Study On Solid-liquid Stirred Tanks By Fully Resolved Direct Numerical Simulation Based On Lattice Boltzmann Method

Solid-liquid stirred tanks are widely used in chemical,metallurgical,pharmaceutical industry and environmental engineering.The study of particle dynamics in solid-liquid stirred tank is critical to its design,scale-up and operation optimization.The study of solid-liquid stirred tanks mainly includes two interrelated scientific problems:solid-liquid mixing characteristics and particle dynamics.To be more specific,the solid-liquid mixing characteristics mainly focus on the movement of particles in a stirred tank,including the suspension of heavy particles,the drawn-down of light particles and the aggregation of particles in a stirred tank.This kind of study is very significant to the use of stirred tanks in engineering;And the study of particle dynamics focuses on the interaction forces exerted on particles in a stirred tank,which provides important information for stirred tank simulation.For the research problems mentioned in the above,this thesis mainly focuses on the phenomenon of particles aggregation and particle dynamics in the stirred tank,because we notice that these two problems have the common ground that the experiment and traditional simulation methods have encountered great difficulties in studying these two problems.The lack of proper research methods leads to few studies about these subjects reported,and many technical problems still need to be solved Recently,as the development of the lattice Boltzmann method(LBM),a novel high resolution direct numerical simulation was proposed to simulate the solid-liquid stirred tank,which is very suitable for studying these two scientific problems in stirred tanks.Therefore,the main idea of this work is to simulate the solid-liquid stirred tank based on the lattice Boltzmann method,aiming at a systematical study of the particle aggregation phenomenon and particle dynamics in a stirred tank.The specific scope and results are as follows:(1)In Chapter 2,as an application of LBM,the influence of microchannel shape and wall properties on the flow flux is studied by LBM coupled with the Shan-Chen model for modeling different hydrophobic channel walls.Firstly,the effect of channel shape and wall properties on the flux in the variable cross-section microchannel is studied.The results show that the hydrophobic surface in the microchannel can increase the fluid flux through the channel,and the flow flux is linearly and positively correlated with the slip length.Moreover,the presence of the inclined hydrophobic wall changes the flow pattern in the channel,so that the flux variation law in the hydrophobic microchannel exhibits a different tendency from a macrochannel.Subsequently,the microchannels with wetting and non-wetting walls are simulated.The results show that the flow flux in a straight hydrophobic channel is linearly related to the length of hydrophobic wall,and has little relation to the staggered arrangement of surface properties.A similar result can be found in the variable cross-section channel,and more non-wetting surface also can improve the flux in such channels.(2)Based on the LBM simulation of single-phase flow mentioned above,a direct numerical simulation program for a stirred tank is established by combining the immersed boundary method and the hard sphere model.The immersed boundary method is used to simulate the solid wall of impeller and particles.The hard sphere model is used here to deal with the collision events of a particle with other particles and solid wall.On this basis,the particle aggregation phenomenon in the low Reynolds number agitation tank is simulated.The effects of initial position of the particles,particle density,particle diameter and stirred tank Reynolds number on particle motion are investigated.The simulation results show that the particles in low Reynolds number agitation tank have their unique equilibrium regions.And the essence of the particle aggregation is that each individual particle in particle swarm approaches gradually the same stable orbit of motion.Particles at different initial positions all have the tendency to move toward to the same equilibrium region,but the particles far from this region require a longer induction time.The location of equilibrium region is related to the particle density and stirred tank Reynolds number.The light particle and high Reynolds number induce an equilibrium region,which is close to the center of vortex of liquid circulation flow,and vice versa.Besides,when the rotation speed of impeller is too fast,the flow in the stirred tank will fluctuate violently,the movement of fluid and particles exhibits more and stronger random fluctuations,and the aggregation of particles does not occur at this condition.In addition,within the particle size range studied in this paper,the particle size has little influence on the equilibrium region.(3)Base on the direct numerical simulation program for stirred tanks developed above,we extend it to simulate a system with more particles for studying the particle dynamics in a stirred tank.Based on the assumption of quasi-steady flow in a stirred tank,the simplified Eulerian-Eulerian equation and the ensemble averaged simulation results are used to analyze the interaction forces exerted on particles in a stirred tank.By comparing the interaction force calculated by the immersed boundary method and the material derivative of solid phase,the rationality of the hypothesis and feasibility of this analysis method are verified.Then the pressure gradient force and drag force in a stirred tank can be obtained through simulation.And the results show that the pressure distribution in a stirred tank is independent from the solid phase properties,but related to the stirred tank Reynolds number.It is interesting to find that the degree of influence of pressure gradient force on the particle motion depends mainly on the particle properties.The drag force in a stirred tank is related to the solid-liquid density ratio and the local particle Reynolds number.With the increase of local particle Reynolds number,the drag force increases firstly and then tends to an asymptotic value.Based on the drag force simulation results,an empirical correlation for stirred tanks is proposed by considering the influence of solid-liquid density ratio,local particle Reynolds number and local liquid energy dissipation.