Magneto-Thermal Stability Of Multifilamentary Composite Nb₃Sn Superconducting Wires In Maglev Systems

With the advancement of global technology and economic strength,people’s demand for long-distance fast travel is growing.Traditional wheel-track high-speed trains are mainly driven forward by the adhesive traction between the wheels and rails,and are therefore subject to speed bottlenecks,driving noise,operating vibration,and hill-climbing ability;therefore,magnetic levitation train systems have been adopted by several countries around the world as a train operation system with better performance.However,compared to ordinary normal conduc-tive materials,coils made with superconducting materials have the advantages of high current density and low transmission loss,and thus can generate larger magnetic fields,resulting in greater levitation and traction forces to achieve higher energy utilization efficiency and higher train operating speeds.Current Nb₃Sn superconducting materials make up for the disadvan-tages of expensive high-temperature superconducting materials and immature manufacturing processes,breaking the dilemma that Nb Ti has reached its physical use limit and becoming the material of choice for manufacturing superconducting coils in superconducting magnetic lev-itation systems.However,during the operation of superconducting maglev trains,the Nb₃Sn superconducting coils on the trains with high currents will experience flux jumps under the high-frequency alternating magnetic field generated by the driving coils on the tracks.The flux jumping will lead to a large influx of flux into the superconductor and thus the current-carrying capacity of the superconducting coil will be rapidly reduced.In addition,the movement of the flux will lead to the release of energy in the form of Joule heat,which will cause the overall temperature of the superconducting coil to rise rapidly and,in more serious cases,burn up the whole coil,both of which will affect the normal use of the superconducting coil and sometimes even cause safety accidents.Therefore,the magnetic thermal stability analysis of Nb₃Sn super-conducting coils is the basis to ensure that the superconducting magnetic levitation system can operate smoothly.In this paper,the multi-physical field coupling model of a two-dimensional multi-filament composite Nb₃Sn superconducting coil in fully uncoupled mode is established under the actual working conditions of the superconducting coil,and its flux jump evolution law under different conditions is studied.First,this paper introduces the computational method to calculate the magneto-thermal re-sponse of Nb₃Sn multi-filamentary composite superconducting wires.The control equations of themethod for calculating the electromagnetic response of the model are established in the finite element software COMSOL Multiphysics through the general form partial differential equation module;then the thermal diffusion equation for calculating the temperature distribu-tion of the model is established through the coefficient form partial differential equation,and the electromagnetic field is coupled with the temperature field through the superconducting instan-ton equation.The magnetic field distribution,current distribution,and heat generation power curves are then calculated using the same method for both two-dimensional methods as well as the three-dimensional twisted model,and the accuracy of our method is verified by comparing them with experimentally derived magnetization curves from other literature.Secondly,the flux jump of Nb₃Sn multi-filamentary composite superconducting wire un-der alternating magnetic field in the completely uncoupled case is simulated using themethod,and the effects of the alternating magnetic field frequency and amplitude on the flux jump of the superconducting wire are analyzed,and the critical threshold curves of the frequency and amplitude of the flux jump occurring in the superconducting wire are plotted.Then the ef-fects of background temperature,flux creep index,and boundary heat transfer coefficient on the flux jump of superconducting lines are investigated.The results show that as the ampli-tude decreases,the critical frequency interval for flux jumping becomes larger and then smaller until a certain critical frequency at which no more flux jumping occurs in the superconducting line.In addition,decreasing the background temperature,increasing the flux creep index,and increasing the boundary heat transfer coefficient are more likely to lead to flux jumps.Finally,the strain field under the electromagnetic force distribution calculated in ABAQUS software was imported into COMSOL software to simulate the flux jumping phenomenon,and the flux jumping problem under the force-electric-magnetic-thermal coupling model of Nb₃Sn multi-filament composite superconducting coil was investigated.The results show that the max-imum stress-strain location in the superconducting coil is distributed in the middle turn of the innermost layer of the coil,and the axial stress-strain distribution is symmetrical.The maximum strain position in the superconducting coil,i.e.,the middle turn of the innermost layer,is more prone to flux jumping.In addition,the small size of the superconducting core wire is effective in suppressing the occurrence of flux jumps.In the small size,the strain causes the flux to change from a jump to a smooth penetration situation,while in the larger size of the superconducting wire,which is more prone to flux jumps,the strain increases the frequency of flux jumps and also makes it more difficult to recover the temperature to the operating temperature after a flux jump occurs.