THE ROLE OF VORTICITY IN TURBULENT, RECTANGULAR, FREE AND WALL JETS

Abstract

Experimental results on the near field development of a rectangular jet with aspect ratio 10 are presented. The jet issues from a sharp-edged orifice attached to a rectangular settling chamber at ReDh ~ 42,000 either in free space or parallel to a flat wall. Measurements on cross plane grids obtained with a twocomponent hot wire anemometry probe, provide information on the three-dimensional characteristics of the flow field. Data were suitably averaged over the symmetrical areas of each cross section. Mean vorticity components and terms of the axial vorticity equation were estimated by interpolation and derivation of the mean velocity measurements. Key features of this type of jet are saddleback mean axial velocity profiles and a predominant dumbbell shape of the axial mean velocity contours. These characteristics are found to be influenced by the axial vorticity distribution, which is related to two terms in the axial mean vorticity transport equation that diffuse fluid from the center of the jet towards its periphery. INTRODUCTION Rectangular free and wall jets have attracted the interest of researchers for many years, since they belong to a class of shear flows which is important for understanding the fundamentals of turbulence but also constitute a generic flow configuration in engineering applications. In the past, experimental studies focussed on the global characteristics of jet velocity decay, growth, the entrainment process and the shape of the mean and turbulent profiles up to the self-similarity zone, while more recent studies focus on the influence of specific inlet and boundary conditions, including aspect ratio, nozzle exit geometry and external boundaries along with the Reynolds number on jet development (see Vouros et al. 2015 and Agelin-Chaab, 2010 for recent reviews). Rectangular free and wall jets present important three dimensional characteristics and although quite early Launder and Rodi (1983) noticed the importance of variables such as the axial vorticity, the available experimental information is rather scarce. Nowadays, it is clear that in order to capture the 3D characteristics of rectangular jets, measurements of the velocity and the vorticity in a volume, i.e. on suitable cross plane grids are required. In this work measurements of the three velocity components, obtained with X-probe hot wire anemometry, on cross plane grids in a free and a wall jet (Schwab, 1986), are further exploited using modern interpolation techniques. The jets are issuing under identical conditions from a 1:10 aspect ratio, sharp-edged, rectangular orifice, at Reh ~ 23,000 based on slot height, h (ReDh ~ 42,000, based on the hydraulic diameter, Dh), indicating that the jets should be fully turbulent, at least beyond the near field (Dimotakis, 2000, Fellouah and Pollard, 2009). The expected symmetries of the distributions are imposed on the experimental data by suitable averaging, taking into account the symmetry properties of each variable. Mean vorticity components and terms of the axial vorticity budget equation are estimated by interpolation and derivation from the mean velocity measurements (Vouros et al. 2015, Panidis et al. 2016). Contour plots of flow characteristics including mean velocity components, normal and shear Reynolds stresses, mean vorticity components and terms of the vorticity budget are presented in the following to discuss the complex underlying flow physics. The configuration of the orifice and the Cartesian coordinate grid used in this work are depicted in fig. 1. In all the following contour plots, a rectangular indicates the location of the exit orifice whereas, black contour lines correspond to streamwise velocity values U/Ucl= 0.5, 0.95 and in some cases 1.05, where Ucl is the local centreline velocity.