稠密气固两相流动的颗粒相二阶矩模型及数值模拟研究
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摘要
气固两相流动现象广泛存在于化工、电力、冶金、食品、制药等领域中,深入认识和掌握气固两相流动的内在机理和规律有着重要的实际意义。随着计算机技术和计算方法的不断发展,数值模拟已成为气固两相流动研究的主要方法之一。但是由于气固系统本身的复杂性,气固两相流动模拟的理论模型仍然有许多值得改进和提高之处。
目前常用的颗粒动理学模型中,仅引入了颗粒温度来描述颗粒速度脉动的强弱,忽略了颗粒速度脉动的各向异性;然而现有的研究表明颗粒速度脉动呈现出较强的各向异性,因此,有必要发展颗粒相二阶矩模型并应用于气固两相流动模拟。
基于颗粒动理学基本原理,本文推导了表征颗粒速度脉动各向异性的二阶矩输运方程,对其中颗粒相本构模型采用动理学方法封闭,对颗粒脉动速度三阶矩分别采用初等输运理论和线性理论进行封闭,建立了适用于稠密气固两相流动模拟的颗粒相二阶矩模型。采用颗粒-壁面碰撞的法向和切向弹性恢复系数,应用动理学方法,推导了颗粒相速度和颗粒脉动速度二阶矩的壁面边界条件。
应用颗粒相二阶矩模型模拟了鼓泡床内的气固两相流动特性。对“布风板”鼓泡床的模拟得到了床内气泡的尾涡型和临近型聚并以及气泡的尾涡截断型和流场拉伸型分裂。模拟得到的颗粒相速度、颗粒温度和颗粒脉动速度关联矩Mxy与实验结果相吻合。通过降低颗粒间碰撞弹性恢复系数可以改变布风板鼓泡床内的气泡运动特征,从而使颗粒速度脉动的各向异性增强。对中心射流鼓泡床,通过采用颗粒动理学模型和颗粒相二阶矩模型模拟对比,发现两者模拟得到的宏观流动行为基本相似,但是射流气泡的大小、颗粒速度脉动的强弱以及速度脉动的各向异性特征具有明显差异,采用颗粒相二阶矩模型能够更好地反映中心射流鼓泡床内颗粒脉动的各向异性行为。
应用颗粒相二阶矩模型模拟了提升管内气固两相流动特性。通过二维提升管内的全流场流动模拟,得到时均颗粒浓度和质量流率的径向分布与实验结果吻合较好,时均的轴向气体压降也与实验结果相一致。对一维提升管内“环-核”型流动的模拟显示,采用不同三阶矩封闭模型的颗粒相二阶矩模型都能够得到颗粒速度脉动的各向异性特征。通过对一维提升管的模拟比较,研究了三阶矩封闭模型中的模型参数以及气固相间曳力、壁面参数和颗粒物性参数对气固两相流动的影响。气固相间作用的耗散项以及颗粒物性参数对气固流动结构和颗粒速度脉动各向异性的影响较大,考虑相间作用的耗散项、减小颗粒直径或降低颗粒-颗粒碰撞弹性恢复系数都会加强颗粒速度脉动的各向异性;颗粒-壁面碰撞的法向弹性恢复系数对流动结构影响较小,而切向弹性恢复系数的影响则较大。
考虑了颗粒速度脉动对气固相间曳力模型的影响,并基于颗粒相二阶矩模型模拟了提升管内气固两相流动。结果表明颗粒的速度脉动增加了气固相间曳力系数的非线性特征,颗粒温度越高,颗粒脉动速度对相间曳力系数的贡献也越大。通过模拟比较,发现考虑颗粒脉动速度对相间曳力系数的影响后,颗粒温度明显降低。提高气体操作速度,颗粒速度脉动对相间曳力系数的影响变得更明显。
Gas-solid two-phase flows are widespread in chemical industry, electric power, metallurgy, food, pharmarcy and other fields. In-depth understand and grasp of the mechanism of gas-solid flows has important significance. With the development of computational fluid dynamics (CFD), numerical simulation has become one of the most promising tools for researching gas-solid flows. However, due to the complexity of gas-solid system, theoretical models for numerical simulation of gas-solid flows are still needed in great improvement and enchancement.
Currently, the commonly used model is based on the kinetic theory of granular flow, in which only the granular temperature is introduced to describe the strength of particle velocity fluctuating. In fact, the fluctuation of particle velocity shows a strong anisotropy from experiments. Therefore, it’s necessary to develop a second-order moment model of particles which could take the anisotropic characteristic of particle velocity fluctuating into account.
With the basic principles of the kinetic theory, the transport equation for the second-order moment of particle fluctuating velocity is present. The solid phase constitutive model is closed with the kinetic approach, and the third-order moment of particle fluctuating velocity is approximated with the elementary transport theory and linear theory respectively. Then the second-order moment model is established for the simulation of dense gas-solid flows. By using the normal and tangiential restitution coefficients of particle-wall collision, the wall boundary condtions for solid phase velocity and second-order moment are also derived with the kinetic approach.
The second-order moment model is applied to simulate the hydrodynamics of gas-solid two-phase flows in bubbling fluidized beds. For the case of freely bubbling fluidized bed with an air distributor, the model predicts the trailing votex type and neighboring type bubble coalescence and trailing votex cut type and flow field stretched type bubble break-up. The time-averaged solid phase velocity and second-order moments of particle velocity are obtained and agree with experimental results. By reducing the restitution coefficient of particle- particle collision, the bubble dynamics in the freely fluidized bed varies a lot, so that the anisotropy of particle velocity fluctuating is strengthed. For the case of the bubbling fluidized bed with a central jet, comparison between anisotripic model and isotropic model shows that both models give similar macroscopic flow structure, but different size of bubble jets, different strength and anisotropic characteristic of particle velocity fluctuating. The anisotropic behaviors of the particle velocity fluctuating is better reflected by using the second-order moment model.
The second-order moment model is used to simulate the hydrodynamics of gas-solid two-phase flows in risers. The time-averaged radial distribution of particle concentration and solid mass flux, axial gas pressure drop in a two-dimensional riser are obtained and agree with experimental results. The simulation of one-dimensional“core-annulus”flow in the riser shows that anisotropic models with different third-order moment closures are able to predict the anisotropic fluctuation of particle velocity. Then the parameters in the third-order moment closures, the interphase interactions, the wall parameters as well as the physical parameters of particles are studied using the anisotropic model. It is found that the drag items in the third-order moment closures effect the gas-solid flow structures, but hardly effect the anistropic characterisc of particle velocity fluctuating. The dissipation item of interphase interaction, the physical parmeters of particles effect both the flow strctures and the anisotropic behaviors of particle velocity fluctuating. Considering the dissipation term of interphase interaction, or reducing the particle diameter or decreasing the restitution coefficient of particle-particle collision would increase the anisotropic of particle velocity fluctuating. Simulation results also show that the flow structure is less affeced by the normal restitution coefficient of particle-wall collision, but is greatly affected by the tangential one.
The effect of particle fluctuating velocity on interphase drag model is then studied by incorporating it into the second-order moment model. Simulation of the gas-solid flow in a riser shows that the particle fluctuating velocity increases the non-linear characteristics of interphase interaction, and the higher of the granular temperature, the greater impact of the particle fluctuating velocity. It’s found that with the contribution of the particle fluctuating velocity, the granular temperature decreases significantly. By increasing the operating gas velocity, the impact of particle fluctuating velocity on interphase interaction becomes more obvious.
目前常用的颗粒动理学模型中,仅引入了颗粒温度来描述颗粒速度脉动的强弱,忽略了颗粒速度脉动的各向异性;然而现有的研究表明颗粒速度脉动呈现出较强的各向异性,因此,有必要发展颗粒相二阶矩模型并应用于气固两相流动模拟。
基于颗粒动理学基本原理,本文推导了表征颗粒速度脉动各向异性的二阶矩输运方程,对其中颗粒相本构模型采用动理学方法封闭,对颗粒脉动速度三阶矩分别采用初等输运理论和线性理论进行封闭,建立了适用于稠密气固两相流动模拟的颗粒相二阶矩模型。采用颗粒-壁面碰撞的法向和切向弹性恢复系数,应用动理学方法,推导了颗粒相速度和颗粒脉动速度二阶矩的壁面边界条件。
应用颗粒相二阶矩模型模拟了鼓泡床内的气固两相流动特性。对“布风板”鼓泡床的模拟得到了床内气泡的尾涡型和临近型聚并以及气泡的尾涡截断型和流场拉伸型分裂。模拟得到的颗粒相速度、颗粒温度和颗粒脉动速度关联矩Mxy与实验结果相吻合。通过降低颗粒间碰撞弹性恢复系数可以改变布风板鼓泡床内的气泡运动特征,从而使颗粒速度脉动的各向异性增强。对中心射流鼓泡床,通过采用颗粒动理学模型和颗粒相二阶矩模型模拟对比,发现两者模拟得到的宏观流动行为基本相似,但是射流气泡的大小、颗粒速度脉动的强弱以及速度脉动的各向异性特征具有明显差异,采用颗粒相二阶矩模型能够更好地反映中心射流鼓泡床内颗粒脉动的各向异性行为。
应用颗粒相二阶矩模型模拟了提升管内气固两相流动特性。通过二维提升管内的全流场流动模拟,得到时均颗粒浓度和质量流率的径向分布与实验结果吻合较好,时均的轴向气体压降也与实验结果相一致。对一维提升管内“环-核”型流动的模拟显示,采用不同三阶矩封闭模型的颗粒相二阶矩模型都能够得到颗粒速度脉动的各向异性特征。通过对一维提升管的模拟比较,研究了三阶矩封闭模型中的模型参数以及气固相间曳力、壁面参数和颗粒物性参数对气固两相流动的影响。气固相间作用的耗散项以及颗粒物性参数对气固流动结构和颗粒速度脉动各向异性的影响较大,考虑相间作用的耗散项、减小颗粒直径或降低颗粒-颗粒碰撞弹性恢复系数都会加强颗粒速度脉动的各向异性;颗粒-壁面碰撞的法向弹性恢复系数对流动结构影响较小,而切向弹性恢复系数的影响则较大。
考虑了颗粒速度脉动对气固相间曳力模型的影响,并基于颗粒相二阶矩模型模拟了提升管内气固两相流动。结果表明颗粒的速度脉动增加了气固相间曳力系数的非线性特征,颗粒温度越高,颗粒脉动速度对相间曳力系数的贡献也越大。通过模拟比较,发现考虑颗粒脉动速度对相间曳力系数的影响后,颗粒温度明显降低。提高气体操作速度,颗粒速度脉动对相间曳力系数的影响变得更明显。
Gas-solid two-phase flows are widespread in chemical industry, electric power, metallurgy, food, pharmarcy and other fields. In-depth understand and grasp of the mechanism of gas-solid flows has important significance. With the development of computational fluid dynamics (CFD), numerical simulation has become one of the most promising tools for researching gas-solid flows. However, due to the complexity of gas-solid system, theoretical models for numerical simulation of gas-solid flows are still needed in great improvement and enchancement.
Currently, the commonly used model is based on the kinetic theory of granular flow, in which only the granular temperature is introduced to describe the strength of particle velocity fluctuating. In fact, the fluctuation of particle velocity shows a strong anisotropy from experiments. Therefore, it’s necessary to develop a second-order moment model of particles which could take the anisotropic characteristic of particle velocity fluctuating into account.
With the basic principles of the kinetic theory, the transport equation for the second-order moment of particle fluctuating velocity is present. The solid phase constitutive model is closed with the kinetic approach, and the third-order moment of particle fluctuating velocity is approximated with the elementary transport theory and linear theory respectively. Then the second-order moment model is established for the simulation of dense gas-solid flows. By using the normal and tangiential restitution coefficients of particle-wall collision, the wall boundary condtions for solid phase velocity and second-order moment are also derived with the kinetic approach.
The second-order moment model is applied to simulate the hydrodynamics of gas-solid two-phase flows in bubbling fluidized beds. For the case of freely bubbling fluidized bed with an air distributor, the model predicts the trailing votex type and neighboring type bubble coalescence and trailing votex cut type and flow field stretched type bubble break-up. The time-averaged solid phase velocity and second-order moments of particle velocity are obtained and agree with experimental results. By reducing the restitution coefficient of particle- particle collision, the bubble dynamics in the freely fluidized bed varies a lot, so that the anisotropy of particle velocity fluctuating is strengthed. For the case of the bubbling fluidized bed with a central jet, comparison between anisotripic model and isotropic model shows that both models give similar macroscopic flow structure, but different size of bubble jets, different strength and anisotropic characteristic of particle velocity fluctuating. The anisotropic behaviors of the particle velocity fluctuating is better reflected by using the second-order moment model.
The second-order moment model is used to simulate the hydrodynamics of gas-solid two-phase flows in risers. The time-averaged radial distribution of particle concentration and solid mass flux, axial gas pressure drop in a two-dimensional riser are obtained and agree with experimental results. The simulation of one-dimensional“core-annulus”flow in the riser shows that anisotropic models with different third-order moment closures are able to predict the anisotropic fluctuation of particle velocity. Then the parameters in the third-order moment closures, the interphase interactions, the wall parameters as well as the physical parameters of particles are studied using the anisotropic model. It is found that the drag items in the third-order moment closures effect the gas-solid flow structures, but hardly effect the anistropic characterisc of particle velocity fluctuating. The dissipation item of interphase interaction, the physical parmeters of particles effect both the flow strctures and the anisotropic behaviors of particle velocity fluctuating. Considering the dissipation term of interphase interaction, or reducing the particle diameter or decreasing the restitution coefficient of particle-particle collision would increase the anisotropic of particle velocity fluctuating. Simulation results also show that the flow structure is less affeced by the normal restitution coefficient of particle-wall collision, but is greatly affected by the tangential one.
The effect of particle fluctuating velocity on interphase drag model is then studied by incorporating it into the second-order moment model. Simulation of the gas-solid flow in a riser shows that the particle fluctuating velocity increases the non-linear characteristics of interphase interaction, and the higher of the granular temperature, the greater impact of the particle fluctuating velocity. It’s found that with the contribution of the particle fluctuating velocity, the granular temperature decreases significantly. By increasing the operating gas velocity, the impact of particle fluctuating velocity on interphase interaction becomes more obvious.
引文
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