Numerical Modeling Of Superconducting Applications : : Simulation Of Electromagnetics, Thermal Stability, Thermo-hydraulics And Mechanical Effects In Large-scale Superconducting Devices / / Bertrand Dutoit, Francesco Grilli and Frederic Sirois.

• Superior document: World Scientific Series In Applications Of Superconductivity And Related Phenomena ; v.4
• VerfasserIn: Dutoit, Bertrand,; Grilli, Francesco,; Sirois, Frederic,
• TeilnehmendeR: Grilli, Francesco,; Sirois, Frederic,
• Place / Publishing House: Singapore : : World Scientific Publishing Company,, 2023.
• Year of Publication: 2023
• Language: English
• Series: World Scientific Series In Applications Of Superconductivity And Related Phenomena
• Physical Description: 1 online resource (328 pages)

This book aims to present an introduction to numerical modeling of different aspects of large-scale superconducting applications: electromagnetics, thermal, mechanics and thermo-hydraulics. The importance of computational modeling to advance current superconductor research cannot be overlooked, especially given the enormous benefits provided by superconductors in many human endeavours, including energy generation, medical treatments, and future electrical technologies.Aimed at graduate students, researchers and practitioners in different fields of applied superconductivity, this book consists of four chapters. The chapter on electromagnetics provides a review of the state-of-the-art modeling of electromagnetic phenomena in superconductors, emphasising the theoretical aspects of the different numerical formulations. This is followed by a chapter on thermal effects, dedicated to the simulation of thermal stability and quench in superconducting magnets, with specific examples of magnets used in particle accelerators. Then, the chapter on mechanics provides details of the modeling of forces and stresses in cables composed of second-generation high-temperature superconducting wires. Finally, the chapter on thermo-hydraulics focuses on the fundamental thermal-hydraulic aspects involved in the cooling of superconducting magnets, with special reference to the issues related to the forced-flow cooling.

Table of Contents

Cover -- Title page -- Copyright -- Contents -- Introduction -- 1. Electromagnetic Modeling of Superconductors -- 1.1. Introduction -- 1.1.1. Maxwell equations in quasimagnetostatics -- 1.1.1.1. Faraday's integral law -- 1.1.2. Macroscopic electromagnetic properties of superconductors -- 1.1.3. Vector and scalar potentials and their relation to the sources -- 1.1.3.1. Long straight conductors (infinite) -- 1.1.3.2. Axial symmetry -- 1.1.4. Solution to the Laplace equation for electrostatics -- 1.1.5. Integral relation between B and J -- 1.1.6. Current potentials -- 1.1.6.1. Divergence-free gauge of T -- 1.1.6.2. Magnetic-field gauge -- 1.1.6.3. Current potential as magnetization -- 1.1.7. Calculation of local dissipation and AC loss -- 1.1.7.1. Fundamental aspects of the local loss dissipation -- 1.1.7.2. Hysteresis loss of magnetic materials -- 1.1.7.3. Conductors and superconductors under uniform applied fields -- 1.2. Analytical Formulas and Main Electromagnetic Behavior -- 1.2.1. Hysteresis currents -- 1.2.1.1. Infinite cylinder under axial applied magnetic field -- 1.2.1.2. Infinite slab under parallel applied field -- 1.2.1.3. Circular wire with transport current -- 1.2.1.4. Elliptical wire with transport current -- 1.2.1.5. Thin strip under applied magnetic field -- 1.2.1.6. Thin strip with transport current -- 1.2.1.7. Universal scaling law for the power-law E(J) relation -- 1.2.2. Eddy currents -- 1.2.2.1. Low-frequency limit -- 1.2.2.2. Whole frequency range -- 1.2.3. Coupling currents -- 1.2.3.1. On the decomposition of AC loss into eddy, coupling, and superconductor contributions -- 1.2.3.2. Two slab filaments connected by normal conductor -- 1.3. Numerical Methods -- 1.3.1. Finite element methods -- 1.3.1.1. H formulation -- 1.3.1.2. A-ϕ formulation -- 1.3.1.3. T-Ω formulation -- 1.3.1.4. Combined formulations.

1.3.2. Variational methods -- 1.3.2.1. J-ϕ formulation -- 1.3.2.2. T formulation -- 1.3.2.3. H formulation -- 1.3.2.4. H-ψ formulation -- 1.3.2.5. Interaction with nonlinear magnetic materials -- 1.3.3. Integro-differential methods -- 1.3.3.1. J integral formulation -- 1.3.3.2. T integral formulation -- 1.3.4. Spectral methods -- 1.3.5. Particular issues for three dimensions -- 1.4. Modeling of Power Applications -- 1.4.1. Numerical modeling of individual wires -- 1.4.1.1. Dependence of Jc on magnetic field -- 1.4.1.2. Dependence of Jc on position -- 1.4.1.3. Simulation of magnetic materials -- 1.4.1.4. Dynamic resistance -- 1.4.2. Interacting tapes -- 1.4.3. 3D modeling -- 1.4.4. Rotating machines -- Acknowledgments -- References -- 2. Introduction to Stability and Quench Protection -- 2.1. Margins to Quench -- 2.1.1. Minimum quench energy -- 2.1.1.1. Numerical modeling of MQE -- 2.1.1.2. MQE simulations -- 2.1.2. Margins in magnet load line -- 2.2. Classifying Quenches -- 2.2.1. Devred's classification of quenches -- 2.2.2. Wilson's classification of quenches -- 2.3. Engineering Methodology in Quench Protection -- 2.3.1. Model -- 2.3.2. Design -- 2.3.3. Simulation -- 2.3.4. Experiment -- 2.4. Numerical Modeling of a Quench Event -- 2.4.1. Input and output of a quench simulation -- 2.4.1.1. Magnetic flux density distribution -- 2.4.1.2. Operation conditions -- 2.4.1.3. Post-processing data -- 2.4.2. Spatial and temporal discretization in a FEM based tool -- 2.4.2.1. Spatial discretization -- 2.4.2.2. Temporal discretization -- 2.4.3. Triggering the quench in the simulation of an HTS magnet -- 2.4.4. Reducing modeling domain to speed up quench simulations for HTS magnets -- 2.4.4.1. Modeling domain -- 2.4.4.2. Simulation results -- 2.4.5. Quench analysis of an R&amp -- D REBCO magnet.

2.5. Design of Quench Protection Heaters for Nb3Sn Accelerator Magnets -- 2.5.1. R&amp -- D of Nb3Sn quadrupole magnet -- 2.5.2. Heater technology and target variables for optimization -- 2.5.3. Modeling the heater's efficiency -- 2.5.4. Guidelines for parametric optimization of heaters -- 2.5.5. Simulations for the LHQ heater design -- 2.5.6. Testing the designed heater layout -- Acknowledgements -- References -- 3. Finite Element Structural Modeling -- 3.1. Introduction -- 3.2. HTS Tapes and Cables -- 3.3. FEA Research Areas -- 3.3.1. Single-tape simulations -- 3.3.2. Cable simulations -- 3.4. Modeling Techniques for Single Tapes -- 3.4.1. Finite element software and settings -- 3.4.2. REBCO-coated conductor architecture -- 3.4.3. Element types -- 3.4.4. Meshing -- 3.4.5. Material properties -- 3.4.6. Boundary conditions and loads -- 3.5. Modeling Techniques for Cables -- 3.5.1. Model simplifications -- 3.5.2. Element types -- 3.5.3. Meshing -- 3.5.4. Material properties -- 3.5.5. Contact relationships -- 3.5.6. Boundary conditions and loads -- 3.6. Postprocessing and Results -- 3.6.1. Simulation output results -- 3.6.2. Critical current prediction -- 3.6.3. Single-tape results -- 3.6.4. Cable results -- References -- 4. Thermal-Hydraulics of Superconducting Magnets -- 4.1. Applications of Superconducting Magnets and Related Topologies/Geometries -- 4.1.1. Magnetically confined nuclear fusion experiments -- 4.1.2. Particle accelerators -- 4.1.3. Others -- 4.1.3.1. Gyrotrons -- 4.1.3.2. Medical -- 4.1.3.3. Power grid -- 4.2. Superconducting Magnet Cooling Methods -- 4.2.1. Cooling fluids -- 4.2.1.1. Helium -- 4.2.1.2. Hydrogen -- 4.2.1.3. Neon -- 4.2.1.4. Nitrogen -- 4.2.2. Cooling options -- 4.2.2.1. Forced flow -- 4.2.2.2. Conduction -- 4.2.2.3. Pool -- 4.2.3. Cryoplant description -- 4.2.3.1. Refrigerator -- 4.2.3.2. SHe loop.

4.2.3.3. Interfaces -- 4.2.4. Solid properties -- 4.2.4.1. Metals -- 4.2.4.2. Superconductor -- 4.2.4.3. Insulations -- 4.3. Modeling -- 4.3.1. Space scales -- 4.3.2. Time scales -- 4.4. Forced-Flow CICC Superconductor Hydraulics -- 4.4.1. Multiple flow regions -- 4.4.1.1. Bundle -- 4.4.1.2. Hole -- 4.4.1.3. Coupling between bundle and hole -- 4.4.2. Friction factors -- 4.5. Forced-Flow CICC Thermal-Hydraulics -- 4.5.1. Heat transfer coolant-solids -- 4.5.2. Heat transfer between different solids -- 4.5.3. Heat transfer between different coolant regions -- 4.6. Heat Transfer Mechanisms in the Magnet -- 4.6.1. Heat transfer within the winding -- 4.6.2. Heat transfer within the magnet structures -- 4.6.2.1. Cooling of the coil casing -- 4.6.3. Heat transfer between structures and winding -- 4.6.3.1. Issues in the ground insulation modeling -- 4.7. Relevant TH Transients -- 4.7.1. Cool down -- 4.7.2. Normal operation -- 4.7.3. Off-normal operation -- 4.7.3.1. Stability and quench -- 4.7.3.2. Fast discharge/current ramps -- 4.7.3.3. Loss of flow/coolant accidents -- 4.8. Available Models and Experimental Facilities -- 4.8.1. Thermal-hydraulic codes -- 4.8.1.1. Venecia -- 4.8.1.2. 4C -- 4.8.1.3. Supermagnet -- 4.8.1.4. Others -- 4.8.2. Conductor test facilities -- 4.8.3. Magnets test facilities -- 4.8.4. Available experiments -- 4.8.4.1. Superconducting tokamaks in operation -- 4.8.4.2. Superconducting stellarators in operation -- References -- Index.