Corrective measures in turbulent pipe flows and extended self-similarity

Significant statistical bias in LDA measurements and how to adequately deal with it is a subtle problem when dealing with turbulent flows. In order to attempt a clarification we have performed measurements on a non-standard " grid experiment" where a clear bias effect is found. We have investigated t he effect of several corrective measures and find that best results, in the sense of having the first moment converge to zero, are obtained when using the time between events as statistical weights. The corrected time series have been used to check for extended self-similarity (ESS). Even though no scaling regime is seen for the third moment and the flow certainly is neith er isotropic nor homogeneous, perfect ESS scaling based on the absolute thi rd moment is observed up to the twelfth moment, extending into a time domai n regime where the Taylor hypothesis of frozen turbulence is obviously viol ated. Reversing the argument this indicates that the correction scheme need ed can be experimentally decided on using the criterion stated above and es pecially so if ESS is to be expected. Finally we have used the corrected da ta to quantify the deviations from Gaussian behavior of the velocity differ ence probability density function for a weakly turbulent flow. Through comp arison with results on the Gaussian-Lorentzian distribution we find that th e even part of the experimental distribution can be reproduced quite well b y a single-parameter family of distributions with second moment equal unity .