重力热管传热过程的数学模型及液氮温区重力热管的实验研究
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摘要
重力热管具有传热效率高、结构简单、成本低廉等突出优点。尽管重力热管已广泛地应用于许多工业设备中,但其内部换热机理非常复杂,影响因素众多且具有较强的关联性,同时存在不同类型的传热极限,导致现有的数学模型对重力热管传热过程的分析尚不完善。与此同时随着超导技术的快速发展,重力热管在可靠性要求高、长距离及狭窄空间下冷量输送等方面有望发挥重要作用。然而,目前以低温流体为工质开展的研究尚不充分,限制了其在低温领域的推广应用。本文以完善重力热管理论模型和探索其在液氮温区的传热特性为目标,主要开展了以下三方面的研究工作：
1、建立了较完善的重力热管稳态数学模型,定量分析了充注率对管内流动形式及冷却温度的影响
充注率是重力热管传热性能最重要的影响因素之一,对管内流动形式和热管冷却温度起着决定性作用。不同充注率条件下,重力热管内液膜与液池的分布呈现多样性。然而,现有的数学模型仅考虑了其中的部分流形,并对液膜和液池不同换热过程的考虑尚不充分,导致它们对充注率影响分析仍不完善。本文根据重力热管冷凝段、蒸发段液膜区和蒸发段液池区的换热机理分别建立了数学模型,全面考虑了重力热管稳定运行时可能存在三种流动形式和过渡期间的三种临界形式,通过热管总质量和能量守恒关系确定不同充注率条件下管内的流动形式及冷却温度。计算结果揭示了与两种临界流动形式相对应的临界充注率的作用,它们分别是重力热管具有最佳冷却性能的充注率和冷却性能与充注率关系发生变化的转折点。经过分析本文获得了可以使重力热管维持稳定高效运行的充注率区间。
2、建立了能够同时预测重力热管干涸极限、携带极限和沸腾极限的稳态数学模型；与临界充注率和传热率的关系综合后,获得了重力热管维持稳定运行的区间
重力热管可能发生的传热极限主要包括干涸极限、携带极限和沸腾极限。目前,预测传热极限的理论模型仅同时包括干涸极限和携带极限,并且对干涸极限的可靠性未得到充分验证。本文根据传热极限的发生机理,提出了干涸比例的概念,将它与通常认为干涸极限的标准-液池完全干涸-综合在一起作为干涸极限的预测准则；推导出最大气体雷诺数关联式作为判断携带极限的准则；将气液两相在竖直管道中流动时环状流起始点空泡系数的经验值引入模型,用来判断液池内流型的转变,并作为预测沸腾极限的准则,从而建立起可以同时分析三种传热极限的数学模型。通过综合临界充注率与传热率的关系,获得了重力热管能够稳定运行的区间,并讨论了工作压力和热管结构尺寸对该区间的影响。
3、以氮为工质对重力热管的传热性能进行了实验研究
现有的实验研究多数是以中温温区普通制冷剂和液体为工质进行的。事实上,工质物性参数和沸腾现象等因素的不同,导致了不同温区热管具有不同的传热特性。然而,目前针对低温流体开展的研究尚不充分。本文设计搭建了低温重力热管实验装置,开展了以氮为工质时其传热性能的研究。实验发现,工作压力在充注率(定义为充注质量全部以液体存在的体积与热管蒸发段体积之比)为18.8%时较稳定；当充注率增加到49.6%时,压力先增加、达到最大值后逐渐减小,在实验研究的传热率范围内压力在系统达到稳定后也趋于稳定；当充注率为62.0%、传热率增加到10 W时,压力达到峰值后,在减小直至稳定的过程中出现波动现象,在传热率增加到15 W时波动强度增加,并未呈现出稳定趋势。通过计算瞬时传热率发现,压力变化特性与其密切相关。传热率较低时两者几乎同时达到峰值,传热率较高时压力峰值略有滞后。通过稳态下实验数据与计算值的比较与分析,本文验证了理论模型、确定了适用于实验条件下的经验系数,为相关研究提供参考。
Two-phase closed thermosyphon (TPCT) has many advantages, such as high efficiency, simple structure, low fabrication cost and so on. Although it has been widely used in many industrial devices, the heat transfer phenomena in a TPCT are complex, and many factors have effects on the heat transfer performance and are related to each other. Besides, there are different types of heat transfer limit. As a result, the available models cannot explain well the heat transfer process in the TPCT. With the rapid development of superconducting technology, the TPCT will play a more important role in high reliability requirement and cooling transfer in long distance and narrow space. However, the existing studies with cryogenic fluid as working fluid are not sufficient, which limits the applications in cryogenic field. The present work focuses on further developing the mathematical model for the TPCT and exploring its heat transfer performance at liquid nitrogen temperature. The following contents are included:
1. Development of a new model for analyzing quantitatively the effects of filling ratio on the flow pattern inside a TPCT and the cooling temperature
Filling ratio is one of the most important factors for the heat transfer performance of a TPCT. It has significant effect on the flow pattern inside and the cooling temperature. For different filling ratios, there are diversiform distributions of liquid film and liquid pool. However, the available models only consider the flow patterns partly, and fail to explain well the different heat transfer mechanisms of liquid film and liquid pool. Consequently, their analyses on the effect of filling ratio are not sufficient. In the present work, based on the different heat transfer mechanisms, the individual models are developed for condenser region, liquid film region and liquid pool region in evaporator, respectively. Three types of flow pattern and three types of critical transition pattern, which could exist in a TPCT in the steady operation, are well considered. The flow pattern and the cooling temperature at different filling ratios can be determined by solving the total mass and energy conservation in the TPCT iteratively. The calculated results explain the effects of two types of critical filling ratio, which are related to the two types of critical transition pattern. One makes the TPCT in the operation with the best cooling performance. The other is the transition point for the different dependence of cooling performance on filling ratio. Finally, the range of filling ratio, which can keep the TPCT in the stable and effective operation, is obtained.
2. Development of a novel model for a TPCT to predict dryout, flooding and boiling limit together. Establishment of the range of a TPCT in the steady operation by combining with the dependence of critical filling ratios on heat transfer rate
There are three types of heat transfer limit, which could happen in the TPCT:dryout limit, flooding limit and boiling limit. At present, the theoretical models for predicting heat transfer limit consider dryout and flooding limit together, and their validities on dryout limit have not been verified. In this work, based on the mechanisms of heat transfer limit, the concept of dryout-ratio is proposed for predicting dryout limit by combining with the general criterion-completely dryout liquid pool utilized in former models. The empirical correlation for the maximum gas Reynolds number is deduced for predicting flooding limit. The empirical void fraction, at the onset of annular flow in vertical liquid-vapor two-phase flow, is introduced into the model as the criterion for flow pattern transition in liquid pool, and predicting boiling limit. Consequently, a novel model, which can predict the three limits together, is developed in this work. By combining with the dependence of critical filling ratios on heat transfer rate, the range of a TPCT in the steady operation is established, and the effects of operating pressure and geometries of a TPCT are also discussed.
3. Experimental investigation on the heat transfer performance of a TPCT with nitrogen as working fluid
At present, the general refrigerants and liquids in the medium temperature range are mostly used as working fluid in the available experimental studies. In fact, some different factors, such as the properties of working fluid, boiling phenomenon and so on, result in the different heat transfer performance of the TPCTs working at different temperatures. However, the available studies with cryogenic fluids are not sufficient to explain the characteristic. In this work, the experimental setup of the cryogenic TPCT is designed and manufactured, and the investigation with nitrogen as working fluid is performed. In the cool-down process, it is observed that the operating pressure keeps relatively steady at the filling ratio (defined as the volume ratio of charged liquid to the evaporator) of 18.8%. When filling ratio is up to 49.6%, the pressure firstly increases to peak value, and then decreases gradually. It finally keeps steady when the system reaches the steady state at the heat transfer rates performed in the experiments. At the filling ratio of 62.0% and the heat transfer rate of 10 W, the pressure reaches the peak and then shows oscillation during decreasing to the steady state. When the heat tranfesr rate is up to 15 W, the amplitude of oscillation is augmented and cannot reach steady state. By calculating the transient heat transfer rate, it is found that the performance of operating pressure is closely related to that. At low heat transfer rate, they almost reach their peak vaules at the same time. At high heat transfer rate, the pressure peak is slightly behind. The comparisons between the model predictions and the experimental results are made and analyzed. The developed models are validated and some empirical values for the experimental condition in this work are determined, which can provide the reference for the relative studies.
1、建立了较完善的重力热管稳态数学模型,定量分析了充注率对管内流动形式及冷却温度的影响
充注率是重力热管传热性能最重要的影响因素之一,对管内流动形式和热管冷却温度起着决定性作用。不同充注率条件下,重力热管内液膜与液池的分布呈现多样性。然而,现有的数学模型仅考虑了其中的部分流形,并对液膜和液池不同换热过程的考虑尚不充分,导致它们对充注率影响分析仍不完善。本文根据重力热管冷凝段、蒸发段液膜区和蒸发段液池区的换热机理分别建立了数学模型,全面考虑了重力热管稳定运行时可能存在三种流动形式和过渡期间的三种临界形式,通过热管总质量和能量守恒关系确定不同充注率条件下管内的流动形式及冷却温度。计算结果揭示了与两种临界流动形式相对应的临界充注率的作用,它们分别是重力热管具有最佳冷却性能的充注率和冷却性能与充注率关系发生变化的转折点。经过分析本文获得了可以使重力热管维持稳定高效运行的充注率区间。
2、建立了能够同时预测重力热管干涸极限、携带极限和沸腾极限的稳态数学模型；与临界充注率和传热率的关系综合后,获得了重力热管维持稳定运行的区间
重力热管可能发生的传热极限主要包括干涸极限、携带极限和沸腾极限。目前,预测传热极限的理论模型仅同时包括干涸极限和携带极限,并且对干涸极限的可靠性未得到充分验证。本文根据传热极限的发生机理,提出了干涸比例的概念,将它与通常认为干涸极限的标准-液池完全干涸-综合在一起作为干涸极限的预测准则；推导出最大气体雷诺数关联式作为判断携带极限的准则；将气液两相在竖直管道中流动时环状流起始点空泡系数的经验值引入模型,用来判断液池内流型的转变,并作为预测沸腾极限的准则,从而建立起可以同时分析三种传热极限的数学模型。通过综合临界充注率与传热率的关系,获得了重力热管能够稳定运行的区间,并讨论了工作压力和热管结构尺寸对该区间的影响。
3、以氮为工质对重力热管的传热性能进行了实验研究
现有的实验研究多数是以中温温区普通制冷剂和液体为工质进行的。事实上,工质物性参数和沸腾现象等因素的不同,导致了不同温区热管具有不同的传热特性。然而,目前针对低温流体开展的研究尚不充分。本文设计搭建了低温重力热管实验装置,开展了以氮为工质时其传热性能的研究。实验发现,工作压力在充注率(定义为充注质量全部以液体存在的体积与热管蒸发段体积之比)为18.8%时较稳定；当充注率增加到49.6%时,压力先增加、达到最大值后逐渐减小,在实验研究的传热率范围内压力在系统达到稳定后也趋于稳定；当充注率为62.0%、传热率增加到10 W时,压力达到峰值后,在减小直至稳定的过程中出现波动现象,在传热率增加到15 W时波动强度增加,并未呈现出稳定趋势。通过计算瞬时传热率发现,压力变化特性与其密切相关。传热率较低时两者几乎同时达到峰值,传热率较高时压力峰值略有滞后。通过稳态下实验数据与计算值的比较与分析,本文验证了理论模型、确定了适用于实验条件下的经验系数,为相关研究提供参考。
Two-phase closed thermosyphon (TPCT) has many advantages, such as high efficiency, simple structure, low fabrication cost and so on. Although it has been widely used in many industrial devices, the heat transfer phenomena in a TPCT are complex, and many factors have effects on the heat transfer performance and are related to each other. Besides, there are different types of heat transfer limit. As a result, the available models cannot explain well the heat transfer process in the TPCT. With the rapid development of superconducting technology, the TPCT will play a more important role in high reliability requirement and cooling transfer in long distance and narrow space. However, the existing studies with cryogenic fluid as working fluid are not sufficient, which limits the applications in cryogenic field. The present work focuses on further developing the mathematical model for the TPCT and exploring its heat transfer performance at liquid nitrogen temperature. The following contents are included:
1. Development of a new model for analyzing quantitatively the effects of filling ratio on the flow pattern inside a TPCT and the cooling temperature
Filling ratio is one of the most important factors for the heat transfer performance of a TPCT. It has significant effect on the flow pattern inside and the cooling temperature. For different filling ratios, there are diversiform distributions of liquid film and liquid pool. However, the available models only consider the flow patterns partly, and fail to explain well the different heat transfer mechanisms of liquid film and liquid pool. Consequently, their analyses on the effect of filling ratio are not sufficient. In the present work, based on the different heat transfer mechanisms, the individual models are developed for condenser region, liquid film region and liquid pool region in evaporator, respectively. Three types of flow pattern and three types of critical transition pattern, which could exist in a TPCT in the steady operation, are well considered. The flow pattern and the cooling temperature at different filling ratios can be determined by solving the total mass and energy conservation in the TPCT iteratively. The calculated results explain the effects of two types of critical filling ratio, which are related to the two types of critical transition pattern. One makes the TPCT in the operation with the best cooling performance. The other is the transition point for the different dependence of cooling performance on filling ratio. Finally, the range of filling ratio, which can keep the TPCT in the stable and effective operation, is obtained.
2. Development of a novel model for a TPCT to predict dryout, flooding and boiling limit together. Establishment of the range of a TPCT in the steady operation by combining with the dependence of critical filling ratios on heat transfer rate
There are three types of heat transfer limit, which could happen in the TPCT:dryout limit, flooding limit and boiling limit. At present, the theoretical models for predicting heat transfer limit consider dryout and flooding limit together, and their validities on dryout limit have not been verified. In this work, based on the mechanisms of heat transfer limit, the concept of dryout-ratio is proposed for predicting dryout limit by combining with the general criterion-completely dryout liquid pool utilized in former models. The empirical correlation for the maximum gas Reynolds number is deduced for predicting flooding limit. The empirical void fraction, at the onset of annular flow in vertical liquid-vapor two-phase flow, is introduced into the model as the criterion for flow pattern transition in liquid pool, and predicting boiling limit. Consequently, a novel model, which can predict the three limits together, is developed in this work. By combining with the dependence of critical filling ratios on heat transfer rate, the range of a TPCT in the steady operation is established, and the effects of operating pressure and geometries of a TPCT are also discussed.
3. Experimental investigation on the heat transfer performance of a TPCT with nitrogen as working fluid
At present, the general refrigerants and liquids in the medium temperature range are mostly used as working fluid in the available experimental studies. In fact, some different factors, such as the properties of working fluid, boiling phenomenon and so on, result in the different heat transfer performance of the TPCTs working at different temperatures. However, the available studies with cryogenic fluids are not sufficient to explain the characteristic. In this work, the experimental setup of the cryogenic TPCT is designed and manufactured, and the investigation with nitrogen as working fluid is performed. In the cool-down process, it is observed that the operating pressure keeps relatively steady at the filling ratio (defined as the volume ratio of charged liquid to the evaporator) of 18.8%. When filling ratio is up to 49.6%, the pressure firstly increases to peak value, and then decreases gradually. It finally keeps steady when the system reaches the steady state at the heat transfer rates performed in the experiments. At the filling ratio of 62.0% and the heat transfer rate of 10 W, the pressure reaches the peak and then shows oscillation during decreasing to the steady state. When the heat tranfesr rate is up to 15 W, the amplitude of oscillation is augmented and cannot reach steady state. By calculating the transient heat transfer rate, it is found that the performance of operating pressure is closely related to that. At low heat transfer rate, they almost reach their peak vaules at the same time. At high heat transfer rate, the pressure peak is slightly behind. The comparisons between the model predictions and the experimental results are made and analyzed. The developed models are validated and some empirical values for the experimental condition in this work are determined, which can provide the reference for the relative studies.
引文
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