对流扩散方程的特征有限元方法以及气泡行为模拟研究
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摘要
本文主要研究了五个不同有限单元的改进特征有限元格式在对流扩散方程中的应用。然后分别采用改进的VOF模型和DPM模型对气泡在离子液体中的运动行为做出数值模拟。采用欧拉-欧拉和群平衡模型(PBM)的耦合模型对离子液体吸收二氧化碳过程中的质量传递以及气液两相流的流场进行了模拟研究。
第二章对对流占优的对流扩散方程分别提出了五节点单元、双线性单元、旋转Q1单元、带限制的旋转Q1单元有限元逼近方法。在整个过程中,利用有限元插值代替了以往文献中收敛分析必不可少的Ritz投影,并且利用插值算子的性质以及平均值技巧来对对流扩散方程进行逼近。与特征扩展混合元的方法相比,当解充分光滑的时候,将空间上L2模的误差估计从O(h)提高到O(h2)阶。与此同时得到了在正则网格下采用协调有限元逼近方程同样的收敛阶。最后针对每一种有限单元进了数值试验验证,通过数值试验验证,我们取得了同理论分析一致的结果。其次对该方程提出了非协调特征扩展混合有限元逼近,得到了与正则网格下的协调扩展混合元逼近格式相同的误差估计并且进行了数值模拟验证。
第三章我们采用改进的VOF模型和DPM模型对离子液体中的气泡行为进行了数值模拟研究。在改进的模型中,除了考虑了重力和表面张力对气泡的影响外,一个新的相间作用力被添加到动量方程中对离子液体中气液界面来进行模拟研究。在DPM模型中引入了一个基于离子液体体系的新曳力模型。在模拟中考虑了气泡在三种不同的离子液体bmimBF4,bmimPF6和omimBF4中的变形、速度、等效直径等因素,并且与实验数据进行对比,取得很好的一致性。此外采用改进的模型,对气泡周围的压强场、速度场进行了预测。通过该工作对了解离子液体中的气泡行为以及为离子液体作为溶剂的鼓泡塔设计提供有力的工具。
尽管利用离子液体从烟道气中捕集二氧化碳是一种新的有效方法,但是关于这种新溶剂的二氧化碳吸收传质特性还没有研究过。在本文第四章中一个耦合的流体动力学模型和群平衡模型用来研究离子液体溶剂吸收二氧化碳的传质特性。考虑到离子液体独特的物理性质,引入了新的曳力模型的欧拉-欧拉模型用来模拟气液两相流体动力学,气泡尺寸大小分布采用群平衡模型来计算。在模拟过程中,气含率、气液相界面积、气泡大小直径分布得到了预测。质量传递速率的计算采用Higbie的渗透理论模型。通过模型获得的数值模拟值与鼓泡塔设备中获得的实验数据取得了很好的一致性。此外通过改进的模型我们获得了二氧化碳吸收过程中气液两相流的压强场和速度场的分布。
Abstr
Five different finite elements for the convection-diffusion problem with a modified charac-teristic finite element scheme are studied in this paper. Then numerical simulations are studied to investigate the motion of bubbles in ionic liquids using an improved volume-of-fluid (VOF) model and DPM model. A coupled Computational Fluid Dynamic (CFD) model and Population Balance Model(PBM) have been applied to study the mass transfer properties for capturing CO2 with ionic liquids solvents.
In Chapter 2, firstly, finite element method for the convection-diffusion problem with a mod-ified characteristic finite element scheme is studied. We discuss five-node element, the constrained rotated Q1 element, bilinear finite element and the popular ratated Q1 element. The O(h2) or-der error estimate in L2-norm with respect to the space, one order higher than the expanded characteristic-mixed finite element scheme with order O(h), and the same as the conforming case for a modified characteristic finite element scheme under regular meshes, is obtained by use of some distinct properties of the interpolation operator and the mean value technique, instead of the so-called elliptic projection, which is an indispensable tool in the convergence analysis of the previous literature. Then some numerical results are provided to verify our theoretical analy-sis. Secondly, we apply a nonconforming finite element to the same equation with the expanded characteristic-mixed finite element scheme with respect to the space. When the requirement of the exact solution's regularity is lower, the optimal estimates are obtained as the same as the pre-vious literature for the conforming finite element under regular meshes. We verify our theoretical analysis with some numerical results.
In Chapter 3, a numerical simulation is studied to investigate the motion of bubbles in ionic liquids using an improved volume-of-fluid (VOF) model and DPM model. In the improved method, besides the gravity and surface tension, a new force between two phases is added to the momentum equation in order to describe the gas-liquid interaction much rigorously in the ionic liquids which possess some special properties compared with the traditional solvents. In DPM model, a new drag force model is added. The deformation, velocity and equivalent diameter of bubble rising in three ionic liquids, i.e., bmimBF4, bmimPF6 and omimBF4 are simulated and the calculation results are agreed well with the experimental data. Furthermore, the detailed velocity fields and pressure fields around the bubble are also predicted with the proposed numerical simulation models. This work is important for understanding the fluid dynamic performance of bubbles in ionic liquids, and could provide a useful tool for designing a bubble column with ionic liquids as its solvents.
Although separating CO2 from flue gas with ionic liquids has been regarded as a new and effective method, the mass transfer properties of the CO2 absorption in these new solvents have still been rarely researched. In Chapter 4, a coupled Computational Fluid Dynamic (CFD) model and Population Balance Model (PBM) have been applied to study the mass transfer properties for capturing CO2 with ionic liquids solvents. Considering the unique properties of ionic liquids, the Eulerian-Eulerian two-flow model with a new drag model is employed for the gas-liquid fluid dynamic simulation. The bubble size distribution is predicted by the PBM method. The gas holdup, interfacial area and bubble size distribution in the bubble column reactor are predicted. The mass transfer rates are estimated with the Higbie's penetration model. Furthermore, the velocity field and pressure field in the reactor are also predicted.
第二章对对流占优的对流扩散方程分别提出了五节点单元、双线性单元、旋转Q1单元、带限制的旋转Q1单元有限元逼近方法。在整个过程中,利用有限元插值代替了以往文献中收敛分析必不可少的Ritz投影,并且利用插值算子的性质以及平均值技巧来对对流扩散方程进行逼近。与特征扩展混合元的方法相比,当解充分光滑的时候,将空间上L2模的误差估计从O(h)提高到O(h2)阶。与此同时得到了在正则网格下采用协调有限元逼近方程同样的收敛阶。最后针对每一种有限单元进了数值试验验证,通过数值试验验证,我们取得了同理论分析一致的结果。其次对该方程提出了非协调特征扩展混合有限元逼近,得到了与正则网格下的协调扩展混合元逼近格式相同的误差估计并且进行了数值模拟验证。
第三章我们采用改进的VOF模型和DPM模型对离子液体中的气泡行为进行了数值模拟研究。在改进的模型中,除了考虑了重力和表面张力对气泡的影响外,一个新的相间作用力被添加到动量方程中对离子液体中气液界面来进行模拟研究。在DPM模型中引入了一个基于离子液体体系的新曳力模型。在模拟中考虑了气泡在三种不同的离子液体bmimBF4,bmimPF6和omimBF4中的变形、速度、等效直径等因素,并且与实验数据进行对比,取得很好的一致性。此外采用改进的模型,对气泡周围的压强场、速度场进行了预测。通过该工作对了解离子液体中的气泡行为以及为离子液体作为溶剂的鼓泡塔设计提供有力的工具。
尽管利用离子液体从烟道气中捕集二氧化碳是一种新的有效方法,但是关于这种新溶剂的二氧化碳吸收传质特性还没有研究过。在本文第四章中一个耦合的流体动力学模型和群平衡模型用来研究离子液体溶剂吸收二氧化碳的传质特性。考虑到离子液体独特的物理性质,引入了新的曳力模型的欧拉-欧拉模型用来模拟气液两相流体动力学,气泡尺寸大小分布采用群平衡模型来计算。在模拟过程中,气含率、气液相界面积、气泡大小直径分布得到了预测。质量传递速率的计算采用Higbie的渗透理论模型。通过模型获得的数值模拟值与鼓泡塔设备中获得的实验数据取得了很好的一致性。此外通过改进的模型我们获得了二氧化碳吸收过程中气液两相流的压强场和速度场的分布。
Abstr
Five different finite elements for the convection-diffusion problem with a modified charac-teristic finite element scheme are studied in this paper. Then numerical simulations are studied to investigate the motion of bubbles in ionic liquids using an improved volume-of-fluid (VOF) model and DPM model. A coupled Computational Fluid Dynamic (CFD) model and Population Balance Model(PBM) have been applied to study the mass transfer properties for capturing CO2 with ionic liquids solvents.
In Chapter 2, firstly, finite element method for the convection-diffusion problem with a mod-ified characteristic finite element scheme is studied. We discuss five-node element, the constrained rotated Q1 element, bilinear finite element and the popular ratated Q1 element. The O(h2) or-der error estimate in L2-norm with respect to the space, one order higher than the expanded characteristic-mixed finite element scheme with order O(h), and the same as the conforming case for a modified characteristic finite element scheme under regular meshes, is obtained by use of some distinct properties of the interpolation operator and the mean value technique, instead of the so-called elliptic projection, which is an indispensable tool in the convergence analysis of the previous literature. Then some numerical results are provided to verify our theoretical analy-sis. Secondly, we apply a nonconforming finite element to the same equation with the expanded characteristic-mixed finite element scheme with respect to the space. When the requirement of the exact solution's regularity is lower, the optimal estimates are obtained as the same as the pre-vious literature for the conforming finite element under regular meshes. We verify our theoretical analysis with some numerical results.
In Chapter 3, a numerical simulation is studied to investigate the motion of bubbles in ionic liquids using an improved volume-of-fluid (VOF) model and DPM model. In the improved method, besides the gravity and surface tension, a new force between two phases is added to the momentum equation in order to describe the gas-liquid interaction much rigorously in the ionic liquids which possess some special properties compared with the traditional solvents. In DPM model, a new drag force model is added. The deformation, velocity and equivalent diameter of bubble rising in three ionic liquids, i.e., bmimBF4, bmimPF6 and omimBF4 are simulated and the calculation results are agreed well with the experimental data. Furthermore, the detailed velocity fields and pressure fields around the bubble are also predicted with the proposed numerical simulation models. This work is important for understanding the fluid dynamic performance of bubbles in ionic liquids, and could provide a useful tool for designing a bubble column with ionic liquids as its solvents.
Although separating CO2 from flue gas with ionic liquids has been regarded as a new and effective method, the mass transfer properties of the CO2 absorption in these new solvents have still been rarely researched. In Chapter 4, a coupled Computational Fluid Dynamic (CFD) model and Population Balance Model (PBM) have been applied to study the mass transfer properties for capturing CO2 with ionic liquids solvents. Considering the unique properties of ionic liquids, the Eulerian-Eulerian two-flow model with a new drag model is employed for the gas-liquid fluid dynamic simulation. The bubble size distribution is predicted by the PBM method. The gas holdup, interfacial area and bubble size distribution in the bubble column reactor are predicted. The mass transfer rates are estimated with the Higbie's penetration model. Furthermore, the velocity field and pressure field in the reactor are also predicted.
引文
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