开口腔内耦合换热的模拟及其解的非线性分析
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摘要
本文用数值方法，研究了开口腔内导热、表面辐射、自然对流的耦合换热问题。电子电气设备的冷却、盾构热环境控制等大量的工程问题，都可以抽象为这种开口腔的耦合换热问题。由于实际工程中要预测发热体和环境的温度，以设计合理的设备结构或创造合适的环境，需要查明这种具有开口的空腔内在各种复杂条件下导热对流和辐射多种换热方式耦合的流动和换热的机理和规律。因此，对这种理论模型进行的研究，具有广泛的工程应用价值。除了工程背景外，这种开口腔内耦合的流动与换热，还表现出了振荡、分岔、混沌等丰富的非线性特性；对其流动和换热机理和特性进行研究，分析其非线性动力学特征，对于更深刻地认识自然，揭示传热学规律和丰富传热学理论，还有更深刻和重要的理论意义。
本文在各种复杂条件下，采用具有QUICK差分格式的SIMPLE方法对开口腔内耦合换热问题进行了数值模拟。首先对具有恒热流和孤立热源的开口腔内自然对流换热进行了数值模拟，给出了相应边界条件和孤立热源的数值处理方法；然后进一步发展处理导热与对流耦合，导热、对流、表面辐射耦合，导热、对流、表面辐射及内部孤立热源耦合等各种较复杂情况的数值处理方法，并对相对应的各种情况进行数值计算；继而，对在各种不同条件下得到的数值模拟结果分析其流动和换热的机理和规律，并进一步进行非线性特性的分析。最后，作为应用，本文对以太阳能热烟囱发电系统为背景的一个模型进行了数值模拟。
本文获得了如下研究结果：
1.对各种条件下的开口腔内流动换热问题建立了计算模型。给出了采用整体求解方法时，处理表面辐射、导热和对流耦合问题的数值处理方法。
2.对恒热流加热开口腔的数值模拟结果表明：在一定Rayleigh数下，存在使腔内与环境质量交换达到最大的腔体深度高度比值。对具有孤立内热源的开口腔自然对流的数值模拟结果表明：在腔体倾斜角不变时，平均Nu数为Ra数的增函数。当Ra>106时，平均Nu数在φ=45°时达到最大值。
3.对导热和对流耦合的倾斜开口腔内的流动和换热进行的数值模拟计算结果表明：对于一个恒壁温加热的耦合开口腔体，无论其倾斜角度是多少，当固体导热系数增大到一定值时，换热就不能被明显地增强；Ra数较小时，换热对倾斜角度的变化较为敏感。随着倾斜角度的减小，换热先增大后减小继而再略微增大。而Ra数较大时，换热经历一个先减弱后增强的过程；对于开口竖直向上的开口腔体，存在一个临界Ra数使腔体内部的流动形式发生变化的临界的Ra数，在本文计算的几何和物理条件下，这个临界Ra数约为11948。
4.对恒热流加热开口腔的耦合换热稳态结果的分析表明：随着导热系数比值(kr)的增大，平均总Nut数也随之增长。在kr超过100时，继续提高导热性能对总体换热的增强效果就不显著了。与无辐射换热的情况相比，有辐射换热时的总平均Nut数增加了大约54.1%到64.0%；
5.对恒壁温加热开口腔的耦合换热非稳态过程分析表明：对一个固定的Ra和kr取值组合，存在一个临界发射率εc。当ε≥εc时，流动与换热的解为非稳态，具体为周期性振荡解或者混沌解。在下壁面形成的热羽流和其相应产生的二次涡流是流动和换热振荡的原因，并且热羽流和二次涡流形成的周期性与Nu数的周期性相对应。
6.对耦合换热计算中出现的三种不同性质的解进行了功率谱分析。对数值模拟解得的平均总Nut数时间序列，采用C-C算法计算嵌入维数和延迟时间，进行了相空间的重构。在重构了的相空间基础上，采用小数据量法求得了不同工况下的最大Lyapunov指数。
7.对太阳能热烟囱系统内流动换热的模拟结果表明，随着加热热流密度的增加，系统空气流量增加，系统出力增加。随着入口高度的增加，系统空气流量相应减小，即系统出力减小。
以上获得的研究成果，可为相关工程问题及进一步的理论分析提供参考。
本文得到了国家自然科学基金面上项目（50576057，50876067），上海教委科研创新重点项目（10ZZ91）和上海市重点学科建设项目资助（J50501）的资助。
Combined heat transfer by natural convection-conduction and surface radiation inan open cavity is studied in this paper. Numerous engineering problems can beabstracted to the combined flow and heat transfer problems such as electronic coolingand thermal environment controlling for shield tunneling. The requirement of predictingthe temperature of heating source and its environment for designing the devices orcontrolling the surroundings asks for the investigate of the mechanism and laws on thecombined flow and heat transfer by natural convection conduction and surface radiationunder various complex conditions. Therefore, the study on the theoretical models hassignificant interest in a range of engineering application. Beside the engineeringapplications, the problem of nature convection in open cavities has abundantcharacteristics of nonlinear dynamic system such as the oscillation and bifurcation. Theanalysis of the nonlinear dynamic characteristic is of great significance for profoundunveiling the flow and heat transfer in open cavities.
Numerical study of natural convection in open cavity under various complexconditions is carried out, using SIMPLE algorithm with QUICK-type discretizationscheme. First, two problems of the natural convections in an open cavity are simulated;one is under a constant flux and the other one is with a discrete heater. The numericalmethod for boundary condition and discrete heater is given. Second, the numericalmethod for natural convection combined with conduction, natural convection combinedwith conduction and surface radiation, natural convection combined withconduction-surface radiation and discrete heater are developed. Then, the flow and heattransfer under various conditions are simulated. Their mechanism and nonlinearcharacteristics are analyzed. Last, a model of flow and heat transfer in the solar chimneysystem is numerically simulated as an application.
The results of the studies are as following:
1. Simulation models under various conditions are built. Numerical method forcoupling convection conduction and surface radiation is given under whole-domaincalculation method.
2. For pure natural convection under a constant flux, the numerical results indicatethat: for the1st problem, at a certain Ra, there is a critical B to maximize the masstransfer between the cavity and ambient; for the natural convection in an open cavity with an isolated heating source, the numerical results indicate that Nu is anincreasing function of Ra under a constant inclined angle; when Ra>106, Nureaches its maximum at φ=45°.
3. The numerical results of natural convection combined with conduction in inclinedopen cavities indicate that, the heat transfer cannot be enhanced further when theconductivity exceed a certain value. The flow pattern in an upward opening cavityis bifurcated at a critical Rac, the Racis about11948under the conditions ofcalculation geometry.
4. The numerical results of heat transfer of the cavity with constant flux indicate that,the heat conduction of conductive wall increases total heat transfer, but its effect isclose to a limit when conductivity ratio exceeds100. The sum of increasing effectof radiation and conduction is ranged from54.1%to64.0%.
5. The numerical results of heat transfer of the cavity with isothermal wall that, for afixed combination of Ra and kr, there is a critical emissivity εc, when ε≥εcthesolution of the flow and heat transfer is unsteady. For the unsteady state, the flowand heat transfer are periodic oscillating or chaotic. The oscillations of flow andheat transfer are caused by the thermal plumes at the bottom wall. If the formationof thermal plumes is periodic.
6. Power Spectra Analysis is carried out for the unsteady-state solution of coupledheat transfer in open cavity. The phase spaces of the time series of averaged totalNu is reconstructed with C-C method and the largest Lyapunov Exponents iscalculated based on the reconstructed phase space using Small Data Sets method.
7. Numerical simulation of flow and heat transfer in solar chimney system indicatethat the output of solar chimney and the mass flux are increasing functions of theheat flux of the bottom, and the entrance height is about20m to maximize the massflux.
The results can be further used for the engineering applications and theoreticalanalysis.The financial support from the Chinese National Natural Science Foundationunder Grants50576057and50876067, Shanghai Education Commission Key Project ofScientific Research No.10ZZ91and Shanghai Key Subjects Construction Project No.J50501.
本文在各种复杂条件下，采用具有QUICK差分格式的SIMPLE方法对开口腔内耦合换热问题进行了数值模拟。首先对具有恒热流和孤立热源的开口腔内自然对流换热进行了数值模拟，给出了相应边界条件和孤立热源的数值处理方法；然后进一步发展处理导热与对流耦合，导热、对流、表面辐射耦合，导热、对流、表面辐射及内部孤立热源耦合等各种较复杂情况的数值处理方法，并对相对应的各种情况进行数值计算；继而，对在各种不同条件下得到的数值模拟结果分析其流动和换热的机理和规律，并进一步进行非线性特性的分析。最后，作为应用，本文对以太阳能热烟囱发电系统为背景的一个模型进行了数值模拟。
本文获得了如下研究结果：
1.对各种条件下的开口腔内流动换热问题建立了计算模型。给出了采用整体求解方法时，处理表面辐射、导热和对流耦合问题的数值处理方法。
2.对恒热流加热开口腔的数值模拟结果表明：在一定Rayleigh数下，存在使腔内与环境质量交换达到最大的腔体深度高度比值。对具有孤立内热源的开口腔自然对流的数值模拟结果表明：在腔体倾斜角不变时，平均Nu数为Ra数的增函数。当Ra>106时，平均Nu数在φ=45°时达到最大值。
3.对导热和对流耦合的倾斜开口腔内的流动和换热进行的数值模拟计算结果表明：对于一个恒壁温加热的耦合开口腔体，无论其倾斜角度是多少，当固体导热系数增大到一定值时，换热就不能被明显地增强；Ra数较小时，换热对倾斜角度的变化较为敏感。随着倾斜角度的减小，换热先增大后减小继而再略微增大。而Ra数较大时，换热经历一个先减弱后增强的过程；对于开口竖直向上的开口腔体，存在一个临界Ra数使腔体内部的流动形式发生变化的临界的Ra数，在本文计算的几何和物理条件下，这个临界Ra数约为11948。
4.对恒热流加热开口腔的耦合换热稳态结果的分析表明：随着导热系数比值(kr)的增大，平均总Nut数也随之增长。在kr超过100时，继续提高导热性能对总体换热的增强效果就不显著了。与无辐射换热的情况相比，有辐射换热时的总平均Nut数增加了大约54.1%到64.0%；
5.对恒壁温加热开口腔的耦合换热非稳态过程分析表明：对一个固定的Ra和kr取值组合，存在一个临界发射率εc。当ε≥εc时，流动与换热的解为非稳态，具体为周期性振荡解或者混沌解。在下壁面形成的热羽流和其相应产生的二次涡流是流动和换热振荡的原因，并且热羽流和二次涡流形成的周期性与Nu数的周期性相对应。
6.对耦合换热计算中出现的三种不同性质的解进行了功率谱分析。对数值模拟解得的平均总Nut数时间序列，采用C-C算法计算嵌入维数和延迟时间，进行了相空间的重构。在重构了的相空间基础上，采用小数据量法求得了不同工况下的最大Lyapunov指数。
7.对太阳能热烟囱系统内流动换热的模拟结果表明，随着加热热流密度的增加，系统空气流量增加，系统出力增加。随着入口高度的增加，系统空气流量相应减小，即系统出力减小。
以上获得的研究成果，可为相关工程问题及进一步的理论分析提供参考。
本文得到了国家自然科学基金面上项目（50576057，50876067），上海教委科研创新重点项目（10ZZ91）和上海市重点学科建设项目资助（J50501）的资助。
Combined heat transfer by natural convection-conduction and surface radiation inan open cavity is studied in this paper. Numerous engineering problems can beabstracted to the combined flow and heat transfer problems such as electronic coolingand thermal environment controlling for shield tunneling. The requirement of predictingthe temperature of heating source and its environment for designing the devices orcontrolling the surroundings asks for the investigate of the mechanism and laws on thecombined flow and heat transfer by natural convection conduction and surface radiationunder various complex conditions. Therefore, the study on the theoretical models hassignificant interest in a range of engineering application. Beside the engineeringapplications, the problem of nature convection in open cavities has abundantcharacteristics of nonlinear dynamic system such as the oscillation and bifurcation. Theanalysis of the nonlinear dynamic characteristic is of great significance for profoundunveiling the flow and heat transfer in open cavities.
Numerical study of natural convection in open cavity under various complexconditions is carried out, using SIMPLE algorithm with QUICK-type discretizationscheme. First, two problems of the natural convections in an open cavity are simulated;one is under a constant flux and the other one is with a discrete heater. The numericalmethod for boundary condition and discrete heater is given. Second, the numericalmethod for natural convection combined with conduction, natural convection combinedwith conduction and surface radiation, natural convection combined withconduction-surface radiation and discrete heater are developed. Then, the flow and heattransfer under various conditions are simulated. Their mechanism and nonlinearcharacteristics are analyzed. Last, a model of flow and heat transfer in the solar chimneysystem is numerically simulated as an application.
The results of the studies are as following:
1. Simulation models under various conditions are built. Numerical method forcoupling convection conduction and surface radiation is given under whole-domaincalculation method.
2. For pure natural convection under a constant flux, the numerical results indicatethat: for the1st problem, at a certain Ra, there is a critical B to maximize the masstransfer between the cavity and ambient; for the natural convection in an open cavity with an isolated heating source, the numerical results indicate that Nu is anincreasing function of Ra under a constant inclined angle; when Ra>106, Nureaches its maximum at φ=45°.
3. The numerical results of natural convection combined with conduction in inclinedopen cavities indicate that, the heat transfer cannot be enhanced further when theconductivity exceed a certain value. The flow pattern in an upward opening cavityis bifurcated at a critical Rac, the Racis about11948under the conditions ofcalculation geometry.
4. The numerical results of heat transfer of the cavity with constant flux indicate that,the heat conduction of conductive wall increases total heat transfer, but its effect isclose to a limit when conductivity ratio exceeds100. The sum of increasing effectof radiation and conduction is ranged from54.1%to64.0%.
5. The numerical results of heat transfer of the cavity with isothermal wall that, for afixed combination of Ra and kr, there is a critical emissivity εc, when ε≥εcthesolution of the flow and heat transfer is unsteady. For the unsteady state, the flowand heat transfer are periodic oscillating or chaotic. The oscillations of flow andheat transfer are caused by the thermal plumes at the bottom wall. If the formationof thermal plumes is periodic.
6. Power Spectra Analysis is carried out for the unsteady-state solution of coupledheat transfer in open cavity. The phase spaces of the time series of averaged totalNu is reconstructed with C-C method and the largest Lyapunov Exponents iscalculated based on the reconstructed phase space using Small Data Sets method.
7. Numerical simulation of flow and heat transfer in solar chimney system indicatethat the output of solar chimney and the mass flux are increasing functions of theheat flux of the bottom, and the entrance height is about20m to maximize the massflux.
The results can be further used for the engineering applications and theoreticalanalysis.The financial support from the Chinese National Natural Science Foundationunder Grants50576057and50876067, Shanghai Education Commission Key Project ofScientific Research No.10ZZ91and Shanghai Key Subjects Construction Project No.J50501.
引文
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