基于格子Boltzmann方法模拟热毛细对流

发布时间：2018-03-03 15:43

本文选题：格子Boltzmann方法　切入点：两相流　出处：《重庆大学》2015年博士论文　论文类型：学位论文

【摘要】：气液界面(自由液面)或者液液界面的流体力学问题广泛存在于自然界与工业生产实践中。流体的界面是一个相到另一个相之间很薄的过渡区域,分子间的相互作用力在这个过渡区域宏观上表现为表面张力,其大小一般是温度和浓度的函数。其中,流体界面上的非均匀温度引起的切向表面张力梯度会驱动流体流动,这种流动称为热毛细对流。在微重力或微尺度条件下,重力和浮力对流体流动的影响极度地减弱,热毛细流可能成为主要的对流。在热毛细对流问题中,温度梯度引起的非均匀表面张力即驱动流体流动又影响界面形状,这两者的动态耦合使热毛细对流的数值模拟成为计算流体动力学长期以来的一个重要挑战。基于格子Boltzmann方法(Lattice Boltzmann Method:LBM),本文发展了考虑界面动态变形的热毛细对流问题的计算方法,其中两种不相溶的流体流动采用多松弛不可压缩LBM方法模拟,界面的动态变形则采用相场法进行捕捉。通过自主开发的程序包,本文数值模拟研究了双液滴热毛细迁移与合并,以及双层环形液池内热毛细对流和界面变形耦合过程。本文的主要工作与贡献如下:(1)首先简要地介绍了LBM方法,推导了格子Boltzmann方程恢复到宏观Navier-Stokes方程的过程,并建立了不可压缩多松弛LBM模型。随后,对经典流动问题进行数值模拟,验证了多松弛不可压缩LBM基础模型及其程序的正确性。(2)基于上述LBM基础模型,建立了两种不同的耦合模型用于模拟考虑界面动态变形的等温两相流问题,两种模型中均采用LBM方法求解两相流流场,而界面运动则分别通过Front Tracking方法和相场法捕捉。最后基于OpenMP并行技术对自主开发的三维问题程序包实现并行计算。(3)在LBM耦合相场法模型中进一步引入能量方程研究热毛细对流问题。建立了轴对称坐标系下的LBM模型,两相流流场采用LBM进行模拟,相场方程和能量方程则采用有限差分法求解。在模型中根据相场方程得到的指示函数,通过引入界面力模型(Continuum Surface Force:CSF)实现法向和切向表面张力的计算。(4)系统地研究了双液滴的热毛细迁移及合并过程。首次通过数值模拟揭示了Marangoni数和Capillary数对两液滴合并过程的影响。研究表明在随Marangoni数增大,尾随液滴更难追上前导液滴并与之合并。此外,随Capillary数增大前导液滴的变形更明显,同样尾随液滴亦更难追上前导液滴并与之合并,同时液滴之间合并的持续时间也随Capillary数增大而增加。(5)系统地研究了多种因素对双层环形液池内热毛细对流和界面变形的影响。结果表明上层流体具有较大的密度或者粘性时,下层流体的流动强度被明显削弱,但液液界面的变形程度也随之增加。不同Capillary数对流动强度的影响较小但对界面变形的影响却非常明显。
[Abstract]:The hydrodynamic problems of the gas-liquid interface (free liquid level) or liquid-liquid interface are widespread in nature and industrial production practice. The interface of the fluid is a thin transition region from one phase to the other. The intermolecular interaction in this transition region is characterized by surface tension, which is generally a function of temperature and concentration, in which the gradient of tangential surface tension caused by the inhomogeneous temperature at the interface of the fluid drives the fluid flow. This flow is called thermocapillary convection. Under microgravity or microscale conditions, the effect of gravity and buoyancy on fluid flow is extremely attenuated, and the hot capillary convection may become the main convection. In the case of thermocapillary convection, The inhomogeneous surface tension caused by temperature gradient not only drives the fluid flow but also affects the interface shape. The dynamic coupling of the two makes the numerical simulation of thermocapillary convection an important challenge in computational fluid dynamics for a long time. Based on lattice Boltzmann method: LBMM, a method for calculating thermocapillary convection considering the dynamic deformation of interface is developed in this paper. Two kinds of insoluble fluid flow are simulated by multi-relaxation incompressible LBM method, and the dynamic deformation of interface is captured by phase field method. The main work and contribution of this paper are as follows: firstly, the LBM method is briefly introduced, and the process of restoring the lattice Boltzmann equation to the macroscopic Navier-Stokes equation is derived. The incompressible multi-relaxation LBM model is established. Then, the numerical simulation of the classical flow problem is carried out to verify the correctness of the multi-relaxation incompressible LBM basic model and its program. Two different coupling models are established to simulate the isothermal two-phase flow problem considering the dynamic deformation of the interface. In both models, the LBM method is used to solve the two-phase flow field. The interface motion is captured by the Front Tracking method and the phase field method respectively. Finally, the parallel computation of the self-developed 3D problem package based on OpenMP parallel technology is realized. 3) the energy equation research is further introduced into the LBM coupled phase field method model. In this paper, the LBM model in axisymmetric coordinate system is established for the problem of thermal capillary convection. The two-phase flow field is simulated by LBM, and the phase field equation and energy equation are solved by finite difference method. The calculation of normal and tangential surface tension by introducing the interfacial force model (Continuum Surface Force: CSF) is used to systematically study the migration and merging process of two droplets. For the first time, the combination of Marangoni number and Capillary number on two droplets is revealed by numerical simulation. Study shows that with the increase of Marangoni number, The trailing droplets are more difficult to track and merge with the lead droplets. In addition, the deformation of the lead droplets is more obvious with the increase of the Capillary number, and it is also more difficult for the trailing droplets to track and merge with the trailing droplets. At the same time, the duration of coalescence between droplets also increases with the increase of Capillary number.) the effects of various factors on the convection and interface deformation in a double-layer annular liquid tank are systematically studied. The results show that the upper layer fluid has a higher density or viscosity. The flow strength of the lower layer fluid is obviously weakened, but the deformation degree of the liquid-liquid interface is also increased. The influence of different Capillary numbers on the flow strength is relatively small, but the effect on the interface deformation is very obvious.
【学位授予单位】：重庆大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O359

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