Particle Image Velocimetry Experiments And Direct Numerical Simulations Of Solid-liquid Mixing In Stirred Tanks With Settling Particles

Solid-liquid mixing is very common in both industrial processes and daily life,for example,petrochemical engineering,hydrometallurgy,wastewater treatment,crystallization reaction,papermaking process,biopharmaceutical industry and food processing.Compared with liquid single-phase mixing,the mixing between solids and liquid is more complicated due to the collisions among particles as well as the interactions between the solid particles and the liquid.The solid-liquid two-phase flow affects the rates of momentum,mass and heat transfer as well as the chemical reactions in stirred tanks significantly.Therefore,it is very relevant to investigate the hydrodynamic behaviors of either the liquid or the solid particles in stirred tanks.In this paper,the Particle Image Velocimetry(PIV)technique and the Lattice Boltzmann Method(LBM)are used to perform the experiments and the numerical simulations in stirred tanks with settling particles under different operating conditions to investigate the hydrodynamic behaviors of the continuous phase as well as the dispersed phase.When applying the laser-based optical imaging technique,for example the PIV,to solid-liquid stirred tanks,a main limiting factor is the solids concentration which was always limited less than 1%by volume in most previous investigations.The reason for this is that the particles will obstruct and scatter the laser light and this kind of obstruction and scattering will get more and more severe with the rise of solids volume fractions.This kind of phenomenon will lead to erroneous velocity measurements and poor signal-to-noise ratios.In order to overcome this problem and increase the solids volume fractions in solid-liquid stirred tanks,the Refractive Index Matching(RIM)method is adopted.When investigating the solid-liquid mixing in a turbulent stirred tank in this paper,the phenyl silicone oil was chosen as the continuous phase to match the refractive index of the silica glass spheres.In this way,the solids volume fraction was increased up to 8%in this study.The diameter of the spheres in this study is 8 mm,which is much bigger than those in most previous investigations(usually less than 1 mm).The resolutions of both the PIV experiments and the LBM direct numerical simulations are high enough to resolve the liquid flow fields in the whole stirred tank including those around and among the spheres.Therefore,this makes it possible to study the solid-liquid interactions,particle distributions,mean liquid velocities and liquid turbulence on particle scale for the first time.The PIV experimental results showed that the exist of particles hindered the nearby liquid flow fields and at the same time the mean velocities,root-mean-square(rms)velocities and turbulent kinetic energy(TKE)of the liquid all decreased with the rise of solids volume fractions.The simulated results agreed quite well with the experimental data in aspect of averaged particle distributions,rms velocities and TKE of the liquid.However,when it comes to mean liquid velocities,the simulated results did not show an obvious decline with the rise of solids volume fractions,which is inconsistent with the experimental data.In most cases of solid-liquid mixing,the flow regime is either laminar or turbulent.However,operations under transitional flow conditions are receiving more and more attention.When scaling up from bench scale to pilot scale,results obtained for transitional flow at bench scale need to be carefully interpreted before applying them to-fully turbulent-pilot scale conditions.Therefore,it is important to investigate the process of solid-liquid suspension in stirred tanks with transitional flows with an emphasis on the way liquid and solids interact.In this paper,the sucrose and sodium chloride aqueous solution and the silica glass spheres were chosen as the continuous phase and dispersed phase respectively to carry out RIM in the transitional stirred tank.The maximum solids volume fraction was up to 8%in this study.The liquid flow fields around and among the particles were also highly resolved in both the PIV experiments and the LBM direct numerical simulations.With the solids volume fraction rising from 0%to 8%,the maximum decline of the liquid TKE values reached 39%and 21%for the experiments and simulations,respectively,and the maximum decline of the mean liquid velocities was 12%and 3%for the experiments and simulations,respectively.In addition,the simulated results agreed quite well with the experimental data in aspect of instantaneous and averaged particle distributions,which showed that the particle concentrations were pretty high underneath the impeller and in the region near the tank walls.For the first time,the high-frequency PIV technique was used to investigate the start-up of particles suspension and the evolutions of liquid flow fields with solids volume fraction up to 20%and the number of the particles up to 8.266×104.The‘mapping function'model,which is used to deal with the interactions between the solid particles and the liquid,combined with LBM was used to perform the simulations under the same operating conditions as those in the high-frequency PIV experiments.The particle volumes as well as the interactions between the particles and the liquid were included in the simulations.The simulated results agreed quite well with the experimental data.This is the basic to extend the numerical simulations of solid-liquid mixing in stirred tanks from bench scale to industrial scale.