基于LBM的两组分混合气体微流动的数值研究
发布时间：2018-09-19 15:56
【摘要】：两组分混合气体在微、纳尺度系统中的流动是自然界和工程实践中常见的一类流动,它广泛存在于页岩气开采,燃料电池研发等领域。在对这类流动问题的数值研究存在多种方法,而与传统的数值方法相比,近十年来发展起来的格子Boltzmann方法(Lattice Boltzmann Method, LBM)以其跨尺度特性,良好的计算并行性和复杂边界的适用性等,已被证实适用于这类混合气体的微尺度流动,因而这种方法成为我们研究这一问题的一种重要手段。目前,虽然研究人员采用LBM在混合气体的微尺度流动相关领域获得了一些研究成果,但仍然有一些基本问题尚未解决。本文正是以这些问题作为切入点,在完善原有的多松弛时间(multiple relaxation times, MRT) LBM相关模型理论的基础上,对两组分混合气体的微尺度流动问题进行深入的研究。本文的研究内容主要包含以下几个方面： 第一,研究了两组分混合气体的整体流动状况,将其看作单组分气体的流动现象。采用考虑壁面截断效应的微尺度多松弛格子Botlzmann模型,对气体在微管道中流动所特有的沿流向非线性压力分布的变化进行了研究,并模拟分析了不同的稀薄效应和压缩效应下的压力分布变化趋势,及在前人工作中被忽视的管道长宽比的影响。研究结果表明：通过对沿流向压力分布的研究能够很好的解释气体微尺度流动中流量的非常规变化；管道的宽长比这一实际因素与压力分布和流量的变化成二次幂函数的关系,同时这种影响只有在克努森数大于一定值时才能够被忽略。 第二,基于对混合气体内部因素影响的考虑,研究了两组分混合气体在微尺度流动中所特有的组分浓度分离现象。我们首先在原有的两组分混合气体的LBE(Lattice Boltzmann Equation)模型的基础上,耦合了经壁面截断效应修正后的有效松弛时间以及更为精确的二阶滑移速度,使得新的模型能够适用于更加微小系统中的流动,弥补了原有模型的不足。在此新模型的基础上,通过对氦-氩和氖-氩两种混合气体微尺度流动的中的浓度分离过程的模拟,分析了不同的混合气体构成、稀薄效应和压缩效应对两组分混合气体的浓度分离过程及结果的影响。研究结果表明：两组分混合气体中组分分子质量比越大,分离现象越明显；稀薄效应和压缩效应对浓度分离过程的作用则正好相反,克努森数的增大会增强分离效应,但是压力比的增加却会减弱这一效应。 第三,在对混合气体内部因素的研究的基础上,对管壁的粗糙效应这一外部因素的影响进行了研究。首先,为了在复杂的壁面状况下实现精确的滑移边界条件,把离散-反弹格式边界条件(Diffuse-Bounce-Back, DBB)扩展到两组分的LBE模型中,从而得到了一类能够处理复杂边界和大Kn数流动问题的两组分混合气体的格子Boltzmann模型。基于本文所提出的模型和边界条件,研究了不同粗糙程度的微管道中两组分混合气体的流动,从流量这一宏观量的变化出发,分析了每种因素对混合气体微尺度流动传输过程的影响。研究结果表明：随着粗糙度的增加,粗糙效应对混合气体中的不同组分的流量均成下降趋势；然而各组分的流量间有存在着明显的差异,这一差异又受到组分分子质量比和组分浓度的共同影响；同时随着克努森数的增加,在其小于0.1时,流量下降非常明显,而但克努森数大于0.1时,其作用会随稀薄效应的增强而减弱。 最后,基于以上的二维流动分析,对两组分混合气体的在不同截面形状管道中的三维流动进行了模拟。我们首先把改进后的二维的两组分混合气体的格子Boltzmann模型以及DBB边界条件扩展到三维领域,得到了一种适用于三维流动的两组分混合气体的LBE模型和边界条件。采用此三维模型,通过对两种不同截面形状的三维微管道中两组分混合气体流动的模拟,综合分析了内部因素,壁面因素和截面形状等因子对混合气体的流量和浓度分离过程的影响。研究结果表明：同等截面积下,模拟工况中的三角形截面管道中的流量会高于正方形截面管道中的流量,但是混合气体在三角形截面管道中的浓度分离程度却会比在正方形截面管道中的低,同时这两种影响均受到稀薄效应的限制的,会随着稀薄效应的增强而减弱。 总之,本文由简入繁,从整体研究到局部考虑再回到整体研究,采用格子Boltzmann方法(LBM)方法由浅入深的对两组分混合气体的微尺度流动与传输的机理进行了研究,加深了对这类复杂流动问题的认识。为LBM在混合气体微尺度流动研究中的应用做出了有意义的创新与尝试,也为后续更进一步的研究和探讨奠定了坚实的基础。
[Abstract]:The flow of two-component gas mixtures in micro-and nano-scale systems is a common flow in nature and engineering practice. It is widely used in shale gas exploitation and fuel cell research and development. The Lattice Boltzmann Method (LBM) has been proved to be suitable for the micro-scale flow of such mixed gases due to its cross-scale characteristics, good computational parallelism and applicability to complex boundary conditions. Therefore, this method has become an important means for us to study this problem. Some research results have been obtained in the field of micro-scale flow, but there are still some basic problems unsolved. This paper takes these problems as the breakthrough point to study the micro-scale flow of two-component gas mixture on the basis of improving the original multi-relaxation time (MRT) LBM related model theory. The research contents of this paper mainly include the following aspects:
Firstly, the whole flow state of two-component gas mixture is studied as a single-component gas flow phenomenon. A micro-scale multi-relaxation lattice Botlzmann model considering wall truncation effect is used to study the variation of nonlinear pressure distribution along flow direction peculiar to gas flow in micro-pipes, and the difference between them is simulated and analyzed. The results show that the study of the pressure distribution along the flow direction can well explain the unconventional change of the flow rate in the gas micro-scale flow, and the width-to-length ratio of the pipeline is a practical factor and the pressure distribution. It is a quadratic power function with the change of flow rate, and this effect can be ignored only when Knudsen number is greater than a certain value.
Secondly, based on the consideration of the influence of the internal factors of the gas mixture, the phenomenon of component concentration separation in the micro-scale flow of two-component gas mixture is studied. Firstly, the effective relaxation time corrected by the wall truncation effect is coupled with the LBE (Lattice Boltzmann Equation) model of two-component gas mixture. The new model makes up for the shortcomings of the original model by making use of the second-order slip velocity more accurately. Based on the new model, the concentration separation process in the micro-scale flow of helium-argon and neon-argon mixtures is simulated and the composition of different mixtures is analyzed. The results show that the bigger the molecule mass ratio, the more obvious the separation phenomena are; the opposite is true for the rarefaction effect and compression effect, and the increase of Knudsen number will enhance the separation process. Effect, but the increase of pressure ratio will weaken this effect.
Thirdly, on the basis of the study of the internal factors of the gas mixture, the influence of the outer factors on the roughness effect of the pipe wall is studied. Firstly, in order to realize the precise slip boundary condition under the complicated wall conditions, the discrete-bounce scheme boundary condition (DBB) is extended to the two-component LBE model from A lattice Boltzmann model for two-component gas mixtures with complex boundary conditions and large Kn numbers is obtained. Based on the model and boundary conditions proposed in this paper, the flow of two-component gas mixtures in microchannels with different roughness is studied. From the variation of flow rate as a macroscopic quantity, each factor is analyzed. The results show that the roughness effect decreases with the increase of the roughness, but there are obvious differences among the components, which are influenced by the molecular mass ratio and the concentration of the components. At the same time, with the increase of Knudsen number, when the Knudsen number is less than 0.1, the flow rate decreases obviously, but when the Knudsen number is greater than 0.1, its effect will weaken with the increase of thinning effect.
Finally, based on the above two-dimensional flow analysis, the three-dimensional flow of two-component gas mixture in a pipe with different cross-section shapes is simulated. The LBE model and boundary conditions for gas mixtures were used to simulate the flow of two components in a three-dimensional microchannel with two different cross-sectional shapes. The effects of internal factors, wall factors and cross-sectional shapes on the flow and concentration separation process were analyzed. Under the condition of equal cross-section, the flow rate in the triangular section pipe under the simulated working condition is higher than that in the square section pipe, but the concentration separation degree of the mixed gas in the triangular section pipe is lower than that in the square section pipe. At the same time, both effects are limited by the rarefaction effect, and will follow the rarefaction effect. Increase and weaken.
In summary, this paper studies the mechanism of micro-scale flow and transport of two-component gas mixtures from shallow to deep by using the lattice Boltzmann method (LBM) from simplicity to complexity, from overall to local considerations and then back to the overall study. It deepens the understanding of this kind of complex flow problems. The application has made a meaningful innovation and attempt, and laid a solid foundation for further research and discussion.
【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TM911.4;TQ021.1
本文编号：2250592
[Abstract]:The flow of two-component gas mixtures in micro-and nano-scale systems is a common flow in nature and engineering practice. It is widely used in shale gas exploitation and fuel cell research and development. The Lattice Boltzmann Method (LBM) has been proved to be suitable for the micro-scale flow of such mixed gases due to its cross-scale characteristics, good computational parallelism and applicability to complex boundary conditions. Therefore, this method has become an important means for us to study this problem. Some research results have been obtained in the field of micro-scale flow, but there are still some basic problems unsolved. This paper takes these problems as the breakthrough point to study the micro-scale flow of two-component gas mixture on the basis of improving the original multi-relaxation time (MRT) LBM related model theory. The research contents of this paper mainly include the following aspects:
Firstly, the whole flow state of two-component gas mixture is studied as a single-component gas flow phenomenon. A micro-scale multi-relaxation lattice Botlzmann model considering wall truncation effect is used to study the variation of nonlinear pressure distribution along flow direction peculiar to gas flow in micro-pipes, and the difference between them is simulated and analyzed. The results show that the study of the pressure distribution along the flow direction can well explain the unconventional change of the flow rate in the gas micro-scale flow, and the width-to-length ratio of the pipeline is a practical factor and the pressure distribution. It is a quadratic power function with the change of flow rate, and this effect can be ignored only when Knudsen number is greater than a certain value.
Secondly, based on the consideration of the influence of the internal factors of the gas mixture, the phenomenon of component concentration separation in the micro-scale flow of two-component gas mixture is studied. Firstly, the effective relaxation time corrected by the wall truncation effect is coupled with the LBE (Lattice Boltzmann Equation) model of two-component gas mixture. The new model makes up for the shortcomings of the original model by making use of the second-order slip velocity more accurately. Based on the new model, the concentration separation process in the micro-scale flow of helium-argon and neon-argon mixtures is simulated and the composition of different mixtures is analyzed. The results show that the bigger the molecule mass ratio, the more obvious the separation phenomena are; the opposite is true for the rarefaction effect and compression effect, and the increase of Knudsen number will enhance the separation process. Effect, but the increase of pressure ratio will weaken this effect.
Thirdly, on the basis of the study of the internal factors of the gas mixture, the influence of the outer factors on the roughness effect of the pipe wall is studied. Firstly, in order to realize the precise slip boundary condition under the complicated wall conditions, the discrete-bounce scheme boundary condition (DBB) is extended to the two-component LBE model from A lattice Boltzmann model for two-component gas mixtures with complex boundary conditions and large Kn numbers is obtained. Based on the model and boundary conditions proposed in this paper, the flow of two-component gas mixtures in microchannels with different roughness is studied. From the variation of flow rate as a macroscopic quantity, each factor is analyzed. The results show that the roughness effect decreases with the increase of the roughness, but there are obvious differences among the components, which are influenced by the molecular mass ratio and the concentration of the components. At the same time, with the increase of Knudsen number, when the Knudsen number is less than 0.1, the flow rate decreases obviously, but when the Knudsen number is greater than 0.1, its effect will weaken with the increase of thinning effect.
Finally, based on the above two-dimensional flow analysis, the three-dimensional flow of two-component gas mixture in a pipe with different cross-section shapes is simulated. The LBE model and boundary conditions for gas mixtures were used to simulate the flow of two components in a three-dimensional microchannel with two different cross-sectional shapes. The effects of internal factors, wall factors and cross-sectional shapes on the flow and concentration separation process were analyzed. Under the condition of equal cross-section, the flow rate in the triangular section pipe under the simulated working condition is higher than that in the square section pipe, but the concentration separation degree of the mixed gas in the triangular section pipe is lower than that in the square section pipe. At the same time, both effects are limited by the rarefaction effect, and will follow the rarefaction effect. Increase and weaken.
In summary, this paper studies the mechanism of micro-scale flow and transport of two-component gas mixtures from shallow to deep by using the lattice Boltzmann method (LBM) from simplicity to complexity, from overall to local considerations and then back to the overall study. It deepens the understanding of this kind of complex flow problems. The application has made a meaningful innovation and attempt, and laid a solid foundation for further research and discussion.
【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TM911.4;TQ021.1
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3 刘超峰;倪玉山;;The effect of surface roughness on rarefied gas flows by lattice Boltzmann method[J];Chinese Physics B;2008年12期
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