Particle image velocimetry measurements of vortex structures in stilling basin of multi-horizontal submerged jets*

CHEN Jian-gang (陈剑刚)

State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China

Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu 610041, China,

E-mail: chenjg@yeah.net.

ZHANG Jian-min (张建民), XU Wei-lin (许唯临), LI Shuai (栗帅), HE Xiao-long (何小泷)

State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China

Particle image velocimetry measurements of vortex structures in stilling basin of multi-horizontal submerged jets*

CHEN Jian-gang (陈剑刚)

State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China

Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu 610041, China,

E-mail: chenjg@yeah.net.

ZHANG Jian-min (张建民), XU Wei-lin (许唯临), LI Shuai (栗帅), HE Xiao-long (何小泷)

State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China

(Received August 13, 2012, Revised November 21, 2012)

Measurements of turbulent flow fields in a stilling basin of multi-horizontal submerged jets were made with the singlecamera Particle Image Velocimetry (PIV). The particle images were captured, processed, and subsequently used to characterize the flow in terms of the 2-D velocity and vorticity distributions. This study shows that the maximum close-to-bed velocity in the stilling basin is approximately reduced by 60%, comparing to the jet velocity at the outlet of orifices. The jet velocity is distributed evenly at the latter half of the stilling basin and the time-averaged velocity of the cross section is reduced by 77%-85%, comparing to the jet velocity at the outlet of orifices. These results show that the vortices with horizontal axes are continuously repeated during the form-merge-split-disappear process. The vertical vortices are continuously formed and disappeared, they appear randomly near the slab and intermittently reach the slab of the stilling basin. The range of these vortices is small. Vortices with horizontal axes and vertical vortices do not coincide in space and the vortices with horizontal axes only affect the position of the tail of the vertical vortices attached to the slab of the stilling basin.

multi-horizontal submerged jets, Particle Image Velocimetry (PIV), vortex structure, stilling basin, hydraulic jump

Introduction

A hydraulic jump is the rapid transition from a supercritical flow to a subcritical free-surface flow and is characterized by the strong turbulence and the air bubble entrainment. A hydraulic jump stilling basin is an important type of energy dissipation structures in hydraulic projects[1]. These structures are subjected to considerable pressure fluctuations because of the dynamics of the turbulence inside the hydraulic jump[2]. Unlike the ski-jump energy dissipater, the underflow energy dissipater has the following features: a stable flow pattern, a high energy dissipation ratio and the weak atomization. However, the close-to-bed velocity is high in a routine hydraulic jump stilling basin. To some extent, the practical engineering applications of these stilling basins are limited, especially in the case of a high water head and a large unit discharge. More than 50% of hydraulic projects with a dam height of less than 100 m use the hydraulic jump energy dissipation. However, the use of the hydraulic jump energy dissipation in dams with heights greater than 100 m is not so common. Many stilling basin slabs would be destroyed in practical projects during their early operation[3,4]. Thus, in many practical projects, the conventional hydraulic jump energy dissipation is not practical.

In this situation, multi-horizontal submerged jetswere proposed as a new type of energy dissipater. They were much studied, with some useful conclusions. Zhang et al.[5,6]derived theoretical equations for the sequent depth and the energy dissipation ratio for submerged hydraulic jumps in the stilling basin of multi-horizontal submerged jets. Deng et al.[7]made a series of experimental studies related with the characteristics of multi-horizontal submerged jets. They found that the flow patterns were quite stable in the presence of changes of the tail water level, under the condition of a large aspect ratio in the stilling basin. Sun et al.[8]found that the contracted orifice width would lead to stable flow patterns in the stilling basin, and increases of the energy loss and reductions of atomization. Huang et al.[9]studied the effect of the drop height on the close-to-bed velocity in the stilling basin. The velocity field in the stilling basin of multi-horizontal submerged jets was studied by using numerical simulations, which showed that there was no perforative vertical whirl in the stilling basin and that the vortex would dissociate on the slab instead of remaining fixed at a particular location[10-13]. However, this conclusion was not verified by experiments.

Fig.1 Schematic diagram of experimental flume

Table 1 Detailed characteristics of the experiments

Because of the complex vortex structure and the strong air entrainment in the stilling basin, it is difficult to create the structure and the intensity of the vortex using routine test methods. With the development of the flow field measurement technology, newmethods were developed, such as the Laser Doppler velocimetry (LDV) and the PIV. In recent years, the technique of the PIV has developed rapidly and has been widely used for the measurement of the flow velocity because it can measure the whole flow field instantaneously[14-16]. In the present work, the detailed hydraulic characteristics of the vortex structure are studied experimentally by using the PIV instrumentation, which is better suited to capture the characteristics of flow dynamics than point measurement techniques such as the LDV and the hot-wire anemometry[17].

This new type of energy dissipater is applied in practical engineering applications. The velocity at the outlet of the crest overflowing orifices and the middischarge orifices is approximately 45 m/s. The Jinsha River, where the hydraulic engineering structure is located, is a sediment-laden river. The vortices in the stilling basin would cause abrasion and damage the slab and the sidewall, which warrants a further study. In this paper, the new nonintrusive technique of the PIV is used to study the vortex characteristics in the stilling basin of multi-horizontal submerged jets.

Fig.2 Streamwise velocity profiles at different locations

1. Experimental setup and PIV measurements

1.1 Experimental setup

The experimental setup, shown in Fig.1, was constructed in the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University. The test flume was made of Plexiglas. The test section consists of a head-water reservoir, a flood discharging section, a stilling basin and a downstream reach. The flood discharging section includes 6 crest overflowing orifices and 5 mid-discharge orifices, which are alternately arranged. The chute widths of the crest overflowing orifices and the mid-discharge orifices are 0.04 m and 0.03 m, respectively. The stilling basin is 1.14 m long and 0.54 m wide. The distances from the inlet of the crest overflowing orifices and the mid-discharge orifices to the slab of the stilling basin are 0.545 m and 0.30 m, respectively. The drop heights of the outlet of the crest overflowing orifices and the mid-discharge orifices are1=S0.08 m and2=S 0.04 m, respectively. The distance from the slab of the stilling basin to the top of the end sill is 0.125 m. The Reynolds number Re=Umaxh/ν[18]is approximately 1.28×105, sufficiently large to neglect the scale effects. Umaxis the maximum time-averaged velocity at the outlet of the jets, h is the water depth at the outlet of the orifices, and ν is the kinematic water viscosity. If the flow follows the quadratic resistance law, i.e., if Re is sufficiently large, the viscous forces can be ignored. The Reynolds number generally satisfies the guidelines recommended by Bose and Hager[19], who proposed a minimum Reynolds number of 105. At theend of the downstream flume, the tail water could be adjusted by a moveable gate. The detailed characteristics of the experiments are shown in Table 1.

Fig.3 The streamlines of vortices with horizontal axes at different times for Run 1 (Y=0.25m)

1.2 PIV method

The velocity was measured with a PIV system, manufactured by TSI, Inc.. Hollow glass beads with a diameter of 10 μm-15 μm and a specific density of 1.05×103kg/m3-1.15×103kg/m3were used in the flow as the tracer particles in the lower Froude number experiments. Particles of this size and density are expected to follow the flow faithfully in this application. In the highest Froude number experiments, however, the significant entrainment of large air bubbles would preclude the use of standard particles. To circumvent this experimental difficulty, the fluorescent particles and a camera filter were used. This combination of particles and filter proves successful in screening out the harmful bubble reflections while transmitting the images of the seed particles. The illuminated layer can be either horizontal or vertical, which allows the measurement of the flow field along the (,)XY and (,)XZ planes. The laser light sheet is produced by a double-pulsed Nd-Yag laser with an energy level of 120 mJ per pulse. The laser light sheet with a thickness of 0.001 m is oriented through the axis of the jet with the camera perpendicular to it. The image calibration is done by taking a picture of a steel ruler with 0.001 m divisions, and it was confirmed that there was negligible distortion over the field of view. All images were acquired with a Nikor charge-coupled device (Powerview Plus 4MP CCD) camera (2 048×2 048 pixels) operating ina dual mode. The object distance is adjusted to achieve the field of view required for each image. The image pairs are acquired at each location with a sampling rate of 4 Hz. With the laser light illumination, two frames could be immediately captured by the camera and then transferred to the processor for crosscorrelation computations. With the correlation analysis, outliers are rejected using the cellular neural network method with a variable threshold technique. Rejected vectors are replaced using a Gaussian-weighted mean of their neighbors. The PIV data are then smoothed to remove the high wave number noises. The steamlines are obtained using Tecplot software embedded in the PIV system.

2. Experimental results and analyses

2.1 Streamwise velocity profiles

In these results, the origin of the coordinate system is the point of intersection between the centerline of the slab and the drop. The streamwise direction -XY is the spanwise direction, and Z is the vertical direction (see Fig.1). To delineate the flow structure, the streamwise (-)XZ velocity profiles along the centerline of the jet are captured up to /X1=10S with three different runs. The vertical profiles of the streamwise velocity at different streamwise locations are shown in Fig.2. The origin of the coordinate system is the intersection of the drop and the centerline of the slab of the stilling basin, where X is the distance from the measuring points to the drop, Y is the distance from the measuring points to the centerline of the stilling basin and Z is the distance from the measuring point to the slab. 1S represents the drop height of the crest overflowing orifices, 2S represents the drop height of the mid-discharge orifices2(=S 0.5S1), U represents the streamwise time-averaged velocity at different locations,maxU represents the maximum time-averaged velocity at the outlet of the jets, and experimental represents the experimental value obtained by using the PIV and WSP stands for the free surface in the stilling basin, measured by using a point gauge in routine model tests.

It can be seen in Fig.2(a) that the velocity decays rapidly as1/XS increases, while the location of the maximum velocity moves down at first and then moves up slightly. Depending on the fact whether the streamlines in the stilling basin are parallel or not, the velocity may or may not be distributed evenly. Thus, the velocity is distributed evenly in the stilling basin when X/S1＞8.0. At the same time, the time-averaged velocity in the stilling basin is approximately 0.20Umax. The main jets are closer to the slab because the drop height is lower in Run 2 than in Run 1. The main jets impact the slab approximately at 1/=XS4.5, and the close-to-bed velocity is approximately 0.30Umax. After the velocity spreads evenly, the timeaveraged velocity in the stilling basin is approximately 0.23Umax, as shown in Fig.2(b). Meanwhile, the velocity of the reverse flow is greater in the upper part of the flow, and the characteristics of the hydraulic jumps are clearly seen on the streamwise profile. The axial velocity of the crest overflowing orifices in Run 3 spreads faster than that in Run 1, as shown in Fig.2(c). The mainstream of the crest overflowing orifices and the mid-discharge orifices impact the slab at the location X/S1=2.0 and X/S1=3.0, respectively. Meanwhile, the close-to-bed velocity is approximately 0.40Umaxat this location. When the jet flow establishes an even distribution, the time-averaged velocity of the cross section is approximately 0.15Umax.

In the three different runs, the main jets are located on the foreside of the stilling basin, as1/XS increases, the main jets continuously diffuse in the stilling basin. The velocity is distributed evenly in the stilling basin when X/S1＞8.0, and the time-averaged velocity of the cross section in the stilling basin is approximately (0.15-0.23)Umax. The velocity variation process of the main jets in Run 3 is different from those in Runs 1 and 2. In Run 3, the main jets dive faster than those in Runs 1 and 2, because of the interaction between the two main jets in the water body, located in the crest overflowing orifices and the middischarge orifices. The close-to-bed velocity in the impact zone is higher in Run 3 than that in Runs 1 and 2. The decay distance of the velocity does not increase when the number of jet orifices increases. This result indicates that the strong mixing is enhanced because of the interaction of the jets in the crest overflowing orifices and the mid-discharge orifices. From the perspective of the energy dissipation and compared with Runs 1 and 2, Run 3, with the same length as Runs 1 and 2, displays the “1+1>2” effect.

2.2 Characteristics of vortices with horizontal axis

The streamlines of vortices with a horizontal axis generated at different points in time by the Tecplot software are shown in Fig.3 for Run 1.The vortices merge and split as well as form and decay within this region of the foreside of the stilling basin. A 0.08 m× 0.05 m vortex with a horizontal axis occurs in the turbulent shear layer near the side-wall at T=(t0+0)s and disappears at T=(t0+1.0)s . However, at T= (t0+2.5)s , two vortices of different sizes occur in the turbulent shear layer, and then, the two vortices mergeinto one vortex. As the time progresses, the vortices continuously form and disappear. The boundary conditions are complicated and strongly turbulent in the stilling basin, therefore, the interaction among the vortices is very strong, and the vortex structure is not regular.

Soon after the appearance of a large vortex in the turbulent shear layer, it will split into smaller vortex structures. The vortex in the turbulent shear layer continuously repeats the process of form-merge-split-disappear. Vortices with horizontal axes are not fixed in one place, rather, they move in a range of 0mX＜＜0.25 m. The distance from the vortex center to the slab of the stilling basin changes continuously. The maximum tangential velocities of the vortices with horizontal axes, near the side-wall of the stilling basin, are approximately 0.50 m/s, 0.35 m/s and 0.71 m/s in Runs 1, 2 and 3, respectively. Compared with the jet flow velocity at the outlet of the orifices (approximately 3.18 m/s), the tangential velocities of the vortices are small in the three different runs. Thus the presence of the vortices with horizontal axes in the stilling basin would not cause the abrasion destruction on the side-wall and the drop.

2.3 Characteristics of vertical vortices

The streamlines of the vertical vortices in the stilling basin are shown in Fig.4 for Run 3. During most of the run, there is a clear vortex structure near the slab of the stilling basin, which indicates that the vertical vortex has reached the slab. The range of the vertical vortex near the slab is approximately 0.025 m×0.025 m, and the location of the vertical vortex changes continuously. Vertical vortices, near the drop, form continuously and then disappear. While some of the vertical vortices form and then immediately disappear, others last for a short time, which indicates that the vertical vortex near the slab of the stilling basin is intermittent and that the vortices above the slab do not appear to be in a fixed location. The vertical vortex is mainly affected by the complex boundary conditions and the strong turbulence in the stilling basin. Because of the asymmetric and random flow patterns in the stilling basin, the vertical vortices appear randomly near the slab.

Fig.5 The movements of vertical vortices with different Z values in the stilling basin for Run 3

The transmission process of the vertical vortices with different distances from the measuring lane to the slab of the stilling basin is shown in Fig.5. It can be seen that a vertical vortex between the main jets moves toward the slab then disappears in the water body (Fig.5). While the vertical vortices formed under the main jets reach the slab of the stilling basin, the maximum range of the vertical vortices is approximately 0.025 m×0.025 m, and they are weak in intensity. The maximum tangential velocities of the vertical vortices in the stilling basin are approximately 0.09 m/s, 0.22 m/s and 0.42 m/s in Runs 1, 2 and 3, respectively. Compared with the maximum close-to-bed velocity near the slab of the stilling basin (approximately 1.28 m/s), the tangential velocity of the vortices is much lower in all three runs. Thus, the presence of the vertical vortices does not cause much abrasion destruction on the slab of the stilling basin of multi-horizontal submerged jets.

3. Conclusions

PIV measurements of a hydraulic jump in the stilling basin of multi-horizontal submerged jets were made, and the vortex structures are studied. Our conclusions are as follows:

(1) In Run 1, the main jets do not clearly impact the slab of the stilling basin. When the downstream water level is low, the flow in the stilling basin has the characteristics of a surface flow pattern. In Run 2, the main jet impacts the slab approximately at1/=XS 4.5, to form a wall jet. The maximum close-to-bed velocity in the stilling basin is approximately 0.4Umaxin Run 3. In the three different runs, the velocity is distributed evenly in the stilling basin when1/XS＞8.0, and the time-averaged velocity of the cross section in the stilling basin is approximately (0.15-0.23)Umax.

(2) The vortex with a horizontal axis in the turbulent shear layer continuously repeats the form-mergesplit-disappear process. Multiple vortices in the instantaneous flow field occur at the same time, and the size and shape of the vortices change continuously.

(3) Vertical vortices appear between the main jets. They move toward the slab and then disappear in the water body. The vertical vortex formed under the main jets reaches the slab of the stilling basin, and the size of the vortex is approximately 0.025 m×0.025 m. The vertical vortices form and disappear continuously and they appear randomly near the slab.

(4) The vortices with a horizontal axis and the vertical vortices do not coincide in space. The vortices with horizontal axes only affect the position of the tail of the vertical vortices attached to the slab of the stilling basin. The scale and the intensity of the vortex near the drop, the side-wall and the slab are small and weak, the vortex structure has only a slight effect on the stability of the drop, the side-wall and the slab of the stilling basin. The vortices in the stilling basin of multi-horizontal submerged jets do not cause a severe abrasion destruction on the slab, the side-wall or the drop.

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10.1016/S1001-6058(11)60396-0

* Project supported by the National Natural Science Foundation of China (Grant Nos. 51279118, 50479062) and the Key Projects in the National Science and Technology Pillar Program (Grant No. 2008BAB29B04).

Biography: CHEN Jian-gang (1982-), Male, Ph. D., Assistant Researcher

ZHANG Jian-min, E-mail: zhangjianmin@scu.edu.cn