Numerical simulation of quench propagation in superconducting magnets by using high order methods

In this study, numerical simulation is applied to compressible helium flow and coupled heat transfer in cable-in-conduit superconductor (CICC). Helium flow in CICCs and quench propagation simulation are relevant engineering problems. These flows have high Reynolds number and low Mach number. The large non-linear source terms due to Joule heating and friction force introduce difficulties for most numerical techniques. The main consideration in this dissertation is to seek some numerical methods with high accuracy (resolution) and efficiency.; In the first part of this study, a simple physical model, the energy balance model, was proposed for the first time to track the superfluid helium (He II) and normal helium (He I) fronts, which is very critical to simulate He II/He I transition in large-scale superconducting magnets. This new model was used to analyze the thermal stability (quench behavior) of the NHMFL 45-T hybrid magnets system. This model resulted in high efficiency of numerical simulation of thermal stability analysis compared to complicated 1D quench propagation model. Besides, adaptive mesh techniques were introduced to improve numerical efficiency. This model was successfully predicted quench behavior, right protection, and showed that index heating was the cause to drive quench in the NHMFL 45-T hybrid magnets system.; In the second part of this study, two high-order methods were applied to simulate quench propagation in CICC magnets. The main consideration in this dissertation was to seek some numerical methods with high accuracy (resolution) and efficiency. The first high-order finite different methods, dispersion-relation-preserving (DRP) schemes were used to simulate quench propagation in CICC at the early phase in order to decrease the phase errors (dispersion errors). High-order methods were introduced for the first time to simulate quench propagation in superconducting magnets. This research was focusing on the early phase of quench propagation, which helps to understand the quench propagation mechanism. Detailed numerical algorithm was discussed, and numerical benchmarking results were obtained. We conclude that the research on the early phase of quench propagation is an important issue to understand quench propagation in detail.; The second high-order methods, discontinuous Galerkin (DG) spectral element methods (SEM) were applied to overcome numerical difficulties encountered by most classical methods. DG-SEM is very robust to simulate quench propagation for which traditional methods were only highly efficient either at early stage or later stage of quench propagation in CICC. Detailed numerical benchmarks showed that DG-spectral element methods have advantages in dealing with large non-linear source term problems (quench propagation) by avoiding artificial damping and keeping the system numerical conservation. DG-spectral element methods showed high accuracy (high resolution in large gradient regions), they also demonstrated high numerical stability for large external disturbances. DG-spectral element methods can be parallelized to speed up the simulation while retaining high accuracy. (Abstract shortened by UMI.)...