The Operational Envelope of Cylindrical Thermocouples: A Coupled Analysis of Aerodynamic Recovery Factor and Structural Deflection Limits

The selection of a temperature probe for aerodynamic applications involves a critical trade-off between the measurement accuracy and structural robustness. While the existing literature typically treats thermal performance and structural limits as isolated problems, this study bridges this gap by introducing a novel coupled experimental framework in which the aerodynamic and structural performance of the probes are characterized and interpreted jointly. Three unshielded, cylindrical K-type thermocouples (diameters: D = 0.5, 1.0, and 1.5 mm) were tested in a freejet facility across a Mach number range of M = 0.05 to 0.50, corresponding to a probe Reynolds number range of ReD≈ 500 to 16,200, at a free cantilever length of L = 70 mm for aerodynamic characterization and L = 20–70 mm for structural characterization. Tests were conducted at a total temperature of approximately To ≈ 291 − 294 K, continuously monitored throughout each run. The recovery factor was highest for the 0.5 mm probe (r ≈ 0.4–0.55) and comparable for the 1.0 mm and 1.5 mm probes (r ≈ 0.29–0.34), such that the largest diameter did not produce the lowest value. Structurally, the 0.5 mm probe reached its deflection limit at M ≈ 0.22, while the 1.0 mm probe remained stable to M ≈ 0.36, for a free length of 70 mm. By treating probe selection as a constrained selection problem rather than an ad hoc decision, this study provides a quantitative operational envelope—a critical, data-driven framework for researchers to balance sensor accuracy and physical viability in aerodynamic testing.