Turbulent Flow in Stirred Vessels

Turbulent Flow in Stirred Vessels Turbulence parameters such as intensity and scale of turbulence, correlation coefficients, and... 

Basara et al [3] simulated single- and two-phase turbulent flows in stirred vessels equipped with six- and four blade Rushton-t3q)e turbines using the sliding mesh impeller method. To describe turbulence in the liquid phase a standard k-e model was used for single phase calculations and an extended k-e model was employed for the two-phase simulations. These simulations were performed in transient mode with 1 (ms) time steps. The whole calculation contains 3900 time steps, which means approximately 4s of real time and 17 complete rotations of the impeller. One such simulation took 13 days of CPU time using an Intel single processor with 2.6 GHz). The flow patter predictions were compared with experimental data and fair agreement was obtained. It was stated that the standard k-e model over-predicted the... 

Molen, van der, k. andMAANEN, VAN, H. R. E. Chem. Eng. Sci. 33 (1978) 1161. Laser-Doppler measurements of the turbulent flow in stirred vessels to establish scaling rules. 

Turbulent Flow in Stirred Vessels Turbulence parameters... 

In addition, it is dubious whether this new correlation due to Brucato et al. (1998) should be used in any Euler-Lagrangian approach and in LES which take at least part of the effect of the turbulence on the particle motion into account in a different way. So far, the LES due to Derksen (2003, 2006a) did not need a modified particle drag coefficient to attain agreement with experimental data. Anyhow, the need of modifying particle drag coefficient in some way illustrates the shortcomings of the current RANS-based two-fluid approach of two-phase flow in stirred vessels. 

Gosman, A.D., Lekakou, C., Politis, S., Issa, R.I. and Looney, M.K. (1992), Multi-dimensional modeling of turbulent two-phase flows in stirred vessels, AIChE J., 38, 1946-1956. 

T irbulent Flow in Stirred Vessels Turbulence parameters such as intensity and scale of turbulence, correlation coefficients, and energy spectra nave been measured in stirred vessels. However, these characteristics are not used directly in the design of stirred vessels. 

Gosman AD, Lekakou C, Polits S, Issa RI, Looney MK (1992) Multidimensional Modeling of Turbulent Two-Phase Flows in Stirred Vessels. AIChE J 38(12) 1946-1956... 

Smith, G. W., L. L. Tavlarides and J. Placek, Turbulent flow in stirred tanks scale-up computations for vessel hydrodynamics, Chem. Eng. Comm., 93, 49-73 (1990). 

Sahu, A. K., and J. B. Joshi, Simulation of Flow in Stirred Vessels with Axial Flow Impellers Effects of Various Numerical Schemes and Turbulence Model Parameters, J. Amer. Chem. Soc., in press. 

Such spatial variations in, e.g., mixing rate, bubble size, drop size, or crystal size usually are the direct or indirect result of spatial variations in the turbulence parameters across the flow domain. Stirred vessels are notorious indeed, due to the wide spread in turbulence intensity as a result of the action of the revolving impeller. Scale-up is still an important issue in the field of mixing, for at least two good reasons first, usually it is not just a single nondimensional number that should be kept constant, and, secondly, average values for specific parameters such as the specific power input do not reflect the wide spread in turbulent conditions within the vessel and the nonlinear interactions between flow and process. Colenbrander (2000) reported experimental data on the steady drop size distributions of liquid-liquid dispersions in stirred vessels of different sizes and on the response of the drop size distribution to a sudden change in stirred speed. 

CFD might provide a way of elucidating all these spatial variations in flow conditions, in species concentrations, in bubble drop and particle sizes, and in chemical reaction rates, provided that such computational simulations are already capable of reliably reproducing the details of turbulent flows and their dynamic effects on the processes of interest. This Chapter reviews the state of the art in simulating the details of turbulent flows and turbulent mixing processes, mainly in stirred vessels. To this end, the topics of turbulence and CFD both need a separate introduction. 

Even nowadays, a DNS of the turbulent flow in, e.g., a lab-scale stirred vessel at a low Reynolds number (Re = 8,000) still takes approximately 3 months on 8 processors and more than 17 GB of memory (Sommerfeld and Decker, 2004). Hence, the turbulent flows in such applications are usually simulated with the help of the Reynolds Averaged Navier- Stokes (RANS) equations (see, e.g., Tennekes and Lumley, 1972) which deliver an averaged representation of the flow only. This may lead, however, to poor results as to small-scale phenomena, since many of the latter are nonlinearly dependent on the flow field (Rielly and Marquis, 2001). 

In whichever approach, the common denominator of most operations in stirred vessels is the common notion that the rate e of dissipation of turbulent kinetic energy is a reliable measure for the effect of the turbulent-flow characteristics on the operations of interest such as carrying out chemical reactions, suspending solids, or dispersing bubbles. As this e may be conceived as a concentration of a passive tracer, i.e., in terms of W/kg rather than of m2/s3, the spatial variations in e may be calculated by means of a usual transport equation. 

Venneker, B. C. H., Turbulent flow and gas dispersion in stirred vessels with pseudo plastic fluids , Ph.D. Thesis, Delft University of Technology, Delft, Netherlands (1999). 

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