Assessment of Unsteady Pressure Measurement Uncertainty: Part 2 — Virtual Three Hole Probe

With the advancements in miniaturization and temperature capabilities of piezo-resistive pressure sensors, pneumatic probes — which are the long established standard for flow-path pressure measurements in gas turbine environments — are being replaced with unsteady pressure probes. On the other hand, any measured quantity is by definition inherently different from the ‘true’ value, requiring the estimation of the associated errors for determining the validity of the results and establishing respective confidence intervals. In the context of pressure measurements, the calibration uncertainty values, which differ from measurement uncertainties, are typically provided. Even then, the lack of a standard methodology is evident as uncertainties are often reported without appropriate confidence intervals. Moreover, no time-resolved measurement uncertainty analysis has come to the attention of the authors. The objective of this paper is to present a standard method for the estimation of the uncertainties related to measurements performed using single sensor unsteady pressure probes, with the help of measurements obtained in a one and a half stage low pressure high speed axial compressor test rig as an example. The methodology presented is also valid for similar applications involving the use of steady or unsteady sensors and instruments. The static calibration uncertainty, steady measurement uncertainties and unsteady measurement uncertainties based on phase-locked and ensemble averages are presented by the authors in [1]. Depending on the number of points used for the averaging, different values for uncertainty have been observed, underlining the importance of having greater number of samples. For unsteady flows, higher uncertainties have been observed at regions of higher unsteadiness such as tip leakage vortices, hub corner vortices and blade wakes. Unfortunately, the state of the art in single-sensor miniature unsteady pressure probes is comparable to multi-hole pneumatic probes in size, preventing the use of multi-hole unsteady probes in turbomachinery environments. However, the angular calibration properties of a single sensor probe obtained via an aerodynamic calibration may further be exploited as if a three-hole directional probe is employed, yielding corrected total pressure, unsteady yaw angle, static pressure and Mach number distributions based on the phase-locked averages with the expense of losing the time-correlation between the virtual ports. The aerodynamic calibration and derivation process are presented together with the assessment of the uncertainties associated to these derived quantities in this contribution. In the virtual three-hole mode, similar to that of a single-sensor probe, higher uncertainty values are observed at regions of higher unsteadiness.