Theoretical estimation of quench occurrence and propagation based on generalized thermoelasticity for LTS/HTS tapes triggered by a spot heater

Abstract

The present study deals with the thermal characteristics and mechanical behaviors of low/high temperature superconducting (LTS/HTS) composite tapes during quench processes triggered by a spot heater. Based on the generalized thermoelastic theory, a dynamic thermoelastic model with a relaxation time is developed which takes into account the temperature dependence and finite speed of heat propagation for the superconducting tapes under cryogenic condition. The analyses were performed using the finite element method to solve the coupled differential equations of dynamic heat conduction and elastic equilibrium. The results show that the thermoelastic behaviors exhibit a strong relevance to quench characteristics of the superconductors. As a quench occurs, the thermoelastic strain-rate has an obvious jumping variation with the instant of time of its peak being fortunately coincident with the time at which the critical temperature is reached. Such a jumping change of strain-rate could be a way of estimation and detection of quench occurrence, and the theoretical predictions coincide with the existing experimental observations on thermoelastic strain-rate in LTS magnets. For a HTS tape, the thermoelastic strain-rate or temperature-rate variation and a small jump also are illustrated as the quench occurrence is determined. Additionally, the normal zone propagation velocities for the LTS/HTS tapes are predicted by the critical temperature and thermoelastic strain-rate to show quite good agreements with the results evaluated by Wilson’s formula for a LTS tape or the experimental measurements for a HTS tape. The influences of the relaxation time of heat conduction and thermoelastic coupling on the thermal distribution and strain profile are also discussed in details.