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

Abstract

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.