Statistical properties of attached and separated wall flows

Abstract

The aim of this work is to study the flow field and wall pressure fluctuations induced by quasi-­‐two-­‐dimensional incompressible turbulent boundary layers overflowing a forward-­‐facing step (FFS). Preliminary to the study of the FFS flow, our attention is oriented to the characterization of incoming boundary layer. It is a zero pressure gradient turbulent boundary layer at high Reynolds numbers (Reθ = 3940 and 7257, based on momentum thickness), and the reason why we study this type of flows is not only to determine the properties of the flow impacting the obstacle but also to validate the experimental set-­‐up and the novel method of investigation adopted in the present approach. A time-­‐resolved two-­‐dimensional particle image velocimetry measurements is used. The boundary layer is obtained on the flat wall of a very large recirculating water channel available at INSEAN (Istituto Nazionale Per Studi Ed Esperienze Di Architettura Navale) and is investigated on a streamwise–wall-­‐ normal plane. Statistical moments of velocity are determined with the aim to analysing high-­‐Reynolds-­‐number effects in profiles obtained in a direction orthogonal to the wall. A careful analysis of the mean velocity profiles for the measured average velocity indicates departures from the classical logarithmic law towards the power law or parametric models. Such a departure seems to be independent on the specific parameters used in model laws. Instantaneous velocity fields are deeply analysed to derive information on the dynamic processes involving the generation and evolution of near-­‐wall vortical structures. Different vortex eduction methods are implemented including Reynolds decomposition, vorticity, invariants of velocity gradient tensor and wavelet tools and compared. The agreement of the results achived with these methods is rather good, so all of them are used to derive information on wall dynamics. Independtly of the Reynolds numbers, packets of vortical structures are observed to form and to evolve aligned more or less at an angle of 30˚ with respect to wall. In order to quantify the importance of such ‘coherent’ phenomena over the entire range of turbulent structures, probability density functions of the vortical structure size (obtained from wavelet analysis) are determined. The results show the existence of a hierarchical relation between coherent vortices, the average vortex size being almost equal to 1/10 of the boundary layer displacement thickness. The measured data are consistent with the formation of about seven large ‘children’ vortices from each ‘parent’ vortex. After concluding the study of the attached flow of TBL and after have confirmed the goodness of the methodology and the experimental set-­‐up used we went to study the forward facing step flows. The study of the separated flow is focussed on the statistical characterization of the pressure fluctuations that are measured upstream and downstream of an instrumented FFS step model installed inside a large scale recirculation water tunnel. Two-­‐dimensional (2D) velocity fields are measured as well close to the step via 2D particle image velocimetry (PIV). The overall flow physics is studied in terms of averaged velocity and vorticity fields for different Reynolds numbers based on the step’s height. The wall pressure statistics are analyzed in terms of several indicators, including the root mean square and probability density functions of the pressure fluctuations, demonstrating that the most relevant flow structure is the unsteady recirculation bubble formed at the reattachment region downstream of the step. Pressure spectra and cross correlations are computed as well, and the convection velocity characterizing the propagation of hydrodynamic perturbations is determined as a function of the distance to the vertical side of the step. The simultaneous measurement of time-­‐resolved PIV fields and wall pressure signals enabled us to compute the pressure/velocity cross correlations in the region downstream of the step and substantiated the relevant role played by the recirculation bubble.