Breakup Mechanism Of Fluid Particle And Population Balance Modeling In Particle-Laden Turbulent Flow

The fluid particle breakage significantly increases the surface area at the interfaces and thus contributes to the heat and mass transfer processes in particle laden-turbulent flow,which is commonly found in nature and engineering applications.The particle breakage problem has been one of the most important issues in the fields of environment,chemical engineering and energy that remains to be studied.In this dissertation,the deformation/breakage mechanism of the liquid particle caused by turbulence in process industry is explored by theoretical analysis and population balance modeling.The efficient numerical method and stochastic algorithms for population balance problems with growth processes are developed.A theoretical model is proposed for the particle deformation induced by turbulent fluctuations based on the particle-eddy interaction model and dimensional analysis.The effect of surface deformation on the breakage rate of the liquid particle is quantitatively analyzed.The mean surface deformation ratio of the liquid particle according to the present model for the air-water system is in good agreement with available results.Further analysis indicates that the minimum energy required for particle breakage is significantly dependent on the surface deformation,which is underestimated in previous breakup models.Also,results show that these models have the sensitivity of the integration limits.This work not only provides a good prediction of fluid particle deformability but also gives us further insight into the breakage mechanism of the liquid particle in particle-laden turbulent flows.Considering the deformation properties of the liquid particle during the particle-eddy interaction process,a breakup model(DB model)for the liquid particle in turbulent dispersions is developed.In particular,the characteristic sizes of the effective colliding eddies contributing to the particle breakup process are computed based on the change of the surface energy in this work.Compared with experimental data,the predicted breakage rate and daughter size distribution show a good agreement.The model makes good predictions of the total breakage rate,the daughter size distribution as well as the contribution of effective eddies to the total breakage rate.This work reveals the competitive mechanism between the equal-sized breakup and the unequal-sized breakup.The DB model offers a more fundamental breakup kernel for the population balance model.A Monte Carlo method for the simulation of breakage based on weighted simulation particles and a reconstruction scheme(RSMC)is proposed.Key elements of the reconstruction scheme include segment storage strategy,collapse strategy,weight control strategy and Ghost class recovery strategy.The quantitative evaluation method for computation accuracy is introduced.The RSMC method is verified by a series of classic cases with known analytical solutions.The numerical results show high accuracy compared with the analytical solutions.It is demonstrated that the new RSMC method can optimize the computational speed and accuracy by using the Ghost class particles(or zero-weighted particles),and advantages at excellent numerical accuracy and stability,with particularly less statistical simulation noise over several conventional Monte Carlo approaches.Based on several breakup models and the proposed RSMC method,the dynamic evolution of particle size distribution is studied numerically in a stirred tank.Both the evolution characteristics of particle size distribution and the predictive capabilities of different breakup models are investigated.The numerical results show that the volume cumulative distribution and Sauter average diameter by the DB model are in good agreement with the experimental data.The maximum stable particle size and the minimum particle size model can effectively improve the numerical calculation accuracy of some previous breakup models.However,the predicted volume cumulative distribution is relatively scattered.Further study reveals that the effect of different breakup models on the predictions of particle size distribution is greater than that on the Sauter mean diameter.To solve population balance problems with complex breakage,coagulation,and nucleation processes,the efficient Hybrid Monte Carlo method with the reconstruction scheme(RHMC)is proposed.The coalescence criteria of the weighted particle pair and a fast acceptance-rejection(AR)technique are introduced.The RHMC algorithm is verified by comparison with analytic solutions of a series of classic cases.The simulation results show that the symmetry coalescence criterion has a clearer physical meaning and a better prediction than the non-symmetry one.We obtain excellent results for several test problems on simultaneous coagulation and breakage.Furthermore,the event-driven RHMC algorithm is applied to the numerical study of coagulation and nucleation processes successfully.It is found that the RHMC algorithm has low statistical noise,high accuracy,and long-term calculation stability.