Improving heat transfer in stirred tanks cooled by helical coils

Improving heat transfer in stirred tanks cooled by helical coils

S.M.C.P.Pedrosa; J.R.Nunhez^*

Faculdade de Engenharia Química, UNICAMP, Cx. P 6066, 13083-970, Campinas - SP, Brazil. http://www.feq.unicamp.br/~nunhez. E-mail: [e-mail], E-mail: [e-mail]

ABSTRACT

Stirred Tank Reactors are extensively used in chemical industries. When they are used for highly exothermic reactions, jackets or coils are employed for heat removal. Internal coils can be either helical or axial and they considerably affect the flow inside the reactor because they impose an additional resistance to flow circulation. The aim of this work is to show that the design of vessels cooled by helical coils can be further improved. The design of these reactors follows very much the geometry proposed by Oldshue and Gretton (1954), and some minor modifications in the coil arrangements are likely to improve internal circulation inside these vessels mainly in the region between coils and wall of the vessel. Results show a gain in performance when small alterations are made specially in the shape of the coil arrangement.

Keywords: heat transfer, stirred tanks, helical coils, reactor design and computational fluid dynamics.

INTRODUCTION

The performance of stirred tanks is greatly affected by the location of their internals and their mode of operation. When these vessels are used for highly exothermic reactions, it is common to use either jackets or internal coils for temperature control. Both arrangements have positive influences and drawbacks in controlling bulk temperature, and they should be weighed carefully before deciding which arrangement should be chosen in any design.

For reacting fluids under laminar flow, jacketed vessels have the tendency to affect the flow at the bottom and walls of the vessel, since the low temperature in these regions causes the fluid to have a higher viscosity incomparison to the rest of the vessel. The flow inside stirred vessels with internal helical coils is much more affected than jacketed vessels because the coils pose a resistance to fluid circulation. This means that the number and location of the coils, as well as tube radius and coil helix diameter are important design parameters for such systems. All these factors have an influence on the flow and heat transfer inside the tank.

When jacketed vessels are employed for reactions under laminar flow, there is a temperature peak inside the vessel at the centers of the recirculation zones of the secondary flow, since heat transfer in stirred tanks - in these circumstances - is dominated by the secondary flow. If coils are used, the temperature peak is not necessarily at the center of the recirculation zones, because the heat transfer is greatly affected by the coils. The amount of coils and their design will determine the heat transfer area inside the tank. On the one hand, it is desirable to have as many coils as possible for it increases the heat transfer area but, on the other hand, the smaller the number of coils and its diameter is, the better the circulation and mixing inside the tank. An optimum design for coiled vessels should provide an arrangement with a high internal heat transfer coefficient, which means that the heat generated by the reaction would be removed by a smaller heat transfer area. Since heat transfer is flow dependent, any design improvement for these systems will depend heavily on a detailed knowledge of how flow is affected by the location of the internals of the reactor.

Oldshue and Gretton (1954) suggested a coiled vessel arrangement which was later presented by Uhl and Gray in a book that has become a reference for reactor design (Uhl and Gray, 1966). The primary concern of this research is to show that there are some deficiencies in the internal circulation (which reflects in the heat transfer)for the geometry suggested by Oldshue and Gretton. In their experimental work, Oldshue and Gretton investigated transitional and turbulent flow. This computational work investigates only laminar flow. Even though results indicate improvement in the internal flow under laminar conditions, they cannot be directly extended to turbulent conditions. However, a point should be made: similar flow patterns are expected for both flow regimes, as can bee seen in many works reported in the literature [Gosman et al, 1992; Brucato et. al., 1998]. Since the geometry of the tank with helical coils is the same for both laminar and turbulent flow, the same limitations which are present for laminar flow are also present for turbulent flow. Therefore, studying the fluid circulation inside the coiled tank for laminar flow will provide insights which will be beneficial for understanding how internal flow of vessels with helical coils can be improved_also for turbulent flow. The results for turbulent flow, however, have to be further investigated to confirm how much the flow is affected under these conditions.

Street (1991), Street and McGreavy (1991) and Nunhez and McGreavy (1994) have indicated in their work that no coils should be placed at the impeller blades height because fluid circulation is restricted and overall heat transfer is poor, even though there is an excellent local heat transfer at the coil close to the impeller tip region, where the flow generated by the radial turbine impeller is discharged. This is due to the fact that the sweeping flow at the impeller region is at a high speed and it looses momentum when it encounters the coils placed between the impeller blades and the wall of the vessel. If no coils are placed there, momentum is lost only at the walls and, as a result, fluid circulation away from the impeller will be increased and the overall heat transfer improved. This aspect, however, has not been studied previously, and this work has been addressed to demonstrate it by simulating the momentum, mass and energy transfer inside the reactor.

MODELING AND SIMULATION

The problem under investigation is three-dimensional and can be applied to both Newtonian and non-Newtonian flow, even though the experimental work by Oldshue and Gretton (1954) analyses only Newtonian fluids. For a preliminary investigation, a two-dimensional axisymmetric model has been considered. This means that the radial, axial and tangential velocities will be determined on a two-dimensional grid, making this a pseudo three-dimensional model. Even though this model is a simple representation for the flow, i.e., a single-phase two dimensional model, previous published work shows that the approach is accurate enough to give a good representation for the flow behavior inside stirred tanks and indicates how internal fluid circulation and hence heat transfer can be improved by rearranging the location of internal coils (Pedrosa and Nunhez (2000), Pedrosa et al. (2000), Nunhez and McGreavy (1995), Nunhez and McGreavy (1994), Street (1991), Kuncewics(1992) and Ruhbart and Böhme (1992)).

The critical part of the axisymmetric model is the application of the boundary conditions for the impeller blades in order to give a reasonable representation of the effect of the blades. The approach used by Kuncewicz (1992) was adopted. The idea is to input the momentum at the impeller in an averaged sense, that is, the tangential velocity profile is input in the whole swept volume of the impeller, but fluid is allowed to circulate in the impeller blade region in the radial and axial directions. By imposing the tangential velocity profile in the whole sweeping volume where the blades rotate, the typical radial flow of Rushton turbines is captured. Results show that it gives a good representation for the flow patterns and serves as basis for geometry selection. The reaction heat effect, at this stage, is represented by a heat source in bulk. These aspects can be further refined at a later stage by both a three-dimensional model and a more detailed reaction model.

Figure 1 shows the tank used by Oldshue and Gretton (1954) and Table 1 gives its geometrical dimensions.

The mass, linear momentum and energy balances for steady state operation are expressed in terms of a Eulerian frame of reference. The detailed derivations are given in texts such as Bird et al (1960).

The reader should notice that the axial axis coincides with the shaft. The governing model equations are given below:

Linear Momentum Balance

Radial

Angular

Axial

These are the well known Navier-Stokes equations which describe laminar Newtonian flow. It should be noticed that the gravitational term is not present in the axial component of the momentum conservation. This is because this term is small when compared to the convective term of the Navier Stokes equations, even if the flow regime is laminar. Other authors use the same simplification in flow calculations under laminar conditions (Street, D, 1991, Foumeny et al, 1993.). If it is considered, problems in arriving at converged solutions can arise. This term can have some importance if the vessel is tall.

The energy equation presents some simplifications. The thermal viscous dissipation term is not present in the equations. Welty et al (1976) comments that this term can have strong influence for highly viscous and supersonic flow. Simulations have been performed considering this term and they proved to be negligible in relation to other terms, even though the results are not shown in this paper.

MASS CONSERVATION

ENERGY CONSERVATION

The stress components are:

The fluid properties and other important parameters are:

The non-Newtonian viscosity is given by the Power law model:

The parameters used are n = 0.5, 1 or 1.5 (see Tables 3 and 4).

As already pointed out, the experimental work by Oldshue and Gretton investigated only Newtonian fluids. However, this work also investigated how non-Newtonian fluids behave inside stirred tanks cooled by helical coils. The experimental work by Oldshue and Gretton analyzed viscosities up to 400 centipoises. However, they pointed out that the range of application of their work should hold up to 10.000 centipoises based on data reported by Uhl (1953).

Oldshue and Gretton (1954) used baffles in their work and this cannot be satisfactorily modeled on a two dimensional grid. This aspect has to be considered in more detail using a full three-dimensional since baffles improve mixing by both avoiding vortex formation and by generating a radial velocity component. Nevertheless, the two dimensional model for the secondary flow of the turbine impeller presented in this work gives a good flow representation and presents the main design features that can improve flow circulation.

BOUNDARY CONDITIONS

Free Surface

At the liquid free surface there is no shear stress, which is acceptable for Reynolds numbers (based on impeller tip speed) below 300 (Edwards and Wilkinson, 1972). Therefore a flat surface is assumed and axial velocity is null.

Bottom and Walls of the Vessel

There is no slip, so the velocity is null.

Coil Tubes

There is no slip.

Impeller Blades

The approach of Kuncewicz (1992), is used. He assumes that the blades can be approximated by a momentum which acts equally in the whole swept volume where the blades rotate and he uses a coefficient varying between 0 and 1, which is dependent on the number of blades and can be thought of as a drag coefficient which accounts for the blade effect. For the numerical implementation of this boundary condition the blade is thought of as having zero thickness. In the blade it is specified the tangential velocity profile (rotational speed of the impeller) and fluid is allowed to circulate in the angular and radial directions._This approximation is able to provide a good representation for the flow patterns of turbine impellers.

Coil Tubes

It is assumed that cooling liquid flows inside the coils to maintain temperature constant at 10 ⁰C.

Bottom and Walls of the Vessel

The vessel walls were assumed to be at constant temperature of 10 ⁰C.

At the walls of the vessel the boundary condition is:

At the coils the boundary condition is:

and at the free surface is:

The equations are solved numerically by the finite volume method and the simulations are performed using the CFX-4.2 package by AEA, which has been successfully used for many flow problems. It uses the SIMPLEC algorithm by van Doormaal and Raithby (1984) to the velocity/pressure coupling, which is a variation of the SIMPLE algorithm first developed by Patankar and Spalding (1983) and Patankar (1983). The dissipative upwind scheme was applied for the convective terms in the model equations.

RESULTS AND DISCUSSION

In order to determine a good number of finite volumes, several grids were used and the approach used by Foumeny et al. (1993) and Nunhez and McGreavy (1994, 1995) to guarantee mesh independent results was adopted. Table 3 presents the results for the temperature using mesh densities of 5264 and 10604 control volumes. The temperature differences for the two meshes give a maximum of approximately 1.5 ⁰C for the maximum temperature, and all the other results give a smaller difference. The temperature is the investigated variable, which is more affected by mesh density; so if it keeps independent on mesh density, the results for the other variables are also mesh independent. The small difference in temperature for the finer and coarser meshes indicates that results given for the smaller density are satisfactory for this preliminary investigation. Therefore a mesh density of 5264 control volumes is used. Figure 2 shows the mesh used for the calculations.

Figures 3 and 4 show the generated velocity field by both geometries. It is apparent that velocities are higher in the proposed geometry for the same rotational speed of the impeller. Flow is specially improved in the regions away from the impeller and between the coils and wall. This is so because the proposed geometry provides better fluid circulation. This happens because the small design modification of removing coils placed at the impeller blade height promotes internal flow. The conventional designs have coils at the blades height which reduces the average velocity of the fluid discharged by the impeller when it encounters the coils. As a consequence, there is a tendency for the fluid to stagnate between the coils and the wall of the vessel. Figure 3, which shows the conventional design, indicates that the center of the recirculation zones of the secondary flow for the impeller moving at 60 rpm is located before the centerline of the coil helix (the recirculation zones are located between coils and impeller shaft). The proposed modification for the same conditions gives the secondary flow shown in Figure 4. The center of the recirculation zones, in this case, moves closer to the wall and is located near the coil helix. This in itself indicates that the flow is more convective, since it is well known that the recirculation zones move closer to the vessel wall with the increasing of rotational speed. Additionally, the velocities near the free surface of the tank are higher for the proposed geometry.

Figures 5 shows the temperature contour plot for the proposed geometry. The difference in temperatures for both geometries under the same operational conditions is shown in Table 4.

The maximum and average temperatures for both geometries are very similar, but an important point is that the proposed geometry has a considerably smaller heat transfer area because, apart from having two coils less than the conventional arrangement studied by Oldshue and Gretton (1953), the diameter of the tube for this work is 0.04 m, and the work of Oldshue and Gretton uses 0.05 m. The total coils area for the arrangement of Oldhue and Gretton is 8,5 m² and the coils area for the proposed arrangement is 5,5m². From the results, an averaged heat transfer coefficient has been determined considering the mean fluid temperature and the proposed geometry has a considerable higher heat transfer coefficient. It seems that the improved overall heat transfer coefficient is mainly due to the increased fluid circulation near vessel walls (see Figures 3 and 4).

CONCLUDING REMARKS

The pseudo three-dimensional model presented in this work gives a good representation for the flow and temperature fields for disk turbine impellers under laminar flow and helps to determine design features, which improve fluid circulation inside coiled stirred tank reactors equiped with radial impellers. Results show that coiled vessels have better fluid circulation if no coils are placed at the impeller blades height (for radial impellers). As a consequence, the internal heat transfer inside the vessel is improved, as reflected by a higher overall heat transfer coefficient, as indicated in Table 4.

A full three-dimensional model investigating also turbulent flow has been started. Experimental data will be provided by a Brazilian impeller design company.

ACKNOWLEDGEMENTS

The authors would like to thank CAPES, FAEP (UNICAMP) and FAPESP for the grants received for this project.

NOMENCLATURE

Greek Letters

Received: December 10, 1999

Accepted: September 15, 2002

• Bird, R. B., Stewart, W. E. and Lightfoot, E. N. Transport Phenomena. New York, John Wiley & Sons, Inc., (1960).
• Brucato, A., Ciofalo, M.; Grisafi, F. and Micale, G., Numerical prediction of flow fields in baffled stirred vessels: A comparison of alternative modeling approaches. Chemical Engineering Science, Vol.53, n21, pp3653-3684, 1998
• Edwards, M. F and Wilkinson, W. L., Heat Transfer in Agitated Vessels - Part i. The Chemical Engineer, 310-319 (1972).
• Foumeny, E. A, Holiday, S. O. and. Sandhu, K. S., Prediction of flow patterns in polymerization systems using cfd". In 8^th International Conference on Numerical Methods in Laminar and Turbulent Flow, Swansea - England. 517-528 (1993).
• Gosman, A. D., Lekakou, C., Politis, S. and Issa, R. I., Multidimensional Modeling of Turbulent Two-Phase Flows in Stirred Vessels. AIChE Journal, 38,Nº12, 1946-1956 (1992).
• Kuncewicz, C., Three-Dimensional Model of Laminar Liquid Flow for Paddle Impellers and Flat-Blade Turbines. Chem. Eng. Sci., 47, Nº 15/16, 3959-3967(1992).
• Nunhez, J. R., The Influence of Geometric Factors on the optimum Design of Stirred Tank Reactors. PhD thesis, The University of Leeds (1994).
• Nunhez, J. R. and McGreavy, C.,. A Comparison of the Heat Transfer in Helical Coils and Jacketed Stirred Tank Reactors. Brazilian Journal of Chemical Engineering. 12, No 1, (1995).
• Oldshue, J. Y. and Gretton, A T., Helical Coil Heat Transfer in Mixing Vessels. Chem. Eng. Progress, 50, Nº 12,615-621(1954).
• Patankar, S. V., Numerical Heat Transfer and Fluid Flow. Hemisphere, (1983).
• Patankar, S. V. and Spalding, D. B., A Calculation Procedure for Heat, Mass and Momentum transfer in three Dimensional Parabolic Flows. J. Heat Mass Transfer, 15,1781-1806, (1983).
• Street, D. A., Computational Modelling of Stirred Reaction Vessels. PhD thesis, The University of Leeds, (1991).
• Street, D. A. and C. McGreavy, C., A Model of the Heat Transfer in Internally Cooled Reaction Vessels. In E. A. Foumeny and P. J. Heggs, editors, Heat Exchange Engineering, 2, 279-302, (1991). Ellis Horwood Ltd.
• Tatterson, G., editor: Industrial Mixing Technology: Chemical and Biological Applications. Title of the Chapter: The Influence of Geometric Factors on The Optimum Design of Stirred Tank Reactors, volume 89 of AICHE Symposium Series. AICHE (1994).
• Uhl, V. and Gray, Mixing: Theory and Practice, volume I, chapter5. Academic Press, London (1966).
• Van Doormaal, J. P. and Raithby, G. D., Enhancements of the Simple Method Predicting Incompressible Fluid Flows". Numerical Heat Transfer, 7,147-163 (1984).
• Welty, J. R., Wicks, C. E. and Wilson, R. E., Fundamentals of Momentum, Heat & Mass Transfer. New York, John Wiley & Sons, (1976).

*

To whom correspondence should be addressed

Publication Dates

• Publication in this collection
  25 June 2003
• Date of issue
  June 2003

History

• Accepted
  15 Sept 2002
• Received
  10 Dec 1999