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The hydrodynamic study is simulated using Eulerian—Eulerian multiphase model. The phases, in this model, are treated as inter- penetrating continua represented by a volume fraction at each point of the system. The Reynolds averaged mass and momentum balance equations are solved for each of the phases. The governing equations are given below:
Continuity equation:
Momentum equation:
However, this model shows potentially erratic behaviour in where q is 1 or 2 for primary or secondary phase, respectively, o: is
close-to-zero shear rate and high concentration zones. volume fraction, p is density,
The dependency of the drag on the turbulence was numerically and is shared by both the phases,
velocity vector, P is pressure stress tensor because of
investigated by Khopl‹ar et al. [3] by conducting experiments using Viscosity and velocity fluctuations, g is gravity, f „ is force due to single phase flow through regularly arranged cylindrical objects. A turbulent dissipation, ft is external force, f ,/ , is lift force, f „p , is relationship between the drag, particle diameter and ltolmogorov virtual mass force and Y z is interphase interaction force.
length scale was fit into the expression given by Brucato et al. The Stf ess—strain tensor is due to viscosity and Reynolds stres- [11]. They found that the drag predicted by the original Brucato ses that include the effect of turbulent fluctuations. Using the drag model needs to be reduced by a factor of 10. This modified Boussinesq's eddy viscosity hypothesis the closure can be given Brucato model was then used for the simulation of liquid flow field to the above momentum transfer equation. The equation can be gi- in stirred tanl‹s [2]. I r was able to capture the hey features of liquid ven as:
phase mixing process.
Panneerselvam et al. [12] used the Brucato drag law to simulate 7é v/v solids in liquid. MRF approach was used with Eulerian—Eule—
rian model. There was mismatch in the radial and tang ntia COC‘ where p is the shear viscosity, i is bull‹ viscosity and I is the unit
ponents of velocity at impeller plane. This discrepancy was t attributed to the turbulent fluctuations that dominate the impeller
tensor.
region, which the model was not able to capture successfully.
Guha [ 13] conducted numerical simulations and assessed dif—
3.2. Equations for turbulence
ferent approaches viz. LES and Eulerian—Eulerian (using Schiller— i‹-c mixture turbulence and l‹—s dispersed turbulence models are Nauman drag model) to simulate turbulent solid—11 U1d flOW in used in the present study. The mixture turbulence model assumes low solid loading (TO by volume) stirred tank by comparing with the domain as a mixture and solves for J‹ and c values which are results from the CARPT experiment. Either of the simulation ap— common for both the phases. In the dispersed turbulence model, proach was not able to predict a stronger lower circulation loo