二维方腔热对流系统中纳米颗粒混合及凝并特性的数值模拟

徐飞彬; 周全; 卢志明

doi:10.6052/0459-1879-15-062

二维方腔热对流系统中纳米颗粒混合及凝并特性的数值模拟

doi: 10.6052/0459-1879-15-062

上海市应用数学和力学研究所, 上海200072

基金项目: 国家自然科学基金资助项目(11272196,11332006).

详细信息

通讯作者:
卢志明,教授,主要研究方向:湍流理论,计算流体力学和环境流体力学.E-mail:zmlu@shu.edu.cn

中图分类号: O359+.1
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出版历程
- 收稿日期: 2015-02-26
- 修回日期: 2015-06-15
- 刊出日期: 2015-09-18

NUMERICAL SIMULATION OF BROWNIAN COAGULATION AND MIXING OF NANOPARTICLES IN 2D RAYLEIGH-B?NARD CONVECTION

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China

Funds: The project was supported by the National Natural Science Foundation of China (11272196, 11332006).

摘要

摘要: 采用泰勒展开矩方法对二维瑞利-贝纳德热对流系统(1×10⁶ ≤Ra ≤1 ×10⁸) 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Ra, 斯密特数Sc_M, 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Ra和Sc_M的增大呈对数率减小, 随着Da的增大呈线性增大
- 泰勒展开矩方法 /
- 纳米颗粒 /
- 瑞利-贝纳德热对流 /
- 混合 /
- 凝并 /
- 数值模拟
Abstract: In the present simulations, the first three moments of the particle size distribution of nanoparticles in a two dimensional Rayleigh-Bénard 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 nanoparticles 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 coefficients 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, Sc_M and Da is also determined numerically. The results show that the time decreases logarithmically when Ra and Sc_M increase, while it increases linearly when Da increases.
- TEMOM /
- nanoparticle /
- Rayleigh-B′enard convection /
- mixing /
- coagulation /
- numerical simulation

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