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

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Virginia Tech

Flow temperature sensing remains important for many hypersonic aerodynamics and propulsion applications. Flight test applications, in particular, demand robust and accurate sensing, making thermocouple sensors attractive. Even for these extremely well-developed sensors, the prediction of stresses (hoop, radial, and axial) within thermocouple sheaths for custom-configured probes remains a topic of great concern for ensuring adequate lifetime of sensors. In contemporary practice, high-fidelity simulations must be run to prove if a new design will work at all, albeit at significant time and expense. Given the time and money 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 Thesis address the need for hypersonic flow temperature sensor structural predictions which are compatible with rapid design iteration. The derivation and implementation of a new analytical, low-order model to predict stresses (hoop, radial, and axial) within the sheath of a thermocouple are provided. The analytical model is compared to high-fidelity ANSYS mechanical simulations as well as simplified experimental data. The predictions using the newly developed structural low-order model are in excellent agreement with the numerically simulated results and experimental results with an absolute maximum percent error of approximately 4% and 9.5%, respectively, thus validating the model. A MATLAB GUI composed of the combination of a thermal low-order model outlined in additional references [1] through [6] and the new structural low-order model for thermocouples was developed. This code is capable of solving a highly generalized version of the 1-D pin fin equation, allowing for the solution of the temperature distribution in a sensor taking into account conduction, convection, and radiation heat transfer which is not possible with other existing analytical solutions. This temperature distribution is then used in the analytical structural low-order model. This combination allows for the thermal and structural performance of a thermocouple to be found analytically and compared quickly with other designs.

Thermocouples, Survivability, Low-Order Modeling, Lamé’s Stresses, Hypersonics, High-Temperature