中文摘要：

采用泰勒展开矩方法对二维瑞利-贝纳德热对流系统（1×10^6≤Ra≤1×10^8）中纳米颗粒群的混合和凝并特性进行了数值模拟．结果显示颗粒群随时间演化经历了扩散阶段、混合阶段、充分混合阶段3个阶段，随着颗粒群混合和凝并的进行，颗粒数目浓度减少，颗粒群的平均体积增大；得到了颗粒分布函数各特征量与温度相关系数以及各特征量的空间分布标准偏差在3个阶段的不同特征；得到了颗粒分布函数各阶矩以及平均体积长时间演化的渐近行为，结果与零维渐近解析解一致．最后，本文进一步研究了无量纲数（包括瑞利数砌，斯密特数scM，达姆科勒数Da）对颗粒群达到自保持分布时间的影响，发现该时间随着尺口和SCM的增大呈对数率减小，随着Da的增大呈线性增大．

英文摘要：

In the present simulations, the first three moments of the particle size distribution of nanoparticles in a two dimensional Rayleigh-Benard convection system are calculated with the combination of SIMPLE algorithm and the Tayler-series expansion method of moments （TEMOM） to probe into Brownian coagulation and mixing of nanoparticles. Driven by Brownian coagulation, diffusion and thermal convection, the number concentration of nanoparficles decreases, while the average volume increase generally as time goes on. The temporal evolution of nanoparticles can be divided into three stages, named the diffusion stage, the mixing stage and the fully mixing stage respectively. The correlation coef- ficients between moments of nanoparticles and the temperature, and relative standard deviation of moments experience distinct characteristics in three stages. The long-time behavior for moments of nanoparticles is obtained and is in good agreement with the asymptotic solution. Finally, the time to attain such an asymptotic solution is investigated and its dependence on Ra, S CM and Da is also determined numerically. The results show that the time decreases logarithmically when Ra and S CM increase, while it increases linearly when Da increases.