Numerical Simulation Of Micro-mixing In Stirred Tanks

Stirred tanks are widely used in process industries as typical reactive-mixing equipments.The quality of desired or target products and the cost for processing are directly associated with the hydrodynamics,mixing and mass transfer characteristics therein.Especially for the mixing-sensitive chemical process with side-reactions,if the reactants added into the reactor fail to achieve the molecular-level homogeneity quickly,the local mixing conditions around the feed pipe exit will have a significant influence on the yield and quality of desirable products and the process stability.Intensive and thorough studies on different mixing scales,especially on micro-mixing which directly affects chemical reactions,will benefit remarkably the design,optimization and scale-up of industrial stirred-tank reactors and the process intensification.The major objective of this work is to investigate the turbulent reactive flows in single-and multi-phase stirred tanks numerically.It is expected to understand the effect of micro-mixing on the selectivity of complicated multiple reactions systems and analyze the practical problems with the proper micro-mixing models.The primary findings are listed as follows.(1)In this work,a new micro-mixing simulation method combining the Engulfment model(E-model)with computational fluid dynamic(CFD)is proposed and applied to investigate the micro-mixing in semi-batch stirred tanks.The new modeling approach describes the macro-and micro-scale segregation of materials with the mixture fraction and its variance.The micro-mixing effects on the course of the hydrolysis of ethyl chloroacetate in competition with the neutralization of sodium hydroxide and the iodide/iodate reaction coupled with the neutralization reaction are examined respectively.The numerical predictions of segregation index at different impeller speeds,feed locations and feed concentrations are in good agreement with the reported experimental data.This practical method does not need any parameter obtained from experiment and requires low computational costs,making it more suitable for studying micro-mixing in industrial scale reactors.(2)Based on the Eulerian-Eulerian multi-fluid model with using the mixture fraction and its variance,the CFD method combining with the E-model is extended to a two-phase form which is used to simulate the micro-mixing effects on the course of parallel competing chemical reactions in semi-batch gas-liquid and solid-liquid stirred tanks,respectively.The flow field is obtained with the two-phase k-ε turbulent model and a model of variable bubble size is adopted to predict the bubble size distribution for the gas-liquid system.Compared with experimental data,the multi-phase numerical method shows the satisfactory predicting capability.The trends of predicted segregation index are captured under different solid concentrations,gas flow rates,feed positions,and so on.For the gas-liquid system,the turbulent level near the free surface is apparently strengthened with the increase of gassing rate and the consumption time for every added reactant element decreases due to the enhanced mixing,but the micro-mixing with feeding reactant near the impeller has no significant improvement.For the solid-liquid system,when the solid cloud is formed at high solid holdups,the flow velocity in the clear liquid layer is notably reduced,so the reactions proceed more slowly in this almost stagnant zone near the surface.(3)By solving the Reynolds-averaged transport equations of the mixture fraction and its variance,the feed pipe backmixing is investigated with CFD simulation.The qualitative characteristics with the presence of feed pipe backmixing are presented in this work and the quantitative simulation results are compared with the relevant experimental data.The flow characteristics inside the feed pipe close to its opening is notable under backmixing.There is a vortex inside the feed pipe and the vortex will occupy the entire exit cross-section of feed pipe under the condition of serious backmixing.The value of mean mixture fraction is apparently smaller than one inside the feed pipe due to backmixing of fluid into the feed pipe,and the high values of mixture-fraction variance gradually move from the inside of feed pipe to its opening with the decrease of feed pipe diameter and the increase of feed rate.(4)The two-environment DQMOM-IEM(Direct quadrature method of moments combining with the interaction by exchange with the mean micro-mixing model)model is implemented for the first time to predict quantitatively the effects of mixing on the distribution of products in a semi-batch stirred-tank reactor.The predictive behavior of DQMOM-IEM micro-mixing model used for stirred tank is verified with the experimental data.The higher the agitation speed is,the lower the yield of by-product.At the relatively low feed velocity,the feed stream is more easily dispersed into the mainstream to benefit in maximizing the yield of the desired product,so the segregation index of mixing-sensitive parallel competitive chemical reactions decreases with the increase of feed time.Furthermore,the visualization of reaction plume presented in this work shrinks toward the feed pipe exit where the mixture fraction variance is large.(5)The DQMOM-IEM micro-mixing model is applied for the first time to simulate the novel reactive-PLIF(Planar laser-induced fluorescence)experiment in an un-baffled stirred tank.For this real complex reactive system,all the reactants concentrations are related to the mixture fraction and reaction progress variables after detailed derivation.The effects of impeller speed and off-bottom clearance on the mixing and fast chemical reactions occurring simultaneously are investigated and compared with the experimental data.By using the mixture fraction and reaction progress variables,the descriptions of the Fenton reaction and oxidation reaction of Rhodamine B are formulated.The quenching process of fluorescence signal can be visualized by solving the probability,probability weighted mixture fraction and reaction progress variables used in the two-environment DQMOM-IEM micro-mixing model.With the increase of impeller speed,both the physical mixing time and the reactive mixing time are reduced due to the enhanced turbulence level.The impeller off-bottom clearance plays an significant role on the flow pattern,so the reactive time is sensitive to the impeller off-bottom clearance and there exists a optimized operating position which needs the minimum quenching time of fluorescent emission of Rhodamine B.Compared with the predicted results neglecting the concentration fluctuations,the significant effect of micro-mixing on the course of chemical reactions is apparent.Hence,the DQMOM-IEM micro-mixing model is useful to describe the sub-grid mixing and close the non-linear chemical source term.The program and the deducing method to express the concentrations of reactants with mixture fraction and reaction progress variables can be used not only to simulate the reactive PLIF progress,but also to calculate other mixing-sensitive reactions applied in chemical industries.