多相和多组分流动中热质传递的Lattice Boltzmann方法的数值研究
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摘要
Lattice Boltzmann Method(LBM)方法作为一种特殊的数值方法,以其自然并行、几何边界易处理、程序简单等诸多优点在输运问题,尤其在多相流、多孔介质、对流扩散和化学反应等问题模拟上体现了较大的优势及很强的适应性,展示了其广阔的应用前景。基于以上背景和推进该数值方法与工程应用接轨的思路,本文分别以超重力旋转填充床中液相膜流态下的微观混合,以及核池沸腾中气泡的增长、运动和变形等物理问题为研究背景,针对其中复杂多变的界面行为,包括可溶的多组分界面和不互溶的多相流界面,依托LBM方法的优势和特点,对界面的变化以及界面传质和传热等物理过程进行数值研究。根据实际问题的需要,先后提出、改进和联合了不同的LBM模型。利用这些模型数值研究相关问题,所获结果不仅为LBM在多相多组分流领域的实用化奠定了一些基础,也为相关领域实验和理论研究提供了有意义的参考。
为检验LBM多组分流模型在复杂流动中的适应性和对应复杂边界处理的便捷性,依托超重力旋转填充床的工业背景,对床内液相膜流动状态下建立的液相组分间层状扩散反应模型进行合理扩展,将对流传质引入模型建立对流扩散传质模型。以此模型为基础对填料丝的强化对流传质作用进行了数值研究。通过引进反映宏观混合效率的函数,量化分析了填料丝形状和尺寸在其强制对流传质中的作用。结果对旋转填充床的填料设计及其传质的数值研究工作有参考价值,对其它填料的设计亦有启示作用。
由于LBM多组分模型在研究组分传质时缺乏对流动混合效率的记忆性,本文构造了串行竞争反应的LBM模型。应用该模型分别对填料主体区和端效应区的微观混合和化学反应进行了数值研究。在主体区,采用层状扩散模型进行了模拟,与对应实验结论和其它数值结果比对分析,证明了算法的有效性。在端效应区,基于强制对流扩散反应模型对端效应区的强制对流传质和化学反应进行了积极的探索。初步探索了填料丝的强制对流传质作用,证明了LBM模型对该问题的适应性。同时模拟结果对研究分散后液体微元的传质有参考意义,为研究分散传质奠定了基础。为进一步研究填料丝形状和几何尺寸对其强制对流作用的影响提供了有利的数值工具,另外该模型可以在相似的传质和化学反应系统中推广应用。
为研究LBM的传热模型,本文将改进的LBM方程引入LBM热模型,在对应的宏观传热方程中消除了一阶非线性误差项,以此为思路提出了两个二阶精度热模型。通过Rayleigh-Benard对流数值试算,初步探索了这两个二阶精度和对应一阶精度热模型的传热特征和适应性,并做了对比分析。在Ra数极高或热传导系数极大时,采用这三个热模型计算的Nu数与经验值均有较大偏差。分析LBM对应宏观热传导方程的截断误差后,本文在平衡分布函数中引进一个调节因子。通过调节对应宏观传热方程的截断误差项系数,很好的校正了Nu数的计算偏差,提高了热模型模拟精度,拓展了模拟范围,增强了LBM作为一个数值方法在解决传热问题中的适应性。
联合上述热模型,对大密度比多相流LBM模型进行改造,构造了一个能描述传热主导相变的大密度多相流LBM复合模型。在复合模型中,基于Stefan边界假设以传热主导相变,相变作为一个源项被添加在C-H方程中以相序参数的变化来描述两相相变,同时在LBM热模型中考虑对应的相变潜热。这种相变处理方式可以自动追踪相变引起的界面变化,比其它处理方法简洁且物理背景清晰。应用该复合模型数值研究了过热液体中单气泡增长、运动和变形机理与气液两相物理参数(如动力粘性系数、表面张力和Jacob数等)的相互关系。
通过联合和调整Briant的部分浸润性边界处理,本文应用多相流复合LBM模型对水平过热壁面上气泡的增长和跃离进行了数值研究。其中关于气泡跃离直径的研究呈现了正确的参数关联,证明了复合模型对该问题的适应性。以此为基础,进一步研究了气泡的合并对增长和跃离的影响。
Lattice Boltzmann method(LBM) has recently begun to receive considerable attention as a possible alternative to conventional computational fluid dynamics(CFD) for simulating fluid flow.These algorithms have shown great promise for simulating flow in topologically complicated geometries,such as those encountered in porous media,and for simulations of multiple components or multiphase flow with heat and mass transfer,where there are few viable alternatives using conventional CFD method.
Based on the lattice Boltzmann method,the research work focuses on the numerical investigation of heat and mass transfer in flows with multiple components and phases encountered in the rotating packed-bed and nucleate pool boiling,as follows:
Using the lattice Boltzmann method ofmulticomponent flows,the liquid mass transfer in the forced convection and diffusion resulted by the column wire packing was simulated in the rotating packed-bed.By introducing a function which reflects the efficiency of the mixing,the relationships were analyzed and compared for the liquid mass transfer and the role of the convection in the wire packing with different size and form.Numerical simulation results can be considered as available data for improving the design of the packing and for studying on the mass transfer in the rotating packed-bed.
The Lattice Blotzmann scheme for the serial competitive reaction is constituted.Based on the layer model that describes the reaction-diffusion without convection,the serial competitive reaction in the central zone of the Rotating Packed-bed is simulated.Its numerical results show the quantitative agreement with that in Ref.1 and demonstrate the scheme is efficient.Analyzing the experimental work in ref.1 and a model is developed to describe the reaction-diffusion with the forced convection resulted by the Packing wire.The model is suitable for study the mass transfer in the forced convection at the edge of the Rotating Paced-bed and is founded on a hypothesis that the several times larger size liquid is continue media than of the Packing wire.Applying the LB scheme the serial competitive reaction at the edge of the Rotating Packed-bed is simulated and the mass transfer in the forced convection resulted by the Packing wire is studied.Its results provide reference for the study on the scattered mass-transfer and the design of the Rotating Packing-bed.
A parameter is added into lattice Boltzmann thermal models so that the models possess second-order accuracy.The models are employed to simulate the Rayleigh-Benard convection heat transfer for identifying abilities and are compared with its original model.As a result,it was found that there is error of computed Nu numbers for all three models when the Ra number and the thermal diffusivity become very bigger.After analyzing truncation error of the corresponding heat-transfer equation in macro scale,an adjusting parameter is introduced into the equilibrium distribution function in the paper.As a result,the computed error of the Nu number is eliminated by applying the parameter to adjust the coefficient of the truncated error.Improvements mentioned above show that the LBM heat-transfer models extends its simulation range and boosts up its applicability.
Combining with the lattice Boltzmann thermal model,the lattice Boltzmann multiphase model with a large density ratio can be extended to describe the phenomenon of phase change with mass and heat transferring through the interface.Based on the Stefan boundary condition, the phase change is considered as change of the phase order parameter and is disposed as a source term of the Cahn-Hilliard(C-H) equation.The change of the interfacial position with the time is obtained as a part of the solution of the combined lattice Boltzmann equations. This hybrid model is applied to simulate the motion and growth of a vapor bubble as it rises through a uniformly superheated liquid.At the same time,parametric studies affected on the bubble growth,deformation and rising in the different surface tension forces and kinetic viscosities are also presented.
Improving the Briant's treatment of the partial wetting boundaries,the hybrid model is applied to simulate the growth and departure of the single vapor bubble on the superheat wall. The numerical results exhibit correct parametric dependencies of the departure diameter as the experimental correlation in recent literature and show the hybrid model is suitable and feasible.On this basis,parametric studies on the growth,coalescence and departure of the twin-bubble on the horizontal wall are also presented.
The content about thesis chapters is arranged as follows:
The research background and the LBM review are summarized in Chapter 1.The LBM principle and its boundary treatment are introduced in Chapter 2.The numerical investigations and its results are presented in Chapter 3,4,5 and 6,respectively.The conclusions and prospect are provided in Chapter 7.
为检验LBM多组分流模型在复杂流动中的适应性和对应复杂边界处理的便捷性,依托超重力旋转填充床的工业背景,对床内液相膜流动状态下建立的液相组分间层状扩散反应模型进行合理扩展,将对流传质引入模型建立对流扩散传质模型。以此模型为基础对填料丝的强化对流传质作用进行了数值研究。通过引进反映宏观混合效率的函数,量化分析了填料丝形状和尺寸在其强制对流传质中的作用。结果对旋转填充床的填料设计及其传质的数值研究工作有参考价值,对其它填料的设计亦有启示作用。
由于LBM多组分模型在研究组分传质时缺乏对流动混合效率的记忆性,本文构造了串行竞争反应的LBM模型。应用该模型分别对填料主体区和端效应区的微观混合和化学反应进行了数值研究。在主体区,采用层状扩散模型进行了模拟,与对应实验结论和其它数值结果比对分析,证明了算法的有效性。在端效应区,基于强制对流扩散反应模型对端效应区的强制对流传质和化学反应进行了积极的探索。初步探索了填料丝的强制对流传质作用,证明了LBM模型对该问题的适应性。同时模拟结果对研究分散后液体微元的传质有参考意义,为研究分散传质奠定了基础。为进一步研究填料丝形状和几何尺寸对其强制对流作用的影响提供了有利的数值工具,另外该模型可以在相似的传质和化学反应系统中推广应用。
为研究LBM的传热模型,本文将改进的LBM方程引入LBM热模型,在对应的宏观传热方程中消除了一阶非线性误差项,以此为思路提出了两个二阶精度热模型。通过Rayleigh-Benard对流数值试算,初步探索了这两个二阶精度和对应一阶精度热模型的传热特征和适应性,并做了对比分析。在Ra数极高或热传导系数极大时,采用这三个热模型计算的Nu数与经验值均有较大偏差。分析LBM对应宏观热传导方程的截断误差后,本文在平衡分布函数中引进一个调节因子。通过调节对应宏观传热方程的截断误差项系数,很好的校正了Nu数的计算偏差,提高了热模型模拟精度,拓展了模拟范围,增强了LBM作为一个数值方法在解决传热问题中的适应性。
联合上述热模型,对大密度比多相流LBM模型进行改造,构造了一个能描述传热主导相变的大密度多相流LBM复合模型。在复合模型中,基于Stefan边界假设以传热主导相变,相变作为一个源项被添加在C-H方程中以相序参数的变化来描述两相相变,同时在LBM热模型中考虑对应的相变潜热。这种相变处理方式可以自动追踪相变引起的界面变化,比其它处理方法简洁且物理背景清晰。应用该复合模型数值研究了过热液体中单气泡增长、运动和变形机理与气液两相物理参数(如动力粘性系数、表面张力和Jacob数等)的相互关系。
通过联合和调整Briant的部分浸润性边界处理,本文应用多相流复合LBM模型对水平过热壁面上气泡的增长和跃离进行了数值研究。其中关于气泡跃离直径的研究呈现了正确的参数关联,证明了复合模型对该问题的适应性。以此为基础,进一步研究了气泡的合并对增长和跃离的影响。
Lattice Boltzmann method(LBM) has recently begun to receive considerable attention as a possible alternative to conventional computational fluid dynamics(CFD) for simulating fluid flow.These algorithms have shown great promise for simulating flow in topologically complicated geometries,such as those encountered in porous media,and for simulations of multiple components or multiphase flow with heat and mass transfer,where there are few viable alternatives using conventional CFD method.
Based on the lattice Boltzmann method,the research work focuses on the numerical investigation of heat and mass transfer in flows with multiple components and phases encountered in the rotating packed-bed and nucleate pool boiling,as follows:
Using the lattice Boltzmann method ofmulticomponent flows,the liquid mass transfer in the forced convection and diffusion resulted by the column wire packing was simulated in the rotating packed-bed.By introducing a function which reflects the efficiency of the mixing,the relationships were analyzed and compared for the liquid mass transfer and the role of the convection in the wire packing with different size and form.Numerical simulation results can be considered as available data for improving the design of the packing and for studying on the mass transfer in the rotating packed-bed.
The Lattice Blotzmann scheme for the serial competitive reaction is constituted.Based on the layer model that describes the reaction-diffusion without convection,the serial competitive reaction in the central zone of the Rotating Packed-bed is simulated.Its numerical results show the quantitative agreement with that in Ref.1 and demonstrate the scheme is efficient.Analyzing the experimental work in ref.1 and a model is developed to describe the reaction-diffusion with the forced convection resulted by the Packing wire.The model is suitable for study the mass transfer in the forced convection at the edge of the Rotating Paced-bed and is founded on a hypothesis that the several times larger size liquid is continue media than of the Packing wire.Applying the LB scheme the serial competitive reaction at the edge of the Rotating Packed-bed is simulated and the mass transfer in the forced convection resulted by the Packing wire is studied.Its results provide reference for the study on the scattered mass-transfer and the design of the Rotating Packing-bed.
A parameter is added into lattice Boltzmann thermal models so that the models possess second-order accuracy.The models are employed to simulate the Rayleigh-Benard convection heat transfer for identifying abilities and are compared with its original model.As a result,it was found that there is error of computed Nu numbers for all three models when the Ra number and the thermal diffusivity become very bigger.After analyzing truncation error of the corresponding heat-transfer equation in macro scale,an adjusting parameter is introduced into the equilibrium distribution function in the paper.As a result,the computed error of the Nu number is eliminated by applying the parameter to adjust the coefficient of the truncated error.Improvements mentioned above show that the LBM heat-transfer models extends its simulation range and boosts up its applicability.
Combining with the lattice Boltzmann thermal model,the lattice Boltzmann multiphase model with a large density ratio can be extended to describe the phenomenon of phase change with mass and heat transferring through the interface.Based on the Stefan boundary condition, the phase change is considered as change of the phase order parameter and is disposed as a source term of the Cahn-Hilliard(C-H) equation.The change of the interfacial position with the time is obtained as a part of the solution of the combined lattice Boltzmann equations. This hybrid model is applied to simulate the motion and growth of a vapor bubble as it rises through a uniformly superheated liquid.At the same time,parametric studies affected on the bubble growth,deformation and rising in the different surface tension forces and kinetic viscosities are also presented.
Improving the Briant's treatment of the partial wetting boundaries,the hybrid model is applied to simulate the growth and departure of the single vapor bubble on the superheat wall. The numerical results exhibit correct parametric dependencies of the departure diameter as the experimental correlation in recent literature and show the hybrid model is suitable and feasible.On this basis,parametric studies on the growth,coalescence and departure of the twin-bubble on the horizontal wall are also presented.
The content about thesis chapters is arranged as follows:
The research background and the LBM review are summarized in Chapter 1.The LBM principle and its boundary treatment are introduced in Chapter 2.The numerical investigations and its results are presented in Chapter 3,4,5 and 6,respectively.The conclusions and prospect are provided in Chapter 7.
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