(126f) Analysis of Velocity PDFs and Higher Order Statistics in Polymer-Modified Channel Flow Turbulence
In an effort to further understand the impact of viscoelasticity in modifying inertial turbulence, leading to drag reduction, we present here further statistical evaluation of velocity data collected during large scale numerical simulations of turbulent viscoelastic flow in a channel using the Giesekus constitutive model. More specifically, we examine the way the probability distribution functions (PDF) of the velocity and velocity derivatives and their corresponding 3rd and 4th moments are changed at various distances from the wall. Those PDFs were studied in the past primarily in Newtonian turbulence were they have been found to significantly depart from normal (Gaussian) statistics, as a result, in part, of the intermittency in the flow and the influence of coherent motions on local statistics. Just last year we have reported their study with the presence of polymers and found that those nonGaussian characteristics were even more pronounced, in accordance to the higher intermittency of viscoelastic turbulent flow(1).
In the present work we further quantify these polymeric effects on the velocity and velocity derivatives PDFs. For the first time, we focused on the shape of the most pronounced nonGaussian effects, the ?fat? tails. As a result to ?fat? tails, the probability of otherwise characterized as very improbable events (excursions tens of standard deviations away from the mean) become for these particular distributions much more likely and fairly plausible. Whereas before the analysis was based on an ad-hoc standard histogram procedure, which is for these rare events full of noise and ambiguity, we developed here a much more systematic procedure based on an analysis of the cumulative probability functions and on the implementation of rigorous statistical criteria for rare events, like the Hill estimator. We show that, with viscoelasticity and at certain locations near the wall, the PDFs exhibit ?fat? tails falling with a power law and sufficiently slow so that some of their higher moments (above 3) are not even finite. The more general implications of this work to the modeling of viscoelastic turbulence are going to be underlined.
(1) G. Samanta, K.D. Housiadas, R.A. Handler and A.N. Beris, 2009, ?Effects of Viscoelasticity on the Probability Density Functions in Turbulent Channel Flow,? Phys. Fluids, 21: article 115106.