摘要
Rayleigh-Bénard对流常见于自然界和各种工程应用中，并受到广泛研究，常由温度场或浓度场的不均匀性引发。传热与传质过程，尤其对应Rayleigh-Bénard 对流过程，具有一定相似性。一些Rayleigh-Bénard对流在传热（如自然对流）中已经广泛应用的分析方法或理论，如熵产率分析，有望用于解决界面传质领域的问题。而本文的研究成功例证了这一思路：首次将熵产分析引入到对界面传质Rayleigh-Bénard对流的研究并提出新的观点。这对引入更多新研究角度或分析方法到界面传质Rayleigh-Bénard对流研究中具有一定启发意义。
对于传热Rayleigh-Bénard对流的研究中，通过与文献比较，全面的验证了基于ANSYS Fluent无量纲模拟稳态对流的可靠性。在此基础上，对方腔内变物性低Pr数流体自然对流进行研究，发现热导率对局部传热熵产率分布影响最大，且变物性对平均Nu数影响可能存在协同或抵消作用。最后借助量阶分析和均匀试验设计得到各物性对平均Nu数的通用半理论半经验数学表达式。
对于传质Rayleigh-Bénard对流的研究，基于ANSYS Fluent对CO2-乙醇吸收体系的界面传质Rayleigh-Bénard对流进行原始变量数值模拟，在对流过程与传质效果分析中发现新生对流胞极大地强化传质过程。首次得到Rayleigh-Bénard 对流中质量传递和粘性耗散这两个不可逆过程的熵产率，并从非平衡热力学角度对其进行分析。液层中局部传质和粘性熵产率均出现特征分布，并对其进行成因分析。全局传
质和粘性熵产率随时间变化在对流前后，即对应分子扩散主导阶段和对流主导阶段，分别呈现出不同趋势。相对于纯扩散过程，Rayleigh-Bénard对流的引发改变了系统不可逆过程路径而实现传质强化，体现为全局总熵产率随时间的差异性变化。
本文的创新性主要有三点：首次将熵产分析引入到界面传质Rayleigh-Bénard 对流研究中，提供了基于非平衡热力学的新研究视角；将热函数推广到变物性自然对流中，提出描述流体流动的动量流函数，解决流函数对可压缩流体的不适用性；验证了基于ANSYS Fluent无量纲模拟的可靠性，并提出界面传质Rayleigh-Bénard对流的相关变量无量纲化的初级方案，为进一步无量纲研究提供了基础。
关键词：Rayleigh-Bénard对流，自然对流，界面传质，变物性，无量纲化，
熵产分析，非平衡热力学
ABSTRACT
Rayleigh-Bénard convection is common in nature and engineering applications and has been extensively studied, often caud by the inhomogeneity of temperature field or concentration field. Heat and mass transfer process, especially their corresponding Rayleigh-Bénard convection process, has similarities to some extent. Some analytical methods and theories of Rayleigh-Bénard
convection like entropy generation analysis widely ud in heat transfer process, such as natural convection, are potential to solve some problems in interfacial mass transfer process. And this study provided a good example of this idea: entropy generation analysis was first introduced into Rayleigh-Bénard convection in interfacial mass transfer process with fresh insights obtained, which enlightens and updates the application of more new rearch perspectives or analytical methods into Rayleigh-Bénard convection in interfacial mass transfer process.
In the study of Rayleigh-Bénard convection in heat transfer process, the reliability of dimensionless simulation of stable convection bad on ANSYS Fluent was verified comprehensively by comparing with many literatures. And on this basis, the study of the effects of property variations on natural convection for low Prandtl number liquids in a square enclosure found that thermal conductivity had the greatest influence on local entropy generation rate, and the effects of property variations on average Nuslt number may augment or counteract each other. Finally, a general mathematical expression of average Nuslt number which is half theoretical and half empirical in nature was obtained through scale analysis and uniform experiment design.
In the study of Rayleigh-Bénard convection in mass transfer process, interfacial Rayleigh-Bénard convection in CO2-ethanol absorption system was simulated with primitive variables bad on ANSY
S Fluent. It was found that the new ont of convection cells greatly enhanced the mass transfer process. The entropy generation rate of two irreversible process of Rayleigh-Bénard convection: mass transfer and viscous dissipation, was firstly obtained and analyzed from the perspective of non-equilibrium thermodynamics. The characteristic distributions of entropy generation rate due to mass transfer and friction in local liquid layer were found and their caus were analyzed. And the variation of global entropy generation rate due to mass transfer and friction with time showed different trends respectively before and after the ont of
convection, corresponding to molecular diffusion-dominated pha and convection-dominated pha. Compared with pure diffusion, the ont of Rayleigh-Bénard convection changed the path of irreversible process to achieve mass transfer enhancement, embodied in the variation of global total entropy generation rate.
The innovations of this paper contains three aspects. Firstly, entropy generation analysis was first introduced into Rayleigh-Bénard convection in interfacial mass transfer process, which provided a new perspective bad on non-equilibrium thermodynamics. Secondly, the theory of heatfunction was promoted to natural convection in variable properties system, and momentum stream function on behalf of fluid flow was propod to solve the limitation when applying stream function to compres
sible fluid. Thirdly, the reliability of dimensionless simulation bad on ANSYS Fluent was verified, and initial attempts at nondimensionalization of variables related to Rayleigh-Bénard convection in interfacial mass transfer process were made, which laid the foundation of further dimensionless rearch.
KEY WORDS: Rayleigh-Bénard convection, Natural convection, Variable properties, Nondimensionalization, Entropy generation analysis, Non-equilibrium thermodynamics
目录
第1章文献综述 (1)
1.1 引言 (1)
1.2 Rayleigh-Bénard对流研究进展 (1)
1.2.1 腔内传热Rayleigh-Bénard对流 (2)
1.2.2 界面传质Rayleigh-Bénard对流 (4)
1.3 无量纲数及相关分析 (6)
1.3.1 量纲分析 (6)
1.3.2 量阶分析 (7)
1.3.3 方程无量纲化 (8)
1.4 熵产生及其分析方法 (11)
1.4.1 热力学基础 (11)
1.4.2 熵产含义 (13)
1.4.3 熵产分析 (14)
1.5 本文主要工作及意义 (15)
第2章无量纲模拟方腔内Rayleigh-Bénard对流的可行性验证 (17)
2.1 物理模型及网格划分 (17)
2.2 数值计算模型 (18)
2.2.1 基本控制方程 (18)
2.2.2 流函数方程 (20)
2.2.3 热函数方程 (21)
2.2.3 熵产率表达式 (22)
2.2.5 努塞尔数 (23)
2.2.6 求解方案 (23)
2.3 模拟结果验证 (24)
2.3.1 Nu数验证 (24)
2.3.2 流函数验证 (25)
2.3.3 热函数验证 (26)
2.3.4 熵产率验证 (27)
2.4 计算过程验证 (29)
2.4.1 控制方程 (29)
2.4.2 验证结果 (30)
2.5 本章小结 (31)
第3章方腔内变物性低Pr流体的层流自然对流 (33)
3.1 流体变物性描述 (33)
3.2 物理模型与网格划分 (36)
3.3 计算模型 (37)
3.3.1 控制方程 (37)
3.3.2 动量流函数方程 (39)
3.3.3 热函数方程 (40)
3.3.4 熵产率表达式 (41)
3.3.5 努塞尔数 (43)
3.3.6 求解方案 (44)
3.4 液态金属Na在不同方腔温差下的自然对流 (44)
3.4.1 温差3K的方腔内对流分析 (45)
3.4.2 温差300K的方腔内对流分析 (48)
3.5 物性对低Pr流体的方腔内自然对流的影响 (51)
3.5.1 单一物性变化对自然对流影响 (51)
3.5.2 两物性共同变化对自然对流影响 (59)
3.6 物性变化对自然对流的综合影响 (60)
3.6.1 量阶分析 (60)
3.6.2 均匀试验设计 (62)
3.6.3 拟合结果 (63)
3.7 本章小结 (63)
第4章CO2-乙醇体系界面吸收过程Rayleigh-Bénard对流 (65)
4.1 物理模型 (65)
4.2 数值计算模型 (67)
4.2.1 控制方程 (67)
4.2.2 熵产率表达式 (67)
4.3 界面扰动模型 (70)
4.4 模型验证 (71)
4.4.1 求解方案 (71)
4.4.2 网格无关性验证 (71)
