A correlation to calculate time constant of thermocouples

Abstract

A time constant is the dynamic response time of a thermocouple measuring unsteady flow fields. The measured temperature of a thermocouple is the bead temperature, which is determined by the energy conservation of the bead. Heat transfer of the bead includes convective and radiative heat exchange with the flow, heat conduction with the wires, and surface radiation with the environment. These heat transfer modes affect both the bead temperature and its time constant. The novelty of the paper is to derive a correlation for calculating the time constant of a thermocouple based on the bead energy conservation, covering a wide range of conditions and explicitly reflecting the contribution of surface radiation and conduction. The correlation involves the parameter β related to surface radiation and the parameter cl related to conduction. The correlation for β is obtained by fitting the time constant of small beads in the flows with step change parameters using CFD simulations, while the parameter cl is obtained by fitting the time constant of thermocouples under varying flow conditions using CFD simulations. The relative errors between the calculated time constants with the correlation and those of the CFD simulations are less than 19%. The CFD simulations indicate that the time constants considering radiation and conduction are 33–49% of those considering only the effect of convection for the tested cases. The S type and K type thermocouples were used to measure the standard Hencken flames. By applying current loads and then removing them, the dynamic response curves and the time constants of the thermocouples are obtained. The maximum errors between the calculated time constants with the correlation and the experimental values are less than 10%.