Performance analysis of various impellers in stirred tank by using CFD.

Sivakumar, C. ; Kumar, R. Sasi

Introduction

Impellers are the most important parts in a stirred tank. Mixing vessels vary in shape and size, from cylindrical to square. There are also a large range of impellers that can be used: radial flow impellers such as the Rushton Turbine move the fluid out radially, axial flow impellers move the fluid out in an axial direction, and mixed flow impellers generate both radial and axial motion. These three types of impellers are generally much smaller than the tank and cause fluid motion by stirring at high speeds. Other types of impellers, such as helical screw, helical ribbon, and anchors, sweep the entire volume of the tank and so run at much slower speeds due to their size and power consumption. Impeller location is not always constant: the most common orientation is with the impeller entering from the top in the centre of the vessel. Eccentric and nonvertical impeller positions have been used to generate motion within non baffled tanks that mimic, with some success, the flow patterns in baffled tanks. Side entering impellers are also used for highly viscous materials such as paper pulp. Baffles are used when mixing with the smaller impellers described above to help improve mixing when flow is seen throughout the entire vessel, and also to prevent solid body rotation. Correct choice of equipment is made dependant on the type of fluid to be mixed. This paper discusses the performance analysis of various impellers in stirred tank.

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A various literature is available on detailed velocity fields in mixing tanks agitated by various impellers. Jaworski et al. (1991) used an LDV system, measured the turbulent velocity field in a mixing vessel agitated by a 45[degrees] pitched turbine with 6 blades. Weetman and Oldshue. (1988) presented correlations for power, flow and shear characteristics of a 6-bladed disc turbine, a hydrofoil axial flow impeller (A310) and a pitch bladed turbine, measured through an automated LDV system. Similarly Nouri and Whitelaw (1990) and many others have presented the flow field and impeller characteristics through LDV measurements. Yianneskis et al. (1987) showed detailed flow structures of the tip vortices attached to a Rushton turbine (6-bladed). Schafer et al. (1997) conducted similar laser doppler velocimetry measurement on the same type of 6-bladed Rushton turbine. They presented time-mean velocity vector field and turbulent kinetic energy contour. The measurements captured the angular flow variation through synchronizing LDA sampling with a shaft encoder. In comparison with most other measured velocity fields, the resolution of LDA point measurements is exceptionally high. Fine flow structures including the trailing vortices at the blade tip were characterized. They determined energy dissipation distribution through calculating the velocity strain field.

Dyster et al. (1993) measured the radial discharge velocities of a Rushton turbine for Reynolds number from 5 to 5x104, using water, glycerol of different concentrations. They presented the mean centre-line velocity profile, i.e. the impeller centre radial velocity profile along the radial direction. They also presented power and flow number correlations with Reynolds number, for Newtonian fluids. Although the flow fields of many impellers have been investigated. Wu and Pullum (2000) developed an analysis method based on a blade element theory. The method permits rapid prediction of impeller pumping performance through calculation.

Although the flow fields of many impellers have been investigated. Wu and Pullum (2000) developed an analysis method based on a blade element theory. The method permits rapid prediction of impeller pumping performance through calculation.

Impeller Selection

The following points are necessary to select the impellers. They are

* Mixing is the key to process design. Impeller selection is a key to mixer design.

* How impellers convert energy into fluid motion is fundamental to their ability to provide a predictable process result.

* All the energy (P) applied by any mixing impeller produces a pumping effect (Q) and a velocity head (H), so that P [alpha] QH

* Knowledge of how this balance of energy distribution can change with impeller geometry is fundamental to mixer design. Lightning has used its extensive knowledge of impeller fluid mechanics to develop a family of efficient, process specific, impellers.

Computational Fluid Dynamics

The equations for fluids are quite complex and can be difficult to solve, especially if the geometry of a problem is intricate. The equations are nonlinear in the acceleration term (convection term), have singularities for high Reynolds Numbers (which appears in the N-S equations in the form of 1/Re), and the pressure difference terms are difficult to solve in combination with the fluid's motion. By making use of computers as a computational tool, we can "solve" these equations of motion in nearly any arbitrary situation.

The Reynolds average Navier- stokes equations are solved with the standard k-e turbulence model, for which the continuity equation is

[partial derivative]p / [partial derivative]t div ([pU.sub.I]) = 0,

Where U is the mean velocity vector and p is the fluid density. The momentum equation is

[[partial derivative]pU.sub.i] / [partial derivative]t + div ([pU.sub.i][U.sub.i]) = dp / [dx.sub.i] + [div[tau].sub.ij] + [F.sub.B],

Where [rho] is the pressure [[tau].sub.ij] is the Reynolds stress; and [F.sub.a] represents the controls and centrifugal forces. For the multiple frames of reference approach, the transient terms are zero. However the controls ([F.sub.c]) and centrifugal ([F.sub.ce]) forces are important. The transient terms are retained in the case of the sliding grid approach.

Numerical Methods

The numerical simulation of the flow and mixing in the stirred vessel has been performed using ANSYS-CFX5 (ANSYS, 2003). This is a general purpose commercial CFD package that solves the NavierStokes equations using a finite volume method via a coupled solver. The analysis procedure has been carried out in two steps. Firstly the velocity and pressure fields in the tank are solved. These values are then used to calculate particle trajectories with the flow field.

Methods of Measuring Liquid velocity

The flow characteristics of stirred vessels have been studied by many investigators using different velocity measuring devices. The first velocity measurement in a stirred vessel carried out by using the light streak method (Sachs, 1954). Improved version was used by Cutter (1966). Pitot tubes (Nagata, 1955) and hot wire anemometer (Bowers, 1965) were other types of instruments employed in the early studies on the measurements of the flow fields in mixing tanks.

None of the above devices are entirely satisfactory. Ideally a measurement device should not interface with the flow field and should permit the measurement of instantaneous velocities. Among the non-invasive and instantaneous methods, the Laser Doppler Velocimetry (LDV) in which velocity is measured using the Doppler shift of the laser beams crossing the flow field, is the most common method used in velocity measurements of the complex flows.

LDV was used by Rao and Brodkey (1972), Riet and Soots (1989), Wu and Petterson (1989), Kresta and Wood (1983). Nevertheless the flow in the stirred vessel is highly unsteady and time varying large scale motions dominate the flow. Since the LDV measures velocities on a plane, characterizing the entire flow field requires long experimental times. In addition LDV cannot be used in opaque media.

Therefore Bakker et al. (1996), Ward (1995) were the first to use Particle Image Velocimetry (PIV) to study the two dimensional flow pattern along the center plane in the vessel. PIV is quite different from the LDV methods. LDV provides instantaneous velocity field snapshot in a plane but PIV provides overall flow fields with spatially resolved eddies but with low temporal resolution.

Flow Patterns in Stirred Vessel

According to the main directions of the streamlines in the vessel, there are three principal types of flow. These are tangential flow, radial flow and axial flow.

Tangential flow

Tangential flow, where the liquid flows parallel to the path is shown in Figure 2. When the flow is predominantly tangential, discharge of liquid from the impeller to the surroundings is small. Tangential flow takes place in a paddle type impeller running at a speed, which is not sufficient to produce a noticeable action of the centrifugal force.

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Axial flow is defined as having the majority of the flow in a direction parallel to the agitator shaft and tank wall. It is most useful for general mixing and solids suspension, and is in fact the most widely used flow pattern. An illustration of this pattern is provided in Figure 3.

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Radial flow is defined by having the impeller discharge normal to the shaft. It is used for applications requiring shear, gas dispersion (which does not actually require shear) and mixing at very low liquid levels. An illustration of this flow pattern is provided in Figure 4.

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Mixed flow is somewhere between axial and radial flow. The impeller discharge is about 45 degrees to the agitator shaft. It can be used for general purpose design. The main use today is in applications where surface vortexing is desirable, such as in incorporating dry powders or pulling in gasses from above the liquid surface. Care must be taken using this flow pattern for solids suspension; if the impeller is too large or too high off bottom, flow reversal will occur, leading to a pile of solids forming in the bottom center of the tank. Figure 5 illustrates this flow pattern.

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Power number, NP

This is defined by NP = P/pN3D5. It is proportional to the ratio of power draw to liquid density and impeller parameters, including shaft speed. Its principal use is to calculate power draw. Various power numbers are given in Table 1

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Pumping Number, NQ

This is defined by NQ = Q/ND3. It may be thought of as being proportional to the ratio of the impeller pumping rate to the impeller swept displacement. Its principle use is to calculate flows and characteristic velocities inside an agitated tank. The pumping number is used for calculations in flow velocity controlled problems, such as liquid blending and motion. It is a function of impeller type, Reynolds number and geometric parameters. Pumping number is constant in both turbulent and laminar flow, but it varies in the transition flow range. It is much higher in turbulent flow than in laminar. In addition, it is mostly independent of geometric effects in laminar flow but shows a decreasing value with increasing D/T in turbulent flow, indicating that the return flow impedes the discharge flow as the impeller gets larger, especially for axial flow impellers.

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Experimental Method

Laser Doppler Velocimetry

Laser Doppler Velocimetry is a means by which velocity in a fluid can be determined optically, and hence, without interfering with the fluid itself. The process involves measuring the Doppler shift of the laser radiation that is scattered by the moving particles. The optical system used for Laser Doppler Velocitometry in this laboratory.

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Particle Image Velocimetry

Particle Image Velocimetry (PIV) is another optical technique similar to LDV for measuring fluid velocity and flow patterns. The method uses a laser sheet projected into the vessel, a fast CCD camera at right angles to the laser sheet captures many imagesover a period of time of small tracer particles (~60um) in the mixing fluid passing through the laser sheet. From these interactions, 2D velocity fields can be obtained (Kukura et al., 2002). La Fontaine and Shepherd, 1996, measured flow fields in a stirred tank and were able to identify stagnant flow regions, circulation loops and the turbulent flow. Bakker et al., 1996, and Sheng et al., 1998, measure the flow fields generated in a stirred tank with a pitch blade turbine and an axial impeller respectively.

PIV is a good technique to obtain velocity instantaneous fields within a given measurement plane and in this sense is a more rapid technique than LDV, however the accuracy in the recorded velocitie values are not as good. PIV has the same difficulties that LDV has in that it is an optical technique so the fluid must be transparent.

Velocities and Turbulent Kinetic Energy

Velocities for each of the velocity components in the down, up and reverse modes. In all three pumping configurations, the r.m.s. velocities are considerably higher in the discharge stream of the impeller than in the bulk of the tank. In the up-pumping and reverse modes, the high r.m.s. velocity region around the impeller is more spread out than in the down-pumping mode. Even though the r.m.s. velocities observed in the bulk of the tank are significantly smaller than the maximums found in the discharge flow, the difference between the component values varies noticeably. Table 1 gives the maximum r.m.s values for each impeller configuration. From these results, it is reserved that the flow induced by these two impellers in the three different configurations is in general, not isotropic. Mishra et al.15 have also observed that the flows induced byan APV-B2 impeller in both the up- and down-pumping configurations are not isotropic.

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Mixing time calculation:

Mixing efficiency of evaluated by calculating the homogenization energy from the dimensionless mean kinetic energy dissipation rate,[??].. The torque on the wall baffles was used to calculate power from Eq. (1), and this was in turn used to compute [??] from Eq.. 2. The power number predictions obtained using this method were much closer to the experimental results than those obtained from the local simulation values of the turbulent kinetic energy dissipation rate.

Power (P) exerted on the baffles was calculated as:

P=2[PI]MN (1)

where M is the torque and the mean kinetic energy dissipation rate is given by:

[??] = p/[V.sub.T[rho]] (2)

where [V.sub.T] is the fluid volume. The homogenization energy ([eta]) was calculated as a product of the kinetic energy dissipation rate and mixing time:

[eta] = [[??].sub.90] (3)

where [[??].sub.90] is the time required to achieve 90% homogenization. The mixing time required to achieve 90% homogenization ([[??].sub.90]), for example, is the time it takes for the fluctuation of the response signal to be below 10% of the concentration achieved at perfect mixing.

Conclusion

The quality of mixing is influenced by the performance of the mixing tanks, and this has been a subject of investigation for many years. Many impeller types have been employed to improve mixing in either a single-phase or multiphase system. However, the efficiency of mixing achieved in such systems depends on the geometry of the tank and impeller, as well as on the properties of the fluid. The conventional methods of evaluating the quality of mixing, namely of mixing time and power, may not provide sufficient information for the optimal design of such systems.

This review shows that modern techniques, such as LDV and CFD, can reveal the salient design features of the system. In particular, these studies have revealed mixing maldistribution features such as dead zones in the conventional stirred tank configurations. It has been further shown that the tank and impeller configurations that have over the years been regarded as standard may not provide the optimal operating condition with regards to system homogeneity and power consumption. The current research trend on stirred tanks shows that the simultaneous application of LDV and CFD techniques can provide detailed data for the system scale up. This can reduce the cost of a mixing process and improve product quality. The information on the fluid-flow pattern in tanks stirred by impellers mounted on multiple shafts still is lacking.

References

[1] Dyster, K. N., Koustakos, E., Jaworski, Z. and Nienow, A. W., "An LDA Study of the Radial Discharge Velocities Generated by A Rushton Turbine: Newtonian Fluids, Re>=5", Trans I Chem E, 71, Part A, Jan. 1993, 11-23.

[2] Jaworski, J., A. W. Nienow, and N. K. Dyster, "An LDA Study of the Turbulent Flow Field in a Baffled Vessel Agitated by an Axial, Down-pumping Hydrofoil Impeller," The Canadian J. Chem. Eng., 74, 3 (1996).

[3] Jaworski, Z., A. W. Nienow, E. Koutsakos, K. Dyster, and W. Bujalski, "An LDA Study of Turbulent Flow in a Baffled Vessel Agitated by a Pitched Blade Turbine," Chem. Eng. Res. Design, 64(A4), 313-320 (1991).

[4] Nienow, A W., "The Suspension of Solid Particles", in "Mixing in the Process Industries", N. Hamby, M. F. Edward and A. W. Nienow, Eds. (1992).

[5] Nienow A. W. "Hydrodynamics of stirred bioreactors" Appl. Mech. Rev., Vol. 51 No 1., Jan 1998.

[6] Nouri, J. M., and J. H. Whitelaw, "Flow Characteristics of Stirred Reactors with Newtonian and Non- Newtonian Fluids," AIChE J., 36(4), 627 (1990).

[7] Schafer, M., Hofken, M. and Durst, "Detailed LDV Measurements for Visualisation of The Flow Field Within A Stirred-Tank Reactor Equippied with A Rushton Turbine", Trans IchemE, Vol. 75 Part A, 729-736, Nov. (1997).

[8] Stoots, Carl M. and Calabrese R. V., "Mean Velocity Field Relative to a Rushton Turbine Blade", AIChE J., 41(1), 1-11 (1995).

[9] Weetman, R. J., and J. Y. Oldshue, "Power, Flow and Shear Characteristics of Mixing Impellers," Proc. 6th European Conf. on Mixing, Pavia, Italy, 24-26 May 1988.

[10] Wu, J. and Pullum, L., "Performance Analysis of Axial Flow Mixing Impellers", AIChE Journal, 46 No.3, pp489-498, 2000.

[11] Wu, J., Zhu, Y., Bandopadhayay, P. C., Pullum, L. and Shepherd, I. C., "Solids Suspension with Axial Flow Impellers", AIChE J. 46(3), 647-650 (2000a).

[12] Zwietering, T, N., "Suspension of Solids in Liquid by Agitators", Chem. Eng. Sci. 8, 244-253 (1958).

[13] Yianneskis, M., Z. Popiolek, and J. H. Whitelaw, "An Experimental Study of the Steady and Unsteady Flow Characteristics of Stirred Reactors," J. Fluid Mechanics, 175, 537 (1987).

(1) C. Sivakumar and (2) R. Sasi Kumar

(1) Ist year M.E, Engineering Design, K.S.R. College of Technology, Tiruchencode-637 215, Namakkal District, Tamil Nadu, India E-mail: sivachelliah@yahoo.com

(2) Associate Professor, Department of Mechanical Engineering, K.S.R. College of Technology, Tiruchencode-637 215, Namakkal District, Tamil Nadu, India

Table 1: Turbulent Power Numbers.

D/T Narrow Wide Pitched Rushton
 Hydrofoil Hydrofoil Blade 6-blade

0.25 0.33 1.06 1.37 5.5
0.3 0.32 1.05 1.37 5.5
0.4 0.29 1.0 1.37 5.5
0.5 0.27 0.98 1.37 5.5

Table 2: Generic" Turbulent Pumping Numbers

D/T Narrow Wide Pitched Rushton
 Hydrofoil Hydrofoil Blade 6-Blade

0.25 0.57 0.80 0.88 0.72
0.3 0.55 073 0.80 0.72
0.4 0.53 0.63 0.68 0.72
0.5 0.51 0.56 0.60 0.72