Steady-state error analysis and modeling of water-cooled shielded multi-probe thermocouples

Water-cooled probes resolve operational issues in high-temperature environments but increase steady-state errors, reducing the accuracy of existing models. Therefore, a new steady-state error prediction model incorporating the effects of water cooling is essential. This study employs numerical simulation to analyze the steady-state error magnitude and variation of Water-Cooled Shielded Multi-Probe Thermocouples (WSMTC) at Mach numbers of 0.2 to 0.5. The results indicate that water cooling can increase the probe's steady-state error by a factor of three. To address this issue, we analyzed the probe's flow and heat transfer characteristics. The WSMTC configuration parameters were integrated into the steady-state error prediction model. Additionally, the radiation error prediction model was improved to account for radiative heat transfer between the thermocouple junction, shield, turbine engine casing walls, and surrounding fluid, considering their significant temperature differences. Finally, a steady-state error prediction model for various measurement probes was developed using a multi-fin parallel approach. The constructed model exhibits a maximum error of less than 5 K (0.3% of the total temperature), demonstrating high precision.