TY - JOUR

T1 - PIV uncertainty propagation

AU - Sciacchitano, Andrea

AU - Wieneke, Bernhard

PY - 2016/6/29

Y1 - 2016/6/29

N2 - This paper discusses the propagation of the instantaneous uncertainty of PIV measurements to statistical and instantaneous quantities of interest derived from the velocity field. The expression of the uncertainty of vorticity, velocity divergence, mean value and Reynolds stresses is derived. It is shown that the uncertainty of vorticity and velocity divergence requires the knowledge of the spatial correlation between the error of the x and y particle image displacement, which depends upon the measurement spatial resolution. The uncertainty of statistical quantities is often dominated by the random uncertainty due to the finite sample size and decreases with the square root of the effective number of independent samples. Monte Carlo simulations are conducted to assess the accuracy of the uncertainty propagation formulae. Furthermore, three experimental assessments are carried out. In the first experiment, a turntable is used to simulate a rigid rotation flow field. The estimated uncertainty of the vorticity is compared with the actual vorticity error root-mean-square, with differences between the two quantities within 5-10% for different interrogation window sizes and overlap factors. A turbulent jet flow is investigated in the second experimental assessment. The reference velocity, which is used to compute the reference value of the instantaneous flow properties of interest, is obtained with an auxiliary PIV system, which features a higher dynamic range than the measurement system. Finally, the uncertainty quantification of statistical quantities is assessed via PIV measurements in a cavity flow. The comparison between estimated uncertainty and actual error demonstrates the accuracy of the proposed uncertainty propagation methodology.

AB - This paper discusses the propagation of the instantaneous uncertainty of PIV measurements to statistical and instantaneous quantities of interest derived from the velocity field. The expression of the uncertainty of vorticity, velocity divergence, mean value and Reynolds stresses is derived. It is shown that the uncertainty of vorticity and velocity divergence requires the knowledge of the spatial correlation between the error of the x and y particle image displacement, which depends upon the measurement spatial resolution. The uncertainty of statistical quantities is often dominated by the random uncertainty due to the finite sample size and decreases with the square root of the effective number of independent samples. Monte Carlo simulations are conducted to assess the accuracy of the uncertainty propagation formulae. Furthermore, three experimental assessments are carried out. In the first experiment, a turntable is used to simulate a rigid rotation flow field. The estimated uncertainty of the vorticity is compared with the actual vorticity error root-mean-square, with differences between the two quantities within 5-10% for different interrogation window sizes and overlap factors. A turbulent jet flow is investigated in the second experimental assessment. The reference velocity, which is used to compute the reference value of the instantaneous flow properties of interest, is obtained with an auxiliary PIV system, which features a higher dynamic range than the measurement system. Finally, the uncertainty quantification of statistical quantities is assessed via PIV measurements in a cavity flow. The comparison between estimated uncertainty and actual error demonstrates the accuracy of the proposed uncertainty propagation methodology.

KW - linear error propagation

KW - particle image velocimetry

KW - spatial resolution

KW - uncertainty propagation

KW - uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=84978878126&partnerID=8YFLogxK

UR - http://resolver.tudelft.nl/uuid:b44a7c7a-fece-4dec-905b-c0f84c39c389

U2 - 10.1088/0957-0233/27/8/084006

DO - 10.1088/0957-0233/27/8/084006

M3 - Article

AN - SCOPUS:84978878126

VL - 27

JO - Measurement Science and Technology

JF - Measurement Science and Technology

SN - 0957-0233

IS - 8

M1 - 084006

ER -