Evaluation of the topological characteristics of the turbulent flow in a 'box of turbulence' through 2D time-resolved particle image velocimetry

The experimental evaluation of the topological characteristics of the turbulent flow in a 'box' of homogeneous and isotropic turbulence (HIT) with zero mean velocity is presented. This requires an initial evaluation of the effect of signal noise on measurement of velocity invariants. The joint probability distribution functions (pdfs) of experimentally evaluated, noise contaminated, velocity invariants have a different shape than the corresponding noise-free joint pdfs obtained from the DNS data of the Johns Hopkins University (JHU) open resource HIT database. A noise model, based on Gaussian and impulsive Salt and Pepper noise, is established and added artificially to the DNS velocity vector field of the JHU database. Digital filtering methods, based on Median and Wiener Filters, are chosen to eliminate the modeled noise source and their capacity to restore the joint pdfs of velocity invariants to that of the noise-free DNS data is examined. The remaining errors after filtering are quantified by evaluating the global mean velocity, turbulent kinetic energy and global turbulent homogeneity, assessed through the behavior of the ratio of the standard deviation of the velocity fluctuations in two directions, the energy spectrum of the velocity fluctuations and the eigenvalues of the rate-of-strain tensor. A method of data filtering, based on median filtered velocity using different median filter window size, is used to quantify the clustering of zero velocity points of the turbulent field using the radial distribution function (RDF) and Voronoo analysis to analyze the 2D time-resolved particle image velocimetry (TR-PIV) velocity measurements. It was found that a median filter with window size 3 x 3 vector spacing is the effective and efficient approach to eliminate the experimental noise from PIV measured velocity images to a satisfactory level and extract the statistical two-dimensional topological turbulent flow patterns.