NEAR FREE

NEAR FREE-SURFACE FLOW CHARACTERISTICS IN A JET AGITATED TANK

Aldo Tamburrino¹, Alan Mourgues² and Claudio Aravena²

¹Associate Professor, ²Research Assistant

Water Resources and Environmental Division, Department of Civil Engineering, University of Chile, Casilla 228-3, Santiago-CHILE, Phone (56-2) 696 8448,

Fax: (56-2) 689 4171 E-mail: atamburr@cec.uchile.cl

Abstract: Preliminary results of an experimental study carried out in a tank filled with water agitated by means of jets located at the bottom are reported in this paper. Flow visualization and PIV techniques were used to characterize the flow near the free surface. From the velocity records, the turbulent kinetic energy and velocity spectra were computed. They show the energy decay and its redistribution having place close to the free surface. Flow visualization allowed us to define a flow pattern formed by a series of quasi-periodical events near the free surface.

Keywords: turbulence, flow Structures. jet agitated tank. turbulent kinetic energy. turbulence decay.

1 INTRODUCTION AND OBJECTIVES

Phenomena occurring at and near the free surface of turbulent flows play an important role in the mass and heat transfer mechanisms across the air-water interface. A better knowledge of the flow field close to the free surface, and the turbulent structures taking place close to it, will help us for a better understanding of the transport mechanisms.

Although turbulent flows have been studied more than a century, there is no a general description of them yet. The equations governing the phenomenon have been analyzed in detail, but for practical purposes, there always is a need for some empirical data.

Near the free surface there is an interaction between the surface and the vortices generated by the turbulence. During the last 30 years there have been an special interest for understanding the mechanisms and parameters involved in this process. Most of the approaches developed to explain the flow behavior near the free surface consider eddies generated in the outer region and reaching the surface. Komori et al. (1989) propose that large scale eddies intermittently reach the interface, renew it, and go back to the bulk of the fluid. According to Rashidi and Banerjee´s model (1988), the fluid ejected from the bottom reach the free surface, interacting with the interface, where the large eddies break down in smaller ones, generating a large velocity gradient close to the free surface, and the fluid move downwards. Bernal and Kwon (1988) visualized the evolution of vortical rings generated close to the free surface, with axis parallel to it, and found that the ring vortex lines opened during the interaction with the free surface. The resulting field is composed by vortices attached to the surface, with their ends starting and finishing in the interface. According to Dommermuth (1991), presence of U shaped vortices explain the surface eddies observed in clean or contaminated free surfaces.

The objective of this paper is to present preliminary results of an experimental study carried out in jet agitated tanks in order to visualize and quantify the turbulent structures at and near the free surface.

2 EXPERIMENTAL SET-UP, FLOW CONDITIONS AND METHODOLOGY

Experiments were performed in two perspex tanks 50´50 cm² and 95´95 cm² base area and 70 cm height. Nozzles (2.9 mm diameter) were located at the bottom, spaced 5 cm from each other. Water was alternatively injected and evacuated through the nozzles, circulating in a closed circuit. Thus, a zero net discharge is obtained in horizontal planes, parallel to the bottom.

Water depth was maintained at 44 cm and jet velocity ranked from 0.72 to 1.74 m/s. Velocity at and near the free surface in vertical and horizontal planes was computed from PIV measurements. Velocity in the bulk of the fluid was obtained by a 3D acoustic Doppler velocimeter (SonTek).

The vertical plane used for flow visualization was 5 cm wide and 4 cm height and it was located in the middle of the tank, with its longitudinal side in the centerline. In the PIV technique, 300 image pairs were digitized, corresponding to 5 minutes length record. 10 mm aluminum flakes were used as tracers. The jet velocity from the injecting nozzles was 0.72 m/s. Time series for the vertical and horizontal velocities in the vertical plane were generated at the nodes of a grid defined in the visualization plane, allowing us to compute temporal mean velocities, turbulence intensities or rms (root mean square) values, turbulent kinetic energy, and frequency velocity spectra.

The velocity field at the free surface for a 1.74 cm/s jet velocity was obtained after digitizing the motion of 0.1 mm perspex tracers. Wavenumber spectra for the horizontal velocities and vorticity were also computed.

3 RESULTS

From the movies taken in the vertical plane, a quasi-periodic sequence of large events close to the free surface and reaching it was observed, which can be described in terms of four stages as follows (see Fig.1):

(1) An upward motion. A very strong vertical motion approximates towards the free surface.

(2) The velocity changes direction, from vertical to horizontal motion, and small vortices are formed near the free surface.

(3) The velocity presents a disordered pattern, with sudden changes of its direction.

(4) A sweeping motion, where large scale vortices literally “sweeps” the vortices close to the free surface or the disordered pattern of stage 3). The dominant motion is horizontal.

The sequence is not always 1)-2)-3)-4). Sometimes, before stage 4) is reached, another upward motion 1) comes, generating small vortices, close to the free surface. The frequency of events type 1) is about three times higher than the frequency of events type 4).

The free surface effect upon the turbulent kinetic energy, K made dimensionless with the jet velocity, V_ch , is presented in Fig. 2. According to this result, an energy decay is found in the surface influenced layer. Results obtained by other authors indicating a weak increasing of K in this layer (Grisenty and George, 1991) would be consequence of energy production associated to large scale secondary currents arising from the boundary effects imposed by the lateral walls and the free surface.

In the flow visualization experiments, deformation of vortices with horizontal axes moving upwards due to their interaction with the free surface was observed. The vortices decrease their vertical dimensions and increase the horizontal ones. As a result, a redistribution of K, from the vertical to the horizontal velocity fluctuations occurs. This effect can be observed in Fig. 3, where the spectra of the vertical velocity fluctuations, G_w’w’ , and the horizontal velocity spectra, G_u’u’ , at different vertical locations (z/H, H = 44 cm) is presented. As the eddies get closer to the free surface, the kinetic energy due to the vertical velocity fluctuations decrease with respect to the energy associated to the horizontal fluctuations, as a result of the velocity intensity transfer from the z to the x direction.

Regarding the measurements at the free surface, a velocity field is presented in Fig. 4. For the sake of clearness, in this figure vectors were drawn in a mesh coarser than that used in the computations. From the vector orientation is possible to find an upwelling region in the center of the tank and a strong downwelling area centered at (25, 44). Around the tank perimeter, vortices with vertical axis are detected. Due to the stabilizing affects of the walls in the corners, the most permanent vortices (in shape and duration) are precisely those located in the corners. Those vortices are usually the bigger ones.

From the free surface data, wavenumber spectra for the horizontal velocities and vorticity at the free surface were determined and they are given in Figs. 5 and 6. In those figures, the spectra was made dimensionless with the square of the rms value of the corresponding velocities or vorticity fluctuations. Computations were performed along the X and the Y axis, defining the wavenumbers k_x and k_y , respectively. As it is expected, in both figures all the data collapses into one curve, due to the indifference in choosing the X or Y axis.

4 CONCLUSION

A quasi-periodic flow pattern was detected near the free surface. Characteristics of this pattern are a strong vertical motion in which fluid coming from the bulk reaches the free surface, generating small eddies near the surface, and a “sweeping” motion, with a dominant horizontal velocity, removing the eddies. This process can be associated to the renewal phenomenon, that has importance in the mass and heat transfer mechanisms across the interface. During this process, ascending vortices increase their horizontal size and reduce their vertical ones, redistributing the turbulent kinetic energy, increasing the energy associated to the horizontal velocity fluctuations and damping the vertical fluctuations.

Visualization and measurements at the free surface show regions associated to the upwelling motion (where the flow separates) and regions of downwelling movement (where the flow converges). Vortical motions are observed, with more stable eddies located in the corners of the tank.

Acknowledgements

The authors acknowledge the support given by the Chilean Fund for Science and Technology by means of the Grant Fondecyt 1990025.

References

Bernal, L.P. and J.T. Kwon (1988) “Vortex ring dynamics at a free surface”, Phys. Fluids A (1)3,449-451.

Dommermuth D.C.(1991) “The formation of U-shaped vortices on vortex tubes impinging on a wall with applications to free surfaces”, Phys. Fluids A (4)4,757-769.

Grisenti, M., and J. George (1991) “Hydrodynamics and mass transfer in a jet-agitated vessel”, in Air-Water Mass Transfer, S.C. Wilhelms and J.S. Gulliver (Eds.), ASCE, 94-105.

Komori, S., Y. Murakami and H. Ueda (1989) “The relationship between surface-renewal and bursting motions in an open channel flow”, J. Fluid Mech. (203),103-123.

Rashidi, M. and S. Banerjee (1988) “Turbulence structure in free-surface channel flows”, Phys. Fluids (31)9,2491-2503.