Assessment of Unsteady Pressure Measurement Uncertainty—Part I: Single Sensor Probe

Abstract

With the advancements in miniaturization and temperature capabilities of piezoresistive 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. 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 (LP) 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 average (PLA) and ensemble average are presented in this contribution. 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 multihole pneumatic probes in size, preventing the use of multihole 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 PLAs 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 by the authors in Dell'Era et al. (2016, “Assessment of Unsteady Pressure Measurement Uncertainty—Part II: Virtual Three Hole Probe,” ASME J. Eng. Gas Turbines Power, 138(4), p. 041602). In the virtual three-hole mode, similar to that of a single sensor probe, higher uncertainty values are observed at regions of higher unsteadiness.

Characterization of Periodic Incoming Wakes in a Low-Pressure Turbine Cascade Test Section by Means of a Fast-Response Single Sensor Virtual Three-Hole Probe

“…/d ≈ 25) would lead to significant errors in the measurement of the time mean total pressure downstream of the bars if one was to use a conventional pneumatic (directional) probe [2]. For this reason, a directional probe with a single fast-response pressure sensor has been used in a virtual three-hole mode, as described by Mersinligil et al [8] and by Dell'Era et al [9,10].…”

Uncertainty quantification for aerodynamic pressure probes, using adaptive quasi-Monte Carlo

“…In this approach the Gaussian error propagation (GEP) formula is used to combine the elemental uncertainties. The propagation of uncertainties for a 1-sensor UPP, employing the ASME PTC 19.1 standard, is described in [12,13]. The two standards group the uncertainties in a different fashion but treat them similarly; propagating the uncertainties using a Taylor's series expansion.…”

“…Typically, a first order approximation of the Taylor's series can be used if the measurement model is assumed linear, as in [12,13]. If the linearization of the model provides poor representation or the output probability density function (PDF) departs appreciably from Gaussianity, higher order terms of the expansion need to be included [2].…”

A Fast Measuring Method for the Inner Diameter of Coaxial Holes

“…As the confused structure of coaxial hole parts, the contact probes cannot get all coordinates of measured points in some deep holes. Pneumatic gauging has the advantages of non-contact and high precision [7], its precision can commonly achieve 0.5 μm accuracy. Excessive air tightness limits the measuring clearance to less than 100 μm, which results in a small redundancy space for measuring operations.…”