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