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Electrothermics

Book Description

This book concerns the analysis and design of induction heating of poor electrical conduction materials.

Some innovating applications such as inductive plasma installation or transformers, thermo inductive non-destructive testing and carbon-reinforced composite materials heating are studied. Analytical, semi-analytical and numerical models are combined to obtain the best modeling technique for each case. Each model has been tested with experimental results and validated. The principal aspects of a computational package to solve these kinds of coupled problems are described.

In the first chapter, the mathematical tools for coupled electromagnetic and thermal phenomena are introduced. In Chapter 2, these tools are used to analyze a radio frequency inductive plasma installation. The third chapter describes the methodology of designing a low frequency plasma transformer. Chapter 4 studies the feasibility of the thermo inductive technique for non-destructive testing and the final chapter is dedicated to the use of induction heating in the lifecycle of carbon-reinforced composite materials.

Contents

1. Thermal and Electromagnetic Coupling, Javad Fouladgar, Didier Trichet and Brahim Ramdane.

2. Simplified Model of a Radiofrequency Inductive Thermal Plasma Installation, Javad Fouladgar and Jean-Pierre Ploteau.

3. Design Methodology of A Very Low-Frequency Plasma Transformer, Javad Fouladgar and Souri Mohamed Mimoune.

4. Non Destructive Testing by Thermo-Inductive Method, Javad Fouladgar, Brahim Ramdane, Didier Trichet and Tayeb Saidi.

5. Induction Heating of Composite Materials, Javad Fouladgar, Didier Trichet, Samir Bensaid and Guillaume Wasselynck

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Introduction Induction Heating: Principles and Applications
    1. I.1. Principle
    2. I.2. Characteristics
    3. I.3. Power supply
    4. I.4. Industrial potential of induction
    5. I.5. Bibliography
  5. Chapter 1 Thermal and Electromagnetic Coupling
    1. 1.1. Introduction
    2. 1.2. Electromagnetic problem
      1. 1.2.1. Local formulation of the electromagnetic problem
        1. 1.2.1.1. Maxwell’s equation
        2. 1.2.1.2. Interaction between electromagnetic waves and materials
        3. 1.2.1.3. Vector and scalar potentials
      2. 1.2.2. Boundary conditions
        1. 1.2.2.1. Boundary conditions between two different media
        2. 1.2.2.2. Boundary conditions at the domain’s limits
      3. 1.2.3. Functional spaces
      4. 1.2.4. Tonti diagrams
      5. 1.2.5. Different formulations of the electromagnetic field
        1. 1.2.5.1. Magnetostatic formulation
        2. 1.2.5.2. Magnetostatic formulation in magnetic vector potentials
        3. 1.2.5.3. Magnetodynamic formulation
        4. 1.2.5.4. Magnetodynamic formulation in A-V
        5. 1.2.5.5. Magnetodynamic formulation in T–T0–φ
        6. 1.2.5.6. Formulation in H-φ [DUL 96]
        7. 1.2.5.7. Uniqueness conditions
      6. 1.2.6. Time harmonic form
        1. 1.2.6.1. Maxwell’s equations in the time harmonic form
        2. 1.2.6.2. Electromagnetic power
    3. 1.3. Thermal problem
    4. 1.4. Magnetothermal coupling
    5. 1.5. Solving the electromagnetic and thermal equations
      1. 1.5.1. Analytic methods
        1. 1.5.1.1. Transient state
        2. 1.5.1.2. Harmonic state
      2. 1.5.2. Semi-analytic methods
        1. 1.5.2.1. Shell elements and surface impedance methods
        2. 1.5.2.2. Generalized shell element formulation of a conductive plate
        3. 1.5.2.3. Moment method
          1. 1.5.2.3.1. Interactions between circuit elements
          2. 1.5.2.3.2. Axisymmetrical case
      3. 1.5.3. Numerical models
        1. 1.5.3.1. Finite volume method without velocity terms
        2. 1.5.3.2. Finite volume method with a velocity term
        3. 1.5.3.3. Finite element method
          1. 1.5.3.3.1. Nodal form functions
          2. 1.5.3.3.2. Edge form functions
          3. 1.5.3.3.3. Facet form functions
          4. 1.5.3.3.4. Volume form functions
          5. 1.5.3.3.5. Integral formulation
    6. 1.6. Conclusion
    7. 1.7. Bibliography
  6. Chapter 2 Simplified Model of a Radiofrequency Inductive Thermal Plasma Installation
    1. 2.1. Introduction
    2. 2.2. Plasma and its characteristics
      1. 2.2.1. Plasmas
      2. 2.2.2. Properties of thermal plasma
      3. 2.2.3. Inductive thermal plasma
      4. 2.2.4. Thermal inductive plasma installation
      5. 2.2.5. Inductive thermal plasma start-up and maintenance
        1. 2.2.5.1. Plasma start-up
        2. 2.2.5.2. Plasma maintenance
    3. 2.3. Modeling a plasma installation
      1. 2.3.1. Torch simulation
        1. 2.3.1.1. Simplification
        2. 2.3.1.2. Solving the electromagnetic equation
        3. 2.3.1.3. Solving the heat equation
    4. 2.4. Calculating charge impedance
      1. 2.4.1. Results
      2. 2.4.2. Local validations
        1. 2.4.2.1. Magnetic field measurement method
        2. 2.4.2.2. Temperature measurement method
        3. 2.4.2.3. Results
    5. 2.5. Generator model
      1. 2.5.1. Triode generator
      2. 2.5.2. Modeling the HF generator in the steady state
        1. 2.5.2.1. Principle of the developed model
        2. 2.5.2.2. Triode modeling
        3. 2.5.2.3. Quasi-analytic generator simulation
        4. 2.5.2.4. Results
      3. 2.5.3. Complete simulation of a thermal plasma installation
        1. 2.5.3.1. Coupling algorithm
        2. 2.5.3.2. Validation of the complete installation simulation model
        3. 2.5.3.3. Calculating the installation’s efficiency
    6. 2.6. Conclusion
    7. 2.7. Bibliography
  7. Chapter 3 Design Methodology of a Very Low-Frequency Plasma Transformer
    1. 3.1. Introduction
    2. 3.2. Different types of very low-frequency applicators
      1. 3.2.1. Choice criterion of very low-frequency plasma applicators
    3. 3.3. Simplified analytical model for analysis and preliminary design
      1. 3.3.1. Hypotheses
      2. 3.3.2. System equation
      3. 3.3.3. Plasma maintenance criterion
      4. 3.3.4. Flaws of the linear model
    4. 3.4. Nonlinear model
      1. 3.4.1. Nonlinear model results
    5. 3.5. Plasma stability in the transitory and sinusoidal states
      1. 3.5.1. Transitory state
      2. 3.5.2. Sinusoidal state
    6. 3.6. Advanced inductive plasma transformer model
      1. 3.6.1. Displacement current
      2. 3.6.2. Electromagnetic equation formulation
        1. 3.6.2.1. Introducing a voltage source
      3. 3.6.3. Thermal equation formulation
      4. 3.6.4. Coupling algorithm for the electromagnetic and thermal equations
      5. 3.6.5. Results of the 3D model
      6. 3.6.6. Impact of the number of arms of the magnetic core on the electric field distribution
    7. 3.7. Plasma initialization
      1. 3.7.1. Initialization with a capacitive discharge
      2. 3.7.2. Initialization with an inductive discharge
      3. 3.7.3. Towards an inductive ignitor
    8. 3.8. Conclusion
    9. 3.9. Bibliography .
  8. Chapter 4 Non Destructive Testing by Thermo-Inductive Method
    1. 4.1. Introduction
    2. 4.2. Principles of the thermo-inductive method
      1. 4.2.1. Installation schematic
      2. 4.2.2. Describing the technique’s elements
        1. 4.2.2.1. Induction generator
        2. 4.2.2.2. The inductor
        3. 4.2.2.3. The infrared camera
        4. 4.2.2.4. The specimen to inspect
      3. 4.2.3. The stimulation modes
        1. 4.2.3.1. Modulated stimulation mode
        2. 4.2.3.2. Pulse stimulation mode
        3. 4.2.3.3. Pulse phase mode
    3. 4.3. Basic thermo-inductive technique theory
      1. 4.3.1. One-dimensional models for the propagation of the thermal wave in a continuous medium
        1. 4.3.1.1. Propagation of thermal waves in a semi-infinite medium excited by a constant flux
          1. 4.3.1.1.1. Sinusoidal flux (modulated mode)
          2. 4.3.1.1.2. Pulse flux
          3. 4.3.1.1.3. Pulse phase mode
        2. 4.3.1.2. Propagation of thermal waves in a semi-infinite plate with a horizontal flaw
          1. 4.3.1.2.1. Modulated excitation mode
          2. 4.3.1.2.2. Pulse excitation mode
          3. 4.3.1.2.3. Pulse phase’s excitation mode
      2. 4.3.2. One-dimensional model limitations
      3. 4.3.3. Numerical models
        1. 4.3.3.1. Electromagnetic models
          1. 4.3.3.1.1. A-V formulation
          2. 4.3.3.1.2. T-φ formulation
          3. 4.3.3.1.3. Thermal model
      4. 4.3.4. Magneto-thermal coupling
      5. 4.3.5. Applying numerical model to study the feasibility of the thermo-inductive technique
    4. 4.4. Application of the thermo-inductive method to inspect massive magnetic steel components
      1. 4.4.1. Studied setup
      2. 4.4.2. Flaw’s influence on the distribution of the induced currents and temperature
      3. 4.4.3. Study of the inductor’s influence
        1. 4.4.3.1. Shape and position of the inductor
        2. 4.4.3.2. Air gap between the inductor and the inspected component.
      4. 4.4.4. Choice of induction generator
      5. 4.4.5. Acquisition parameters
      6. 4.4.6. Influence of the heating time and the electromagnetic frequency
        1. 4.4.6.1. Heating time
        2. 4.4.6.2. Electromagnetic frequency
      7. 4.4.7. Influence of the flaw’s geometry
        1. 4.4.7.1. Influence of the flaw depth/flaw length ratio
        2. 4.4.7.2. Flaw orientation
      8. 4.4.8. Experimental results
    5. 4.5. Comparison with infrared thermography
      1. 4.5.1. Studied setup
    6. 4.6. Applications on composite materials
      1. 4.6.1. Study of composite materials
        1. 4.6.1.1. Studied setup
        2. 4.6.1.2. Study of the inductor’s influence
        3. 4.6.1.3. Influence of the electromagnetic frequency and heating time
        4. 4.6.1.4. Influence of the flaw depth
        5. 4.6.1.5. Influence of flaw thickness
        6. 4.6.1.6. Influence of the delamination width
      2. 4.6.2. Experimental study
        1. 4.6.2.1. Inspection of the drilled plate
        2. 4.6.2.2. Inspection of the plate with a hole opening on a surface
    7. 4.7. Conclusion and general instructions
      1. 4.7.1. Discussion on the choice of induction generator and inductor
      2. 4.7.2. Discussion on data acquisition
      3. 4.7.3. Flaw characterization
        1. 4.7.3.1. Surface flaws
        2. 4.7.3.2. Deep flaws
        3. 4.7.3.3. Delaminations
    8. 4.8. Bibliography
  9. Chapter 5 Induction Heating of Composite Materials
    1. 5.1. Introduction
    2. 5.2. Composite materials
      1. 5.2.1. Composite material definition
      2. 5.2.2. Composite material constituents
        1. 5.2.2.1. The matrix
        2. 5.2.2.2. The reinforce
      3. 5.2.3. Composite architecture
    3. 5.3. Lifecycle of composite materials
    4. 5.4. Induction and the lifecycle of composite materials
      1. 5.4.1. Mastery of induction heating of composite materials
        1. 5.4.1.1. Simulation tool
        2. 5.4.1.2. Adapting the inductor’s form and frequency to the geometry, the material, and the type of heating
        3. 5.4.1.3. Precise knowledge of the physical properties
    5. 5.5. Identifying the physical properties of composite materials by experimental methods
      1. 5.5.1. Influence of the geometry
      2. 5.5.2. Induced current methods
        1. 5.5.2.1. Measuring the electrical conductivity of a conductive plate
        2. 5.5.2.2. Analytic impedance calculation
        3. 5.5.2.3. 2D numerical method
      3. 5.5.3. Sensitivity analysis
      4. 5.5.4. Impedance measurements
        1. 5.5.4.1. Optimization of the measurement system
        2. 5.5.4.2. Experimentation and results
    6. 5.6. Homogenization techniques
      1. 5.6.1. Inverse problem
        1. 5.6.1.1. Application of the inverse problem to stratifiedcomposite materials
        2. 5.6.1.2. Thermal characteristics
      2. 5.6.2. Dynamic homogenization methods for periodic structures
        1. 5.6.2.1. Homogenization of the electrical conductivity
        2. 5.6.2.2. Thermal properties
        3. 5.6.2.3. Applications to the 2D electromagnetic study of composite materials
        4. 5.6.2.4. Applications to the 2D thermal study of composite materials
        5. 5.6.2.5. Applications to 3D materials
      3. 5.6.3. Homogenization by the representative samples method
        1. 5.6.3.1. The method’s principle
        2. 5.6.3.2. Generating the geometry
        3. 5.6.3.3. Results
        4. 5.6.3.4. Influence of contacts between differently oriented folds
    7. 5.7. Heating composite materials by induction
      1. 5.7.1. Studied setup
      2. 5.7.2. Inductor
      3. 5.7.3. The composite plates
      4. 5.7.4. Experimental validation setup
    8. 5.8. Setup model
      1. 5.8.1. Electromagnetic formulation
      2. 5.8.2. Thermal formulation
    9. 5.9. Influence of the folds’ orientation
    10. 5.10. Difficulty of the electrothermal coupling
      1. 5.10.1. Study of the sensitivity of the induced power’s variation as a function of the temperature
    11. 5.11. Validating the electrothermal mode
      1. 5.11.1. 13-fold composite
      2. 5.11.2. 16-fold composite
    12. 5.12. Conclusion
    13. 5.13. Bibliography
  10. List of Authors
  11. Index