
1. Outer boundary A=0
2. Asymmetry axis eY
ef
= 0
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27
Table-IV Lead cable specification
2 (c) 2 (d)
Figure 2(a). Axisymmetric geometry, 2(b) Meshing, 2(c). Magnetic vector potential at 6.55
kHz, 2(d) Magnetic flux density at 6.55 kHz
Sr no Lead Cable Description
1 Material Copper
2 Length 3.61 m
3 Outer diameter 0.025m
4 Thickness 0.001 m
5 Insulation gap 0.015m
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28
2.5 Experiment
Experiments were carried out on vacuum induction melting furance. Schematic diagram of
furnace is shown in the figure (3). 40 kW, 5 kHz, 400 V Power source was connected to the
induction coil. During experiment, various parameters such as Coil current, coil voltage were
measured and recorded at different frequency as shown in figure 4. High frequency current was
measured by rogowaski coil [20]. During experiment, Vacuum below 100 µbar and cooling water
pressure more than 2 kg/cm2
were maintained.
Water coolant
Vacuum
Copper
Induction
coil
Charge
Graphite
crucible
Induction
melting
power
source
3-Phase
mains
power
supply
Melting
vessel
Figure (3). Schematic diagram of Uranium melting
3. RESULT AND ANALYSIS
Experimental results are shown in the figure (4). From figure (4), it is observed that resonance
frequency of series RLC circuit is approximately (6 kHz). As power source output frequency
moves towards resonance frequency, induction coil voltage and current increase.
0 6.8 7.2 7.6 8.0 8.4
0
100
200
300
400
Voltage
Coil
voltage(V)
Frequency(kHz)
0
200
300
400
500
600
700
800
Current
Coil
Current(A)
Figure (4). Coil voltage and coil current during experiment
9. International Journal of Electromagnetics ( IJEL ), Vol 1, No 1, August 2016
29
01 6.8 7.2 7.6 8.0 8.4
0.0
0.70
0.72
0.74
0.76
0.78
0.80
0.82 Copper
Graphite
Skin
Depth(mm)
Copper
Skin
Depth(mm)
Frequency(kHz)
0
14.5
15.0
15.5
16.0
16.5
W
orkpiece
Figure (5). Skin depth at different frequency
In figure (5), it is observed that skin depth in graphite is 20 times more than copper due to high
resistivity of graphite. Figure 6(a) and 6 (b), show the comparison of analytically and numerically
calculated equivalent coil resistance and reactance. The difference between analytical and
numerical resistance and reactance values are less than 7 % and 4 % respectively in specified
frequency range.
0 6.8 7.2 7.6 8.0 8.4
0.00
0.054
0.056
0.058
0.060
0.062
0.064
0.066
Equivalent
coil
resistance(Ohm)
Frequency(kHz)
Analytical
Numerical
6 (a)
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30
0 6.8 7.2 7.6 8.0 8.4
0.00
0.05
0.34
0.36
0.38
0.40
0.42
0.44
0.46
Coil
equivalent
reactance(Ohm)
Frequency(kHz)
Analytical
Numerical
6 (b)
Figure 6(a) coil and workpiece equivalent resistance, 6(b) Coil and workpiece equivalent
reactance
From figure7 (a) and (b), it is observed that analytical and numerical calculated coil voltage and
workpiece power are in good agreement and difference is less than 4% for coil voltage and less
than 2 % for workpiece power in specified frequency range.
0 6.8 7.2 7.6 8.0 8.4
0
80
120
160
200
240
280
Coil
voltage(V)
Frequency(Khz)
Analytical
Numerical
7 (a)
11. International Journal of Electromagnetics ( IJEL ), Vol 1, No 1, August 2016
31
0 6.8 7.2 7.6 8.0 8.4
0
5000
10000
15000
20000
25000
30000
Workpiece
power
(W)
Frequency(kHz)
Numerical
Analytical
7 (b)
Figure (7) (a) Coil voltage, (7) (b) workpiece power calculated by analytical and numerical
methods
Figure (8) shows the workpiece and coil power calculated by eq (7.1) and (7.2) at different
frequency. These data are used to calculate the coil efficiency at different frequencies and found
that coil efficiency is ~81%.
0 6.8 7.2 7.6 8.0 8.4
0
5000
10000
15000
20000
25000
30000
Coil
Power(W)
W
orkpiece
Workpiece
Power(W)
Frequency(kHz)
0
2000
4000
6000
Coilpower
Figure (8) Coil and work piece power at different frequency
12. International Journal of Electromagnetics ( IJEL ), Vol 1, No 1, August 2016
32
0 6.8 7.2 7.6 8.0 8.4
0
100
150
200
250
300
350
400
Coil
Voltage(V)
Frequency(kHz)
Experiment
Numerial
Analytical
Figure (9) Analytically, numerically and experimentally obtained coil voltage
After validation of analytical and numerical model of induction heating process, experiment was
conducted to validate the coil voltage calculated by analytical and numerical method. Figure (9)
shows the comparison of analytical, numerical and experimental coil voltage. In this comparison,
lead impedance is included during analytical and numerical computation, because during
experiment, coil voltages are measured at power source output terminal. From figure (9), it is
observed that results are in good agreement.
4. CONCLUSION
Mathematical modeling and simulation of electromagnetic induction phenomenon in induction
heating process were carried out and results were validated by analytically obtained results.
Experiments were conducted to validate the coil voltage obtained by analytical and numerical
methods at different frequencies. Analytical and numerically calculated workpiece power at
different frequencies is very much close to each other and that is the main concern of induction
heating system designer. This model can be applied to optimize the coil parameters to get the
desired results in induction heating of different kind of materials and avoid the tedious
experiments. This model helps to understand the dynamics of induction heating process in depth.
As these analyses are restricted only to electromagnetic part of induction heating, this can be
further coupled to the power source for transient analysis and heat transfer physics to find out
temperature profile in workpiece.
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