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Mass Transfer in Multiphase Systems and its Applications Part 5

Tham khảo tài liệu 'mass transfer in multiphase systems and its applications part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Toward a Multiphase Local Approach in the Modeling of Flotation and Mass Transfer in Gas-Liquid Contacting Systems 149 The decomposition of the Reynolds stress tensor in a turbulent and pseudo-turbulent contributions with specific transport equation for each part makes possible the computation of the specific scales involved in each part. The determination of these scales allows to describe correctly the different effects of the bubbles agitation on the liquid turbulence structure. 10 100 Fig. 4. Turbulent intensity in single-phase and bubbly boundary layer. 1000 Fig. 5. Turbulent shear stress in single-phase and bubbly pipe flows. If from a theoretical point of view second order is an adequate level for turbulence closure in bubbly flows the implementation of such turbulence models in two-fluid models clearly improves the predetermination of the turbulence structure in different bubbly flow configurations Chahed et al. 2002 2003 . Nevertheless from a practical point of view second order modeling is still difficult to use and turbulence models based on turbulent viscosity concept particularly two-equation models remain widely used in industrial applications. Several two-equation models were developed for turbulent bubbly flows Lopez de Bertodano et al. 1994 Lee et al. 1989 Morel 1995 Troshko Hassan 2001 . All of these models are founded on an extrapolation of single-phase turbulence models by introducing supplementary terms source terms in the transport equations of turbulent energy and dissipation rate. In some models the turbulent viscosity is split into two contributions according to the model of Sato et al. 1981 a turbulent contribution induced by shear and a pseudo-turbulent one induced by bubbles displacements. To adjust the turbulence models some modifications of the conventional constants are sometimes proposed Lee et al. 1989 Morel 1995 . The reduction of second order turbulence modeling developed for two-phase bubbly flows furnish an interpretation of .