Numerical modeling of steady state errors for shielded thermocouples based on conjugate heat transfer analysis

Abstract

In this paper, Conjugate Heat Transfer (CHT) numerical simulation method is implemented to estimate the different sources of steady state errors and their variation characteristics for a typical shielded thermocouple working at free-stream Mach numbers 0.2, 0.3, 0.4, 0.5 and 0.6. 1D physical models with high prediction accuracy and wide applicability, including velocity error model, conduction error model and radiation error model, are proposed. Based on the flow topologies in the shield tube and the Re-Cpb chart by Williamson, the Mach number of the flow around the thermocouple junction is modeled and then a velocity error model is proposed. Temperature deviations between the velocity error model and the CHT simulation results are less than 0.27 K. Considering the actual heat transfer process, a conduction error model is proposed by modeling the heat transfer of the shielded thermocouple as the heat transfer of two fins in series arrangement and propounding a semi-empirical method for predicting the average flow temperature around the shield tube. Temperature deviations between the conduction error model and the CHT simulation results are less than 1.32 K. As for radiation error modeling, the average temperature of the shield tube surface is reasonably estimated, and an equivalent method is introduced to explicitly solve the temperature of shield tube surface with high accuracy. Based on aforementioned parameters, a radiation error model is proposed by evaluating the convective, conductive and radiative heat transfer mechanisms prevalent in the thermocouple junction, shield, duct and flow. Temperature deviations between the radiation model and the CHT simulation results are less than 1.74 K; In order to vindicate the applicability of the proposed models, they are verified at free-stream Mach numbers of 0.1, 0.35 and 0.7. The results show that these models can be used to predict the shielded thermocouple’s steady state errors accurately in a wide Mach number region.