Particle image velocimetry, accuracy of the method with particular reference to turbulent flows
Dam, Charlotte Elgaard
In this thesis we present theoretical predications of the error relative to sampling aread when estimating turbulent parameters, such as the mean and rms value, form Particle Image Velocimetry (PIV) measurements. These results emulate similar time-domain analyses for Laser Doppler Velocimetry (LDA). Homogeneous and shear turbulent flow regimes are considered. The key analysis parameter, the mean square error, leads to an expression for the normalised standard error, The correlation coefficient is a prominent factor in the result and the error is evaluated for three distinct forms of this in one and two dimensions. Furthermore the results are simplified to yield general expressions for the error relative to sampling area given the integral lengthscale and rms turbulence level of the flow. The results are applicable, not only to PIV, but to any measurement method that produces results on a spatial domain. Results from PIV measurements of homogeneous isotropic grid turbulence in air and water are presented. The usefulness of the technique is discussed in terms of; the shape of the curve of the correlation coefficient, the resolution obtained relative to the turbulent lengthscales and coherent structures in the flow, and are, whenever possible, compared to LDA measurements. One of the measurements have been performed as a time series, and a number of vector and velocity plots show both the temporal and spatial development of the flow. In order to verify the theoretical predictions, several measurements of the same flow has been collected and a range of subareas of the total accumulated area has been defined. The relevant parameters and normalized standard error have been calculated for each of the sets of subareas. Given the required factors can be provided, we find the experimental and theoretical results in good agreement, proving this to be a useful result.