湿空气透平（HAT）循环中的工质热物性计算模型和应用研究
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摘要
能源问题直接关系到国家经济发展和国防建设，随着石油资源日益紧张，如何高效节能地利用有限的化石资源是目前阶段的重要课题。现代燃气轮机技术被认为是高效洁净利用化石资源的很好技术，尤其是湿空气透平(HAT)循环被誉为21世纪的新型动力循环。HAT循环的工质是在传统工质中注入水或水蒸气，湿化后可以提高循环的比功和效率，降低污染物的生成。
HAT循环处于高温和高压的工况下，目前已经可以达到1773K和40atm。在这样宽广的温度和压力范围下，湿空气和湿燃气的热物性还没有很完善的计算模型，人们对于传统工质与水蒸气混合而形成的湿工质（湿空气和湿燃气）的研究还很不足，尤其是对于传统工质与水蒸气的混合规律还没有准确的认识与把握。而对于HAT循环的热力学过程的研究和模拟都紧密依赖于准确的工质热物性，但是目前的湿工质热物性研究都还不能满足如此宽广的温度和压力范围。
以往的研究可以分为两大类。第一类是理想混合气体模型，优点是充分利用已有的单组分气体（如干空气、水蒸气、二氧化碳等）的性质，缺点是没有考虑不同组分气体的相互作用和影响，因此结果不够准确。第二类是经验和半经验模型，都把混合气体当作一种假想的纯组分气体，优点是拥有自己的气体状态方程和充分考虑不同组分气体的相互作用，缺点是需要大量的实验数据进行验证和拟合，并且往往只能在较为狭窄的温度和压力范围内适用，不易外推。
本文就HAT循环中的湿空气和湿燃气的热物性的计算模型展开研究，揭示了传统工质（干空气和干燃气）与水蒸气的混合规律,并在上述的宽广的温度和压力范围内提出了准确计算湿工质热物性的方法，其精度与现有的实验数据相比较，比焓、比熵和比容的差别均小于0.1%，因此完全符合工程上的要求。本文的贡献主要在以下四个方面。
首先，本文聚焦于饱和湿空气，利用“半透膜”模型和“实际效果压力”的概念，首次从理论上证明，饱和湿空气中的饱和水蒸气组分的“实际效果压力”正好等于相同温度下的饱和水蒸气的压力。本文首次发现，尽管饱和湿空气中的饱和水蒸气组分与相同温度下独占此相同容积中的饱和水蒸气的“对应状态”相同，即拥有相同的“实际效果压力”和相同的温度，但是两种饱和水蒸气的摩尔数并不相同，前者始终比后者的大一些，这种摩尔数的差别正是由于干空气与饱和水蒸气的相互作用造成的。本文首次提出“改进因子”用于描述干空气对于独占容积的水蒸气的“改进效果”，定量刻画干空气与水蒸气的相互作用的强弱。本文进而提出各个组分气体的“实际效果压力”之和等于总压力的“修正道尔顿分压定律”，并加以论证。一方面，从压力的宏观意义的角度对“修正道尔顿分压定律”进行了理论证明；另一方面，利用数值方法将计算结果与现有的实验数据相比较，从而对“修正道尔顿分压定律”进行了数值证明。
第二，本文将“修正道尔顿分压定律”推广到其他的不饱和湿空气的情形。通过对“改进效果”的物理意义的理解，不饱和湿空气的“改进因子”可以通过合理的计算公式得到。通过对不饱和湿空气的“改进因子”随温度变化的规律，发现“截止温度”是一个极为重要的温度值。“截止温度”为本文首次提出，在数值上等于此时的湿空气总压力所对应的饱和水蒸气的饱和温度。当湿空气温度逐渐升高并且接近于“截止温度”时，“改进因子”会逐渐趋向于1.0000，当温度等于或高于“截止温度”后，“改进因子”始终为1.0000。本文首次发现，当湿空气的温度高于“截止温度”后，干空气与水蒸气的相互作用可以忽略，此时只需要考虑这两种组分气体各自的独占状态即可。至此，所有状态的湿空气热物性都可以计算了。
第三，本文进而研究湿燃气，求解并得到湿燃气的“截止温度”。湿燃气除了含有干空气组分，还含有大量水蒸气和二氧化碳两种实际气体组分，它们都偏离理想气体性质较远。研究发现，在湿燃气总压力恒定的情况下，总压力所对应的饱和水蒸气的饱和温度总是远远高于总压力所对应的饱和二氧化碳的饱和温度。也就是说，随着湿燃气温度的上升，二氧化碳总是比水蒸气更早地体现出“改进因子”趋近于1.0000的特点。因此，湿燃气的“截止温度”可以由总压力所对应的饱和水蒸气的饱和温度决定。当湿燃气的温度高于“截止温度”时，“修正道尔顿分压定律”可以适用于湿燃气，此时各个组分气体的相互作用都可以忽略，而只须考虑各种组分气体的独占状态即可。
第四，本文将湿空气热物性运用于饱和器的计算，将湿燃气热物性运用于透平膨胀做功的计算，得到的计算结果与过去使用的理想模型的计算结果进行详细比较，发现热物性的选择对于循环的计算至关重要，由于热物性模型的选择不同，对于循环的数值模拟的各个结果也会产生各种差异。
总体而言，全文对于饱和湿空气、不饱和湿空气、湿燃气的热物性进行了层层深入的探讨，利用“半透膜”模型对湿空气和湿燃气的热物性进行了解释。其中，“实际效果压力”、“改进因子”、“截止温度”为本文首次提出，着重描述了不同组分气体之间的相互作用，并且结合“修正道尔顿分压定律”及其重要推论，充分利用已有的完备的单组分气体的热物性，本文完整地提供了湿空气和湿燃气的热物性的计算方法。本文研究的结果也适用于其他使用湿空气和湿燃气作为工质的动力机械的热力过程模拟。
National economic development and national defense are both heavily dependent on energy.With the short supply of petroleum resources, how to utilize fossil resources in an efficient andenergy-saving way becomes an imperative task. Modern gas turbine is regarded as an efficient andclean technology to make use of fossil resources. Specifically, Humid Air Turbine (HAT) cycle isregarded as a new type of dynamic cycle in the21stcentury. The working medium of HAT cycle isformed by injecting water or steam into traditional working medium. After humidification, thepower rate and efficacy of the dynamic cycle can be improved, and the formation of pollutantsmay be reduced as well.
The working condition for HAT is at high temperature and high pressure, which alreadyreaches1773K and40atm respectively for current HAT in operation. To date, there is still nosatisfactory calculation model for humid working medium (i.e. humid air and humid combustiongas mixture) in such wide temperature and pressure ranges. The researches on humid workingmedium are not adequate. Specifically, scientists don’t comprehend the behaviors of traditionalworking medium and water vapor in the humid mixture very well. Both study and simulation ofHAT cycle are tightly reliant on accurate thermodynamic properties of humid working medium.However, the current researches on humid working medium do not meet the requirement of suchwide temperature and pressure ranges.
Two types of models are usually applied by past researchers. The first type is the ideal gasmixture model. It fully utilizes the properties of each gas component (e.g. dry air, water vapor andCO2). However, it omits the interactions between different gas components. The thermodynamicproperties obtained by this type of model may not be accurate due to such omissions. The secondtype includes empirical and semi-empirical models. They regard the gas mixture as a pseudo-puregas, which has its own state equation. The results are more accurate because the interactionsbetween different gas components are taken into account. However, the establishment of suchmodel requires a large number of experimental data. This type of model can only be applied inthose experiment-proved temperature and pressure ranges. It cannot be extended to other widerranges.
This thesis studies the thermodynamic properties of humid working medium in HAT cycle,demonstrates the behaviors of dry working medium (i.e. dry air and dry combustion gas mixture)and water vapor in the humid gas mixture, and proposes a new calculation model for humidworking medium in the above-mentioned wide temperature and pressure ranges in HAT cycle. Theerror of my proposed model is less than0.1%compared to existing experimental data, so it fullymeets the engineering standard. The main contributions of this thesis are in the following fouraspects.
First, this thesis focuses on saturated humid air. It establishes the semi-permeable membranemodel and the concept of “actual effective pressure”. It is for the first time to prove the “actualeffective pressure” of water vapor in the saturated humid air exactly equal to the saturationpressure of existing alone saturated water vapor at the same temperature. Furthermore, it isdiscovered that although the saturated water vapor in the saturated humid air is at “CorrespondingState” to the saturated water vapor existing alone in the same volume at the same temperature, themol numbers of two types of saturated water vapor are different. The mol number of saturatedwater vapor in the saturated humid air is always larger than the mol number of the saturated watervapor existing alone. The difference of mol numbers are attributed to the interaction between dryair and water vapor.“Improvement Factor” is proposed to describe the “Improvement Effect” ofmol number increase of the existing alone water vapor caused by dry air quantitatively. Then theRevised Dalton’s Partial Pressure Law proposes that the summation of “actual effective pressures”of each gas component equals the total pressure. This law is proved on two hands. On the onehand, it is proved by the macro physical meaning of pressure. On the other hand, it is proved bythe numerical calculation results of my model compared to existing experimental data.
Second, this thesis extends the Revised Dalton’s Partial Pressure Law to unsaturated humidair. In accordance to the physical meaning of “Improvement Effect”, the “Improvement Factors”for unsaturated humid air can be obtained in reasonable ways. Through the study of “Improvement Factors” in unsaturated humid air with the increase of temperature, it is discovered that “CuttingOff Temperature” is a crucial benchmark.“Cutting Off Temperature” is proposed for the first time,the value of which is exactly equal to the saturation temperature of the existing alone saturatedwater vapor corresponding to the total pressure of humid air. When the temperature of humid airincreases and approaches the “Cutting Off Temperature”, the “Improvement Factors” will movetowards1.0000. When the temperature is equal to or higher than the “Cutting Off Temperature”,the “Improvement Factor” will always be1.0000. It is for the first time to discover that theinteraction between dry air and water vapor may be omitted when the temperature of humid air ishigher than “Cutting Off Temperature”. Under such circumstances, it is only required to considerthe existing alone status of each gas component. Thus, thermodynamic properties of all kinds ofhumid air are able to be calculated smoothly.
Third, this thesis studies humid combustion gas mixture and obtains its “Cutting OffTemperature”. Humid combustion gas mixture contains not only dry air but also large amount ofwater vapor and CO2, both of which are real gas components and deviate from ideal gas behaviorsnotably. Through in-depth research, it is found out that when the total pressure of humidcombustion gas mixture is fixed, the saturation temperature of existing alone saturated water vaporcorresponding to the fixed total pressure is always much higher than the saturation temperature ofexisting alone saturated CO2corresponding to the same total pressure. In other words, in thehumid combustion gas mixture, the “Improvement Factor” of CO2always approaches1.0000much earlier than that of water vapor. Therefore, the “Cutting Off Temperature” of humidcombustion gas mixture can be determined by the saturation temperature of existing alonesaturated water vapor corresponding to the total pressure. When the temperature of humidcombustion gas mixture is higher than the “Cutting Off Temperature”, Revised Dalton’s PartialPressure Law can be applied. Under such circumstances, the interaction between different gascomponents may be omitted. As long as the existing alone status of each gas component isobtained, the thermodynamic properties of humid combustion gas mixture can be thoroughlysolved.
Fourth, this thesis applies the thermodynamic properties of humid air developed by my modelto the saturator calculation and applies the thermodynamic properties of humid combustion gasmixture to the turbine calculation. The calculation results obtained by my model are compared tothe results by ideal gas mixture model in detail. It is found that the selection of an accurate modelfor thermodynamic properties of working medium is of vital importance. By means of differentmodels, the simulation results of many output parameters in HAT cycle will be different to variousextents.
In conclusion, this thesis studies saturated humid air, unsaturated humid air and humidcombustion gas mixture step by step. The semi-permeable membrane model is fully utilized toexplain the thermodynamic behaviors of humid air and humid combustion gas mixture. Suchconcepts as “actual effective pressure”,“Improvement Factor” and “Cutting Off Temperature” areproposed for the first time. This thesis describes the interaction between different gas componentsin detail. The proposition and proof of Revised Dalton’s Partial Pressure Law and the importantdeductive relationship of this law are both crucial. They provide the theoretical foundation to linkthe thermodynamic behavior of the humid gas mixture and the thermodynamic behaviors of its gascomponents. Thus, we can may full use of the well-equipped thermodynamic properties of eachexisting alone gas component to get the thermodynamic properties of humid gas mixture. Thisthesis provides a complete model for calculation of thermodynamic properties of humid air andhumid combustion gas mixture. The results of this thesis may also be fit for other types ofthermodynamic process simulation whose working mediums are humid air or humid combustiongas mixture.
HAT循环处于高温和高压的工况下，目前已经可以达到1773K和40atm。在这样宽广的温度和压力范围下，湿空气和湿燃气的热物性还没有很完善的计算模型，人们对于传统工质与水蒸气混合而形成的湿工质（湿空气和湿燃气）的研究还很不足，尤其是对于传统工质与水蒸气的混合规律还没有准确的认识与把握。而对于HAT循环的热力学过程的研究和模拟都紧密依赖于准确的工质热物性，但是目前的湿工质热物性研究都还不能满足如此宽广的温度和压力范围。
以往的研究可以分为两大类。第一类是理想混合气体模型，优点是充分利用已有的单组分气体（如干空气、水蒸气、二氧化碳等）的性质，缺点是没有考虑不同组分气体的相互作用和影响，因此结果不够准确。第二类是经验和半经验模型，都把混合气体当作一种假想的纯组分气体，优点是拥有自己的气体状态方程和充分考虑不同组分气体的相互作用，缺点是需要大量的实验数据进行验证和拟合，并且往往只能在较为狭窄的温度和压力范围内适用，不易外推。
本文就HAT循环中的湿空气和湿燃气的热物性的计算模型展开研究，揭示了传统工质（干空气和干燃气）与水蒸气的混合规律,并在上述的宽广的温度和压力范围内提出了准确计算湿工质热物性的方法，其精度与现有的实验数据相比较，比焓、比熵和比容的差别均小于0.1%，因此完全符合工程上的要求。本文的贡献主要在以下四个方面。
首先，本文聚焦于饱和湿空气，利用“半透膜”模型和“实际效果压力”的概念，首次从理论上证明，饱和湿空气中的饱和水蒸气组分的“实际效果压力”正好等于相同温度下的饱和水蒸气的压力。本文首次发现，尽管饱和湿空气中的饱和水蒸气组分与相同温度下独占此相同容积中的饱和水蒸气的“对应状态”相同，即拥有相同的“实际效果压力”和相同的温度，但是两种饱和水蒸气的摩尔数并不相同，前者始终比后者的大一些，这种摩尔数的差别正是由于干空气与饱和水蒸气的相互作用造成的。本文首次提出“改进因子”用于描述干空气对于独占容积的水蒸气的“改进效果”，定量刻画干空气与水蒸气的相互作用的强弱。本文进而提出各个组分气体的“实际效果压力”之和等于总压力的“修正道尔顿分压定律”，并加以论证。一方面，从压力的宏观意义的角度对“修正道尔顿分压定律”进行了理论证明；另一方面，利用数值方法将计算结果与现有的实验数据相比较，从而对“修正道尔顿分压定律”进行了数值证明。
第二，本文将“修正道尔顿分压定律”推广到其他的不饱和湿空气的情形。通过对“改进效果”的物理意义的理解，不饱和湿空气的“改进因子”可以通过合理的计算公式得到。通过对不饱和湿空气的“改进因子”随温度变化的规律，发现“截止温度”是一个极为重要的温度值。“截止温度”为本文首次提出，在数值上等于此时的湿空气总压力所对应的饱和水蒸气的饱和温度。当湿空气温度逐渐升高并且接近于“截止温度”时，“改进因子”会逐渐趋向于1.0000，当温度等于或高于“截止温度”后，“改进因子”始终为1.0000。本文首次发现，当湿空气的温度高于“截止温度”后，干空气与水蒸气的相互作用可以忽略，此时只需要考虑这两种组分气体各自的独占状态即可。至此，所有状态的湿空气热物性都可以计算了。
第三，本文进而研究湿燃气，求解并得到湿燃气的“截止温度”。湿燃气除了含有干空气组分，还含有大量水蒸气和二氧化碳两种实际气体组分，它们都偏离理想气体性质较远。研究发现，在湿燃气总压力恒定的情况下，总压力所对应的饱和水蒸气的饱和温度总是远远高于总压力所对应的饱和二氧化碳的饱和温度。也就是说，随着湿燃气温度的上升，二氧化碳总是比水蒸气更早地体现出“改进因子”趋近于1.0000的特点。因此，湿燃气的“截止温度”可以由总压力所对应的饱和水蒸气的饱和温度决定。当湿燃气的温度高于“截止温度”时，“修正道尔顿分压定律”可以适用于湿燃气，此时各个组分气体的相互作用都可以忽略，而只须考虑各种组分气体的独占状态即可。
第四，本文将湿空气热物性运用于饱和器的计算，将湿燃气热物性运用于透平膨胀做功的计算，得到的计算结果与过去使用的理想模型的计算结果进行详细比较，发现热物性的选择对于循环的计算至关重要，由于热物性模型的选择不同，对于循环的数值模拟的各个结果也会产生各种差异。
总体而言，全文对于饱和湿空气、不饱和湿空气、湿燃气的热物性进行了层层深入的探讨，利用“半透膜”模型对湿空气和湿燃气的热物性进行了解释。其中，“实际效果压力”、“改进因子”、“截止温度”为本文首次提出，着重描述了不同组分气体之间的相互作用，并且结合“修正道尔顿分压定律”及其重要推论，充分利用已有的完备的单组分气体的热物性，本文完整地提供了湿空气和湿燃气的热物性的计算方法。本文研究的结果也适用于其他使用湿空气和湿燃气作为工质的动力机械的热力过程模拟。
National economic development and national defense are both heavily dependent on energy.With the short supply of petroleum resources, how to utilize fossil resources in an efficient andenergy-saving way becomes an imperative task. Modern gas turbine is regarded as an efficient andclean technology to make use of fossil resources. Specifically, Humid Air Turbine (HAT) cycle isregarded as a new type of dynamic cycle in the21stcentury. The working medium of HAT cycle isformed by injecting water or steam into traditional working medium. After humidification, thepower rate and efficacy of the dynamic cycle can be improved, and the formation of pollutantsmay be reduced as well.
The working condition for HAT is at high temperature and high pressure, which alreadyreaches1773K and40atm respectively for current HAT in operation. To date, there is still nosatisfactory calculation model for humid working medium (i.e. humid air and humid combustiongas mixture) in such wide temperature and pressure ranges. The researches on humid workingmedium are not adequate. Specifically, scientists don’t comprehend the behaviors of traditionalworking medium and water vapor in the humid mixture very well. Both study and simulation ofHAT cycle are tightly reliant on accurate thermodynamic properties of humid working medium.However, the current researches on humid working medium do not meet the requirement of suchwide temperature and pressure ranges.
Two types of models are usually applied by past researchers. The first type is the ideal gasmixture model. It fully utilizes the properties of each gas component (e.g. dry air, water vapor andCO2). However, it omits the interactions between different gas components. The thermodynamicproperties obtained by this type of model may not be accurate due to such omissions. The secondtype includes empirical and semi-empirical models. They regard the gas mixture as a pseudo-puregas, which has its own state equation. The results are more accurate because the interactionsbetween different gas components are taken into account. However, the establishment of suchmodel requires a large number of experimental data. This type of model can only be applied inthose experiment-proved temperature and pressure ranges. It cannot be extended to other widerranges.
This thesis studies the thermodynamic properties of humid working medium in HAT cycle,demonstrates the behaviors of dry working medium (i.e. dry air and dry combustion gas mixture)and water vapor in the humid gas mixture, and proposes a new calculation model for humidworking medium in the above-mentioned wide temperature and pressure ranges in HAT cycle. Theerror of my proposed model is less than0.1%compared to existing experimental data, so it fullymeets the engineering standard. The main contributions of this thesis are in the following fouraspects.
First, this thesis focuses on saturated humid air. It establishes the semi-permeable membranemodel and the concept of “actual effective pressure”. It is for the first time to prove the “actualeffective pressure” of water vapor in the saturated humid air exactly equal to the saturationpressure of existing alone saturated water vapor at the same temperature. Furthermore, it isdiscovered that although the saturated water vapor in the saturated humid air is at “CorrespondingState” to the saturated water vapor existing alone in the same volume at the same temperature, themol numbers of two types of saturated water vapor are different. The mol number of saturatedwater vapor in the saturated humid air is always larger than the mol number of the saturated watervapor existing alone. The difference of mol numbers are attributed to the interaction between dryair and water vapor.“Improvement Factor” is proposed to describe the “Improvement Effect” ofmol number increase of the existing alone water vapor caused by dry air quantitatively. Then theRevised Dalton’s Partial Pressure Law proposes that the summation of “actual effective pressures”of each gas component equals the total pressure. This law is proved on two hands. On the onehand, it is proved by the macro physical meaning of pressure. On the other hand, it is proved bythe numerical calculation results of my model compared to existing experimental data.
Second, this thesis extends the Revised Dalton’s Partial Pressure Law to unsaturated humidair. In accordance to the physical meaning of “Improvement Effect”, the “Improvement Factors”for unsaturated humid air can be obtained in reasonable ways. Through the study of “Improvement Factors” in unsaturated humid air with the increase of temperature, it is discovered that “CuttingOff Temperature” is a crucial benchmark.“Cutting Off Temperature” is proposed for the first time,the value of which is exactly equal to the saturation temperature of the existing alone saturatedwater vapor corresponding to the total pressure of humid air. When the temperature of humid airincreases and approaches the “Cutting Off Temperature”, the “Improvement Factors” will movetowards1.0000. When the temperature is equal to or higher than the “Cutting Off Temperature”,the “Improvement Factor” will always be1.0000. It is for the first time to discover that theinteraction between dry air and water vapor may be omitted when the temperature of humid air ishigher than “Cutting Off Temperature”. Under such circumstances, it is only required to considerthe existing alone status of each gas component. Thus, thermodynamic properties of all kinds ofhumid air are able to be calculated smoothly.
Third, this thesis studies humid combustion gas mixture and obtains its “Cutting OffTemperature”. Humid combustion gas mixture contains not only dry air but also large amount ofwater vapor and CO2, both of which are real gas components and deviate from ideal gas behaviorsnotably. Through in-depth research, it is found out that when the total pressure of humidcombustion gas mixture is fixed, the saturation temperature of existing alone saturated water vaporcorresponding to the fixed total pressure is always much higher than the saturation temperature ofexisting alone saturated CO2corresponding to the same total pressure. In other words, in thehumid combustion gas mixture, the “Improvement Factor” of CO2always approaches1.0000much earlier than that of water vapor. Therefore, the “Cutting Off Temperature” of humidcombustion gas mixture can be determined by the saturation temperature of existing alonesaturated water vapor corresponding to the total pressure. When the temperature of humidcombustion gas mixture is higher than the “Cutting Off Temperature”, Revised Dalton’s PartialPressure Law can be applied. Under such circumstances, the interaction between different gascomponents may be omitted. As long as the existing alone status of each gas component isobtained, the thermodynamic properties of humid combustion gas mixture can be thoroughlysolved.
Fourth, this thesis applies the thermodynamic properties of humid air developed by my modelto the saturator calculation and applies the thermodynamic properties of humid combustion gasmixture to the turbine calculation. The calculation results obtained by my model are compared tothe results by ideal gas mixture model in detail. It is found that the selection of an accurate modelfor thermodynamic properties of working medium is of vital importance. By means of differentmodels, the simulation results of many output parameters in HAT cycle will be different to variousextents.
In conclusion, this thesis studies saturated humid air, unsaturated humid air and humidcombustion gas mixture step by step. The semi-permeable membrane model is fully utilized toexplain the thermodynamic behaviors of humid air and humid combustion gas mixture. Suchconcepts as “actual effective pressure”,“Improvement Factor” and “Cutting Off Temperature” areproposed for the first time. This thesis describes the interaction between different gas componentsin detail. The proposition and proof of Revised Dalton’s Partial Pressure Law and the importantdeductive relationship of this law are both crucial. They provide the theoretical foundation to linkthe thermodynamic behavior of the humid gas mixture and the thermodynamic behaviors of its gascomponents. Thus, we can may full use of the well-equipped thermodynamic properties of eachexisting alone gas component to get the thermodynamic properties of humid gas mixture. Thisthesis provides a complete model for calculation of thermodynamic properties of humid air andhumid combustion gas mixture. The results of this thesis may also be fit for other types ofthermodynamic process simulation whose working mediums are humid air or humid combustiongas mixture.
引文
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