Turbulence measurements indicate that, with regard to streamwise turbulence intensity, flow similarity occurs at a certain distance downstream of the orifice. This distance was observed to be x/d ≥110 by Newman et al. (1972), x/h ≥ 60 by Padmanabam & Lakshmana Gowda (1991b), x/d ≥ 40 by Agelin-Chaab & Tachie (2011a), and x/A 0.5 ≥ 30 by Hall & Ewing (2007a). The values of x/d = 110, x/d = 60 and x/d =40 correspond to x/A 0.5≈124, 37 ≤ x/A 0.5 ≤ 67 and x/A 0.5 ≈ 45 respectively, calculated by taking into account the corresponding orifice areas used. These
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differences highlight the influence of the orifice on the flow characteristics. The streamwise turbulence for a three-dimensional circular wall jet was reported by Newman et al. (1972) to be significantly higher (~ 50%) compared to a two-dimensional wall jet, a statement also supported by Abrahamsson et al. (1996).
Using flow visualisation, Newman et al. (1972) observed a strong divergence of the jet pathlines at the wall surface away from the plane of symmetry (see Figure 2.7). Similarly, based on velocity correlation measurements, Davis & Winarto (1980) concluded that the presence of the wall caused an interaction between its surface and the normal component motions towards the surface, which produced “strong out-flow motions along the plane in a symmetrical manner about the plane of symmetry”. They reported the existence of a large-scale motion in a plane perpendicular to the jet flow, indicated by higher levels of measured momentum transport in the lateral direction than in the vertical direction. This motion provides a physical mechanism for the increased mixing parallel to the surface and the resulting high lateral growth rate.
Reviewing the results of Newman et al. (1972) and Davis & Winarto (1980), Launder & Rodi (1983) emphasised the “substantial and sustained streamwise vorticity” created in a three-dimensional wall jet and recognised its importance in the jet’s anisotropic growth pattern. They identified the anisotropy of the Reynolds stresses in the plane at right angles to the flow as one of the potential source of the induced streamwise vorticity. The validity of this statement was confirmed in a computational investigation by Craft & Launder (2001), who attributed the large lateral growth rate entirely to the induced streamwise vorticity.
Figure 2.7: Flow visualisation of the surface pathline pattern of a circular three-dimensional wall jet (by Newman et al., 1972)
An experimental investigation by Iida & Matsuda (1988) also shows evidence of secondary flows, identified by the presence of two pairs of streamwise vortices located in a symmetrical arrangement with respect to the xz plane near the wall (z < zmax) and in
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the mixing region (z>zmax) respectively (see small image in Figure 2.8a, where the vertical and lateral axes are Y and Z respectively, and zmax is denoted as Ym). The
formation mechanism of these vortices was further investigated by Matsuda et al. (1990) for Rej = 1.6×105 and by Ewing & Pollard (1997) for Rej = 2.5×104, using Hot- Wire Anemometry. They found the presence of a large-scale structure very much resembling a horseshoe vortex, which stretched and inclined progressively in the direction of the flow near the surface as it moved downstream (see Figure 2.8a). As a consequence of the inclination, the legs of the horseshoe vortex form counter-rotating quasi-streamwise vortices in the mixing region, identified by Matsuda et al. (1990) as the primary cause of the high lateral growth rate.
Ewing & Pollard (1997) modified the model suggesting that the structures shed by the circular jet were ring-like vortices which interacted with the wall, resulting in the centre of their base being raised off the surface while the outer edges of the base moved closer to the surface. This phenomenon resulted in the formation of two horseshoe vortices, one large near the jet edges and one smaller near the jet centre line, shown with solid and dashed contours respectively in Figure 2.8a. Such modification predicts both pairs of streamwise vortices observed by Iida & Matsuda (1988). Hall & Ewing (2007b) observed a similar pattern of a large horseshoe vortex, associated with the outer shear layers, and a smaller independent structure near the wall.
(a) (b)
Figure 2.8: Proposed models of vortex structures in near-field region of a three-dimensional wall jet according to (a) Matsuda el al., 1990 and (b) Namgyal & Hall, 2013
Y and Z in (a) and y and z in (b) denote the vertical and transverse axes respectively, differing from the notation shown in Figure 2.5
A recent investigation by Hall & Ewing (2010) for square wall jets of Rej = 9×104 showed that the large coherent structures were asymmetric with respect to the jet centre line. Their passage was associated with lateral sweeps of fluid across the entire span of the jet, causing the characteristic large lateral spread.
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Namgyal & Hall (2013) investigated a round wall jet of Rej = 1.2×105 at x/d = 5 using Particle Image Velocimetry attempting to link the formation of mean streamwise vorticity (secondary flow) and the unsteady vorticity of the coherent structures in the near field. They proposed a flow model, shown in Figure 2.8b, which predicts the development of instabilities within the large coherent vortex rings as they travel downstream, which would eventually form into coherent streamwise vortex structures away from the surface, similarly to a free jet. The smaller structures also form streamwise vortex pairs, bound close to the wall, which are not related to the vortices away from the wall, as observed by Hall & Ewing (2007b). Namgyal & Hall (2013) concluded that the coherent vortex structures, formed in the outer shear layers in the near-field region, did not contribute directly to the secondary flow in the plane at right angles to the flow.