A Mathematical Model for the Characterization of Superconducting Level Sensors

An automated level control in cryogenic systems requires a precise and continuous level measurement. If properly characterized, superconducting level sensors are a viable option for the same. The operation of a superconducting level sensor is based on the difference in the heat transfer from the sensor wire to the liquid and the gaseous phases of the cryogen. The higher heat transfer in the liquid phase results in a superconductive status, whereas the lower heat transfer in the gaseous phase results in a normal conductive status with a voltage drop corresponding to the length of the wire in the gaseous phase. Hence, it demands a judicious selection of the sensor and the operational parameters such as the current input, for an accurate level measurement as well as the reduction of the liquid boil off. In this paper, to simulate the operation of a superconducting level sensor, a model has been developed by taking the steady-state heat balance along the sensor wire. It is then used for the investigation of the sensor current, voltage output at various liquid levels, and temperature profile of the sensor wires of NbTi and MgB
₂
/SS level sensors in LHe. Furthermore, design guidelines have been proposed for an MgB
₂
/SS superconducting level sensor for LH
₂
level measurement. The parameters considered for the analysis are the sensor wire diameter and the active length. In addition, the effect of an external resistor on the sensor operation is also studied.