Optimal design of E-type coaxial thermocouples for transient heat measurements in shock tunnels

Coaxial thermocouples have been widely used for transient heat transfer measurements in high-enthalpy shock tunnels. The one-dimensional semi-infinite heat conduction theory is typically used for temperature data processing. However, lateral heat transfer occurs due to material differences between the two electrodes and the junction, causing a deviation in the heat flux measurement from the prediction results of the one-dimensional semi-infinite heat conduction theory. Thus, the lateral heat conduction effect should be investigated to improve the accuracy and reliability of heat flux measurements. In this paper, the heat transfer in E-type (Chromel-Constantan) coaxial thermocouples was analyzed by numerically solving the two-dimensional axisymmetric heat conduction equation with the Du Fort-Frankel scheme. The maximum temperature point on the surface of the coaxial thermocouples shifted to the positive electrode during the heating process. The numerical simulation indicated that the surface temperature of the coaxial thermocouples and the derived heat flux were larger than the theoretical value. The heat flux measurement error of the coaxial thermocouples can be reduced by increasing the width of the positive electrode. Hence, 13 combinations of the diameters of positive electrode and negative electrode were designed for analysis. With the increase of positive electrode diameter or decrease of negative electrode, the heat flux measurement error kept on decreasing, which can be lower than 0.5% in some cases. The results of this study can provide a reference for the design and optimization of coaxial thermocouples.