Analysis of Stresses in Metal Sheathed Thermocouples in High-Temperature Flows

Flight and ground test applications for in-flow and near-wall flow temperature sensing demand robust and accurate sensing, making thermocouple sensors attractive. Even for these extremely well-developed sensors, an accurate prediction of stresses within thermocouple sheaths for custom-configured probes remains a topic of great concern for ensuring an adequate lifetime of sensors. In contemporary practice, high-fidelity simulations must be run to prove survivability, albeit at significant time and expense. Given the resources it takes to run high-fidelity simulations, rapid optimization of sensor configurations is often impossible or, at a minimum, impractical. The developments presented in this paper address the need for high-temperature sensor structural predictions that are compatible with rapid design iteration. The derivation and implementation of a new analytical, low-order model to predict stresses within the sheath of a thermocouple are provided. The analytical model is compared to threedimensional elastic finite element method simulations as well as experimental data from a simplified configuration. The low-order model sheath stress predictions, which are critical to probe survival, are in excellent agreement with the numerically simulated results and experimental results with root-mean-squared percentage errors of approximately 1.2 and 2.6%, respectively, thus, validating the model.