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1、 基于格子 Boltzmann 方法模拟热毛细对流重庆大学博士学位论文学生姓名：谢海琼指导教师：曾 忠业：流体力学学科门类：工 学教 授专重庆大学航空航天学院二一五年九月 Simulation of the ThermocapillaryConvection with Lattice Boltzmann MethodA Thesis Submitted to Chongqing Universityin Partial Fulfillment of the Requirement for theDoctors Degree of EngineeringByHaiqiong XieSupervi
2、sed by Prof. Zeng ZhongSpecialty: Fluid MechanicsCollege of Aerospace Engineering ofChongqing University, Chongqing, ChinaSeptember 2015 中文摘要摘要气液界面（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
3、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
4、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
5、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
6、液滴并与之合并，同时液滴之I 重庆大学博士学位论文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。关键词：格子 Boltzmann 方法，两相流，热毛细对流，相场法，表面张力II 英文摘要ABSTRACTThe fluid dynamics problem involving gas-liquid or liquid-liquid in
7、terface iswidely observed in nature and industrial production. The fluid interface is a thintransition region, the interactive force between molecules behaves macroscopically asthe surface tension. In general, the surface tension depends on the interface temperatureor concentration. The temperature
8、gradient on the interface results in a gradient ofsurface tension along the fluid interface, and it drives melt convection, so-calledthermocapillary flow.Under microgravity or in micro-scale flow, the gravity and buoyancy effect isgreatly reduced, and the thermocapillary flow may become the dominate
9、d convection.In thermocapillary flow, the unbalanced surface tension not only drives the convection,but also affects the interface shape, and the coupling between thermocapillary flow andinterface deformation makes the numerical simulation to become a challenge incomputational fluid dynamics.Based o
10、n the Lattice Boltzmann Method (LBM), the numerical method forthermocapillary flow with considering dynamic interface deformation was developed.The two-phase flow was simulated with LBM, the dynamic interface deformation wascaptured with phase-field method. By using the developed method and code, th
11、ethermocapillary migration of drop, the drops coalescence, and thermocapillary flow inan annular cavity with two liquid layers were investigated numerically.The main works in this paper are summarized as follows:(1) Firstly, the LBM and the relation with the Navier-Stokes equation wereintroduced bri
12、efly, and the incompressible multi-relaxation-time LBM model waspresented. The classical flow problem was simulated by the LBM to valid the modeland code.(2) Based on the above LBM model, two kinds of coupling models for isothermaltwo-phase flow with dynamic interface deformation were developed. The
13、 flow fieldswere obtained from the LBM model, and the interface deformation was captured by thefront tracking technique and phase field method, respectively. The parallel programmingwith OpenMP was implemented for three-dimensional two-phase flow problems.(3) The energy equation was introduced to th
14、e LBM model, which is coupled withphase field method, to simulate thermocapillary flow. The LBM was applied to solveIII 重庆大学博士学位论文the flow field for incompressible binary fluids, and the model was implemented in anaxisymmetric form. Both phase field equation and the energy equation were solved witht
15、he finite difference method. The continuum surface force model was adopted tocompute the normal and tangential surface tension according the order parameter.(4) The thermocapillary migration of drop and the drops interaction weresimulated numerically. The effects of Marangoni number and Capillary numbers on thedrops coalescence were investigated. The results indicate that the drop coalescencebecomes more difficult with a larger Marangoni number. With increasing Capillarynumber, the deformation of the leading drop becomes more o
