基于能量守恒耗散粒子动力学方法的自然对流模拟改进研究

鲁维; 陈硕; 于致远; 赵嘉毅; 张凯旋

doi:10.7498/aps.72.20230495

摘要

能量守恒耗散粒子动力学(eDPD)是一种研究热输运过程的介观尺度数值模拟方法, 然而在eDPD系统内引入Boussinesq假设以研究自然对流问题时, eDPD系统自身的热膨胀性对模拟结果的影响常常被忽略. 首先研究了eDPD系统的热膨胀性, 通过模拟获得eDPD系统的热膨胀系数β; 并由此模拟了不同瑞利数Ra、不同几何结构下的自然对流; 利用eDPD系统自身的热膨胀性, 在不引入Boussinesq假设的前提下获得了合理的温度场和速度场, 与相同Ra数下有限体积法模拟结果相比, 误差明显小于以往研究中相同条件下的对比误差. 研究表明在eDPD系统中引入Boussinesq假设时, 需要考虑eDPD系统自身热膨胀性的影响, 并且进一步对Ra数的计算进行了修正.

关键词:

Abstract

Energy conservation dissipative particle dynamics (eDPD) is a mesoscale numerical simulation method of studying the heat transport process. In previous studies, when the Boussinesq assumption was introduced into the eDPD system to study the natural convection, the system was generally considered to be incompressible, and the effect of the thermal expansion of the eDPD system itself on the simulation results was often neglected, which would cause errors in the simulation. In the present study, the thermal expansion characteristic of the eDPD system is first investigated, and the thermal expansion coefficient β of the eDPD system is obtained by eDPD simulation. Then, based on the thermal expansion characteristic of the eDPD system itself, the natural convection is simulated with different values of Rayleigh number Ra and different geometries, specifically, square cavity, concentric rings, and eccentric rings, and reasonable temperature and velocity fields are obtained, and they are in agreement with the simulated results by the finite volume method (FVM). The error between the eDPD simulation, in which the natural convection is driven by thermal expansion of the eDPD system itself, and FVM simulated result is considerably smaller than the errors observed in previous studies where Boussinesq assumption was directly adopted to simulate natural convection phenomena while neglecting the thermal expansion effect of eDPD system. It is shown that the effect of the eDPD system’s own thermal expansion characteristic needs to be considered when introducing the Boussinesq assumption in the eDPD system, and further, the calculation of the Ra number is modified in this paper.

Keywords:

energy conservation dissipative particle dynamics /
Boussinesq hypothesis /
natural convection /
thermal expansion

作者及机构信息

1.
同济大学航空航天与力学学院力学系, 上海　200092

2.
上海理工大学能源与动力工程学院, 上海　200093

3.
南开大学医学院, 天津　300071

通信作者: 陈硕, schen_tju@tongji.edu.cn

基金项目: 国家自然科学基金(批准号: 11872283, 12002212)和上海扬帆计划 (批准号: 20YF1432800) 资助的课题.

Authors and contacts

1.
Department of Mechanics, School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China

2.
School of Energy and Power Engineering, Shanghai University of Technology, Shanghai 200093, China

3.
School of Medicine, Nankai University, Tianjin 300071, China

Corresponding author: Chen Shuo, schen_tju@tongji.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11872283, 12002212) and the Sailing Program of Shanghai, China (Grant No. 20YF1432800).

文章全文 : translate this paragraph

参考文献

[1]	Hoogerbrugge P J, Koelman J 1992 Europhys. Lett. 19 155 Google Scholar
[2]	Español P, Warren P 1995 Europhys. Lett. 30 191 Google Scholar
[3]	Groot R D, Warren P 1997 J. Chem. Phys. 107 4423 Google Scholar
[4]	Avalos J B, Mackie A D 1997 Europhys. Lett. 40 141 Google Scholar
[5]	Español P 1997 Europhys. Lett. 40 631 Google Scholar
[6]	Ripoll M, Español P, Ernst M H 1998 Int. J. Mod. Phys. C 9 1329 Google Scholar
[7]	Ripoll M, Español P 2001 Int. J. Mod. Phys. C 15 7271 Google Scholar
[8]	Mackie A D, Avalos J B, Navas V 1999 Phys. Chem. Chem. Phys. 1 2039 Google Scholar
[9]	Avalos J B, Mackie A D 1999 J. Chem. Phys. 111 5267 Google Scholar
[10]	Lukes A C J R 2009 J. Heat Trans. 131 033108 Google Scholar
[11]	Homman A, Maillet J, Roussel J 2016 J. Chem. Phys. 144 024112 Google Scholar
[12]	Stoltz G 2017 J. Comput. Phys. 340 451 Google Scholar
[13]	Qiao R, He P 2007 Mol. Simulat. 33 677 Google Scholar
[14]	Abu-Nada E 2010 Mol. Simulat. 36 382 Google Scholar
[15]	Abu-Nada E 2010 Phys. Rev. E 81 056704 Google Scholar
[16]	Abu-Nada E 2011 J. Heat Trans. 133 112502 Google Scholar
[17]	Abu-Nada E 2015 Numer. Heat Tr. A Appl. 67 808 Google Scholar
[18]	Abu-Nada E 2015 Int. J. Therm. Sci. 92 72 Google Scholar
[19]	Mai-Duy N, Phan-Thien N 2013 J. Comput. Phys. 245 150 Google Scholar
[20]	Pan D Y, Phan-Thien N, Mai-Duy N 2013 J. Comput. Phys. 242 196 Google Scholar
[21]	张凯 2017 硕士学位论文 (太原: 中北大学) Zhang K 2017 M. S. Thesis (Taiyuan: North University of China
[22]	Ripoll M 2002 Ph. D. Dissertation (Spain: UNED
[23]	Fan X J, Phan-Thien N, Yong N T, Wu X H, Xu D 2003 Phys. Fluids 15 11 Google Scholar
[24]	Koschmieder E, Pallas S 1974 Heat Mass Transfer 17 991 Google Scholar
[25]	Zhang J , Önskog T 2017 Phys. Rev. E 96 043104 Google Scholar
[26]	曹知红, 罗康, 易红亮 2014工程热物理学报35 1840 Cao Z H, Luo K, Yi H L 2014 J. Eng. Thermophys. 35 1840
[27]	Cao Z H, Luo K, Yi H L 2014 Int. J. Heat Mass Tran. 74 60 Google Scholar

施引文献

图 1 不同压强下eDPD密度随温度的变化

Fig. 1. Density variation of eDPD with temperature at different pressure level.

下载: 全尺寸图片幻灯片

图 2 eDPD系统热膨胀系数随温度的变化

Fig. 2. Variation of thermal expansion coefficient of eDPD system with temperature.

下载: 全尺寸图片幻灯片

图 3 eDPD模拟方腔内RB问题的模型

Fig. 3. Model of eDPD to simulate RB problem in square cavity.

下载: 全尺寸图片幻灯片

图 4 eDPD模拟不同瑞利数下自然对流的温度云图　(a) Ra = 1600; (b) Ra = 1800; (c) Ra = 2000; (d) Ra = 4000

Fig. 4. Temperature clouds of natural convection under different Rayleigh numbers simulated by eDPD: (a) Ra = 1600; (b) Ra = 1800; (c) Ra = 2000; (d) Ra = 4000.

下载: 全尺寸图片幻灯片

图 5 eDPD模拟不同瑞利数下自然对流的速度矢量图　(a) Ra = 1600; (b) Ra = 1800; (c) Ra = 2000; (d) Ra = 4000

Fig. 5. Natural convection velocity vectors at different Rayleigh numbers by eDPD simulations: (a) Ra = 1600; (b) Ra = 1800; (c) Ra = 2000; (d) Ra = 4000.

下载: 全尺寸图片幻灯片

图 6 eDPD模拟Ra为3100时方腔内自然对流的温度云图

Fig. 6. eDPD simulation of the temperature cloud of natural convection in the square cavity when Ra is 3100.

下载: 全尺寸图片幻灯片

图 7 Ra为3100时eDPD和FVM模拟的方腔内自然对流温度等温线对比图

Fig. 7. Comparison of natural convection temperature isotherms in the square cavity simulated by eDPD and FVM at 3100 of Ra.

下载: 全尺寸图片幻灯片

图 8 Ra为7300时eDPD和FVM模拟的方腔内自然对流温度等温线对比图

Fig. 8. Comparison of natural convection temperature isotherms in the square cavity simulated by eDPD and FVM at 7300 of Ra.

下载: 全尺寸图片幻灯片

图 9 Ra为7300时eDPD和FVM模拟的方腔内自然对流速度线对比图　(a) X = 0.5时V_X沿Y方向变化曲线; (b) X = 1.5时V_X沿Y方向变化曲线; (c) X = 0.3时V_Y沿Y方向变化曲线; (d) X = 1.0时V_Y沿Y方向变化曲线

Fig. 9. Comparison of natural convection velocity profile in the square cavity simulated by eDPD and FVM when Ra is 7300: (a) Variation curve of V_Xalong Y-direction at X = 0.5; (b) variation curve of V_Xalong Y-direction at X = 1.5; (c) variation curve of V_Y along the Y-direction at X = 0.3; (d) variation curve of V_Y along the Y-direction at X = 1.0.

下载: 全尺寸图片幻灯片

图 10 同心圆环模型示意图

Fig. 10. Schematic diagram of the concentric ring model.

下载: 全尺寸图片幻灯片

图 11 不同Ra的 eDPD和FVM同心圆环自然对流等温线对比图　(a) Ra = 1000; (b) Ra = 4100; (c) Ra = 7200; (d) Ra = 10400

Fig. 11. Comparison of natural convection isotherms of eDPD and FVM simulation for concentric rings at different Ra: (a) Ra = 1000; (b) Ra = 4100; (c) Ra = 7200; (d) Ra = 10400.

下载: 全尺寸图片幻灯片

图 12 eDPD和FVM偏心圆环自然对流等温线对比图　(a) Ra = 4100; (b) Ra = 10400

Fig. 12. Comparison of eDPD and FVM eccentric circular natural convection isotherms: (a) Ra = 4100; (b) Ra = 10400.

下载: 全尺寸图片幻灯片

图 13 不考虑eDPD自身热膨胀性时同心圆环自然对流等温线对比图

Fig. 13. Comparison of natural convection isotherms in concentric rings without considering the thermal expansion of the eDPD system.

下载: 全尺寸图片幻灯片

图 14 考虑eDPD自身热膨胀性的同时引入Boussinesq假设情况下, 同心圆环自然对流等温线对比图

Fig. 14. Concentric circular natural convection isotherm comparison when considering the combined effect of thermal expansion of eDPD system and Boussinesq assuming.

下载: 全尺寸图片幻灯片

[1]	Hoogerbrugge P J, Koelman J 1992 Europhys. Lett. 19 155 Google Scholar
[2]	Español P, Warren P 1995 Europhys. Lett. 30 191 Google Scholar
[3]	Groot R D, Warren P 1997 J. Chem. Phys. 107 4423 Google Scholar
[4]	Avalos J B, Mackie A D 1997 Europhys. Lett. 40 141 Google Scholar
[5]	Español P 1997 Europhys. Lett. 40 631 Google Scholar
[6]	Ripoll M, Español P, Ernst M H 1998 Int. J. Mod. Phys. C 9 1329 Google Scholar
[7]	Ripoll M, Español P 2001 Int. J. Mod. Phys. C 15 7271 Google Scholar
[8]	Mackie A D, Avalos J B, Navas V 1999 Phys. Chem. Chem. Phys. 1 2039 Google Scholar
[9]	Avalos J B, Mackie A D 1999 J. Chem. Phys. 111 5267 Google Scholar
[10]	Lukes A C J R 2009 J. Heat Trans. 131 033108 Google Scholar
[11]	Homman A, Maillet J, Roussel J 2016 J. Chem. Phys. 144 024112 Google Scholar
[12]	Stoltz G 2017 J. Comput. Phys. 340 451 Google Scholar
[13]	Qiao R, He P 2007 Mol. Simulat. 33 677 Google Scholar
[14]	Abu-Nada E 2010 Mol. Simulat. 36 382 Google Scholar
[15]	Abu-Nada E 2010 Phys. Rev. E 81 056704 Google Scholar
[16]	Abu-Nada E 2011 J. Heat Trans. 133 112502 Google Scholar
[17]	Abu-Nada E 2015 Numer. Heat Tr. A Appl. 67 808 Google Scholar
[18]	Abu-Nada E 2015 Int. J. Therm. Sci. 92 72 Google Scholar
[19]	Mai-Duy N, Phan-Thien N 2013 J. Comput. Phys. 245 150 Google Scholar
[20]	Pan D Y, Phan-Thien N, Mai-Duy N 2013 J. Comput. Phys. 242 196 Google Scholar
[21]	张凯 2017 硕士学位论文 (太原: 中北大学) Zhang K 2017 M. S. Thesis (Taiyuan: North University of China
[22]	Ripoll M 2002 Ph. D. Dissertation (Spain: UNED
[23]	Fan X J, Phan-Thien N, Yong N T, Wu X H, Xu D 2003 Phys. Fluids 15 11 Google Scholar
[24]	Koschmieder E, Pallas S 1974 Heat Mass Transfer 17 991 Google Scholar
[25]	Zhang J , Önskog T 2017 Phys. Rev. E 96 043104 Google Scholar
[26]	曹知红, 罗康, 易红亮 2014工程热物理学报35 1840 Cao Z H, Luo K, Yi H L 2014 J. Eng. Thermophys. 35 1840
[27]	Cao Z H, Luo K, Yi H L 2014 Int. J. Heat Mass Tran. 74 60 Google Scholar

[1]	林源, 胡凤霞, 沈保根. 相变调控、磁热效应和反常热膨胀. 物理学报, 2023, 72(23): 237501. doi: 10.7498/aps.72.20231118
[2]	王秀明, 周吟秋. 基于能量守恒框架下的波动力学理论研究. 物理学报, 2023, 72(7): 074501. doi: 10.7498/aps.72.20212272
[3]	张贝豪, 郑林. 倾斜多孔介质方腔内纳米流体自然对流的格子Boltzmann方法模拟. 物理学报, 2020, 69(16): 164401. doi: 10.7498/aps.69.20200308
[4]	何宗旭, 严微微, 张凯, 杨向龙, 魏义坤. 底部局部加热多孔介质自然对流传热的格子Boltzmann模拟. 物理学报, 2017, 66(20): 204402. doi: 10.7498/aps.66.204402
[5]	刘飞飞, 魏守水, 魏长智, 任晓飞. 基于总能形式的耦合的双分布函数热晶格玻尔兹曼数值方法. 物理学报, 2015, 64(15): 154401. doi: 10.7498/aps.64.154401
[6]	齐聪, 何光艳, 李意民, 何玉荣. 方腔内Cu/Al2O3水混合纳米流体自然对流的格子Boltzmann模拟. 物理学报, 2015, 64(2): 024703. doi: 10.7498/aps.64.024703
[7]	黄鑫, 彭述明, 周晓松, 余铭铭, 尹剑, 温成伟. 黑腔冷冻靶传热与自然对流的数值模拟研究. 物理学报, 2015, 64(21): 215201. doi: 10.7498/aps.64.215201
[8]	王丽莉, 万明杰, 马江将, 蒋刚. U1-xPuxO2热膨胀性质分子动力学模拟研究. 物理学报, 2014, 63(8): 083103. doi: 10.7498/aps.63.083103
[9]	雷娟棉, 杨浩, 黄灿. 基于弱可压与不可压光滑粒子动力学方法的封闭方腔自然对流数值模拟及算法对比. 物理学报, 2014, 63(22): 224701. doi: 10.7498/aps.63.224701
[10]	周婷婷, 黄风雷. HMX不同晶型热膨胀特性及相变的ReaxFF分子动力学模拟. 物理学报, 2012, 61(24): 246501. doi: 10.7498/aps.61.246501
[11]	龚博致, 张秉坚. 水中自然超空泡机理及减阻效应的非平衡分子动力学研究. 物理学报, 2009, 58(3): 1504-1509. doi: 10.7498/aps.58.1504
[12]	孙东科, 朱鸣芳, 杨朝蓉, 潘诗琰, 戴挺. 强制对流和自然对流作用下枝晶生长的数值模拟. 物理学报, 2009, 58(13): 285-S291. doi: 10.7498/aps.58.285
[13]	孙亮, 孙一峰, 马东军, 孙德军. 高瑞利数下水平自然热对流的幂律关系. 物理学报, 2007, 56(11): 6503-6507. doi: 10.7498/aps.56.6503
[14]	邱勋林, 夏钟福, 安振连, 吴贤勇. 热膨胀处理的聚丙烯蜂窝膜驻极体的压电性. 物理学报, 2005, 54(1): 402-406. doi: 10.7498/aps.54.402
[15]	李晓杰. 热膨胀型固体物态方程. 物理学报, 2002, 51(5): 1098-1102. doi: 10.7498/aps.51.1098
[16]	秦晓英. 纳米固体Ag在高温下的热膨胀行为. 物理学报, 1995, 44(2): 244-250. doi: 10.7498/aps.44.244
[17]	卢志超, 鲜于泽, 沈保根. 铁基纳米晶合金的热膨胀研究. 物理学报, 1994, 43(5): 799-802. doi: 10.7498/aps.43.799
[18]	阮耀钟, 李立平, 吴志强, 何平笙. PTS单晶的低温热膨胀系数. 物理学报, 1987, 36(9): 1219-1223. doi: 10.7498/aps.36.1219
[19]	涂相征. 稳定自然对流下的温度梯度液相外延. 物理学报, 1982, 31(1): 78-89. doi: 10.7498/aps.31.78
[20]	杨国琛, 罗辽复, 陆埮. 中间玻色子理论Ⅰ.基本假设和对称性. 物理学报, 1966, 22(9): 1027-1031. doi: 10.7498/aps.22.1027

计量

文章访问数: 1503
PDF下载量: 47
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

基于能量守恒耗散粒子动力学方法的自然对流模拟改进研究