Uncertainty Evaluation on Multi-Hole Aerodynamic Pressure Probes

In the frame of a continuous improving of the performance and of the accuracy in experimental tests, the uncertainty analysis on measurements instrumentation and techniques is of paramount importance. For this reason, since the beginning of the experimental activities at the Fluid Machines Laboratory located at Politecnico di Milano (Italy), this issue was addressed and different methodologies were applied.

In the present paper, a review of the different methodologies used is proposed and for each of them a detailed description is provided. The chosen probes for this investigation are a pneumatic 5 hole probe and fast response 2 sensors probe, the latter applied as a virtual 4 hole probe.

During the calibration of multi-hole probes, a set of calibration coefficients has to be defined to correlate the probe pressure taps readings with the static and total pressures, the flow angles and Mach number.

These calibration coefficients, included in calibration matrices, are then used during the probe application in the experimental rigs to recover the unknown flow properties. 

The uncertainty quantification, needed to find out the final uncertainty on the flow properties, starts with the transducers calibration; the second step is the evaluation of the uncertainty in the calibration matrices to end up with the uncertainty quantification in the unknown flow.

Therefore, the purpose of this paper is to show and discuss three different methodologies for the uncertainty quantification of the flow quantities, highlighting their strengths and weakness.

The easiest methodology consists in applying the probe, after having calibrated it, in a known flow and, by making use of the calibration matrices, evaluating the flow properties: the accuracy is calculated by the difference between the imposed flow quantities and the calculated ones.

One of the widespread methodology makes use of the uncertainty propagation techniques: this methodology is applied both in the calibration process, where the calibration coefficients are calculated and their uncertainty quantified. When the unknown flow is measured, the final uncertainty includes the ones of the actual pressure readings and of the calibration coefficients.

The last methodology makes use of the Monte Carlo based approach, applied both in the calibration phase and in the measuring one. In this methodology, different probability functions have been imposed to the different uncertainty contributions.

The uncertainty contributions during the pressure transducer calibration refers to the analog to digital conversion, the reference transducer, the standard deviation of the voltage signals, the repeatability in the measuring, the transducers linearity. In addition to the aforementioned probes values, for the evaluation of probes uncertainty, the angular positioning, calibration coefficients and nozzle static and total pressures errors have to be included.