容器放气过程的数值模拟及热力学模型研究
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摘要
容器放出法是一种测试气动元件流量特性的方法,因其简便、节能、高效,故具有很高的应用价值。本课题基于国际合作研究项目,对放出法进行了基础理论和实验研究,其目的在于给国际标准组织提交一种通用的测试气动元件流量特性的新方法。本文采用了有限体积数值模拟、试验研究和理论分析相结合的方法,对容器放气过程的速度场和温度场的分布及变化规律、等温容器的特性及等温容器放出法、空容器放气过程的多变指数、放气过程的热力学模型及其应用进行了系统的研究,目的在于全面、直观地认识放气过程,提高放出法的测试精度,研究内容具有重要的理论价值和实际意义。
文中首先建立了容器放气过程的数学模型,通过将等温容器内的填充物简化为一定孔隙率的多孔介质,利用Fluent软件对空容器和等温容器的放气过程进行数值仿真,得到了放气过程中速度场分布、温度场分布以及它们的变化规律。模拟结果表明:(1)速度场主要位于放气口附近很小的区域,容器内大部分区域在放气过程中速度接近于0;(2)容器内的温度场的分布和容器形状有关,最低温度位于容器中心,并且温度梯度随放气过程不断加大;(3)等温容器放气过程的温度变化范围要比空容器小约20倍,非常接近于等温过程。最后,通过实验对仿真结果进行验证,结果表明,容器内压力曲线的仿真结果和实验结果非常吻合,容器内空气的平均温度的仿真结果和实验结果尽管有一定误差,但仍能正确反映温度变化的趋势和规律。其次,等温容器的等温特性直接决定其使用性能。因此,本文对不同条件下等温容器放气过程的温度变化规律进行了全面的研究。实验结果表明,容器内填充细金属丝可以显著增强热交换,使放气过程的温降很小,并可近似为等温过程。但放气过程的温降受到很多因素的影响,在放气初始压力和放气口固定的条件下:填充密度一定时,金属丝的线径越细等温效果越好;填充物只要是金属丝,材质影响不大;金属丝的填充密度越大,等温效果越好。另外,在充气压力和填充密度一定的情况下,放气速度越快,等温性能越差。通过实验可知:在放气初始压力为700kPa、50μm铜丝填充密度0.3kg/L的条件下,要形成等温容器,则容器的容积(L)和放气口的声速流导(×10~(-8)m~3/(s·Pa))的比值必须大于等于6。研究表明等温容器放出法能够用来测量放气电磁阀的声速流导和临界压力比,尽管忽略温度变化会引起一定的误差,但测试结果说明采用全局优化的方法,仍旧能够得到比较准确的结果。
再次,文中还通过“停止法”对空容器放气过程声速段和整个放气过程的多变指数进行了研究。结果表明,容器的放气过程是个多变指数不断变化的过程,多变指数从1.4开始逐渐减小并趋近于1,放气过程中有热交换的存在并随着放气过程不断加强。为了提高定容积放出法的测试精度,把多变指数应用于定容积放出法测试声速流导的数据处理中,提出了部分多变指数法和完全多变指数法,结果证明:完全多变指数法所得的声速流导精确度非常高,且稳定性也很好,随测试时间点的变化幅度小于1.2%。
文中还建立了集总参数法的空容器放气过程的热力学模型,针对模型中的难以测定的换热系数,提出了两种方法:固定换热系数模型和基于大空间自然对流换热模型。对于固定换热模型,根据停止放气后的压力曲线得到此过程的换热系数,并把这个换热系数作为放气过程中的换热系数,基于此模型的放气过程仿真结果要比绝热模型的仿真结果接近试验结果很多。基于大空间自然对流的换热模型中的热交换系数是根据自然对流换热关联式得到的,它随着放气过程的变化而变化,根据这个模型仿真得到压力曲线和温度曲线和试验结果都很一致,说明该模型能够真实反映放气过程的热交换。
论文最后把基于大空间自然对流换热的放气热力学模型和放气压力曲线相结合,由放气的初始状态递推得到放气过程中容器内空气的平均温度和放气过程的多变指数,计算结果和实验结果非常一致,说明此方法可以替代“停止法”来确定放气过程的平均温度。基于放气热力学模型,根据放气压力曲线,通过分段函数优化的方法来辨识放气阀的声速流导和临界压力比,得到的结果和ISO6358所测的结果基本相同。研究表明,基于模型辨识的方法要比ISO6358简单、节能,且精度不低于ISO6358标准中A级精度。
Discharge method is one of methods to measure the flow rate characteristics of pneumatic components. Being simple, energy-saving and efficient, it is also highly applicable. In this internationally coordinated research project, theoretical and experimental study on the discharge method were carried out in order to provide International Organization for Standardizaion (ISO) with a novel and general-purpose method for measuring flow rate characteristics of pneumatic components. By combining finite volume simulation, theoretical analysis along with experimental study, the following specifics were systematically studied in this paper: the distribution and evolution of the velocity and temperature fields during discharge, the isothermal chamber characteristics and isothermal discharge method, the polytropic exponent, the thermodynamic model during discharge as well as their applications. The objective of this study is to accurately and roundly understand the process of discharge and improve the measurement accuracy and repeatability, which are of great theoretical and practical significance.
At first, the physical models for empty and isothermal chambers have been established under the assumption that the stuffers in the isothermal chamber serve as porous media, numerical simulations were thus carried out with Fluent software. The velocity and temperature distribution and their profiles are obtained. Simulation results indicate that the velocity gradient locates primarily at the vicinity of discharge orifice while the velocity in the chamber is almost uniformly zero. The temperature distribution in the chamber is associated with the shape of the chamber. The lowest temperature is located at the center of chamber, with increasing temperature gradient during the process of discharge. The temperature drop of isothermal chamber is about 20 times less than that of empty tank, which indicate that the discharge process of isothermal chambers is very close to isothermal process. To validify the simulation results, the experimental pressure curves in the chambers agree well with the simulations. Despite a certain error, simulations of the average air temperature profiles inside the chamber during discharge exhibit the same evoluting trend and norm to those by experiments.
Secondly, the temperature change of isothermal chambers is critical to their usability and it is therefore systematically studied under various conditions. The results show that the metal thread stuffed in chamber can greatly enhance heat transfer during discharge, which can dramatically decrease the temperature drop so that the discharge process can be regarded as an isothermal process. The isothermal characteristic of isothermal chamber is influenced by many factors under fixed charge pressure and discharge orifice. The material has little effect on isothermal characteristic as long as the stuffer is metal. The finer metal thread and the higher stuff density yield better isothermal characteristic. The higher discharge velocity, the worse isothermal characteristic is. Under the condition of an initial pressure 700 kPa and a stuff density 0.3kg/L of copper threads, the ratio of chamber volume (L) and the sonic conductance (×10-8m3/(s·Pa)) should be greater than or equal to 6 in order to be eligibly treated as an isothermal chamber. The isothermal chamber discharge method can be used to measure the sonic conductance and critical pressure ratio of the discharge valve. Although neglecting temperature change might lead to some error, the accurate results can be obtained with global optimization.
Next, the polytropic exponent during sonic discharge and the whole discharge is studied experimentally. The polytropic exponent during discharge keeps varying from 1.4 to 1, indicating the existence of heat transfer as the heat flux enhances with the progression of the discharge. Furthermore, by appling the polytropic exponent to the data processing of discharge method in order to improve the accuracy of constant volume discharge method, partial polytropic exponent method and complete polytropic exponent method are proposed. The accuracy and stability of sonic conductance obtained with complete polytropic exponent are very high, at a standard deviation of less than 1.2% throughout the whole measurement process.
In addition, the thermodynamic model for tank discharge is founded with lumped parameter. In order to determine the heat transfer coefficient which is difficult to obtain experimentally, two kinds of heat transfer models were given: fixed heat transfer coefficient model and natural convection model. In the fixed heat transfer coefficient model, the coefficient is determined with the pressure curve after stopped discharge. The discharge process was simulated with this model, and the result is very close to that of the experiments when compared with the simulation results of the adiabatic model. The heat transfer coefficient in the natural convection model is determined on the basis of relationship of natural-convection, and it changes with the discharge process. The pressure and temperature curve obtained with simulation based on this model match well with those of the experiments, which indicated that natural convection model can reflect the real discharge quite well.
At last, by combining the discharge thermodynamic model base on natural convection with the discharge pressure curve, the temperature and polytropic exponent during discharge can be obtained from initial state,which were quite closed to those from experiments. Therefore,it can be concluded that this method can be a very good substitute to the“stop method”in determining the average temperature during discharge. The sonic conductance and critical pressure ratio of discharge valve can be identified by optimization based on discharge thermodynamic model and discharge pressure curve, where the results are basically the same as those by ISO 6358. This identification method is simpler and more energy-saving than ISO 6358, and its accuracy is equal or higher than that the A grade in ISO 6358.
文中首先建立了容器放气过程的数学模型,通过将等温容器内的填充物简化为一定孔隙率的多孔介质,利用Fluent软件对空容器和等温容器的放气过程进行数值仿真,得到了放气过程中速度场分布、温度场分布以及它们的变化规律。模拟结果表明:(1)速度场主要位于放气口附近很小的区域,容器内大部分区域在放气过程中速度接近于0;(2)容器内的温度场的分布和容器形状有关,最低温度位于容器中心,并且温度梯度随放气过程不断加大;(3)等温容器放气过程的温度变化范围要比空容器小约20倍,非常接近于等温过程。最后,通过实验对仿真结果进行验证,结果表明,容器内压力曲线的仿真结果和实验结果非常吻合,容器内空气的平均温度的仿真结果和实验结果尽管有一定误差,但仍能正确反映温度变化的趋势和规律。其次,等温容器的等温特性直接决定其使用性能。因此,本文对不同条件下等温容器放气过程的温度变化规律进行了全面的研究。实验结果表明,容器内填充细金属丝可以显著增强热交换,使放气过程的温降很小,并可近似为等温过程。但放气过程的温降受到很多因素的影响,在放气初始压力和放气口固定的条件下:填充密度一定时,金属丝的线径越细等温效果越好;填充物只要是金属丝,材质影响不大;金属丝的填充密度越大,等温效果越好。另外,在充气压力和填充密度一定的情况下,放气速度越快,等温性能越差。通过实验可知:在放气初始压力为700kPa、50μm铜丝填充密度0.3kg/L的条件下,要形成等温容器,则容器的容积(L)和放气口的声速流导(×10~(-8)m~3/(s·Pa))的比值必须大于等于6。研究表明等温容器放出法能够用来测量放气电磁阀的声速流导和临界压力比,尽管忽略温度变化会引起一定的误差,但测试结果说明采用全局优化的方法,仍旧能够得到比较准确的结果。
再次,文中还通过“停止法”对空容器放气过程声速段和整个放气过程的多变指数进行了研究。结果表明,容器的放气过程是个多变指数不断变化的过程,多变指数从1.4开始逐渐减小并趋近于1,放气过程中有热交换的存在并随着放气过程不断加强。为了提高定容积放出法的测试精度,把多变指数应用于定容积放出法测试声速流导的数据处理中,提出了部分多变指数法和完全多变指数法,结果证明:完全多变指数法所得的声速流导精确度非常高,且稳定性也很好,随测试时间点的变化幅度小于1.2%。
文中还建立了集总参数法的空容器放气过程的热力学模型,针对模型中的难以测定的换热系数,提出了两种方法:固定换热系数模型和基于大空间自然对流换热模型。对于固定换热模型,根据停止放气后的压力曲线得到此过程的换热系数,并把这个换热系数作为放气过程中的换热系数,基于此模型的放气过程仿真结果要比绝热模型的仿真结果接近试验结果很多。基于大空间自然对流的换热模型中的热交换系数是根据自然对流换热关联式得到的,它随着放气过程的变化而变化,根据这个模型仿真得到压力曲线和温度曲线和试验结果都很一致,说明该模型能够真实反映放气过程的热交换。
论文最后把基于大空间自然对流换热的放气热力学模型和放气压力曲线相结合,由放气的初始状态递推得到放气过程中容器内空气的平均温度和放气过程的多变指数,计算结果和实验结果非常一致,说明此方法可以替代“停止法”来确定放气过程的平均温度。基于放气热力学模型,根据放气压力曲线,通过分段函数优化的方法来辨识放气阀的声速流导和临界压力比,得到的结果和ISO6358所测的结果基本相同。研究表明,基于模型辨识的方法要比ISO6358简单、节能,且精度不低于ISO6358标准中A级精度。
Discharge method is one of methods to measure the flow rate characteristics of pneumatic components. Being simple, energy-saving and efficient, it is also highly applicable. In this internationally coordinated research project, theoretical and experimental study on the discharge method were carried out in order to provide International Organization for Standardizaion (ISO) with a novel and general-purpose method for measuring flow rate characteristics of pneumatic components. By combining finite volume simulation, theoretical analysis along with experimental study, the following specifics were systematically studied in this paper: the distribution and evolution of the velocity and temperature fields during discharge, the isothermal chamber characteristics and isothermal discharge method, the polytropic exponent, the thermodynamic model during discharge as well as their applications. The objective of this study is to accurately and roundly understand the process of discharge and improve the measurement accuracy and repeatability, which are of great theoretical and practical significance.
At first, the physical models for empty and isothermal chambers have been established under the assumption that the stuffers in the isothermal chamber serve as porous media, numerical simulations were thus carried out with Fluent software. The velocity and temperature distribution and their profiles are obtained. Simulation results indicate that the velocity gradient locates primarily at the vicinity of discharge orifice while the velocity in the chamber is almost uniformly zero. The temperature distribution in the chamber is associated with the shape of the chamber. The lowest temperature is located at the center of chamber, with increasing temperature gradient during the process of discharge. The temperature drop of isothermal chamber is about 20 times less than that of empty tank, which indicate that the discharge process of isothermal chambers is very close to isothermal process. To validify the simulation results, the experimental pressure curves in the chambers agree well with the simulations. Despite a certain error, simulations of the average air temperature profiles inside the chamber during discharge exhibit the same evoluting trend and norm to those by experiments.
Secondly, the temperature change of isothermal chambers is critical to their usability and it is therefore systematically studied under various conditions. The results show that the metal thread stuffed in chamber can greatly enhance heat transfer during discharge, which can dramatically decrease the temperature drop so that the discharge process can be regarded as an isothermal process. The isothermal characteristic of isothermal chamber is influenced by many factors under fixed charge pressure and discharge orifice. The material has little effect on isothermal characteristic as long as the stuffer is metal. The finer metal thread and the higher stuff density yield better isothermal characteristic. The higher discharge velocity, the worse isothermal characteristic is. Under the condition of an initial pressure 700 kPa and a stuff density 0.3kg/L of copper threads, the ratio of chamber volume (L) and the sonic conductance (×10-8m3/(s·Pa)) should be greater than or equal to 6 in order to be eligibly treated as an isothermal chamber. The isothermal chamber discharge method can be used to measure the sonic conductance and critical pressure ratio of the discharge valve. Although neglecting temperature change might lead to some error, the accurate results can be obtained with global optimization.
Next, the polytropic exponent during sonic discharge and the whole discharge is studied experimentally. The polytropic exponent during discharge keeps varying from 1.4 to 1, indicating the existence of heat transfer as the heat flux enhances with the progression of the discharge. Furthermore, by appling the polytropic exponent to the data processing of discharge method in order to improve the accuracy of constant volume discharge method, partial polytropic exponent method and complete polytropic exponent method are proposed. The accuracy and stability of sonic conductance obtained with complete polytropic exponent are very high, at a standard deviation of less than 1.2% throughout the whole measurement process.
In addition, the thermodynamic model for tank discharge is founded with lumped parameter. In order to determine the heat transfer coefficient which is difficult to obtain experimentally, two kinds of heat transfer models were given: fixed heat transfer coefficient model and natural convection model. In the fixed heat transfer coefficient model, the coefficient is determined with the pressure curve after stopped discharge. The discharge process was simulated with this model, and the result is very close to that of the experiments when compared with the simulation results of the adiabatic model. The heat transfer coefficient in the natural convection model is determined on the basis of relationship of natural-convection, and it changes with the discharge process. The pressure and temperature curve obtained with simulation based on this model match well with those of the experiments, which indicated that natural convection model can reflect the real discharge quite well.
At last, by combining the discharge thermodynamic model base on natural convection with the discharge pressure curve, the temperature and polytropic exponent during discharge can be obtained from initial state,which were quite closed to those from experiments. Therefore,it can be concluded that this method can be a very good substitute to the“stop method”in determining the average temperature during discharge. The sonic conductance and critical pressure ratio of discharge valve can be identified by optimization based on discharge thermodynamic model and discharge pressure curve, where the results are basically the same as those by ISO 6358. This identification method is simpler and more energy-saving than ISO 6358, and its accuracy is equal or higher than that the A grade in ISO 6358.
引文
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