Direct numerical simulations of solid-liquid suspension in a transitional stirred tank

Abstract

Solid-liquid stirred tanks are very common in industrial process, for example pharmaceutical engineering, water treatment and crystallization. In these operating units, solid-liquid two-phase flows affect the rates of momentum, mass and heat transfer as well as the chemical reactions significantly. The flow regime in most investigations of solid-liquid suspension is either laminar or turbulent, however the transitional regime is also very important especially when scaling up from bench scale to pilot scale. Therefore, it is important to investigate the hydrodynamic characteristics of solid-liquid suspension in a transitional stirred tank. In this work, the lattice Boltzmann method was used to solve the liquid flow field. The uniform, cubic grids were applied with grid spacing Δ and time step Δ t representing the lattice units in space and time respectively. The stirred tank is a cubic tank with a flat bottom, whose height and side length of the bottom are both equal to 264 Δ. The impeller is a 45° pitched-blade turbine with diameter D =189.6 Δ; width of the impeller blade W =38.4 Δ and it operates under the down-pumping configuration. The impeller-based Reynolds number is 1334, which indicates that the flows belong to transitional regime. The particles are all equally sized solid spheres with diameter d p=9.6 Δ. As for the boundary conditions in this work, the half-way bounce-back rule was used to form the no-slip boundary conditions at all tank walls including top, bottom and side walls. The immersed boundary method was applied to impose the no-slip boundary conditions at the particles surface and the impellers surface. When it comes to the collisions, a hard-sphere collision algorithm based on the two-parameters model (restitution coefficient and friction coefficient) was adopted to carry out the collisions among the particles as well as the collisions between the particles and the tank walls. The collisions between the particles and the impeller were performed by using a soft-sphere collision model. In addition, the lubrication force was applied to deal with the close-range hydrodynamic interaction between the solid surfaces. This paper mainly did the simulations for different solids volume fractions Φ =0%, 1%, 5% and 8% at impeller angle θ =30° and at the same time resolved the impeller angles to 0°, 30° and 60° for solids volume fraction Φ =5%. In terms of simulated results, at first we compare the instantaneous liquid flow field between the single-phase system and the solid-liquid two-phase system, which shows that the exist of particles clearly hindered the liquid flow field especially in the impeller-discharge region. This paper also compares the averaged hydrodynamic characteristics between the single-phase system and the solid-liquid two-phase system. The results show that the averaged liquid velocity did not change obviously with the rise of solids volume fraction from 0% to 1%, however, when the solids volume fraction rose up to 5% or even higher to 8%, the averaged liquid velocity decreased obviously in the impeller-discharge region as well as the region near the bottom of the stirred tank at impeller angles θ =30°. Finally, the turbulent kinetic energy (TKE) of the liquid is compared qualitatively and quantitatively and it shows that the TKE values decreased significantly with the rise of solids volume fraction at impeller angle θ =30°. The peak TKE values decreased more than 50% with the rise of impeller angle θ from 0° to 30° for solids volume fraction Φ =5%, however the peak TKE values did not change obviously with the impeller angle θ rising from 30° to 60°.