鼓泡塔反应器气液两相流数值模拟模型及应用
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摘要
鼓泡塔反应器因结构简单、传质传热效率高等优点而大量应用于石油化工、能源、环境、生物工程等领域。深入研究该类反应器的流体力学行为,可以为优化反应器操作、设计高效的反应器结构以及拓展鼓泡塔的应用范围提供依据。鼓泡塔液相流动由气相驱动,两相之间作用强烈,因而流体力学行为非常复杂；又因大量气泡的存在使得实验研究非常困难。近年来,随着计算流体力学的发展和相关的物理模型不断完善,数值模拟已逐渐成为鼓泡塔研究的重要手段。本文以鼓泡塔PX氧化反应器放大设计为背景,开展鼓泡塔反应器的数值模拟研究,以指导反应器设计。
双流体模型因假定离散气泡相为拟流体,气相与液相互相渗透,因此计算量较小,工业应用潜力大。针对当前鼓泡塔模拟中模型问题以及存在的不足,本文采用双流体模型开展了以下的工作。
对气液两流模拟中的各物理模型进行了详细的数值模拟实验,定量考察了它们的作用。结果发现,湍流模型和升力是模拟鼓泡流摆动周期的关键,而虚拟质量力的作用不大。对于单孔局部通气鼓泡塔,只有考虑升力或湍流扩散力才能合理模拟气相分散；而对于底部均匀进气鼓泡塔,不考虑升力或湍流扩散力也能获得与实验比较接近的模拟结果。
为预测气泡直径,对考虑气泡聚并与破碎的单方程气泡界面浓度模型进行了研究,并编写了该模型的相关计算程序,最后耦合该模型与CFD双流体模型对鼓泡塔进行模拟。计算结果表明：整体气含率、局部气含率、局部气／液相速度和液相湍流动能的模拟结果与实验数据吻合较好,但气／液相雷诺应力模拟结果与实验值相差较大。
为模拟气泡尺寸分布,对气泡群平衡模型(BPBM模型)进行了系统研究。建立了完整的SBPBM模型数值实现算法,编写相关计算程序。并通过综合考虑气泡自由运动空间以及气泡的有效湍动运动距离对气泡碰撞效率的影响,对Prince聚并模型进行修正。在SBPBM-CFD耦合模型框架上,采用标准Luo&Svendsen与标准Prince模型组合以及标准Luo&Svendsen与修正Prince模型组合分别对同一鼓泡塔进行了数值模拟。结果表明,标准模型预测的气泡直径随表观气速先增大后减少；而修正模型预测的气泡直径基本上随表观气速增大而增大。
在SBPBM模型的基础上,本文首次提出并建立了双气泡相-群平衡模型(TBPBM),编制了该模型的数值算法和计算程序。并耦合TBPBM模型与CFD双流体模型对鼓泡塔进行了数值模拟。发现TBPBM模型明显改善了平均气泡尺寸模型和SBPBM模型的模拟结果,且TBPBM模型模拟的气泡尺寸大于SBPBM模型。文中还详细考察了边界条件、网格、数值格式对BPBM模型模拟结果的影响,结果表明它们对模拟结果的影响非常严重,特别是体积分数方程的离散格式和网格的影响更是显著,并由此提出了一种较优的网格划分方案。
应用CFD模拟较系统的研究了带短导流筒内构件的鼓泡塔和多种气体分布器。结果发现,在鼓泡塔底部安装短导流筒,能在不降低气含率情况下,显著提高液相循环速度以及瞬时液相速度,将改善普通鼓泡塔的固相悬浮性能。气体分布器的模拟结果表明分布器形式和管式分布器的通气管位置严重影响了鼓泡塔的流体力学、混合以及气泡尺寸分布；文中通过CFD数值模拟,对四管分布器通气管安装位置提出了优化,并且CFD优化结果与实验结论吻合较好,说明可以通过CFD模拟对鼓泡塔反应器进行优化设计。
基于气泡破碎时湍流涡最小能量密度约束条件对Luo&Svendsen破碎模型了进行修正。然后,采用SBPBM-CFD双流体耦合模型以及修正的Luo&Svendsen模型和Prince聚并模型对鼓泡塔的放大效应进行了三维数值模拟研究。模拟结果表明：塔径对整体气含率的影响可以忽略,但气含率径向分布随塔径的增大逐渐均匀；鼓泡塔中心液速是塔径的1／3次方的函数；塔径对平均气泡尺寸及其分布有一定的影响,但不显著。塔径对流型有显著影响,小直径鼓泡塔内(D=440mm)液相沿鼓泡塔中心扭曲上升；而在大塔内,液相贴壁面垂直上升,形成大尺度的整体循环。
Bubble column reactors are widely employed in petrochemical, energy, environmental and bio-engineering processes because of their features of being geometrically simple and superior gas-liquid interfacial mass and heat transfer. A fundamental investigation and understanding of fluid dynamics in bubble column reactors would be very beneficial to the optimization of operation, design of high efficiency reactor structure and extension of their applications. As the main flow inside bubble column is driven by rising bubbles, hydrodynamics involved exhibits complicated status due to the interaction and strong coupling between liquid and gas phases. In addition, the presence of a large amount of bubbles or bubble clusters causes bubble reactors to be opaque. These factors make it extremely difficult to experimentally study the details of flow patterns in bubble columns. Recent progress on CFD modeling and the knowledge of bubble dynamics has made this possible, i.e. the use of numerical simulation as an important tool to investigate multiphase flow behavior in bubble column reactors. This dissertation attempts to use numerical modeling approach to study the fluid dynamics in bubble columns, in particular seeking for scale-up modelling of PX oxidation reactors.
This project has employed two-fluid model in all of the simulations due to its lower requirement for computational resource and potential for industrial applications. The model regards the dispersed bubble phase as a pseudo-fluid and postulates the gas and liquid phases to be permeable.
In view of the existing difficulties and problems encountered in CFD modelling of flows in bubble columns, this dissertation has firstly conducted detailed numerical modelling experiments to quantitatively study the effects of different physical models currently employed in CFD modelling, in particular the interfacial force models and turbulence models in the simulations of gas-liquid flows. The examples to refelect these effects have been demonstrated in Chapter 3. The modelling results have clearly indicated that the turbulence model and lift force are the key factors influencing predictions of dynamic fluctuation behavior of bubble plume in bubble columns. The influence of added-mass force can be negligible. For a bubble column equiped with a single-pipe sparging gas distributor at the centre of the bottom of the bubble column, the simulation shows that it is necessary to include both the lift force and turbulent dispersion force in the modeling in order to obtain the reasonable gas phase distributions. While for a bubble column with an uniform gas sparger, reasonable simulation results can be still obtained when excluding the lift force and turbulent dispersion force in the two-fluid model.
A single scalar transport equation which describes bubble size changes characterised by bubble interfacial areas was incorporated into the simulations through UDF subroutines. The effect of bubble coalescence and break-up was taken into consideration in the adopted models. The predicted time-averaged axial liquid velocities, gas hold-up and gas phase interfacial areas were compared with the available experimental results. It was revealed from the simulation that the predicted overall gas holdup, local gas holdup, local phase velocities and liquid phase turbulence kinetic energy are in good agreement with the experimental data while the Reynolds stresses for both gas and phases are poorly estimated, very likely due to the lost of the details of instantaneous flow in time-averaging process for deriving the k～εturbulent model.
The bubble population balance model (BPBM or referred to as SBPBM in Chapter 6 of the dissertation) was systemically studied in Chapter 5 in order to properly predict the bubble size distribution in bubble columns. A numerical method to realise single-bubble-phase population balance model (SBPBM) was proposed and a corresponding code for execution of such method was programmed. Modification to "Prince bubble coalescence model" was introduced to account for the effect of the free-moving space among bubbles and effective bubble migration due to turbulence on the efficiency of bubble collision. In simulations, cases of both the use of Luo & Svendsen's model together with Prince's model and adoption of the modified Prince model were tested for prediction of hydrodynamics in a bubble column. The simulations show that the use of the original "Prince model" predicts that the mean bubble size increases initially but decreases with the increase of superficial velocity. However, adoption of the modified Prince's model forecasts that the mean bubble size increases with the increase of superficial velocity, consistent with the experimental observations reported in the literature.
Based on the applications of the SBPBM model and perception of its limitations, an improved model to describe bubble size distribution-two-bubble-phase population balance model (TBPBM) was proposed in Chapter 6. The corresponding numerical method for exectution of such model was also developed and incorporated into the self-coding of UDF subroutines in a similar way to the work done based on the SBPBM model. The TBPBM model coupled with two-fluid model was used to simulate the flow inside a bubble column. The simulation has clearly demonstrated that the adoption of the TBPBM model significantly improves the predictions in comparison to the use of the mean bubble size model and SBPBM model. The mean bubble size predicted by using the TBPBM model is apparently larger than that by using the SBPBM model, consistent with the practical observations. Detailed examinations have been also performed in Chapter 6 to look into the influence of the boundary conditions, mesh size and numerical schemes adopted in the modelling on the simulations using the BPBM model. The obtained results indicate that the mesh size and numerical schemes employed in the simulations have a significant impact on gas holdup prediction since the volume fraction transport equation is susceptible to mesh size and the numerical schemes. As a result, a better meshing method was proposed.
Based on the investigations in the preceding chapters, CFD modelling approach was employed to systemically assess the influence of adoption of a short size draft tube and configurations of gas distributors on fluid dynamic in bubble columns. Simulation results demonstrate that allocation of a short draft tube which is fixed in the lower part of the bubble column can remarkably increase the liquid circulation velocity and instantaneous velocity without reduction of the overall gas holdup, clearly being beneficial to suspension of solid particles in the bubble column. CFD simulation also shows that the configurations of gas distributor and the allocation of gas sparging pipes have a vital impact on flow patterns, mixing time and bubble sizes in the bubble column. An optimal allocation for four sparging pipe gas distributor in the bubble column is obtained by CFD modelling, which agrees well with the experimental observation.
Finally, a modification to "Luo & Svendsen's bubble breakup model" was proposed to account for the constraint of eddy energy density limiting the the minmum fragmentation fration of a bubble, i.e. the energy density of an eddy (ρ1uγ2/2) should be larger than the capalliary force (σ/dmin) of the smaller fragmental daughter bubble. On this basis, three-dimensional numerical simulations of four different diameters of bubble columns were conducted to investigate the scale-up effect using the SBPBM model and the modified "Luo & Svendsen's bubble breakup model" together with "Prince coalescence model". The simulations show that the effect of the bubble column diameter on the overall gas holdup may be negligible, but the radial profiles of time-averaged local gas holdup become flatter when bubble column diameter increases. Furthermore, the predicted time-averaged axial liquid velocity in bubble column center was found to be proportional to the cubic root of the bubble column diameter. The simulations reveal that the diameter of a bubble column also affects the bubble size and bubble distributions but the effect is not notale as expected. However, significant differences of flow patterns in different bubble columns are predicted, indicating that the induced liquid flows up in the bubble column center with a meandering way for small diameter bubble column reactors, and a large circulation loop with induced liquid flowing up along the bubble column wall for larger bubble columns.
双流体模型因假定离散气泡相为拟流体,气相与液相互相渗透,因此计算量较小,工业应用潜力大。针对当前鼓泡塔模拟中模型问题以及存在的不足,本文采用双流体模型开展了以下的工作。
对气液两流模拟中的各物理模型进行了详细的数值模拟实验,定量考察了它们的作用。结果发现,湍流模型和升力是模拟鼓泡流摆动周期的关键,而虚拟质量力的作用不大。对于单孔局部通气鼓泡塔,只有考虑升力或湍流扩散力才能合理模拟气相分散；而对于底部均匀进气鼓泡塔,不考虑升力或湍流扩散力也能获得与实验比较接近的模拟结果。
为预测气泡直径,对考虑气泡聚并与破碎的单方程气泡界面浓度模型进行了研究,并编写了该模型的相关计算程序,最后耦合该模型与CFD双流体模型对鼓泡塔进行模拟。计算结果表明：整体气含率、局部气含率、局部气／液相速度和液相湍流动能的模拟结果与实验数据吻合较好,但气／液相雷诺应力模拟结果与实验值相差较大。
为模拟气泡尺寸分布,对气泡群平衡模型(BPBM模型)进行了系统研究。建立了完整的SBPBM模型数值实现算法,编写相关计算程序。并通过综合考虑气泡自由运动空间以及气泡的有效湍动运动距离对气泡碰撞效率的影响,对Prince聚并模型进行修正。在SBPBM-CFD耦合模型框架上,采用标准Luo&Svendsen与标准Prince模型组合以及标准Luo&Svendsen与修正Prince模型组合分别对同一鼓泡塔进行了数值模拟。结果表明,标准模型预测的气泡直径随表观气速先增大后减少；而修正模型预测的气泡直径基本上随表观气速增大而增大。
在SBPBM模型的基础上,本文首次提出并建立了双气泡相-群平衡模型(TBPBM),编制了该模型的数值算法和计算程序。并耦合TBPBM模型与CFD双流体模型对鼓泡塔进行了数值模拟。发现TBPBM模型明显改善了平均气泡尺寸模型和SBPBM模型的模拟结果,且TBPBM模型模拟的气泡尺寸大于SBPBM模型。文中还详细考察了边界条件、网格、数值格式对BPBM模型模拟结果的影响,结果表明它们对模拟结果的影响非常严重,特别是体积分数方程的离散格式和网格的影响更是显著,并由此提出了一种较优的网格划分方案。
应用CFD模拟较系统的研究了带短导流筒内构件的鼓泡塔和多种气体分布器。结果发现,在鼓泡塔底部安装短导流筒,能在不降低气含率情况下,显著提高液相循环速度以及瞬时液相速度,将改善普通鼓泡塔的固相悬浮性能。气体分布器的模拟结果表明分布器形式和管式分布器的通气管位置严重影响了鼓泡塔的流体力学、混合以及气泡尺寸分布；文中通过CFD数值模拟,对四管分布器通气管安装位置提出了优化,并且CFD优化结果与实验结论吻合较好,说明可以通过CFD模拟对鼓泡塔反应器进行优化设计。
基于气泡破碎时湍流涡最小能量密度约束条件对Luo&Svendsen破碎模型了进行修正。然后,采用SBPBM-CFD双流体耦合模型以及修正的Luo&Svendsen模型和Prince聚并模型对鼓泡塔的放大效应进行了三维数值模拟研究。模拟结果表明：塔径对整体气含率的影响可以忽略,但气含率径向分布随塔径的增大逐渐均匀；鼓泡塔中心液速是塔径的1／3次方的函数；塔径对平均气泡尺寸及其分布有一定的影响,但不显著。塔径对流型有显著影响,小直径鼓泡塔内(D=440mm)液相沿鼓泡塔中心扭曲上升；而在大塔内,液相贴壁面垂直上升,形成大尺度的整体循环。
Bubble column reactors are widely employed in petrochemical, energy, environmental and bio-engineering processes because of their features of being geometrically simple and superior gas-liquid interfacial mass and heat transfer. A fundamental investigation and understanding of fluid dynamics in bubble column reactors would be very beneficial to the optimization of operation, design of high efficiency reactor structure and extension of their applications. As the main flow inside bubble column is driven by rising bubbles, hydrodynamics involved exhibits complicated status due to the interaction and strong coupling between liquid and gas phases. In addition, the presence of a large amount of bubbles or bubble clusters causes bubble reactors to be opaque. These factors make it extremely difficult to experimentally study the details of flow patterns in bubble columns. Recent progress on CFD modeling and the knowledge of bubble dynamics has made this possible, i.e. the use of numerical simulation as an important tool to investigate multiphase flow behavior in bubble column reactors. This dissertation attempts to use numerical modeling approach to study the fluid dynamics in bubble columns, in particular seeking for scale-up modelling of PX oxidation reactors.
This project has employed two-fluid model in all of the simulations due to its lower requirement for computational resource and potential for industrial applications. The model regards the dispersed bubble phase as a pseudo-fluid and postulates the gas and liquid phases to be permeable.
In view of the existing difficulties and problems encountered in CFD modelling of flows in bubble columns, this dissertation has firstly conducted detailed numerical modelling experiments to quantitatively study the effects of different physical models currently employed in CFD modelling, in particular the interfacial force models and turbulence models in the simulations of gas-liquid flows. The examples to refelect these effects have been demonstrated in Chapter 3. The modelling results have clearly indicated that the turbulence model and lift force are the key factors influencing predictions of dynamic fluctuation behavior of bubble plume in bubble columns. The influence of added-mass force can be negligible. For a bubble column equiped with a single-pipe sparging gas distributor at the centre of the bottom of the bubble column, the simulation shows that it is necessary to include both the lift force and turbulent dispersion force in the modeling in order to obtain the reasonable gas phase distributions. While for a bubble column with an uniform gas sparger, reasonable simulation results can be still obtained when excluding the lift force and turbulent dispersion force in the two-fluid model.
A single scalar transport equation which describes bubble size changes characterised by bubble interfacial areas was incorporated into the simulations through UDF subroutines. The effect of bubble coalescence and break-up was taken into consideration in the adopted models. The predicted time-averaged axial liquid velocities, gas hold-up and gas phase interfacial areas were compared with the available experimental results. It was revealed from the simulation that the predicted overall gas holdup, local gas holdup, local phase velocities and liquid phase turbulence kinetic energy are in good agreement with the experimental data while the Reynolds stresses for both gas and phases are poorly estimated, very likely due to the lost of the details of instantaneous flow in time-averaging process for deriving the k～εturbulent model.
The bubble population balance model (BPBM or referred to as SBPBM in Chapter 6 of the dissertation) was systemically studied in Chapter 5 in order to properly predict the bubble size distribution in bubble columns. A numerical method to realise single-bubble-phase population balance model (SBPBM) was proposed and a corresponding code for execution of such method was programmed. Modification to "Prince bubble coalescence model" was introduced to account for the effect of the free-moving space among bubbles and effective bubble migration due to turbulence on the efficiency of bubble collision. In simulations, cases of both the use of Luo & Svendsen's model together with Prince's model and adoption of the modified Prince model were tested for prediction of hydrodynamics in a bubble column. The simulations show that the use of the original "Prince model" predicts that the mean bubble size increases initially but decreases with the increase of superficial velocity. However, adoption of the modified Prince's model forecasts that the mean bubble size increases with the increase of superficial velocity, consistent with the experimental observations reported in the literature.
Based on the applications of the SBPBM model and perception of its limitations, an improved model to describe bubble size distribution-two-bubble-phase population balance model (TBPBM) was proposed in Chapter 6. The corresponding numerical method for exectution of such model was also developed and incorporated into the self-coding of UDF subroutines in a similar way to the work done based on the SBPBM model. The TBPBM model coupled with two-fluid model was used to simulate the flow inside a bubble column. The simulation has clearly demonstrated that the adoption of the TBPBM model significantly improves the predictions in comparison to the use of the mean bubble size model and SBPBM model. The mean bubble size predicted by using the TBPBM model is apparently larger than that by using the SBPBM model, consistent with the practical observations. Detailed examinations have been also performed in Chapter 6 to look into the influence of the boundary conditions, mesh size and numerical schemes adopted in the modelling on the simulations using the BPBM model. The obtained results indicate that the mesh size and numerical schemes employed in the simulations have a significant impact on gas holdup prediction since the volume fraction transport equation is susceptible to mesh size and the numerical schemes. As a result, a better meshing method was proposed.
Based on the investigations in the preceding chapters, CFD modelling approach was employed to systemically assess the influence of adoption of a short size draft tube and configurations of gas distributors on fluid dynamic in bubble columns. Simulation results demonstrate that allocation of a short draft tube which is fixed in the lower part of the bubble column can remarkably increase the liquid circulation velocity and instantaneous velocity without reduction of the overall gas holdup, clearly being beneficial to suspension of solid particles in the bubble column. CFD simulation also shows that the configurations of gas distributor and the allocation of gas sparging pipes have a vital impact on flow patterns, mixing time and bubble sizes in the bubble column. An optimal allocation for four sparging pipe gas distributor in the bubble column is obtained by CFD modelling, which agrees well with the experimental observation.
Finally, a modification to "Luo & Svendsen's bubble breakup model" was proposed to account for the constraint of eddy energy density limiting the the minmum fragmentation fration of a bubble, i.e. the energy density of an eddy (ρ1uγ2/2) should be larger than the capalliary force (σ/dmin) of the smaller fragmental daughter bubble. On this basis, three-dimensional numerical simulations of four different diameters of bubble columns were conducted to investigate the scale-up effect using the SBPBM model and the modified "Luo & Svendsen's bubble breakup model" together with "Prince coalescence model". The simulations show that the effect of the bubble column diameter on the overall gas holdup may be negligible, but the radial profiles of time-averaged local gas holdup become flatter when bubble column diameter increases. Furthermore, the predicted time-averaged axial liquid velocity in bubble column center was found to be proportional to the cubic root of the bubble column diameter. The simulations reveal that the diameter of a bubble column also affects the bubble size and bubble distributions but the effect is not notale as expected. However, significant differences of flow patterns in different bubble columns are predicted, indicating that the induced liquid flows up in the bubble column center with a meandering way for small diameter bubble column reactors, and a large circulation loop with induced liquid flowing up along the bubble column wall for larger bubble columns.
引文
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