Design of experiments

Abstract

A statistical tool called design of experiments (DOEs) is introduced for uncertainty quantification in particle image velocimetry (PIV). DOE allows to quantify the total uncertainty as well as the systematic uncertainties arising from various experimental factors. The approach is based on measuring a quantity (e.g. time-averaged velocity or Reynolds stresses) several times by varying the levels of the experimental factors which are known to affect the value of the measured quantity. Then, using Analysis of Variances, the total variance in the measured quantity is computed and hence the total uncertainty. Moreover, the analysis provides the individual variances for each of the experimental factors, leading to the estimation of the systematic uncertainties from each factor and their contributions to the total uncertainty. The methodology is assessed for planar PIV measurements of the flow over a NACA0012 airfoil at 15 degrees angle of attack considering five experimental factors, namely camera aperture, inter-frame time separation, interrogation window size, laser sheet thickness and seeding density. Additionally, the methodology is applied to the investigation by stereoscopic PIV of the flow at the outlet of a ducted Boundary Layer Ingesting propulsor. The total uncertainty in the time-averaged velocity as well as the constituent systematic uncertainties due to the experimental factors, namely camera aperture, inter-frame time separation, interrogation window size and stereoscopic camera angle, are quantified.