微尺度气体流动与传热的直接Monte Carlo方法模拟
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摘要
微尺度气体流动和换热机理的研究是微机电系统(MEMS)和纳机电系统(NEMS)发展中的重要一步。在微尺度条件下,由于特征尺度减小,导致Knudsen数较大,连续性假设不准确。从而基于连续性假设的传统方法不再适用,气体的流动问题须从分子运动的角度加以求解。直接模拟Monte Carlo方法(DSMC)是应用广泛的基于分子运动的统计数值模拟方法。
本文在理论分析的基础上,开发DSMC模拟计算代码,并采用此代码对微尺度下单组份气体、两种气体混合流动和换热等问题进行了模拟分析,并从分子运动的观点讨论其物理机理。以下是主要工作内容:
第一,为了对微尺度气体的流动和传热进行研究,开发了DSMC方法的数值求解代码(C++),并且为代码编写了图形用户界面(GUI),与Bird给出的标准程序相对比,计算结果一致,证明了程序的可靠性。由于C++作为一种面向对象的高级计算机语言,具有强大的生命力,易于扩展,具有良好的继承性和安全性。
第二,对微尺度下气体流动和常规尺度下的稀薄气体流动问题进行分析。为了保证DSMC方法应用于微尺度研究中的有效性,讨论了流动的相似性条件。当应用稀薄气体动力学于微尺度流动中的研究中时,除了要保证三个无量纲参数(Re,Ma,Kn)至少两个相等之外,还应当满足稀疏气体的有效性(δ＞＞d)。除此之外在DSMC的计算中,还必须考虑网格划分、网格内分子数等等条件,以减少模拟计算的误差。
第三,应用自行开发的DSMC程序对微槽道流动、方腔流动进行了数值模拟,讨论和分析了其基本流动问题。在此基础上对两种气体混合流动现象进行研究。对结果的分析中发现气体的进入速度对两种气体的混合距离影响明显,并且对完全混合后的单种气体所占比例影响很大。
第四,为了求解低速和混合尺度下的气体流动问题,改进了离散速度模型,这一模型不同于已有的离散气体模型。将这种模型与数值模拟和理论分析结果的对比表明,离散模型不仅能够模拟低速流动问题,而且还能够模拟Knudsen数从滑移领域到过渡领域内的气体流动,并且计算速度快。
第五,为了研究采用DSMC方法求解近连续流动的低速流动问题,提出EPSM/IP耦合方法,为今后发展连/分子情况下低速的混合领域流动进行了有意义的尝试。
The investigation of micro- and nanoscale gas flow and heat transfer is an important part for the further development of the Microelectromechanical Systems (MEMS) and nano science and technology (NEMS). The Knudsen number is large enough due to the decreased characteristic length and the classical macro-simulation methods are no longer suitable. The flow must be described in the view of molecular dynamics. The direct simulation Monte Carlo method (DSMC) is the one of the most widely used and exact numerical methods for high-Knudsen-number flow.
Based on theoretical analysis, in the present dissertation a code of DSMC with C++ advanced computer language is designed and used in the cases of micro-gas fluid and two kinds of gas mixing. The physical phenomenon of the flow characters and heat transfer is studied in the point view of molecular dynamics. The following is the main clue of the work.
Firstly, in order to use the DSMC method in the micro- and nanoscale gas flow and heat transfer, a code is developed with C++ advanced computer language, and a GUI interface is also developed for the code with QT 4.0. The code is efficient and correct when compared with the Bird's standard code written in Fortran. Because the C++ is based on the Object-Oriented technology, the code can be extended conveniently. Also, it is more safety.
Secondly, the similarity is theoretically analyzed between microscale gas flows and normal-scale rarefied gas flows. In order to make sure the reliability of the similarity, some factors are discussed. When the rarefied gas dynamics is used in studying the micro-gas flow, the dilute gas condition (δ>> d) must be guaranteed. And also, This similarity theory is required that two of the three parameters ( Ma, Re and Kn) are equal. Except that, some factors are also considered, such as the size of grid, the numbers of molecular per cell, time step and so on.
Thirdly, the micro-channel flow and cavity flow were invested by the DSMC code, and the results were discussed and analyzed. After these discussions, two kinds of gas mixing flow are simulated. In the results of binary gas mixture, the speed which is given at the inlet of each kind gas is a very important role, when the number density of each kind of gas is the same before entering the small channel. The full-mixed length will be longer with the increased speed. But this relation is non-linear.
Fourthly, in order to solve the low speed flow in the micro-scale, the discrete velocity model (DVM) is brought out. It is different with the traditional DVM. And comparing this model with theory analysis and numerical solution, in the low speed flow, it shows excellent agreement when Knudsen number from slip region to transfer region. And also it took shorter time to get the solution.
Fifthly, a hybrid method that combining the EPSM and IP methods is considered in solving the near continuum flow region. As comparing with theory analysis, it shows good agreement. It is a beginning for constructing hybrid method for saluting the low speed flow in near continuum region.
本文在理论分析的基础上,开发DSMC模拟计算代码,并采用此代码对微尺度下单组份气体、两种气体混合流动和换热等问题进行了模拟分析,并从分子运动的观点讨论其物理机理。以下是主要工作内容:
第一,为了对微尺度气体的流动和传热进行研究,开发了DSMC方法的数值求解代码(C++),并且为代码编写了图形用户界面(GUI),与Bird给出的标准程序相对比,计算结果一致,证明了程序的可靠性。由于C++作为一种面向对象的高级计算机语言,具有强大的生命力,易于扩展,具有良好的继承性和安全性。
第二,对微尺度下气体流动和常规尺度下的稀薄气体流动问题进行分析。为了保证DSMC方法应用于微尺度研究中的有效性,讨论了流动的相似性条件。当应用稀薄气体动力学于微尺度流动中的研究中时,除了要保证三个无量纲参数(Re,Ma,Kn)至少两个相等之外,还应当满足稀疏气体的有效性(δ＞＞d)。除此之外在DSMC的计算中,还必须考虑网格划分、网格内分子数等等条件,以减少模拟计算的误差。
第三,应用自行开发的DSMC程序对微槽道流动、方腔流动进行了数值模拟,讨论和分析了其基本流动问题。在此基础上对两种气体混合流动现象进行研究。对结果的分析中发现气体的进入速度对两种气体的混合距离影响明显,并且对完全混合后的单种气体所占比例影响很大。
第四,为了求解低速和混合尺度下的气体流动问题,改进了离散速度模型,这一模型不同于已有的离散气体模型。将这种模型与数值模拟和理论分析结果的对比表明,离散模型不仅能够模拟低速流动问题,而且还能够模拟Knudsen数从滑移领域到过渡领域内的气体流动,并且计算速度快。
第五,为了研究采用DSMC方法求解近连续流动的低速流动问题,提出EPSM/IP耦合方法,为今后发展连/分子情况下低速的混合领域流动进行了有意义的尝试。
The investigation of micro- and nanoscale gas flow and heat transfer is an important part for the further development of the Microelectromechanical Systems (MEMS) and nano science and technology (NEMS). The Knudsen number is large enough due to the decreased characteristic length and the classical macro-simulation methods are no longer suitable. The flow must be described in the view of molecular dynamics. The direct simulation Monte Carlo method (DSMC) is the one of the most widely used and exact numerical methods for high-Knudsen-number flow.
Based on theoretical analysis, in the present dissertation a code of DSMC with C++ advanced computer language is designed and used in the cases of micro-gas fluid and two kinds of gas mixing. The physical phenomenon of the flow characters and heat transfer is studied in the point view of molecular dynamics. The following is the main clue of the work.
Firstly, in order to use the DSMC method in the micro- and nanoscale gas flow and heat transfer, a code is developed with C++ advanced computer language, and a GUI interface is also developed for the code with QT 4.0. The code is efficient and correct when compared with the Bird's standard code written in Fortran. Because the C++ is based on the Object-Oriented technology, the code can be extended conveniently. Also, it is more safety.
Secondly, the similarity is theoretically analyzed between microscale gas flows and normal-scale rarefied gas flows. In order to make sure the reliability of the similarity, some factors are discussed. When the rarefied gas dynamics is used in studying the micro-gas flow, the dilute gas condition (δ>> d) must be guaranteed. And also, This similarity theory is required that two of the three parameters ( Ma, Re and Kn) are equal. Except that, some factors are also considered, such as the size of grid, the numbers of molecular per cell, time step and so on.
Thirdly, the micro-channel flow and cavity flow were invested by the DSMC code, and the results were discussed and analyzed. After these discussions, two kinds of gas mixing flow are simulated. In the results of binary gas mixture, the speed which is given at the inlet of each kind gas is a very important role, when the number density of each kind of gas is the same before entering the small channel. The full-mixed length will be longer with the increased speed. But this relation is non-linear.
Fourthly, in order to solve the low speed flow in the micro-scale, the discrete velocity model (DVM) is brought out. It is different with the traditional DVM. And comparing this model with theory analysis and numerical solution, in the low speed flow, it shows excellent agreement when Knudsen number from slip region to transfer region. And also it took shorter time to get the solution.
Fifthly, a hybrid method that combining the EPSM and IP methods is considered in solving the near continuum flow region. As comparing with theory analysis, it shows good agreement. It is a beginning for constructing hybrid method for saluting the low speed flow in near continuum region.
引文
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