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Research Papers: Gas Turbines: Turbomachinery

Evaluation of Measurement Uncertainties for Pneumatic Multihole Probes Using a Monte Carlo Method

[+] Author and Article Information
Magnus Hölle

Institute of Jet Propulsion and Turbomachinery,
RWTH Aachen University,
Templergraben 55,
Aachen 52062, Germany
e-mail: hoelle@ist.rwth-aachen.de

Christian Bartsch

Institute of Jet Propulsion and Turbomachinery,
RWTH Aachen University,
Templergraben 55,
Aachen 52062, Germany
e-mail: christian.bartsch@lhind.dlh.de

Peter Jeschke

Institute of Jet Propulsion and Turbomachinery,
RWTH Aachen University,
Templergraben 55,
Aachen 52062, Germany
e-mail: jeschke@ist.rwth-aachen.de

1Corresponding author.

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received August 8, 2016; final manuscript received December 13, 2016; published online March 7, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(7), 072605 (Mar 07, 2017) (8 pages) Paper No: GTP-16-1395; doi: 10.1115/1.4035626 History: Received August 08, 2016; Revised December 13, 2016

The subject of this paper is a statistical method for the evaluation of the uncertainties for pneumatic multihole probe measurements. The method can be applied to different types of evaluation algorithms and is suitable for steady flow-field measurements in compressible flows. The evaluation of uncertainties is performed by a Monte Carlo method (MCM). Each calibration and measurement input quantity are randomly varied on the basis of its corresponding probability density function (PDF) and propagated through the deterministic parameter evaluation algorithm. Other than linear Taylor series based uncertainty evaluation methods, the MCM features several advantages: it does not suffer from lower-order expansion errors and can therefore reproduce nonlinearity effects. Furthermore, different types of PDFs can be assumed for the input quantities, and the corresponding coverage intervals can be calculated for any coverage probability. To demonstrate the uncertainty evaluation, a calibration and subsequent measurements in the wake of an airfoil with a five-hole probe are performed. The MCM is applied to different parameter evaluation algorithms. It is found that the MCM cannot be applied to polynomial curve fits, if the differences between the calibration data and the polynomial curve fits are of the same order of magnitude compared to the calibration uncertainty. Since this method has not yet been used for the evaluation of measurement uncertainties for pneumatic multihole probes, the aim of this paper is to present a highly accurate and easy-to-implement uncertainty evaluation method.

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Figures

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Fig. 1

Propagation of distributions for N = 3 independent input quantities according to Ref. [12]

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Fig. 2

Flow chart visualizing the evaluation of uncertainties using MCM

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Fig. 3

Five-hole probe: (a) pressure taps and angle convention and (b) probe head

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Fig. 4

MCM model for calibration and measurement

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Fig. 5

Probe calibration setup

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Fig. 6

Measurement in the wake of a symmetrical profile

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Fig. 7

Approximation of polynomial curve fit

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Fig. 8

Φapprox/u(Φcal) for total pressure calibration data at Ma=0.5

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Fig. 9

Convergence history averaged for entire traverse

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Fig. 10

Histogram of static pressure at η=1.2  mm compared to normal PDF

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Fig. 11

Total pressure and 95% cov. interval in the wake

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Fig. 12

Static pressure and 95% cov. interval in the wake

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Fig. 13

Yaw angle and 95% cov. interval in the wake

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Fig. 14

Over 95% cov. interval for ps with u(ηtrav,mea)=0  mm

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Fig. 15

Over 95% cov. interval for α with u(ηtrav,mea)=0  mm

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