This paper presents the often-neglected correlation terms for uncertainty propagation and shows their importance for rigorous uncertainty analysis. It shows that these terms can be leveraged, often through simple experimental design changes to substantially reduce uncertainty. The efficiency equation is particularly suited to this approach, with order of magnitude uncertainty reductions possible. The paper will present this effect from both a theoretical study and from data measured behind a transonic fan during a distortion response program.
The efficiency equation is particularly suited to improving uncertainty by leveraging the correlation terms because the temperature uncertainty contributes most of the overall uncertainty. Systematic error sources usually dominate thermocouple measurement uncertainty because the slow time response leads to small random errors. The partial derivatives with respect to inlet and outlet total temperature have opposite signs. Correlations between these systematic errors are relatively easy to force through using a single data acquisition system and in-situ calibration standard. This paper presents performance comparisons of these effects for thermocouples. For a 1.35 pressure ratio, 85% efficiency fan, the uncertainty can be reduced by correlation from 85% ± 6.7% to 85% ± 0.48% for typical K-type thermocouples.