OFFSET HEIGHT EFFECTS ON TURBULENT CHARACTERISTICS OF SUBMERGED JETS

Abstract

Experimental study of turbulent characteristics of submerged jet near the free surface was carried out at four offset height ratios of 1, 2, 3 and 4. The Reynolds number based on jet exit velocity and nozzle width was 5500. A particle image velocimetry system was used for the velocity measurement. The jet attachment length increased with the offset height. The results showed that the free surface affected the maximum velocity decay and jet spread for the shallower jets. The surface mean velocity and Reynolds normal stresses were quantified and dramatic reduction of surface-normal Reynolds normal stress than its streamwise component was observed in the interaction region. Joint probability density functions were used to investigate the contribution of the turbulent events to Reynolds shear stress. INTRODUCTION Turbulent jets discharged in the vicinity of a free surface are often referred to as submerged jets. Submerged jets have various practical applications which include disposal of industrial effluent into shallow streams, water purification, and in the remote sensing of moving ships. Understanding the mixing characteristics and turbulent structures in submerged jets is important to the design of engineering devices. A schematic diagram of a submerged jet is shown in figure 1. The nozzle of width, d is located near the free surface. The offset height of the center of the nozzle from the free surface is denoted by h. The origin of the Cartesian coordinate system adopted in the present study is located at the center of the nozzle in the jet exit plane; x and y indicate the streamwise and surface-normal direction respectively, U and V indicate the streamwise and surface-normal mean velocities respectively, u and v are the streamwise and surface-normal fluctuating velocities respectively; and Uj is the jet exit velocity. The jet attaches to the free surface upon discharge at the attachment point, xr. The flow field of a submerged jet can be divided into two regions: recirculation region and surface jet region. In the recirculation region, characteristic negative U is found between the upper edge of the jet and the free surface. The streamwise extent of the recirculation region is measured from the nozzle exit to the attachment point and is often reffered to as attachment length. After the recirculation region, surface jet region starts. In the surface jet region, positive U appears at the free surface. One of the salient characteristics of a submerged jet is that the location of local maxumum streamwise mean velocity, Um deviates from the nozzle centerline with the jet development downstream and moves towards the free surface (Anthony and Willmarth, 1992). The dashed line passing through the location of Um as shown in the figure demarcates the two shear layers of the jet. The upper and lower portion of this dashed line is reffered to as upper and lower shear layer, respectively. y0.5 and y0.5 are the distances of the location of 0.5Um measured from the location of Um and the free surface, respectively in the lower shear layer. The mixing characteristics and turbulent structure of free jets have been extensively investigated in the past (e.g., Gutmark et al. 1989; Hussein et al., 1994; Quinn and Militzer, 1988). It is now widely accepted that the entrainment and spreading characteristics of non-circular jets are considerably different from those in a circular nozzle, due largely to the dynamics of coherent structures. Square jets, for instance, have been found to entrain more fluid and spread more rapidly than their circular counterparts because the vortex rings from rectangular nozzles deform more rapidly and to a greater extent than those in circular nozzles (e.g., Gutmark et al. 1989). Although the impact of the turbulent structures on the characteristics of free jets is well documented, much less is known concerning the structure of submerged turbulent jets. The interaction between the vortical structures and the free surface was examined by Anthony and Willmarth (1992) for a submerged round jet placed at depth of h/d = 2. They reported a redistribution of the turbulent kinetic energy from the surface-normal turbulence intensity to the streamwise and spanwise turbulence intensities. Madnia and Bernal (1994) measured the flow characteristics of an axisymmetric jet issuing at various depths (h/d = 1, 1.5, 2.5 and 3.5) beneath and parallel to a free surface. They proposed a model of the free surface as a symmetry plane with the submerged jet interacting with its twin or image jet above the free surface, and h and Ujd/h as the length and velocity scales, respectively, in the surface jet region. Most of the previous studies on submerged turbulent jets used circular nozzles (Madnia and Bernal, 1994; Rainford, and Khan, 2009; Tian et al., 2012; Wallker, et al., 1995). 10 International Symposium on Turbulence and Shear Flow Phenomena (TSFP10), Chicago, USA, July, 2017 2 session.paper The objective of the present study is to investigate the effects of offset height ratio on the mixing characteristics and turbulent structures in a submerged square jet using a particle image velocimetry system. EXPERIMENTAL PROCEDURE The experiments were carried out in an open water channel of length 2500 mm. The cross section of the channel was of dimensions 200 mm × 200 mm. The channel was fabricated from clear acrylic plates that provide easy optical access. A square orifice nozzle of width, d = 10 mm, was used to produce the jet. The following four offset height ratios were tested: h/d = 1, 2, 3 and 4. The Reynolds number (Re) and Froude number (Fr) based on Uj and d were approximately 5500 and 1.7, respectively. A high-resolution particle image velocimetry (PIV) was used to perform the velocity measurements in the vertical symmetry (xy) plane of the jet. The flow was seeded using 10 μm silver coated hollow glass spheres with specific gravity of 1.1. The seeding paricles were illuminated by a 120 mJ per pulse Nd:YAG doublepulsed laser with a wavelength of 532 nm. A 2048 × 2048 pixel CCD camera with pixel pitch of 7.4 μm was used to capture the flow field. The field of view was set to 135 mm × 135 mm. Measurements were carried out in two planes which cover the streamwise extent of the flow field ranging 0 ≤ x/d ≤ 24. Based on an initial convergence test, 5000 image pairs were used to compute the flow statistics. The data were post-processed using the adaptive correlation option of DynamicStudio to obtain the average particle displacement within the interrogation area. The interrogation area size was set as 32 pixels × 32 pixels with 50% overlap in both x and y directions. RESULTS AND DISCUSSION Instantaneous Flow Visualization Figure 2 shows instantaneous velocity vector field for two offset height cases: h/d = 1 and 3 from the jet exit to x/d = 12 which covers recirculation region and a portion of surface jet region. A Galilean decomposition was performed by subtracting a constant convective velocity of 0.15Uj from the instantaneous realizations to reveal small scale vortices propagating at that velocity (Agrawal and Prasad, 2002). The corrugated contour lines of (U-0.15Uj) are also included in the plots to demarcate the turbulent/non-turbulent interface (T/NTI) in the realizations. The contour lines also pass through the centers of the small scale spanwise vortex cores at the edge of the shear layer. Braid-like structures indicated by the darker areas (within 0 < x/d < 7) are also noticed in the plots, which in the vertical symmetry plane, correspond to the vortex rings propagating in the downstream direction. The results presented in figure 2a provide a clear indication that the jet-free surface interaction limits the T/NTI for the shallower jet in the upper shear layer. Attachment Length The attachment length (Lr), measured from the jet exit to the attachment point (xr) is an important characteristic of submerged jets. In the present study, the attachment point was identified as the streamwise location where the streamwise mean velocity profile along the free surface changes from negative to positive value or starts to increase from a nominally zero value. The estimated values of attachment length were Lr/d = 1.0, 6.4, 9.3 and 12.3 for h/d = 1, 2, 3 and 4, respectively. The values are about 14 to 20% higher than those reported by Sankar et al. (2008) for a submerged square jet at Re = 40000. Maximum Velocity Decay and Jet Spread The evolution of the local maximum mean streamwise velocity, Um as a function of x is shown in figure 3a for the four offset heights. Classical scaling Uj and d are used as the velocity and length scale, respectively, for normalization. Um decayed with downstream distance due to the entrainment and mixing of the surrounding fluid with the core jet. The decay rate was estimated by fitting a straight line: Uj/Um = Kd (x/d – c1) in the linear portion of the Um profiles as shown in the figure for h/d = 1, where Kd and c1 represent the decay rate and the kinematic virtual origin, respectively. Kd was estimated as 0.149, 0.176, 0.213 and 0.217 for h/d = 1, 2, 3 and 4, respectively. The increase in the decay rate with the offset height ratio was due to the enhanced entrainment y0.5 h d Uj Recirculation region