A statistical analysis for time-averaged turbulent and fluctuating flow fields using Particle Image Velocimetry

Abstract The significance of the number of vector maps recorded on time-averaged statistics is analysed using Particle Image Velocimetry for a practical application of a radial fan flow. This type of flow has been shown to produce large gradients in both velocity and turbulence intensity, therefore rendering a single-point statistical analysis of the error in time-averaged data unsuitable. First and second order statistics for the entire region of interest have been assessed by varying sample sizes and monitoring the influence on velocity magnitude, turbulence intensities and Reynolds shear stress. Theoretical standard error estimates and an empirical bootstrapping technique have been implemented for determining high confidence levels in the accuracy of the time-averaged quantities. The results illustrate the complex turbulent and fluctuating flows produced by rotating fans, highlighting the requirement to predict sufficient sample numbers during experimentation. In the example presented, and for many practical scenarios where fluctuating flow exists, a trade-off between sample size and accuracy may be necessary using this measurement technique.