Profundidad de Raíces por Planta en (cm):

The term ‘offset jet’ describes a jet originating from an orifice, located at an offset distance of a few orifice diameters d above a flat surface. The features and characteristic regions are shown schematically in Figure 2.9 for a two-dimensional offset jet exiting from an orifice in a vertical wall (offset distance is denoted with b). Because of the offset, the jet travels a certain distance downstream before attaching to the surface. As it travels further, it would eventually acquire the flow characteristics of a wall jet, defining the longitudinal span of the attachment region, also called impingement region, and the start of the wall jet region. The region upstream of the attachment point is characterised by reverse flow. Compared to a free jet, the offset jet is drawn towards the surface by the Coanda effect, causing a downwards jet trajectory as illustrated in Figure 2.9. The Coanda effect is described by Giles (1977) as follows. Due to the presence of the wall surface, less fluid is available for entrainment on the surface side compared to the free side as the jet expands. This causes a partial vacuum or low pressure area between the surface and the jet, which tends to attract the jet towards the surface.

Rajaratnam & Subramanya (1969) and Pelfrey & Liburdy (1986) reported that downstream of a small developing sub-region within the wall jet region, the flow becomes independent of the offset distance. Both observed velocity profile similarity at a distance from the nozzle of x/d ≈ 20d. For an offset of 7d and Rej of 1.5×104, Pelfrey & Liburdy (1986) reported that the jet attached at x/d = 13. In a similar investigation for an offset of 3d and Rej of 1.78×104, Miller & Comings (1960) observed attachment at x/d = 7. In comparison, a turbulent free jet would have a half-width of 3d at x/d ≈ 12 and 7d at x/d ≈ 30, calculated with a half-width spread angle of approximately 12 degrees, given by Tollmien (1945). This difference can be attributed to the Coanda

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effect and the associated downwards trajectory of the jet, causing the jet to attach earlier. Hoch & Jiji (1981) obtained results for the offset jet trajectory in a parallel freestream, varying the orifice offset at 3d, 5.7d and 8.7d and the ratio of ambient velocity to exit jet velocity β between 0 and 0.25. It is evident that up to 5.7d the attachment point is not influenced by the freestream velocity for the range of β tested, while at 8.7d the attachment is delayed further downstream.

More recent investigations on two-dimensional offset jets have been conducted by Nasr & Lai (1998) and Gao & Ewing (2008). Results by Nasr & Lai (1998) showed that the static pressure variation on the wall surface is independent of Reynolds number for Rej > 1.0×104. They also obtained a relationship for the attachment distance variation with offset ratio, shown in Equation 2.6 where the nomenclature of Figure 2.9 is used.

855 . 0 63 . 2        d b d x_r , for b/d ≤ 20 Equation 2.6 Gao & Ewing (2008) concluded that, based on the variation of jet half-width and maximum velocity, five regions in the flow development could be distinguished for small offsets (≤1.7d) – three within the attachment process (x/d≤6), and two describing the development towards a wall jet. The developed wall jet region was observed to be at x/ d ≥ 10.

Figure 2.9: Offset jet features and nomenclature, adapted from Agelin-Chaab & Tachie (2011b)

Considerably less research has been done on three-dimensional offset jets. McLean and Herring (1976) conducted experiments for a single circular jet at a surface offset of 3d and an array of eleven jets, placed uniformly in lateral direction at spacings

z d b xrp x x z0.5 0.5Umax Uj Umax zmax

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of 35d. They used a high exit jet Mach number of 0.89 at Rej ≈ 4.3×104 and reported that the compressibility effects were limited primarily to the potential core region. For a single jet, the maximum velocity decay was observed to be Umax ~ x – 1.23 between 100 ≤

x/d ≤ 200. The measured entrainment rate up to x/d ≤ 150 agreed well with results for a free jet, implying that the wall had very little effect on the total entrainment. For the array of jets, the entrainment rate was reported to fall below the values for a free jet as soon as adjacent jets began to merge, i.e. x/d ≤ 20. Two-dimensionality of the array of jets, in terms of mean flow characteristics, was observed at x/d ≥ 30.

Nozaki (1983) investigated the effects of nozzle shape and Reynolds number on the attachment of an offset jet for rectangular nozzles of aspect ratio between 1 and 8. Within the range 9.5104 ≤ Rej ≤ 1.02×105, he observed no Reynolds number influence on the attachment flow for aspect ratios larger than 2. Furthermore, the flow behaviour of offset jets of nozzle aspect ratio larger than 3 was shown to be approx. two- dimensional. For smaller aspect ratios, Nozaki (1983) proposed correction factors for calculation of the attachment distance downstream of the nozzle as a function of the offset distance, nozzle aspect ratio and Rej.

Davis and Winarto (1980) and Agelin-Chaab & Tachie (2011b) performed similar experiments with a circular nozzle at offsets between 0.5d and 4d. For Rej ≈ 1.7×105, Davis and Winarto (1980) observed both the lateral and vertical growth rates to decrease and increase with increasing offset respectively. The values varied between 0.32 ≤ dy0.5 / dx ≤ 0.23 and 0.037 ≤ dz0.5 / dx ≤ 0.046 for 0.5 ≤ b / d ≤ 4. Agelin-Chaab &

Tachie (2011b) obtained the growth rates dz0.5/dx = 0.055 ± 0.001 and dy0.5 / dx = 0.250

± 0.005 for a Reynolds number range of 1.0×104≤Rej≤2.0×104. Both investigations confirmed only small differences in the growth rates up to b/d = 2, and reported a similar decay of maximum velocity: Umax ~x– 1.15 by Davies and Winarto (1980) and

Umax ~ x – 1.18 ± 0.03 by Agelin-Chaab & Tachie (2011b). The latter ones also observed the growth rates and maximum velocity decay to be nearly independent of Rej for x / d ≥ 73 and b/d ≤ 2. For b/d = 1, 2 and 4, Agelin-Chaab & Tachie (2011b) reported the attachment distance downstream from the nozzle to be xr/d = 1.5, 3.2 and 6.4 respectively, increasing linearly with b/d and remaining nearly constant within the Reynolds number range tested. These values are larger compared to the two- dimensional offset jet values, calculated from Equation 2.6.