| The flame spray pyrolysis(FSP)synthesis method of nanoparticles has the advantages of high synthesis efficiency,scalable,flexible control and low pollution,and is a promising method for functional materials synthesis.But this process is a multi-scale,non-linear,strong turbulent and complex particle dynamics process,and it is difficult to understand and optimize this process with theoretical and experimental methods.Combining computational fluid dynamics(CFD)with population balance modelling(PBM)is an effective method to study the flame spray pyrolysis process and predict the properties of nanoparticle products.There are many CFD methods and many PBM methods.Among these,the LES(large-eddy simulation)method in CFD has high calculation accuracy and moderate calculation cost.The population balance Monte Carlo(PBMC)method in PBM is simple in principle,easy to expand,easy to program,and has high calculation efficiency for multivariable problems.Therefore,the coupled LES-PBMC has great potential for the simulation of FSP process.However,no one has yet used LES-PBMC to study the flame spray pyrolysis process,which is ascribed to,at least,the huge computational cost of multi-dimensional PBMC,and difficulty in coupling LES and PBMC.And this is the first study to adopt PBMC to investigate the flame spray pyrolysis process.In the first place,this study improves the existing multi-dimensional PBMC method from three aspects to improve its calculation efficiency and reduce its numerical errors.First,based on the assumption of particle linear distribution in a grid and the idea of direct compution of particle transport distance among grids,the numerical technique for particle transport among grids,as an important module of multi-dimensional PBMC simulation,was improved to overcome the numerical diffusion problem which exists in those based on the assumption of particle uniform distribution in a grid,and its calculation efficiency was increased by nearly 506 times.Then with the further optimization of majorant kernels,the fast PBMC method for particle coalgulation was improved to increase its calculation efficiency by 4 times meanwhile keep same computational precision.Finally,the numerical technique for population reconstruction in a grid was improved,where the split-merge algorithm was proposed according to the balance in simulation particle weights and the idea of small approximation error.This split-merge algorithm had no random error during the reconstruction process of simulation particle population,and the approximation error is small,and the error will not be amplified as the particle population evolves.The split-merge algorithm can well inherit the information of the original simulation particle population.Then,this study validated the calculation accuracy of the Nonlinear Large Eddy Simulation-Partially Stirred Reactor(NLES-Pa SR)model for the typical operating conditions of pure spray combustion(without the precursor)in a pilot-scale spray pyrolysis burner.And then the NLES-Pa SR model was one-way coupled with the improved multi-dimensional PBMC to study the flame spray pyrolysis process of synthesis of Zr O nanoparticles.The results showed that the flow fields were very similar between the FSP condition of nanoparticles and the corresponding pure spray combustion condition;the improved multidimensional PBMC method can well describe the spatially-inhomogeneous particle transport process among grids;the improved multidimensional PBMC can capture the difference between the average size of primary particles and the average size of nanoparticles from the beginning;the characteristic coagulation rate is lower than the actual coagulation rate,but the characteristic sintering time scale can reflect the sintering situation of nanoparticles well;the average size of primary particles on the axis of the outlet can represent the situation of the entire outlet,but the average size of nanoparticles on the axis of the outlet is lower than the overall average particle size at the outlet. |
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