Eigendecomposition model of resistance temperature detector with applications to S-CO2 cycle sensing

Super-critical carbon dioxide (S-CO2) is a promising thermodynamic cycle for advanced nuclear reactors and solar energy conversion applications. Dynamic control of the proposed recompression S-CO2 cycle is accomplished with input from resistance temperature detector (RTD) measurements of the process fluid. One of the challenges in practical implementation of S-CO2 cycle is high corrosion rate of component and sensor materials. In this paper, we develop a mathematical model of RTD sensing using eigendecomposition model of radial heat transfer in a layered long cylinder. We show that the value of RTD time constant primarily depends on the rate of heat transfer from the fluid to the outer wall of RTD. We also show that for typical material properties, RTD time constant can be calculated as the sum of reciprocal eigenvalues of the heat transfer matrix. Using the computational model and a set of RTD and CO2 fluid thermo-physical parameter values, we calculate the value of time constant of thermowell-mounted RTD sensor at the hot side of the precooler in the S-CO2 cycle. The eigendecomposition model of RTD will be used in future studies to model sensor degradation and its impact on control of S-CO2.