Network of zones

Scientists of the Institute of Science and Technology of UMIST (Manchester, UK) and collaborating laboratories have developed a network-of-zones model (Mann et al, 1981 Mann and Knysh, 1984 Mann and El-Hamouz, 1992, 1995 Mann et al, 1995 Nienow et al, 1992 Togatorop et al, 1994 and Wang and Mann, 1990, 1992). According to this model a reaction volume is represented by an assembly of backmixed zones, each of equal volume. The liquid... 

Mann, R., D. Vlaev, V. Lossev, S. D. Vlaev, J. Zahradnik, and P. Seichter (1997). A network of zones analysis of the fundamentals of gas liquid mixing in an industrial stirred bioreactor. Recent Progres dans le Genie des Procedes 11, 223-230. 

FIGURE 1.7 Network of zones model for stirred reactors 2 x 10 x 10 network. Flow through different zones was specified using experimental measurements (from Mann and Mavros, 1982). 

A different numerical strategy to simulate multiphase mixing was introduced by Mann and Mann and Hackett. The idea of the method, called the network-of-zone, is to subdivide the flow domain in a set of small cells assumed to be mixed perfectly. The cells are allowed to exchange momentum and mass with their neighboring cells by convective and diffusive fluxes. Brucato and Rizzuti and Brucato et al. applied this idea to the modeling of solid-liquid mixing. An unsteady mass balance for the particles was derived to estimate the solid distribution in the vessel, namely ... 

The attractiveness of the network-of-zone method to compute solid-liquid mixing flows resides in its relative simplicity while being capable of capturing the main flow phenomena for a wide range of concentrations. The objective of the present work is to assess the real capability of this approach in the case of a complex mixing problem involving a coaxial mixer. Coaxial mixers are very popular for the preparation of pastes and slurries in the chemical, food, and coating industries. Another mixer setup is also tested. 

Solid-liquid mixing processes can be simulated with good precision when sound CFD methods are used. The application of a combination of the virtual finite element method and the network-of-zone approach was used in this work to analyze the complex flow and suspension mechanisms in a coaxial mixer. Experiments carried on the laboratory scale confirmed fhe validity of the predictions. 

Mann, R. Gas-liquid stirred vessel mixers toward a unified theory based on network-of-zones. Chem. Eng. Res. Des. 1986, 64, 23-34. 

Brucato, A. Rizzuti, L. In The Application of the Network-of-Zones Model to Solid-Liquid Suspensions, Proceedings 6th European Conference on Mixing, Pavia, Italy, 1988 273-280. 

Brucato, A. Magelli, F. Nocentini, M. Rizzuti, L. An application of the network-of-zones model to solids suspension in multiple impeller mixers. Trans. Instn. Chem. Engrs. 1990, 69, Part A, 43-52. 

The logical extension of this approach is to divide the crystallizer into many compartments. This is known as the network of zones approach and has been used suceessfully by Mann (1993). Here, the exchange flows between compartments are not modeled but applied separately, either from a knowledge of the overall flow pattern achieved from experimental measurements or from a CFD flow model. Additionally, rules are applied which describe the turbulent transport of particles and species between zones. 

The inherent problem of all compartment models is the poor spatial resolution. By significantly increasing the number of compartments (up to 40000 zones) the network-of-zone (NOZ) models could overcome this problem [23-25]. However, the problem of identification and physical interpretation of the model parameters remains unchanged. The macromixing effects are reflected in the choice... 

A network-of-zones analysis of the fundamentals of gas-liquid mixing in an industrial stirred bioreactor. Recents Progr. Genie Proced., 11, 223-230. 

Mann, R., and A. E-Hamouz (1991). Effect of macromixing on a competitive consecutive reaction in a semi-batch stirred reactor Paul s iodination experiments interpreted by networks of zones, presented at the 7th European Conference on Mixing, Brugge, Belgium, Sept. 18-20. 

Wang, Y. D., and R. Mann (1990). Mixing in a stirred semi-batch reactor partial segregation for a pair of competing reactions analyzed via networks-of-zones, Inst. Chem. Eng. Symp. Ser., 121(Fluid Mixing 4), 241-258. 

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