分形颗粒在低Reynolds数条件下传热特性

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清华大学辅仁网/2017-07-07

虞君武,何榕(

),张衍国

Heat transfer characteristics of a fractal particle in a low Reynolds number flow

Junwu YU,Rong HE(

),Yanguo ZHANG

Key Laboratory of Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China

摘要:

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文章导读

摘要目前可用的单个颗粒传热计算公式是在假设颗粒为球形颗粒的基础上得到的,但实际颗粒与球体差异很大,其外形很不规则。但在涉及颗粒流的实际工业计算和相关数值模拟计算中,研究者们通常将实际颗粒近似看成球体,而能否简单采用这一球形假设,还有待进一步验证。该文通过自由漫步的方法生成了与实际颗粒很相似的分形颗粒模型,并运用分子运动论和气体扩散理论建立了分形颗粒在低Reynolds数条件下传热计算模型,研究了分形颗粒的传热特性。计算使用的颗粒直径范围为小于5 μm。计算结果表明: 分形颗粒在低Reynolds数条件下进行传热计算时,采用球形假设会产生很大误差,最大误差可达82%; 分形颗粒的比表面积和分形维数对Nu有重要影响。

关键词 ：分形颗粒,分子运动论,分子扩散,传热系数

Abstract：Current heat transfer coefficient formulae for particles are derived from data for spheres. However, a real particle is not a sphere, but an irregular body, so the assumption that the real particle approximates a sphere is questionable in mathematical models. Fractal models, which give shapes similar to real particles, are produced by the random walk method to calculate the heat transfer coefficient of a factual particle in a low Reynolds number flow using kinetic theory and gas diffusion theory. The particle diameter is less than 5 μm. Simulations show that the spherical assumption is not suitable for the fractal particle with a maximum error of 82%. Nu is then greatly influenced by the specific area and fractal dimension.

Key words：fractal particle kinetic theory molecular diffusion heat transfer coefficient

收稿日期: 2013-10-25 出版日期: 2015-03-17

基金资助:国家自然科学基金项目(21376134)

引用本文:

虞君武,何榕,张衍国. 分形颗粒在低Reynolds数条件下传热特性[J]. 清华大学学报（自然科学版）, 2014, 54(6): 781-786.
Junwu YU,Rong HE,Yanguo ZHANG. Heat transfer characteristics of a fractal particle in a low Reynolds number flow. Journal of Tsinghua University(Science and Technology), 2014, 54(6): 781-786.

链接本文:

http://jst.tsinghuajournals.com/CN/或 http://jst.tsinghuajournals.com/CN/Y2014/V54/I6/781

图表:

计盒维数测量原理图^[10]

立方网格内分子运动示意图

随机行走方法生成的分形颗粒模型外观图

计算条件	参数
计算网格数	100×100×100
单位网格长度dl/m	1.0×10^-7
时间步长dt/s	1.0×10^-10
计算压力p/Pa	1.01×10⁵
气体种类	空气
气体导热系数λ/(W·m^-2·K^-1)	0.024
气体主流温度T_g/K	298
固体颗粒自身发热量Q_c/W	2.1×10^-16
碰撞系数ε	根据球颗粒计算结果确定

本文的计算条件参数设置

编号	等效直径 d/10^-7m	分形维数 d_f	比表面积 s/m^-1	Nu
1	47.129	1.038	2 606 506	1.962
2	46.994	1.035	2 867 080	1.539
3	46.801	1.034	3 294 332	1.375
4	46.559	1.030	3 725 234	1.164
5	46.294	1.041	4 300 757	0.990
6	47.287	1.033	4 698 997	0.921
7	46.876	1.050	5 303 618	0.809
8	46.189	1.056	6 067 137	0.694
9	46.770	1.057	6 796 349	0.614
10	46.863	1.069	7 600 208	0.536
11	47.067	1.070	8 479 320	0.496
12	46.560	1.080	9 501 609	0.434
13	47.265	1.091	10 504 268	0.405
14	47.177	1.080	11 919 894	0.390
15	46.278	1.089	13 195 106	0.363
16	47.102	1.096	15 211 813	0.354
17	46.825	1.105	16 606 890	0.370
18	46.615	1.107	18 738 593	0.410
19	46.191	1.125	20 391 450	0.452
20	46.343	1.141	21 462 920	0.515
21	46.163	1.194	23 637 034	0.734
22	46.156	1.253	24 813 829	1.138

不同分形颗粒的分形参数及计算结果

分形颗粒的比表面积s与分形维数d_f的关系

分形颗粒传热Nu与分形维数d_f关系

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