Turbulence Dissipation in Stirred Jars
Publication: Journal of Engineering Mechanics
Volume 132, Issue 11
Abstract
A two-compartment analytical model was developed to estimate the turbulent dissipation rates in a standard jar stirred by a radial impeller. A simple numerical simulation was also performed to support the analytical arguments. Results of the numerical model showed that away from the impeller, the turbulent dissipation rate rapidly decays proportionally with , where is the axial distance. The turbulent velocity away from the impeller region showed a decay proportional to . Although the dissipation rates at the wall boundary layer were higher compared to those in the tank interior, the total energy dissipated in the boundary layer is smaller compared to that expended in the impeller zone.
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Acknowledgments
The writer wishes to extend his gratitude to the anonymous reviewers for their suggestions on a previous version of the paper. The writer also wishes to thank Professor Harindra Fernando, Professor Jorg Imberger, Professor Greg Ivey, and Professor Supachart Chungpaibulpatana for their continued encouragement. Support from Lee Krispin, Jim Johnson, and Matt Obrigkeit of General Motors is gratefully acknowledged.
References
Batchelor, G. K. (1953). The theory of homogeneous turbulence, Cambridge Univ. Press, Cambridge, U.K.
Bittorf, K. J., and Kresta, S. M. (2001). “Three dimensional wall jets: Axial flow in a stirred tank.” AIChE J., 47, 1277–1284.
Cheng, C.-Y., Atkinson, J. F., and Bursik, M. I. (1997). “Direct measurements of turbulence structures in mixing jar using PIV.” J. Environ. Eng., 123, 115–125.
Clark, M. M. (1985). “Critique of Camp and Stein’s rms velocity gradient.” J. Environ. Eng., 111(6), 741–754.
Cleasby, J. L. (1984). “Is velocity gradient a valid turbulent flocculation parameter?” J. Environ. Eng., 110(5), 875–897.
Cornwell, D. A., and Bishop, M. M. (1983). “Determining velocity gradients in laboratory and full-scale systems.” J. Am. Water Works Assoc., 75, 470–475.
Cutter, L. A. (1966). “Flow and turbulence in a stirred tank.” AIChE J., 12, 35–45.
Derksen, J., and van den Akker, H. E. A. (1999). “Large eddy simulations on the flow driven by a Rushton turbine.” AIChE J., 45, 209.
De Silva, I. P. D., and Fernando, H. J. S. (1992). “Some aspects of mixing in a stratified turbulent patch.” J. Fluid Mech., 240, 605–625.
De Silva, I. P. D., and Fernando, H. J. S. (1994). “Oscillating grids as a source of nearly isotropic turbulence.” Phys. Fluids, 6(7), 2455–2464.
Fernando, H. J. S., and De Silva, I. P. D. (1993). “Note on secondary flows in oscillating-grid, mixing box experiments.” Phys. Fluids A, 5(7), 1849–1851.
Gunkel, A. A., and Weber, M. E. (1975). “Flow phenomena in stirred tanks. Part I: The impeller stream.” AIChE J., 21, 931–949.
Han, M., and Lawler, D. F. (1992). “The (relative) insignificance of G in flocculation.” J. Am. Water Works Assoc., 84(10), 79–91.
Hannoun, I. A., Fernando, H. J. S., and List, E. J. (1988). “Turbulence structure near a sharp density interface.” J. Fluid Mech., 189, 189–209.
Hanson, A. T., and Cleasby, J. L. (1990). “The effects of temperature on turbulent flocculation: Fluid dynamics and chemistry.” J. Am. Water Works Assoc., 82(11), 56–73.
Harvey, P. S., and Greaves, M. (1982). “Turbulent flow in an agitated vessel. II: Numerical solution and model predictions.” Trans. Inst. Chem. Eng., 60, 201.
Hudson, H. E. (1981). Water clarification processes, Van Nostrand Reinhold, New York.
Itsweire, E. C., Helland, K. N., and Van Atta, C. W. (1986). “The evolution of grid generated turbulence in a stably stratified fluid.” J. Fluid Mech., 162, 299.
Ju, S. Y., Mulvahill, T. M., and Pike, R. W. (1990). “Three-dimensional turbulent flow in agitated vessels with non-isotropic viscosity turbulence model.” Can. J. Chem. Eng., 68, 3.
Koh, P. T. L., Andrews, J. G. R., and Uhlherr, P. H. T. (1984). “Flocculation in stirred tanks.” Chem. Eng. Sci., 39, 975–985.
Kresta, S. M., Bittorf, K. J., and Wilson, D. J. (2001). “Internal annular wall jets: Radial flow in a stirred tank.” AIChE J., 47, 2390–2401.
Kresta, S. M., and Wood, P. E. (1991). “Prediction of the three-dimensional turbulent flow in stirred tanks.” AIChE J., 37, 448–460.
Lee, K. C., Ng, K., and Yianneskis, M. (1996). “Sliding mesh predictions of the flow around Rushton impellers.” Inst. Chem. Eng. Symp. Ser., 140, 47.
Liem, L. E., Smith, D. W., and Stanley, S. J. (1999). “Turbulent velocity in flocculation by means of grids.” J. Environ. Eng., 125(3), 224–233.
Long, R. R. (1978). “Theory of turbulence in a homogeneous fluid induced by an oscillating grid.” Phys. Fluids, 21, 1887–1888.
Luo, J. Y., Issa, R. I., and Gosman, A. D. (1994). “Prediction of impeller induced flows in mixing vessels using multiple frames of reference.” Inst. Chem. Eng. Symp. Ser., 136, 549–556.
McDougall, T. J. (1979). “Measurements of turbulence in a zero-mean-shear mixed layer.” J. Fluid Mech., 94, 409–431.
Okamoto, Y., Nishikawa, M., and Hashimoto, K. (1981). “Energy dissipation rate distribution in mixing vessels and its effects on liquid-liquid dispersion and solid-liquid mass transfer.” Int. Chem. Eng., 21, 88–94.
Perng, C. Y., and Murthy, M. Y. (1993). “A moving-deforming mesh technique for simulation of flow in mixing tanks.” AIChE Symp. Ser., 89, 37.
Placek, J., and Tavlarides, L. L. (1985). “Turbulent flow in stirred tanks. I: Turbulent flow in the turbine impeller region.” AIChE J., 31, 1113.
Rao, A. R. (1999). “Prediction of reaeration rates in square, stirred tanks.” J. Environ. Eng., 125, 215–223.
Revstedt, J., Fuchs, L, Kovacs, T., and Tragardh, C. (2000). “Influence of impeller type on the flow structure in a stirred reactor.” AIChE J., 46, 2373–2382.
Stanley, S. J., and Smith, D. W. (1995). “Measurement of turbulent flow in standard jar test apparatus.” J. Environ. Eng., 121, 902–910.
Tennekes, H., and Lumley, J. L. (1973). A first course in turbulence, MIT Press, Cambridge, Mass.
Tomi, D., and Bagster, D. F. (1978). “A model of floc strength under hydrodynamic forces.” Chem. Eng. Sci., 30, 269.
Van Der Molen, K., and Van Maanen, H. R. E. (1978). “Laser-Doppler measurements of the turbulent flow in stirred vessels to establish scaling rules.” Chem. Eng. Sci., 33, 1161–1168.
Wu, H., and Patterson, G. K. (1989). “Laser-Doppler measurements of turbulent-flow parameters in a stirred mixer.” Chem. Eng. Sci., 44, 2207–2221.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 132 • Issue 11 • November 2006
Pages: 1260 - 1268
Copyright
© 2006 ASCE.
History
Received: Oct 8, 2003
Accepted: Sep 27, 2005
Published online: Nov 1, 2006
Published in print: Nov 2006
Notes
Note. Associate Editor: Nikolaos D. Katopodes
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