chimney stacks or flames from petrochemical plants, discharge of sewage or waste heat into rivers or oceans, film cooling of turbine blades, thermal plumes rising into cross winds in the atmosphere, exhaust gas discharged to atmosphere from automobile engine, thermal plumes generated near ground level by volcanoes, thunderstorms, or forest fires that can often rise to heights in the atmosphere where significant crossflow exists, etc.
The problem is also important from the fundamental research point of view, as many complex fluid dynamics phenomena such as vortices, flow reversal, entrainment and mixings are involved with it. The problem represents both free-shear flows (jet) and boundary-layer flows (crossflow). After interactions of both the flows, the flow field becomes complex. It is also characterized by the streamline curvature and different types of vortices are formed due to interactions of the jet and crossflow.
The configuration of a rectangular jet in crossflow is shown in Fig. 1.1. The axis of the jet is usually defined as the locus of the maximum velocity or total pressure. The main parameter which characterizes jet in crossflow is the jet-to-crossflow velocity ratio, R (= vj/ua) or the momentum flux ratio J (= R2)
a j
ρ
ρ . The low velocity ratio (R <
0.5) is seen in the case of turbine blade cooling whereas 1< R < 10 is found in the case of jet stabilisation in the combustion chamber. The jet with R > 10 is characterised with free jet characteristics. In confined jets, the normalized wall distance may also be an important factor, if the distance is not too large. In the multiple jets the normalized distance between two jets is an additional parameter. As shown in Fig. 1.1, the whole flow field of a jet in crossflow can be classified in three distinct regions (Demuren, 1986, Sherif and Pletcher, 1990 and Said et al., 2005). In the first region (I), the initially uniform jet flow interacts with the ambient crossflow causing a shear layer to develop at the jet boundaries. Upstream of this region, the crossflow is decelerated and a positive pressure region is formed. The length of the initial region depends on the jet cross-section, velocity ratio and jet discharge Reynolds number. The second region (II) is the main region or the established flow region, where the jet experiences large deflection. Two mechanisms have been claimed in the literature to explain this deflection: (a) the pressure gradient between the upstream (high) and downstream (low) flow over the bottom wall at the jet exit; and (b) the entrainment between the jet flow and the crossflow stream. The second region is complex, being characterized by
the development of turbulence mixing layer around the jet boundaries and the flow becomes fully turbulent. Due to the shearing action of the crossflow, the jet sides experience strong lateral spread. The third region (III) is the far-field region, where the jet axis approaches the crossflow direction asymptotically and the flow field becomes nearly self-similar. In this region, the magnitude and direction of the jet velocity are close to those of the crossflowing stream and it becomes difficult to distinguish between crossflow and jet fluids.
Vortical flow evolution around a jet in crossflow has been of considerable interest for some time and the subject of several investigations. This is mainly due to its wide application in the vast array of engineering problems and the complex mechanisms of interaction between the jet and the cross-stream. The structurally interesting phenomena observed in jet in a crossflow are the formation of (i) roll-up in the jet- shear layer vortices; (ii) formation of the counter-rotating vortex pair; (iii) a horse- shoe vortex system in the crossflow boundary layer upstream from the jet exit; and (iv) the creation of wake vortices (Fric and Roshko, 1994 and Kelso et al., 1996).
Fig.1.2 (reproduced from Fric and Roshko, 1994) shows a schematic of these major vortex systems for a typical round jet in a crossflow. Some of these vortical structures have been found to be responsible for a significant entrainment of the crossflow fluid by the jet as the latter penetrates into the former.
Fig. 1.2: Different vortices associated in the flow field of jet in crossflow (reproduced with permission from Fric and Roshko, 1994).
The shear layer vortices form near the initial region of the jet due to the interaction of the uniform jet velocity and the crossflow. These form on the leeward and
windward edges of the jet and have been attributed to Kelvin-Helmholtz type instabilities (Kelso et al., 1996 and Andreoplous and Rodi, 1984). Due to the adverse pressure gradient upstream of the jet, a horseshoe vortex system is formed which wraps around the base of the jet and travels downstream. The wake vortices form in the second region and at the inner part of the jet. The wake vortices are initiated by the entrainment of the crossflow boundary-layer into the wake and the upward re- orientation of the entrained flow into the wake structures. Lim et al. (1992) observed that the size of the wake region depends upon the velocity ratio (R). For high velocity ratios (R > 2), the jet penetrates significantly into the crossflow and it bends over far enough downstream of the injection hole. Therefore for these types of jets, there is little influence of the wall on its development. Moreover there is a little effect of the crossflow boundary layer characteristics on the flow for high values of R as the jet is able to penetrate through a relatively thin boundary layer. On the other hand for low velocity ratios (R < 1) the jet bends over into the wall at a small downstream distance and then it spreads over the wall. There is a lack of the wake region downstream of the jet injection hole and the jet behaves like a wall jet. In this type of situation, the jet flow is unable to cross the crossflow boundary layer thus producing less complex flow behaviour in the near-field of the jet compared to that with a high value of R.
The counter-rotating vortex pair (CRVP) forms at the vertical plane just after the jet hole and it becomes dominant structures in the downstream of the flow field. These are formed due to both the shearing between the jet and the crossflow and the vorticity issuing from the jet-hole exit (Andreoplous and Rodi, 1984). In fact, this feature appears even in the steady and laminar numerical calculations of the flow, and it seems to be qualitatively independent of the velocity ratio, Reynolds number, and the shape of the nozzle. Besides these four structures, some authors (Kelso et al., 1996, Peterson and Plesniak, 2002, Haven and Kurosaka, 1997, Kuzo, 1995 and Hale et al., 2000) have reported the presence of secondary vortices in the flow field. They have found an additional pair of counter-rotating vortex located between the jet and wall, thus bifurcating the traditional CRVP.
In most practical situations, jets and plumes are either discharged vertically or at an angle to a crossflow. In such flow conditions the jet and crossflow interaction and thermal spread are extremely important flow properties. Accordingly when the temperature field is strongly affected by the velocity field, temperature can be regarded as a passive scalar, it is necessary to understand the mean and fluctuating
characteristics of the thermal spread and mixing in such jets in crossflow. The flow behaviour and heat transfer analysis of a heated jet in crossflow are reported by several researchers (for example by Wark and Foss, 1998, Chen and Hwang, 1991, Sherif and Pletcher, 1991, Nishiyama et al., 1993, Sarkar and Bose, 1995, Hwang and Chiang, 1995, Shi et al., 2003 and Said et al., 2003).
Even though extensive studies have been carried out in the past few decades to investigate the problem of jets in crossflow, some aspects of the flow requires a more detailed investigation. These aspects are in terms of resolving the flow physics, the effects of the geometry of nozzle and dimensions of the flow field etc. One of these aspects is the jet in a narrow channel crossflow and this is the subject of the present investigation.