基于LBM的兩組分混合氣體微流動的數(shù)值研究
發(fā)布時(shí)間：2018-09-19 15:56
【摘要】：兩組分混合氣體在微、納尺度系統(tǒng)中的流動是自然界和工程實(shí)踐中常見的一類流動,它廣泛存在于頁巖氣開采,燃料電池研發(fā)等領(lǐng)域。在對這類流動問題的數(shù)值研究存在多種方法,而與傳統(tǒng)的數(shù)值方法相比,近十年來發(fā)展起來的格子Boltzmann方法(Lattice Boltzmann Method, LBM)以其跨尺度特性,良好的計(jì)算并行性和復(fù)雜邊界的適用性等,已被證實(shí)適用于這類混合氣體的微尺度流動,因而這種方法成為我們研究這一問題的一種重要手段。目前,雖然研究人員采用LBM在混合氣體的微尺度流動相關(guān)領(lǐng)域獲得了一些研究成果,但仍然有一些基本問題尚未解決。本文正是以這些問題作為切入點(diǎn),在完善原有的多松弛時(shí)間(multiple relaxation times, MRT) LBM相關(guān)模型理論的基礎(chǔ)上,對兩組分混合氣體的微尺度流動問題進(jìn)行深入的研究。本文的研究內(nèi)容主要包含以下幾個(gè)方面： 第一,研究了兩組分混合氣體的整體流動狀況,將其看作單組分氣體的流動現(xiàn)象。采用考慮壁面截?cái)嘈?yīng)的微尺度多松弛格子Botlzmann模型,對氣體在微管道中流動所特有的沿流向非線性壓力分布的變化進(jìn)行了研究,并模擬分析了不同的稀薄效應(yīng)和壓縮效應(yīng)下的壓力分布變化趨勢,及在前人工作中被忽視的管道長寬比的影響。研究結(jié)果表明：通過對沿流向壓力分布的研究能夠很好的解釋氣體微尺度流動中流量的非常規(guī)變化；管道的寬長比這一實(shí)際因素與壓力分布和流量的變化成二次冪函數(shù)的關(guān)系,同時(shí)這種影響只有在克努森數(shù)大于一定值時(shí)才能夠被忽略。 第二,基于對混合氣體內(nèi)部因素影響的考慮,研究了兩組分混合氣體在微尺度流動中所特有的組分濃度分離現(xiàn)象。我們首先在原有的兩組分混合氣體的LBE(Lattice Boltzmann Equation)模型的基礎(chǔ)上,耦合了經(jīng)壁面截?cái)嘈?yīng)修正后的有效松弛時(shí)間以及更為精確的二階滑移速度,使得新的模型能夠適用于更加微小系統(tǒng)中的流動,彌補(bǔ)了原有模型的不足。在此新模型的基礎(chǔ)上,通過對氦-氬和氖-氬兩種混合氣體微尺度流動的中的濃度分離過程的模擬,分析了不同的混合氣體構(gòu)成、稀薄效應(yīng)和壓縮效應(yīng)對兩組分混合氣體的濃度分離過程及結(jié)果的影響。研究結(jié)果表明：兩組分混合氣體中組分分子質(zhì)量比越大,分離現(xiàn)象越明顯；稀薄效應(yīng)和壓縮效應(yīng)對濃度分離過程的作用則正好相反,克努森數(shù)的增大會增強(qiáng)分離效應(yīng),但是壓力比的增加卻會減弱這一效應(yīng)。 第三,在對混合氣體內(nèi)部因素的研究的基礎(chǔ)上,對管壁的粗糙效應(yīng)這一外部因素的影響進(jìn)行了研究。首先,為了在復(fù)雜的壁面狀況下實(shí)現(xiàn)精確的滑移邊界條件,把離散-反彈格式邊界條件(Diffuse-Bounce-Back, DBB)擴(kuò)展到兩組分的LBE模型中,從而得到了一類能夠處理復(fù)雜邊界和大Kn數(shù)流動問題的兩組分混合氣體的格子Boltzmann模型�；诒疚乃岢龅哪Ｐ秃瓦吔鐥l件,研究了不同粗糙程度的微管道中兩組分混合氣體的流動,從流量這一宏觀量的變化出發(fā),分析了每種因素對混合氣體微尺度流動傳輸過程的影響。研究結(jié)果表明：隨著粗糙度的增加,粗糙效應(yīng)對混合氣體中的不同組分的流量均成下降趨勢；然而各組分的流量間有存在著明顯的差異,這一差異又受到組分分子質(zhì)量比和組分濃度的共同影響；同時(shí)隨著克努森數(shù)的增加,在其小于0.1時(shí),流量下降非常明顯,而但克努森數(shù)大于0.1時(shí),其作用會隨稀薄效應(yīng)的增強(qiáng)而減弱。 最后,基于以上的二維流動分析,對兩組分混合氣體的在不同截面形狀管道中的三維流動進(jìn)行了模擬。我們首先把改進(jìn)后的二維的兩組分混合氣體的格子Boltzmann模型以及DBB邊界條件擴(kuò)展到三維領(lǐng)域,得到了一種適用于三維流動的兩組分混合氣體的LBE模型和邊界條件。采用此三維模型,通過對兩種不同截面形狀的三維微管道中兩組分混合氣體流動的模擬,綜合分析了內(nèi)部因素,壁面因素和截面形狀等因子對混合氣體的流量和濃度分離過程的影響。研究結(jié)果表明：同等截面積下,模擬工況中的三角形截面管道中的流量會高于正方形截面管道中的流量,但是混合氣體在三角形截面管道中的濃度分離程度卻會比在正方形截面管道中的低,同時(shí)這兩種影響均受到稀薄效應(yīng)的限制的,會隨著稀薄效應(yīng)的增強(qiáng)而減弱。 總之,本文由簡入繁,從整體研究到局部考慮再回到整體研究,采用格子Boltzmann方法(LBM)方法由淺入深的對兩組分混合氣體的微尺度流動與傳輸?shù)臋C(jī)理進(jìn)行了研究,加深了對這類復(fù)雜流動問題的認(rèn)識。為LBM在混合氣體微尺度流動研究中的應(yīng)用做出了有意義的創(chuàng)新與嘗試,也為后續(xù)更進(jìn)一步的研究和探討奠定了堅(jiān)實(shí)的基礎(chǔ)。
[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.
【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TM911.4;TQ021.1
本文編號：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.
【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TM911.4;TQ021.1
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3 劉超峰;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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