The computation team in Professor Schwartz’s research group mainly focuses on developing computational models and performs simulation-based analyses for superconductivity technology. Our aim is to develop advanced models and modeling techniques and integrate them to form a series of analysis and design tools for scientific research and industrial engineering; and to develop novel methods to solve various important engineering issues in superconductivity technology, such as effective quench detection and protection in high temperature superconducting magnetic energy storage (SMES) systems.

Modeling and simulation is an indispensable part in the process of research and design of superconducting technology and devices. Building a superconducting device such as a high-field magnet can be very expensive in term of material cost and risk management. The potential of damaging a superconducting magnet by strong Lorentz forces and catastrophic quenching during normal operation implies that traditional design process that relies on building and testing multiple prototypes to adjust design parameters is out of the question. In this situation, careful design analysis must be done before the magnet is put into fabrication. A design analysis must ensure that the to-be-built magnet is properly cooled and it can withstand strong mechanical stresses generated by Lorentz forces and is properly protected when a quench is effectively detected. The ultimate goal is to design and build the target magnet that perform reliably and meet all target specifications. This kind of analysis can be a daunting task as it involves multiphysics calculations that couple electromagnetics, thermal physics and even structural mechanics and fluid dynamics, subjected to complicated design considerations. As a result, it can only be done computationally via modeling and simulation.

Computational modeling and simulation allows researches and engineers to investigate numerically nearly all physical behaviors occur inside an object under study. These behaviors, such as stresses and strains inside a laminated composite conductor, oftentimes are extremely difficult or expensive, if not impossible, to be observed by direct experimental means. The ability to observe any behavior allows one to gain valuable insight into the underlying working principles, understand the effects of environmental parameters and identify causes of problems by experimenting with different parameters at the clicks of a few keystrokes.

Experiment is an important and complimentary part of modeling and simulation. Once a new model is built, it must be validated against some trusted results to ensure that it approximates physical phenomena with reasonable accuracy. The results used for validation can be obtained either from analytical equations, from other validated computational models or more trustable, from experiments. The computational and experimental teams in Schwartz’s research group work closely with each other. When needed, the experimental teams conduct proprietary experiments to generate validation results, and the computational team performs simulations to help choosing experimental parameters and instruments, and also to gain better understanding of experimental results.

**Summary of computational projects**

Our computational team has developed novel finite element models from different superconductor related projects funded by DoE, AFRL and ARPA-E. These models have put NCSU in a leading edge of superconductivity technology research. The past, ongoing and future modeling and simulation projects initiated in Schwartz’s research group are summarized below

**Three-dimensional quench analysis of superconducting conductors and coils:**

Quench is one of the major reliability concerns in operating superconducting devices. A quench is an avalanche phenomenon that happens inside a superconducting conductor when current originally transporting in a superconducting layer is redistributed to a normal metal around a temperature hot-spot, causing joule heating in the normal metal to further increase the hot-spot peak temperature and volume. If uncontrolled, the growing temperature during a quench can damage a superconducting conductor. The situation is even more serious in an active high-field superconducting coil. When a quench happens, the enormous amount of stored magnetic energy will dissipate over the small but slowly enlarging hot-spot volume, thus causing catastrophic meltdown in the coil if the quench is left uncontrolled.

The purpose of this project is to understand computationally how a quench happens and behaves inside a high temperature superconducting coated conductor and coil, how do variations in geometrical and material properties affect the quench behavior and what can be done to improve the thermal stability of a superconducting devices.

Our team has successfully developed a novel mixed-dimensional modeling approach that allows models consisted of laminated high-aspect-ratio thin layers to be built in three dimension. It is a notorious problem to build such models in mesh-based numerical techniques such as finite element method. The new modeling approach is used to build three-dimensional REBCO coated conductor quench models. The same modeling approach is generalized into a multiscale, modularized approach that allows full-scale model such as a magnet coil to be built hierarchically by using the conductor model as a basic building block. This modularized approach allows physical behavior to be observed in multiple scales—from micrometer to full device scale.

**Three-dimensional structural analysis:**

Strong Lorentz forces generated by a high-field magnet and thermal stresses/strains generated during a quench and cooling process can cause undesired mechanical damages such as crack and delamination in a conductor. Time-varying magnetic load generated by the Lorentz forces during charge/discharge cycles of a SMES can also cause fatigue failures. These mechanical failures can cause performance degradation and even total failure to a superconducting device.

The purpose of this work is to study how stresses/strains are generated inside conductors and coils at different stages of manufacturing and operation, and how mechanically more robust conductors and coils can be built. Based on the mixed-dimensional and modularized modeling concepts used for the quenching models, our team has successfully developed structural conductor and full-scale coil models. Stress/strain analyses down to the individual laminated high-aspect-ratio thin layers are performed starting from the conductor fabrication process, to the bending process in coil winding stage, then to cooling, quenching and finally cyclic loading in fatigue analysis.

**Quench detection based on distributed temperature sensing using Rayleigh back scattering:**

Due to slow quench propagation speed in high temperature superconducting conductors, quench detection has been an intense research and engineering topic. Conventional detection methods that based on detecting minor voltage changes are inefficient and sensitive to electromagnetic interferences. Muons Inc. purposed a Rayleigh scattering based optical fiber distributed temperature sensing technology for quench detection. This method allow a quench detection mechanism to monitor continuously the temperature profile along the entire length of the fiber, which is co-wound with the winding conductor or attached at strategic locations of a coil. This allows an effective and efficient, safe and reliable detection method immune to electromagnetic interference to be designed. NCSU’s computational efforts in this project is to perform computational analysis on a sample coil to characterize the coil’s quench behavior and to find methods to define the specifications for data acquisition and processing (DAQ) required for reliable and safe quench detection and protection.

**Computational design analysis of a novel, high performance SMES system:**

This effort uses electromagnetic, thermal and structural analyses to study and characterize the electrical, thermal and structural behaviors of a novel SMES technology. The analyses allows engineers to survey the feasibility of a certain design approach and select appropriate design parameters that results in satisfied performance of a purposed SMES design. Optimization is also performed to select design parameters such as shape factor that gives maximal stored energy/cost-weight factor and better structural integrity.

**AC losses analysis:**

This ongoing work focuses on developing new modeling methods for calculating electromagnetic field and AC losses occur in superconducting coated composite conductor which is composed of laminated high-aspect-ratio thin films.

**Optimization and parameter identification:**

One of our future computational efforts will focus on making simulation-based optimization a practical tool for designing large scale superconducting devices. An optimization process performs iteratively hundreds to thousands of searches through the design parameter space to find a local or ultimately, a global solution that satisfies the objective function subjected to design constraints. Each search involves a full-scale forward simulation of the model, which may take many hours to complete. This computation intensive task renders optimization with full-scale model impractical. One promising approach to overcome this problem is using model reduction techniques to reformulate the full-scale model with a surrogate model of much smaller scale. This will speed up each forward simulation step in the optimization process many order of magnitude in computational speed, thus making the optimization a practical task.

Even a model built with accurate governing equations which describe the underlying physics is only as accurate as the material properties it is using. Oftentimes, some of the material properties used in a model are unavailable simply because they are too new or very difficult to be obtained experimentally. Our team has developed computational techniques to estimate the unknown properties of the materials in question. One way to do this kind of parameter identification is to perform inverse simulation with least-square optimization to “curve-fitting” the simulation results against some experimentally observable parametric results.