微重力环状热毛细对流及不稳定性研究 | |
Alternative Title | Investigation of the Annular Thermocapillary Flow and Instability Analysis under Microgravity Condition |
何蒙 | |
Thesis Advisor | 陈启生 |
2019-05-30 | |
Degree Grantor | 中国科学院大学 |
Place of Conferral | 北京 |
Subtype | 博士 |
Degree Discipline | 流体力学 |
Keyword | 微重力 热毛细对流 谱方法 数值模拟 线性稳定性分析 |
Abstract | 本文采用数值模拟与理论分析的方法，分别研究了微重力环境下环形液池热毛细对流、圆盘间热毛细对流以及UCM流体热毛细液层及其不稳定性特征。 建立了环形液池热毛细对流、圆盘间热毛细对流以及UCM流体热毛细液层的物理模型。通过谱方法得到了环形液池热毛细对流和圆盘间热毛细对流的速度场与温度场。采用线性小扰动不稳定分析方法对环形液池热毛细对流、圆盘间热毛细对流以及UCM流体热毛细液层的不稳定性机理进行了深入研究。 对于环形液池热毛细对流，通过数值模拟得到了不同Prandtl数，不同深宽比下的热毛细对流的基本流场与温度场。通过线性稳定性分析方法研究了环形液池热毛细对流的失稳机理。发现对于小Prandtl数流体，浅液池与深液池中存在两种扰动形态。对于Pr = 1，临界毛细雷诺数随深宽比的增大先减小然后增大，再减小。对于Pr = 6.8，临界毛细雷诺数随着深宽比的增大而减小。研究了外圆柱旋转对流动稳定性的影响，发现在浅液池中，外壁的旋转使得流动更易失稳；而在深液池中，外圆柱的旋转能够提高流动稳定性。对于Pr = 0.1，在浅液池中，外壁的低速旋转使得流动更易失失稳，而高速旋转则可提高流动的稳定性。通过能量分析进一步深入研究流动失稳机理。发现扰动能量由粘性耗散，表面张力做功，和扰动流与基本流间的相互作用组成。小Prandtl数情形下，扰动能量的增长几乎完全由扰动流与基本流间的相互作用项提供。对于Pr = 0.1，旋转使得扰动流与基本流间的相互作用减弱，而热毛细力效应增强。Pr = 6.8时，扰动流与基本流间的相互作用较小，表面张力径向与周向做功对小扰动的能量变化起到主导作用。 通过线性稳定性分析方法研究了圆盘间热毛细对流的失稳机理。发现当Pr £ 0.01时，当两端圆盘静止时，圆盘间热毛细对流最不稳定模态为稳定态的二次流动。当两端圆盘沿相反方向转动时，圆盘间热毛细对流的分叉主要是由轴对称状态向三维振荡态发展。流动最不稳定形态表现为热流体波。Coriolis数对流动失稳的临界频率影响显著，热流体波的传播方向会在大Coriolis数情形下发生改变。对于大Prandtl数流体，流动失稳机理为热流体波。研究了随着圆盘旋转产生的二次涡对流动稳定性的影响。发现二次涡能够显著增强流动的稳定性。能量分析表明，对于小Prandtl数流体，中等旋转使得热毛细流动更加稳定。对于大Prandtl数流体，扰动能量最主要的来源是扰动与基本流的相互作用项在垂直方向上的分量，它也对扰动能量的增长贡献最大。 通过线性稳定性分析方法研究了UCM流体热毛细液层的失稳机理。发现失稳形式为弹性波失稳，其小扰动增长速率随波数的增大而增大。并且UCM流体不存在临界Marangoni数，而是存在临界波数。能量分析表明弹性波的扰动能量主要来自于扰动应力做功，而热毛细力做功、扰动流与基本流的相互作用均可忽略不计。 |
Other Abstract | Thermocapillary convection in annular pools, thermocapillary convection between disks and thermocapillary liquid layers for UCM fluid are investigated using numerical simulation and linear stability analysis. The physical model of thermocapillary convection in annular pools, thermocapillary convection between disks and thermocapillary liquid layers for UCM fluid are established. The velocity and temperature fields of thermocapillary convection in annular pools and thermocapillary convection between disks are obtained through spectral method. The instability mechanism of thermocapillary convection in annular pools, thermocapillary convection between disks and thermocapillary liquid layers for UCM fluid are studied. The basic flow patterns and temperature fields of thermocapillarity convection in annular pools with different prandtl numbers and aspect ratios are obtained by numerical simulation. It is found that for small Prandtl number, there are two kinds of perturbations in shallow and deep pools. For Pr = 1, critical capillary Reynolds number first decreases, then increases and then decreases with the increase of aspect ratio. For Pr = 6.8, the critical capillary Reynolds number decreases with the increase of aspect ratio. The influence of rotation of outer cylinder on flow stability is studied. In deep pools, the rotation of the outer cylinder can stablize the flow . For Pr = 0.1, in the shallow pool, the low-speed rotation of the outer wall makes the flow more unstable, while the high-speed rotation can stablize the flow. The mechanism of flow instability is further studied by energy analysis. It is found that the disturbance energy is composed of viscous dissipation, the work done by surface tension and the interaction between the perturbation flow and the basic flow. In the case of small Prandtl number, the increase of perturbation energy is almost completely provided by the interaction between the perturbation flow and the basic flow. For Pr = 0.1, the interaction between the perturbation flow and the basic flow decreases with the rotation, while the effect of thermocapillary force increases. When Pr = 6.8, the interaction between the perturbation flow and the basic flow is small, and the works done by surface tension in the radial and azimuthal directions play leading roles in the energy increaseof the small perturbation. The instability mechanism of thermocapillarity convection between disks is studied using linear stability analysis. It is found that for Pr £ 0.01, when the disks at both ends are stationary, the most unstable mode of thermocapillary convection between disks is a stationary secondary flow. When the two disks rotate in opposite directions, the bifurcations of thermocapillarity convection between the disks mostly develop from axisymmetric states to a three-dimensional oscillatory ones. The most unstable mode is usually a traveling hydrothermal wave. Coriolis number has a significant effect on the critical frequency of flow instability, and the propagation direction of hydrothermal wave changes under the condition of a large Coriolis number. For large Prandtl number fluid, the flow instability mechanism is due to hydrothermal waves. The influence of secondary vortex on the flow stability is studied. It is found that the secondary vortex can significantly enhance the flow stability. Energy analysis shows that for small Prandtl number fluids, moderate rotation makes the thermocapillary flow more stable. For large Prandtl number fluids, the main source of perturbation energy is the the interaction between the perturbation flow and the basic flow in axial direction,. The instability mechanism of the thermocapillary layer for UCM fluid is studied using linear stability analysis. It is found that the form of instability is due to elastic waves, and its growth rate increases with the increase of wave number. However, there is no critical Marangoni number in UCM fluid, but the critical wave numbers are obtained. Energy analysis shows that the perturbation energy of elastic wave mainly comes from the work done by the perturbation stress, while the work done by thermocapillary force and the interaction between the perturbation flow and the basic flow are negligible. |
Language | 中文 |
Document Type | 学位论文 |
Identifier | http://dspace.imech.ac.cn/handle/311007/79102 |
Collection | 国家微重力实验室 |
Recommended Citation GB/T 7714 | 何蒙. 微重力环状热毛细对流及不稳定性研究[D]. 北京. 中国科学院大学,2019. |
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