TURBULENCE STRUCTURE IN A JET AGITATED TANK

   Aldo Tamburrino¹,  Javier Pujol²,   Alejandro Muñoz³

¹Associate Professor,  ²Civil Engineer,   ³Research 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: Experimental results obtained in a jet agitated tank are presented in this paper. A tank filled with water is agitated by means of jets located in the bottom. Velocity measurements and flow visualization experiments allowed us to identify a secondary motion scaling with the flow depth, forming well defined cells along the tank diagonals. Turbulence intensity measurements show presence of an homogeneous and isotropic turbulence region, where the kinetic energy decays as the inverse of the square of the distance from the bottom. Relationships to define the location where the homogeneous and isotropic region starts are also found.

Keywords: turbulence, agitated tanks, homogeneous turbulence, isotropic turbulence

1  INTRODUCTION AND OBJECTIVES

Agitated tanks have been used at least since the middle 1950’s (Rouse and  Dodu, 1955) to study turbulence phenomena. Turbulence is generated by agitating the water contained in the tank. Usually, agitation is achieved by grids (Rouse and Dodu, 1955; Bouvard and Dumas, 1967; Thompson and Turner; 1975; Hopfinger and Toly, 1976), but agitation by a jet (Sonin et al., 1986) and microjets (Grisenti and George, 1991) have also been reported.

Agitated tanks present some advantages when compared to another experimental facilities. It is easy to generate different levels of turbulence and the flow in the tank have longer residence times. In addition, isotropic and homogeneous turbulence can be generated easily. Most of the authors have reported that the turbulent kinetic energy (k) decays like z^-2 in the region of isotropic and homogeneous turbulence (z is a vertical axis). This behavior is not valid close to any surface because the turbulence is not isotropic near the surfaces. For free surfaces, there is a damping of the vertical fluctuation and an enhancement of the horizontal ones, as a result of the boundary condition imposed by these kind of boundaries.

The objective of this paper is to present some experimental results regarding the turbulence characteristics of some flows in a tank. Turbulent flows with zero cross sectional mean velocity  are generated by an arrangement of nozzles placed at the bottom.

Four flow regions can be defined in the bulk of fluid: I) Lower region, where zones of high turbulence (injection jet zones) are surrounded by regions of lower turbulence (evacuating flow zones). II) Middle region. Zone where there is a direct interaction of jets.  III) Zone of isotropic and homogeneous turbulence. IV) Surface influenced layer.

This paper refers to the first three regions. Results regarding the fourth region are given in another paper (Tamburrino, Mourgues and Aravena) presented in this Congress.

2  EXPERIMENTAL FACILITY AND FLOW CONDITIONS

The experimental facility is a tank 65 cm height, with a 49 cm squared cross section. Water is injected and evacuated by 2.9 mm nozzles located in the bottom, spaced 5 cm each other. Velocities were recorded by a 3D acoustic Doppler velocimeter (ADV), with a 25 Hz sampling rate. ADV measurements were complemented with flow visualization experiments. An illuminating sheet  was generated by a 5 watt laser source. Aluminum flakes (less than 10 mm size) were used as tracers.

ADV measurements were taken in three equally spaced vertical planes and two horizontal planes located at 15 and 30 cm from the bottom. Velocity was recorded in the nodes of an imaginary grid located in the planes. Distance between nodes was 5 cm.

Experimental conditions are summarized in Table 1. H is the water level in the tank, Q is the discharge, U_c is the mean jet velocity, and n is the kinematic viscosity of water.

3  RESULTS

The temporal mean velocity field was determined from the velocity records. It showed the presence of  four large scale secondary flows oriented along the tank diagonals. Fig. 1 presents the velocity vectors in a diagonal plane, in which two well defined vortices are detected. Fig.2 is a 3-D view of the temporal mean streamlines, showing the vortical motion in the diagonal planes. Flow visualization also showed the secondary cells before described and vortical motions in horizontal planes, with persistent vortices located in the corners. These vortices are smaller than those located along the diagonals, and they are continuously moving back and forth, changing their shape and size.

Turbulent intensity distribution for the three velocity components (U_rms, V_rms, W_rms) for four different locations in a center plane are presented in Fig. 3. One profile is located over an injecting nozzle (distance from a wall: x = 24.5 cm ), another one is over an evacuating nozzle (x = 29.5 cm), and the other profiles are located in positions between nozzles (x = 27.0 cm and x = 32.0 cm).  In the plots: z’ = z/H.

From Fig. 3 it is possible to estimate the height z₀ at which the turbulence is homogeneous and isotropic, and its corresponding turbulence intensity, u₀ . A characteristic length scale is defined from the volumetric discharge in the nozzle, Q_c = pD²U_c/4, and from the specific momentum, M_c = pD²U_c²/4, resulting L_c = p^1/2D/2.

Flow visualization close to the bottom showed that the influence area of the evacuating nozzles is very small when compared to the influence area of the injecting jets. Thus, z₀ was related to the injecting nozzle separation, s.  Figs. 4 and 5 present the relationships found for the dimensionless height and turbulence intensity when the turbulence becomes isotropic and homogeneous. A curve fitting  to the experimental points (without taking into account the point that does not follow the tendency in Fig. 4) gives:

                                         (1)

                                            (2)

A characteristic velocity is defines as u_k = (2 k/3)^1/2 , where k is the turbulent kinetic energy, which can be made dimensionless with the jet velocity U_c. A plot of this dimensionless characteristic velocity against the dimensionless height z/L_c is shown in Fig. 6. The experimental data fit the relationship:

                                                   (3)

In the figure, the straight line corresponds to Eq. 3. The exponent –1 of  this equation is in agreement with the value found by other authors (Hopfinger and Toly, 1976) in grid stirred tanks. Thus the turbulent kinetic energy decay is inversely proportional to the squared distance (k ~ z ^-2), independent of the generating mechanism. Eq. 3 is not valid close to the free surface, since it overestimates the vertical turbulence intensity and underestimates the horizontal ones, as a result of the vertical damping imposed by the free surface and the resulting energy redistribution towards the horizontal components.

4  CONCLUSIONS

Some flow and turbulence characteristics in a jet agitated tank have been experimentally determined.  Presence of large scale secondary cells oriented  along the tank diagonals were detected both visually and from velocity measurements. Smaller vortices continuously moving and changing their shape were observed in the tank corners.

Relationships defining the distance from the bottom at which turbulence becomes homogeneous and isotropic and its associated turbulence intensity value were determined. In this region, turbulence kinetic energy decays as k ~ z ^–2, as it has been found in grid stirred tanks.

Acknowledgements

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

References

BOUVARD, M. etH. DUMAS (1967) “Aplication de la méthode du fil chaud a la mesure de la turbulence dans l’éau. Deuxieme Partie”, La Houille Blanche, No. 3, pp. 723-734.

GRISENTE, 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, A.S.C.E., pp. 94-105.

HOPFINGER, E.J.  and J.-A. TOLY (1976) “Spatially decaying turbulence and its relation to mixing accross density interfaces”, J.Fluid Mech., vol 78, part 1, pp. 155-175.

ROUSE, H. et J. DODU (1955) “Diffusion turbulente à travers une discontinuité de densité”, La Houille Blanche, No. 4, pp. 522-532.

SONIN, A.A.; M.A. SHIMKO and H.-H. CHUN (1986) “Vapor condensation onto a turbulent liquid – I. The steady condensation rate as a function of liquid-side turbulence”, Int. J. Heat Mass Transfer, vol. 29, No. 9, pp. 1319-1332.

THOMPSON, S.M. and J.S. TURNER (1975) “Mixing across an interface due to turbulence generated by an oscillating grid”, J.Fluid Mech., vol. 67, part 2, pp. 349-368.

Table 1  Flow Conditions

Fig.1  Velocity field in a diagonal plane experiment aI1

Fig. 2  Streamlines. 3D view

Fig. 3   Turbulence intensity distribution experiment B1.

Fig. 4  Dimensionless distance at which the turbulence is homogeneous and isotropic

Fig. 5  Dimensionless characteristic velocity at Z₀

Fig. 6  Dimensionless turbulence intensity distribution