8TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY - PIV09 Melbourne, Victoria, Australia, August 25-28, 2009 Studying the invariants of the velocity-gradient tensor of a round turbulent jet using Tomo-PIV M.Khashehchi 1 , G.E.Elsinga 1 , H.Bornstein 2 , C.Atkinson 2 , A. Ooi 1 , Ivan Marusic 1 , Julio Soria 2 1 Department of Mechanical Engineering, University of Melbourne, Melbourne, Victoria, 3010, AUSTRALIA imarusic@unimelb.edu.au 2 Laboratory for Turbulence Research in Aerospace and Combustion, Department of Aerospace and Mechanical Engineering, Monash University, Clayton, Victoria, 3800, AUSTRALIA julio.soria@eng.monash.edu.au ABSTRACT Turbulence of the round jet has been assessed using invariants of the velocity gradient tensor. Experimental data, obtained using Tomographic Particle Image Velocimetry (Tomo-PIV), using four PCO-4000 cameras with 11 megapixel resolution, is presented for a seeded free air jet, operating in the turbulent regime and the Re number based on the diameter of the nozzle is 10000. Using the acquired 3-D velocity fields, the local statistical and geometrical structure of three-dimensional turbulent flow can be described by properties of the velocity gradient tensor. The invariants of the velocity gradient (R and Q), rate-of-strain ( s R and s Q ), and rate-of-rotation ( w Q ) tensors are analyzed across the turbulent expanding regions at different distances from the nozzle outlet. More specifically, the JPDF of invariants is computed, which allows a detailed statistical characterization of the dynamics, geometry and topology of the flow during the entrainment process. It should be noted that the results obtained are indicative of the preliminary work in this area. 1. INTRODUCTION After more than one century of research, turbulence is still one of the biggest unsolved problems in fluid flows. The round jet has played a key role in turbulent research since the early work of Liepmann and Laufer[1]. The basic aim of control strategies in the round jet is to evaluate the large scale coherent structures outlined by Burattini [2]. These vortical structures play a major role in transporting mass, heat and momentum in the near field of a jet. Coherent structures result from the initial jet instability (laminar region in this paper) through the selective amplification of small disturbances. A fundamental link between the mechanisms of creating coherent structures and initial conditions is not clear. One possibility is to assess transitional region of the jet which is the region between the near-field, where the flow is dominated by a laminar one dimensional structure and the fully turbulent self-similar region which contains vortical structures. In the transitional region of the turbulent jet, as a result of small disturbances in the mean flow, the vorticity vectors have broken into highly complex structures. In this region it may be possible to observe the evolution of the turbulence into the self similar region and interactions due to vortex dynamics. 1-1-Method Of Velocimetry Evaluating the statistical properties of the spatially developing turbulence requires a technique that can resolve the instantaneous three dimensional flow field, with the proper resolution to obtain reliable statistics. Recently, Elsinga (2007)[3] described the tomographic particle image velocimetry technique (Tomo-PIV) that is capable of measuring all three velocity components in a three- dimensional volume. The technique makes use of several simultaneous views of the illuminated particles and utilises 3D reconstruction of light intensity distribution by means of optical tomography. These reconstructive techniques are also outlined by Atkinson and Soria[4]. 1-2-Study of VGT The study of the invariants of the velocity gradient, rate-of- strain, and rate-of-rotation tensors in turbulent flows has been introduced first by Cantwell, Chong et al.[5], [6-7] and [8]. The invariants are scalar quantities whose values are independent of the orientation of the coordinate system and contain information concerning the rates of vortex stretching and rotation, and on the topology and geometry of deformation of the infinitesimal fluid elements. Furthermore, the analysis of the invariants permits the understanding of these issues using a relatively small number of variables. The invariants have been extensively used in several flow configurations such as isotropic turbulence seen in work by Martín, Nomura and Post, Ooi [9-11], turbulent mixing layers investigated by Soria [12] and turbulent channel flows described by Blackburn et al.[13]. Important information is also obtained by analysing the volume integral of the invariants, as shown by Soria et al.[14] In these studies, several “universal” features of turbulent flows were observed. An example of such a result is the well known “teardrop” shape of the joint probability density function (JPDF) of R and Q . Another area of research involving the invariants has been the identification of the coherent structures in turbulent flows, either to visualize the flow regions associated with the presence of vortex tubes which has been performed by Dubief and Delcayre [15] or to identify the regions responsible for the most important dissipation rates of kinetic energy as discussed by Horiuti[16-17] . This paper represents a first attempt to measure, with Tomo- PIV, the development of turbulence from laminar region through the transitional region of a round jet and analyse the evolution of the invariants of the velocity gradient tensor. Field Code Changed