-
the modified k—r, equations are solved for the continuous phase as is observed in the experiments. The stronger loop is because and the turbulence quantities of dispersed phase are calculated of the high magnitude £fKial velocities stril‹ing the wa s Which 1s using Tchen—theory correlations. It also ta1‹es the fluctuations due not the case in the region above impeller. Comparisons were dolls to turbulence by solving for the interphase turbulent momentum with respect to the solids velocities, turbulent l‹inetic energy, afld transfer. For the sake of brevity, only the equations of mixture solids sojourn times at various parts of the tanl‹. LES predicted model for turbulence are given below. Other equations can be radial velocities fietter than the Euler—Euler in the impeller planés found in the Fluent user guide [14].
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Elsewhere, both the predictions were comparable. It was because
of the high turbulent fluctuations in this region that was not tal‹en into account by the drag formulation used.
D. 'ndnerknr ct aI./ Advanced Powder Technology 23 (20 12) 445—453 447
C „ and Cz,- are constants, cr, and v are turbulent Prandtl numbers.
The mixture density, pz and velocity, fig are computed from the equations below:
Turbulent viscosity, y and turbulence l‹inetic energy, G are computed from equations below:
3.3. Tui bulent dispersion force
In the simulation of solid suspension in stirred tanks, the turbu— lent dispersion force is significant when the size of turbulence ed- dies is larger than the particle size [2]. Its significance is also highlighted in some previous studies [4 5]. The role of this force is also analysed in this study. It is incorporated along with the momentum equation and is given as follows:
where drift velocity, dr is given by,
Dp And D are diffusivities and cr is dispersion Prandtl number.
3.4. Interphase drag force
The drag force represents interphase momentum transfer due to the disturbance created by each phase. For dilute systems and low Reynolds number, particle drag is given by Stokes law and for high Reynolds number, the Schillar Nauman drag model can be used. In the literature review other drag models such as Gidas- pow model [10] and Wen and Yu model [16] have also been dis- cussed. But for stirred tanl‹ systems, there should be a model that tal‹es turbulence into account as with increasing Reynolds number and with the increase in the eddy sizes, the impact of tur- bulence on the drag increases. Considering this Brucato et al. [11 ] proposed a new drag model making drag coefficient as a function of ratio of particle diameter and Itolmogorov length scales. So, with the change in the turbulence at some local point in the system, the drag will also change. The drag coefficient proposed by Brucato et al. is given below:
are available in the literature [17,18]. For the conditions studied in this paper, the drag force calculated using these models was similar to the modified Brucato drag model. Therefore, Brucato and modified Brucato models were used for further study.