复杂边界条件下具有密度极值流体的热对流研究
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摘要
热对流过程广泛存在于各种自然现象和工程技术领域中，其中，封闭腔体内的热对流更是随处可见，因此，一直是学术界研究的热点问题。目前，关于热对流的研究主要是针对密度随温度线性减小的常规流体，对具有密度极值流体热对流的研究主要集中在水平环缝内，而对工程上常见的复杂边界条件下具有密度极值流体的热对流研究很少。本文以相变蓄冷装置中的热对流问题为研究背景，对复杂边界条件下具有密度极值冷水的热对流过程进行了系统研究，得到了不同Rayleigh（Ra）数、密度倒置参数和几何结构下复杂结构环形腔、矩形腔和圆柱形腔内热对流的各种流型结构及其演变规律，分析了各主要参数对复杂结构环形腔内冷水自然对流、矩形及圆柱形腔内冷水Rayleigh-Bénard（R-B）对流流动和传热的影响。本文研究结果对于发展具有密度极值流体自然对流传热理论、拓展R-B对流的研究领域具有重要的科学意义和学术价值，同时，也可以为相变蓄冷装置的工程设计及优化提供理论指导。
首先，对椭圆环形腔内具有密度极值冷水的自然对流进行了数值模拟，得到了不同Ra数、密度倒置参数、椭圆曲率、半径比和旋转角等参数下的流场、温度场及传热特性，讨论了各参数对流动和传热的影响。结果表明，当Ra数较小时，传热以导热为主，随着Ra数的增大，对流传热逐渐占据主导地位，当Ra数超过某一临界值时，流动将转变为非稳态流动。密度倒置参数对流动结构和传热性能具有决定性影响，当密度倒置参数在接近0.5时，流动呈两相互抑制的双胞结构，此时传热能力最差。同时，平均Nusselt（Nu）数随半径比的减小及椭圆曲率的增加而增大；旋转角对流场和温度场影响较大，腔体倾斜时，流场中出现的次级流胞不再成对出现，而是单一地出现在腔体的某一侧，其可使内壁底部区域的局部Nu数增大，但对平均Nu数影响较小。
然后，分析对比了具有不同几何结构的复杂异型腔内、具有密度极值冷水自然对流的流场和温度场的差异，讨论了各种参数对不同异型腔内传热的影响。结果发现，R-C、T-C、E-S和E-T结构环形腔上部或下部区域发生了R-B对流，在较大半径比时，R-C、D-C、T-C、E-S和E-T结构的环形腔内会出现流胞分裂现象。几何结构对传热性能有很大影响，对于外壁为不同几何结构的环形腔，当Ra数较小时，T-C结构传热能力最强，当Ra数较大时，R-C结构传热能力最强。对于内壁为不同几何结构的环形腔，当密度倒置参数较小时，E-D结构传热性能较好，随着密度倒置参数的增大，E-T结构和E-D结构传热能力增强。通过对计算结果的回归整理，得到了各环形腔内冷水自然对流传热关联式。
另外，确定了矩形和圆柱形腔内具有密度极值冷水R-B对流流动的临界条件、可能存在的流型结构以及流型演变过程，结果表明，冷水的密度倒置特性对R-B对流有决定性影响。系统失稳的临界Ra数比常规流体大，且随密度倒置参数的增加而增大。不同密度倒置参数下，对流结构不同，传热能力随密度倒置参数的增大而减小。导热侧壁增强了系统的稳定性，两种热边界条件下流型结构以及分岔序列有很大差别。宽（径）深比的增大会降低系统稳定性，当宽（径）深比较小时，对流结构多为单涡卷和双涡卷结构，且圆柱形腔内R-B对流系统更加稳定；当宽（径）深比较大时，出现了复杂的多涡卷对流结构，圆柱形腔内R-B对流流动结构与矩形腔内的差异较大，在圆柱形腔内R-B对流还出现了中心对称流型。相同Ra数下，多种流型可以稳定共存，且各流型的对流传热能力也存在差异，但这种差异并不大。
最后，对圆柱形腔内具有密度极值冷水R-B对流进行了实验研究，结果表明，实验结果与数值模拟结果吻合较好；壁面平均Nu数都随密度倒置参数的增大而减小，Ra数的增加能显著增强传热能力，径深比的增大也能在一定程度上强化传热。通过对实验结果的回归整理，得到了圆柱形腔内冷水R-B对流传热关联式。
Thermal convection exists widely in all kinds of natural phenomena andengineering technology fields. The natural convection in the closed cavity has become astudy hotspot due to its important applications in engineering. Up to now, many workshave been performed for common fluid that the density of which is considered as alinear function of temperature, and thermal convection of the fluid with the densitymaximum is mainly focused on horizontal annuli. However, research result on thermalconvection of the fluid near its density maximum with complex geometrical and thermalboundary conditions is lacked. In this thesis, a systematic study on thermal convectionof cold water near its density maximum with complex boundary conditions is performed,aiming at the thermal convection in the equipment of phase change cool-thermal energystorage system. The formation and evolution of the flow structures at different Rayleighnumber (Ra), density inversion parameter and geometrical configuration in annularenclosures with various complex configurations, rectangular and cylindrical cavities arepresented. The effect of the main parameters on the natural convection of cold water inannular enclosures with various complex configurations and the Rayleigh-Bénard (R-B)convection of cold water in rectangular and cylindrical cavities is analyzed anddiscussed. The study results can not only has important academic significance ondeveloping the theory of natural convection of the fluid with the density maximum withcomplex configuration and extending the research field of R-B convection, but alsoprovide a reference for design and optimization of phase change cool-thermal energystorage system.
Firstly, a numerical investigation on the natural convection of cold water in ellipticannular enclosures is carried out to obtain the flow and thermal fields and heat transfercharacteristic along the inner wall at different Ra, density inversion parameter, aspectratio, elliptical ratio and inclination angle. Effects of various main parameters on thecharacteristic of flow and heat transfer are discussed. The results indicate thatconduction is the dominant mode of heat transfer at a small Ra, and the convection heattransfer becomes dominant with the increase of Ra. When Ra exceeds to a certain value,the flow is out of stability, but the mechanisms of flow instability are different forvarious density inversion parameters. The flow structure and heat transfer ability dependstrongly on the density inversion parameter. When the density inversion parameter is around0.5, there is a bi-cellular flow pattern consisting of two cells that suppressedeach other, which results in the weakest heat transfer ability. The average Nusseltnumber (Nu) increases with the decrease of the aspect ratio and the elliptical ratio. Theinclination angle modifies the flow and thermal field apparently. The secondary cells donot appear with a pair when the enclosure is tilted, which enhances the local heattransfer ability in the lower region while the overall heat transfer ability is nearlyunaffected.
Secondly, the difference of flow and thermal field and heat transfer ability amongvarious annular enclosures with complex configurations is compared and discussed. Itshows that the R-B convection occurs in the top or bottom region for the R-C, T-C, E-Sand E-T configurations and the cell splitting phenomenon happens at a large aspect ratioin the R-C, D-C, T-C, E-S and E-T configurations. As expected, the wall configurationhas an importanr effect on the heat transfer on the inner wall. For the differentconfiguration of the outer wall, the heat transfer ability of the T-C configuration is thelargest among these configurations at a small Ra while R-C configuration becomes thelargest in heat transfer at a large Ra. For the different inner wall, the E-D configurationachieves the best heat transfer performance in the whole range of the Ra at small densityinversion parameter, and E-T and E-D configurations have the best heat transfer abilityat the large density inversion parameter. Furthermore, the heat transfer correlations forvarious configurations have been proposed by the multi-factor linear regression.
In addition, the thresholds for the onset of convection, the formation and evolutionof complex flow pattern for the R-B convection of cold water with density maximum inrectangular and cylindrical cavities are assured. Results show that the density inversionplays a key role in the R-B convection. The critical Ra for the onset of convection islarger than that of the common fluid, and it increases with the increase of the densityinversion parameter. The flow structures are much more different from each other atdifferent inversion parameters. Conductive sidewall enhances the stability of the R-Bconvection, and the flow structures and bifurcation series are different with the twothermal boundary conditions of sidewalls. The increase of aspect ratio reduces thestability of the flow. When the aspect ratio is small, most of the flow patterns aresingle-roll or two-roll structure. The R-B convection in cylindrical cavity is more stablethan that in rectangular cavity. However, many multiple rolls flow patterns appear, andthe flow structures of cylindrical cavity are much more different from that ofrectangular cavity when the aspect ratio is large. Furthermore, center symmetric flow patterns exist for the R-B convection in cylindrical cavity. At the same Ra, thecoexistence of multiple stable states is observed and the heat transfer rates for thesestates are slightly different from each other.
Finally, an experimental investigation on the heat transfer of the R-B convection ofcold water with the density maximum in the cylindrical cavity is carried out. The resultsof experiment are in good agreement with those of numerical simulation. The averageNu decreases with the increase of density inversion parameter. The increase of Ra canremarkably enhance the heat transfer on the wall while the increase of aspect ratio justenhances the heat transfer ability to a certain extent. Furthermore, the heat transfercorrelation for the R-B convection in the cylindrical cavity has been proposed by themulti-factor linear regression.
首先，对椭圆环形腔内具有密度极值冷水的自然对流进行了数值模拟，得到了不同Ra数、密度倒置参数、椭圆曲率、半径比和旋转角等参数下的流场、温度场及传热特性，讨论了各参数对流动和传热的影响。结果表明，当Ra数较小时，传热以导热为主，随着Ra数的增大，对流传热逐渐占据主导地位，当Ra数超过某一临界值时，流动将转变为非稳态流动。密度倒置参数对流动结构和传热性能具有决定性影响，当密度倒置参数在接近0.5时，流动呈两相互抑制的双胞结构，此时传热能力最差。同时，平均Nusselt（Nu）数随半径比的减小及椭圆曲率的增加而增大；旋转角对流场和温度场影响较大，腔体倾斜时，流场中出现的次级流胞不再成对出现，而是单一地出现在腔体的某一侧，其可使内壁底部区域的局部Nu数增大，但对平均Nu数影响较小。
然后，分析对比了具有不同几何结构的复杂异型腔内、具有密度极值冷水自然对流的流场和温度场的差异，讨论了各种参数对不同异型腔内传热的影响。结果发现，R-C、T-C、E-S和E-T结构环形腔上部或下部区域发生了R-B对流，在较大半径比时，R-C、D-C、T-C、E-S和E-T结构的环形腔内会出现流胞分裂现象。几何结构对传热性能有很大影响，对于外壁为不同几何结构的环形腔，当Ra数较小时，T-C结构传热能力最强，当Ra数较大时，R-C结构传热能力最强。对于内壁为不同几何结构的环形腔，当密度倒置参数较小时，E-D结构传热性能较好，随着密度倒置参数的增大，E-T结构和E-D结构传热能力增强。通过对计算结果的回归整理，得到了各环形腔内冷水自然对流传热关联式。
另外，确定了矩形和圆柱形腔内具有密度极值冷水R-B对流流动的临界条件、可能存在的流型结构以及流型演变过程，结果表明，冷水的密度倒置特性对R-B对流有决定性影响。系统失稳的临界Ra数比常规流体大，且随密度倒置参数的增加而增大。不同密度倒置参数下，对流结构不同，传热能力随密度倒置参数的增大而减小。导热侧壁增强了系统的稳定性，两种热边界条件下流型结构以及分岔序列有很大差别。宽（径）深比的增大会降低系统稳定性，当宽（径）深比较小时，对流结构多为单涡卷和双涡卷结构，且圆柱形腔内R-B对流系统更加稳定；当宽（径）深比较大时，出现了复杂的多涡卷对流结构，圆柱形腔内R-B对流流动结构与矩形腔内的差异较大，在圆柱形腔内R-B对流还出现了中心对称流型。相同Ra数下，多种流型可以稳定共存，且各流型的对流传热能力也存在差异，但这种差异并不大。
最后，对圆柱形腔内具有密度极值冷水R-B对流进行了实验研究，结果表明，实验结果与数值模拟结果吻合较好；壁面平均Nu数都随密度倒置参数的增大而减小，Ra数的增加能显著增强传热能力，径深比的增大也能在一定程度上强化传热。通过对实验结果的回归整理，得到了圆柱形腔内冷水R-B对流传热关联式。
Thermal convection exists widely in all kinds of natural phenomena andengineering technology fields. The natural convection in the closed cavity has become astudy hotspot due to its important applications in engineering. Up to now, many workshave been performed for common fluid that the density of which is considered as alinear function of temperature, and thermal convection of the fluid with the densitymaximum is mainly focused on horizontal annuli. However, research result on thermalconvection of the fluid near its density maximum with complex geometrical and thermalboundary conditions is lacked. In this thesis, a systematic study on thermal convectionof cold water near its density maximum with complex boundary conditions is performed,aiming at the thermal convection in the equipment of phase change cool-thermal energystorage system. The formation and evolution of the flow structures at different Rayleighnumber (Ra), density inversion parameter and geometrical configuration in annularenclosures with various complex configurations, rectangular and cylindrical cavities arepresented. The effect of the main parameters on the natural convection of cold water inannular enclosures with various complex configurations and the Rayleigh-Bénard (R-B)convection of cold water in rectangular and cylindrical cavities is analyzed anddiscussed. The study results can not only has important academic significance ondeveloping the theory of natural convection of the fluid with the density maximum withcomplex configuration and extending the research field of R-B convection, but alsoprovide a reference for design and optimization of phase change cool-thermal energystorage system.
Firstly, a numerical investigation on the natural convection of cold water in ellipticannular enclosures is carried out to obtain the flow and thermal fields and heat transfercharacteristic along the inner wall at different Ra, density inversion parameter, aspectratio, elliptical ratio and inclination angle. Effects of various main parameters on thecharacteristic of flow and heat transfer are discussed. The results indicate thatconduction is the dominant mode of heat transfer at a small Ra, and the convection heattransfer becomes dominant with the increase of Ra. When Ra exceeds to a certain value,the flow is out of stability, but the mechanisms of flow instability are different forvarious density inversion parameters. The flow structure and heat transfer ability dependstrongly on the density inversion parameter. When the density inversion parameter is around0.5, there is a bi-cellular flow pattern consisting of two cells that suppressedeach other, which results in the weakest heat transfer ability. The average Nusseltnumber (Nu) increases with the decrease of the aspect ratio and the elliptical ratio. Theinclination angle modifies the flow and thermal field apparently. The secondary cells donot appear with a pair when the enclosure is tilted, which enhances the local heattransfer ability in the lower region while the overall heat transfer ability is nearlyunaffected.
Secondly, the difference of flow and thermal field and heat transfer ability amongvarious annular enclosures with complex configurations is compared and discussed. Itshows that the R-B convection occurs in the top or bottom region for the R-C, T-C, E-Sand E-T configurations and the cell splitting phenomenon happens at a large aspect ratioin the R-C, D-C, T-C, E-S and E-T configurations. As expected, the wall configurationhas an importanr effect on the heat transfer on the inner wall. For the differentconfiguration of the outer wall, the heat transfer ability of the T-C configuration is thelargest among these configurations at a small Ra while R-C configuration becomes thelargest in heat transfer at a large Ra. For the different inner wall, the E-D configurationachieves the best heat transfer performance in the whole range of the Ra at small densityinversion parameter, and E-T and E-D configurations have the best heat transfer abilityat the large density inversion parameter. Furthermore, the heat transfer correlations forvarious configurations have been proposed by the multi-factor linear regression.
In addition, the thresholds for the onset of convection, the formation and evolutionof complex flow pattern for the R-B convection of cold water with density maximum inrectangular and cylindrical cavities are assured. Results show that the density inversionplays a key role in the R-B convection. The critical Ra for the onset of convection islarger than that of the common fluid, and it increases with the increase of the densityinversion parameter. The flow structures are much more different from each other atdifferent inversion parameters. Conductive sidewall enhances the stability of the R-Bconvection, and the flow structures and bifurcation series are different with the twothermal boundary conditions of sidewalls. The increase of aspect ratio reduces thestability of the flow. When the aspect ratio is small, most of the flow patterns aresingle-roll or two-roll structure. The R-B convection in cylindrical cavity is more stablethan that in rectangular cavity. However, many multiple rolls flow patterns appear, andthe flow structures of cylindrical cavity are much more different from that ofrectangular cavity when the aspect ratio is large. Furthermore, center symmetric flow patterns exist for the R-B convection in cylindrical cavity. At the same Ra, thecoexistence of multiple stable states is observed and the heat transfer rates for thesestates are slightly different from each other.
Finally, an experimental investigation on the heat transfer of the R-B convection ofcold water with the density maximum in the cylindrical cavity is carried out. The resultsof experiment are in good agreement with those of numerical simulation. The averageNu decreases with the increase of density inversion parameter. The increase of Ra canremarkably enhance the heat transfer on the wall while the increase of aspect ratio justenhances the heat transfer ability to a certain extent. Furthermore, the heat transfercorrelation for the R-B convection in the cylindrical cavity has been proposed by themulti-factor linear regression.
引文
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