book

Electrothermics

Name: Electrothermics
Author: Javad Fouladgar
ISBN: 9781848212428

by Javad Fouladgar

March 2012

Intermediate to advanced

276 pages

7h 3m

English

Wiley

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Cover
Title
Copyright
Introduction Induction Heating: Principles and Applications
I.1. Principle
I.2. Characteristics
I.3. Power supply
I.4. Industrial potential of induction
I.5. Bibliography
Chapter 1 Thermal and Electromagnetic Coupling

1.1. Introduction
1.2. Electromagnetic problem
1.2.1. Local formulation of the electromagnetic problem1.2.1.1. Maxwell’s equation 1.2.1.2. Interaction between electromagnetic waves and materials1.2.1.3. Vector and scalar potentials1.2.2. Boundary conditions1.2.2.1. Boundary conditions between two different media1.2.2.2. Boundary conditions at the domain’s limits1.2.3. Functional spaces1.2.4. Tonti diagrams1.2.5. Different formulations of the electromagnetic field1.2.5.1. Magnetostatic formulation1.2.5.2. Magnetostatic formulation in magnetic vector potentials1.2.5.3. Magnetodynamic formulation1.2.5.4. Magnetodynamic formulation in A-V1.2.5.5. Magnetodynamic formulation in T–T0–φ1.2.5.6. Formulation in H-φ [DUL 96]1.2.5.7. Uniqueness conditions1.2.6. Time harmonic form1.2.6.1. Maxwell’s equations in the time harmonic form1.2.6.2. Electromagnetic power
1.3. Thermal problem
1.4. Magnetothermal coupling
1.5. Solving the electromagnetic and thermal equations
1.5.1. Analytic methods1.5.1.1. Transient state1.5.1.2. Harmonic state1.5.2. Semi-analytic methods1.5.2.1. Shell elements and surface impedance methods1.5.2.2. Generalized shell element formulation of a conductive plate1.5.2.3. Moment method1.5.2.3.1. Interactions between circuit elements1.5.2.3.2. Axisymmetrical case1.5.3. Numerical models1.5.3.1. Finite volume method without velocity terms1.5.3.2. Finite volume method with a velocity term1.5.3.3. Finite element method1.5.3.3.1. Nodal form functions1.5.3.3.2. Edge form functions1.5.3.3.3. Facet form functions1.5.3.3.4. Volume form functions1.5.3.3.5. Integral formulation
1.6. Conclusion
1.7. Bibliography
Chapter 2 Simplified Model of a Radiofrequency Inductive Thermal Plasma Installation
2.1. Introduction
2.2. Plasma and its characteristics
2.2.1. Plasmas2.2.2. Properties of thermal plasma2.2.3. Inductive thermal plasma2.2.4. Thermal inductive plasma installation2.2.5. Inductive thermal plasma start-up and maintenance2.2.5.1. Plasma start-up2.2.5.2. Plasma maintenance
2.3. Modeling a plasma installation
2.3.1. Torch simulation2.3.1.1. Simplification2.3.1.2. Solving the electromagnetic equation2.3.1.3. Solving the heat equation
2.4. Calculating charge impedance
2.4.1. Results2.4.2. Local validations 2.4.2.1. Magnetic field measurement method2.4.2.2. Temperature measurement method 2.4.2.3. Results
2.5. Generator model
2.5.1. Triode generator2.5.2. Modeling the HF generator in the steady state2.5.2.1. Principle of the developed model2.5.2.2. Triode modeling2.5.2.3. Quasi-analytic generator simulation2.5.2.4. Results2.5.3. Complete simulation of a thermal plasma installation2.5.3.1. Coupling algorithm2.5.3.2. Validation of the complete installation simulation model2.5.3.3. Calculating the installation’s efficiency
2.6. Conclusion
2.7. Bibliography
Chapter 3 Design Methodology of a Very Low-Frequency Plasma Transformer
3.1. Introduction
3.2. Different types of very low-frequency applicators
3.2.1. Choice criterion of very low-frequency plasma applicators
3.3. Simplified analytical model for analysis and preliminary design
3.3.1. Hypotheses3.3.2. System equation3.3.3. Plasma maintenance criterion3.3.4. Flaws of the linear model
3.4. Nonlinear model
3.4.1. Nonlinear model results
3.5. Plasma stability in the transitory and sinusoidal states
3.5.1. Transitory state3.5.2. Sinusoidal state
3.6. Advanced inductive plasma transformer model
3.6.1. Displacement current3.6.2. Electromagnetic equation formulation3.6.2.1. Introducing a voltage source3.6.3. Thermal equation formulation3.6.4. Coupling algorithm for the electromagnetic and thermal equations3.6.5. Results of the 3D model3.6.6. Impact of the number of arms of the magnetic core on the electric field distribution
3.7. Plasma initialization
3.7.1. Initialization with a capacitive discharge3.7.2. Initialization with an inductive discharge3.7.3. Towards an inductive ignitor
3.8. Conclusion
3.9. Bibliography .
Chapter 4 Non Destructive Testing by Thermo-Inductive Method
4.1. Introduction
4.2. Principles of the thermo-inductive method
4.2.1. Installation schematic4.2.2. Describing the technique’s elements4.2.2.1. Induction generator4.2.2.2. The inductor4.2.2.3. The infrared camera4.2.2.4. The specimen to inspect4.2.3. The stimulation modes4.2.3.1. Modulated stimulation mode4.2.3.2. Pulse stimulation mode4.2.3.3. Pulse phase mode
4.3. Basic thermo-inductive technique theory
4.3.1. One-dimensional models for the propagation of the thermal wave in a continuous medium4.3.1.1. Propagation of thermal waves in a semi-infinite medium excited by a constant flux4.3.1.1.1. Sinusoidal flux (modulated mode)4.3.1.1.2. Pulse flux4.3.1.1.3. Pulse phase mode4.3.1.2. Propagation of thermal waves in a semi-infinite plate with a horizontal flaw4.3.1.2.1. Modulated excitation mode4.3.1.2.2. Pulse excitation mode4.3.1.2.3. Pulse phase’s excitation mode4.3.2. One-dimensional model limitations4.3.3. Numerical models4.3.3.1. Electromagnetic models4.3.3.1.1. A-V formulation4.3.3.1.2. T-φ formulation4.3.3.1.3. Thermal model4.3.4. Magneto-thermal coupling4.3.5. Applying numerical model to study the feasibility of the thermo-inductive technique
4.4. Application of the thermo-inductive method to inspect massive magnetic steel components
4.4.1. Studied setup4.4.2. Flaw’s influence on the distribution of the induced currents and temperature4.4.3. Study of the inductor’s influence4.4.3.1. Shape and position of the inductor4.4.3.2. Air gap between the inductor and the inspected component.4.4.4. Choice of induction generator4.4.5. Acquisition parameters4.4.6. Influence of the heating time and the electromagnetic frequency4.4.6.1. Heating time4.4.6.2. Electromagnetic frequency4.4.7. Influence of the flaw’s geometry4.4.7.1. Influence of the flaw depth/flaw length ratio4.4.7.2. Flaw orientation4.4.8. Experimental results
4.5. Comparison with infrared thermography
4.5.1. Studied setup
4.6. Applications on composite materials
4.6.1. Study of composite materials4.6.1.1. Studied setup4.6.1.2. Study of the inductor’s influence4.6.1.3. Influence of the electromagnetic frequency and heating time4.6.1.4. Influence of the flaw depth4.6.1.5. Influence of flaw thickness4.6.1.6. Influence of the delamination width4.6.2. Experimental study4.6.2.1. Inspection of the drilled plate4.6.2.2. Inspection of the plate with a hole opening on a surface
4.7. Conclusion and general instructions
4.7.1. Discussion on the choice of induction generator and inductor4.7.2. Discussion on data acquisition4.7.3. Flaw characterization4.7.3.1. Surface flaws4.7.3.2. Deep flaws4.7.3.3. Delaminations
4.8. Bibliography
Chapter 5 Induction Heating of Composite Materials
5.1. Introduction
5.2. Composite materials
5.2.1. Composite material definition5.2.2. Composite material constituents5.2.2.1. The matrix5.2.2.2. The reinforce5.2.3. Composite architecture
5.3. Lifecycle of composite materials
5.4. Induction and the lifecycle of composite materials
5.4.1. Mastery of induction heating of composite materials5.4.1.1. Simulation tool5.4.1.2. Adapting the inductor’s form and frequency to the geometry, the material, and the type of heating5.4.1.3. Precise knowledge of the physical properties
5.5. Identifying the physical properties of composite materials by experimental methods
5.5.1. Influence of the geometry5.5.2. Induced current methods5.5.2.1. Measuring the electrical conductivity of a conductive plate5.5.2.2. Analytic impedance calculation5.5.2.3. 2D numerical method5.5.3. Sensitivity analysis5.5.4. Impedance measurements5.5.4.1. Optimization of the measurement system5.5.4.2. Experimentation and results
5.6. Homogenization techniques
5.6.1. Inverse problem5.6.1.1. Application of the inverse problem to stratifiedcomposite materials5.6.1.2. Thermal characteristics5.6.2. Dynamic homogenization methods for periodic structures5.6.2.1. Homogenization of the electrical conductivity5.6.2.2. Thermal properties5.6.2.3. Applications to the 2D electromagnetic study of composite materials5.6.2.4. Applications to the 2D thermal study of composite materials5.6.2.5. Applications to 3D materials5.6.3. Homogenization by the representative samples method5.6.3.1. The method’s principle5.6.3.2. Generating the geometry5.6.3.3. Results5.6.3.4. Influence of contacts between differently oriented folds
5.7. Heating composite materials by induction
5.7.1. Studied setup5.7.2. Inductor5.7.3. The composite plates5.7.4. Experimental validation setup
5.8. Setup model
5.8.1. Electromagnetic formulation5.8.2. Thermal formulation
5.9. Influence of the folds’ orientation
5.10. Difficulty of the electrothermal coupling
5.10.1. Study of the sensitivity of the induced power’s variation as a function of the temperature
5.11. Validating the electrothermal mode
5.11.1. 13-fold composite5.11.2. 16-fold composite
5.12. Conclusion
5.13. Bibliography
List of Authors
Index

Content preview from Electrothermics

3.4. Nonlinear model

In the case of the nonlinear system, the equation of conservation of energy in the steady state is of the form:

[3.25] images

with boundary conditions:

[3.26]

[3.27]

Equation [3.25] can be solved using the finite volumes method:

[3.28] images

where the quantities with the indices w, p, and e represent the values calculated at the left of the current point, those calculated at the current point, and those calculated at the right of the current point, respectively.

Assembling this equation by taking boundary conditions into account, [3.26] and [3.27] result in the following nonlinear equation:

[3.29]

This equation is solved using the iterative algorithm in Figure 3.11.

Figure 3.11. Nonlinear model algorithm

3.4.1. Nonlinear model results

For a given temperature, if we reduce the electric field, we reduce the power injected in the plasma, defined by the term (T)E_e². Decreasing ...

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Electrothermics

by Javad Fouladgar