基于化学势的多相流晶格Boltzmann方法的研究

发布时间：2019-03-14 09:29

【摘要】：自然界普遍存在的多相流现象在工农业生产、科学研究和日常生活中具有广泛的应用,它的相间涉及表面现象、热力学与流体力学的平衡问题,存在传热、传质和化学反应等复杂的物理化学过程,这些效应使得多相流问题的研究变得极为复杂,也正因此,关于多相流现象的研究一直是流体力学领域的热点。计算流体动力学(Computational Fluid Dynamics,CFD)是人们在借助数值与离散的方研究流体运动的长期实践中不断发展形成的一门学科,它在研究包括多相流在内的复杂流体运动方面取得了巨大的成功。然而,由于多相流常常呈现十分复杂的几何界面,且伴随着剧烈的界面拓扑形变(如液滴的聚合与分裂等),传统的CFD方法对多相流的进一步研究将遭遇瓶颈,即复杂几何边界下的Navier-Stokes方程不易求解,对发生剧烈拓扑形变的界面追踪也非常困难。晶格Boltzmann方法(Lattice Boltzmann method,LBM)以分子动力学为基础,是连续Boltzmann方程的一种特殊离散格式,属于新兴的介观方法,兼有连续理论和微观方法的优势,在研究复杂流体运动方面取得了显著成功,尤其是在多相流研究方面具有突出的表现,已经得到了人们的高度认同。与传统的CFD方法相比至少具有如下优势:1.算法简单,无需直接求解复杂的Navier-Stokes方程而仅需求解简单的晶格Boltzmann方程;2.易于处理复杂的几何边界条件,也无需显式地追踪界面,界面的变化自然地蕴含于简单的演化过程;3.LBM的演化具有局域性,非常适合于高性能并行计算等。经过近30年的发展和完善,LBM已经成为了一种新的、不可替代的计算流体动力学方法,在研究多相流方面占据了重要地位,成为了主流的研究方法之一。迄今为止,已经得到人们共同认可、并得到广泛流行与成功应用的LBM多相流模型主要有伪势模型和自由能模型,然而,这两个模型及其后续的改进均不能同时满足伽利略不变性和热力学一致性——伪势模型不具有热力学一致性,而自由能模型则不能满足伽利略不变性。不具有热力学一致性的模型将难以准确地刻画系统的热力学行为,而不满足伽利略不变性的模型则无法精确地描述运动系统的特性。本人参加的课题小组围绕这一问题深入分析了这两个模型的原理,在借助自由能和压力张量计算非理想力的基础上,提出了一种基于压力张量的晶格Boltzmann多相流模型(简称:压力张量模型,EPL,112(2015)44002),并从理论和数值实验的角度验证了新模型既具有热力学一致性又满足伽利略不变性,其算法简单易于实现,且模拟一级相变所得的两相共存曲线与理论吻合更好,有望获得进一步地推广和应用。尽管压力张量模型无论在理论上,还是数值上都有明显优势,也有很好的推广应用前景,然而,本文在深入地研究中发现该模型尚有进一步改进与提升的空间。首先通过压力张量或许并非最佳、更非唯一计算非理想力的有效途径,系统的自由能、化学势和熵等均是能很好描述系统热力学行为的宏观量,尤其是化学势在描述相平衡和化学平衡时具有独特的优势;另一方面,受限多相流系统的流固润湿边界条件采用压力张量难以直接表述,采用有效密度表达也具有一定复杂性,采用化学势描述润湿中固相与液相的相互作用可能更方便。于是,本文从化学势入手对原压力张量模型进行了探索与改进,通过推导获得的基于化学势的非理想力计算公式,构建了基于化学势的晶格Boltzmann多相流模型(简称:化学势模型),同样由化学势出发,发展了一套基于化学势的流固润湿边界条件(简称:化学势润湿边界条件)。经理论和数值实验检验,本文提出的新模型与润湿边界条件主要具有如下优势与特色:1.由于是对原压力张量模型的改进与完善,化学势模型仍然既具有热力学一致性同时又满足伽利略不变性,且化学势模型与润湿边界条件通过化学势在理论上达到了统一与自洽,在数值计算上达到了相互协调与共享。2.化学势模型与润湿边界条件较之压力张量模型算法更简洁,通过典型的van der waals流体一级相变模拟实验表明:新的化学势模型在计算精度、计算效率和稳定性上均有不同程度地提升,充分说明其在数值方面也具有系统的、全面的优势。3.几种常用非理想流体(包括:van der waals,Peng-Robinson,Redlich-Kwong Soave和Carnahan-Starling流体)一级相变和具有不同速度的van der Waals液滴变形模拟表明,化学势模型数值上能很好地描述非理想流体的两相共存现象,也准确地满足伽利略不变性。4.初步应用于固壁表面van der Waals液滴润湿现象的实例充分说明,化学势模型与润湿边界条件的实现与应用方便、可行。数值实验中发现润湿接触角随指定的固壁表面化学势变化几乎是线性的,使得实际应用中通过调整表面化学势以获得所需要的接触角变得十分简单,因此化学势模型与润湿边界条件应用于表面润湿现象的研究具有足够的优势。5.由于化学势是描述热力学系统的一个重要而又普适的宏观量,因此化学势模型及润湿边界条件能够直接推广应用于具有电磁场环境或存在化学反应的多相流系统的研究。以上优势与特色展现了化学势模型与润湿边界条件具有较坚实的理论基础和出色的数值性能,有望在多相流领域中得到普遍地推广与应用。
[Abstract]:The phenomenon of multi-phase flow in nature has a wide application in industrial and agricultural production, scientific research and daily life, and its phases involve surface phenomena, thermodynamic and fluid mechanics balance problems, and there are complex physical and chemical processes such as heat transfer, mass transfer and chemical reaction. These effects make the study of the multi-phase flow problem very complex, and therefore, the research on the multi-phase flow phenomenon has been a hot spot in the field of fluid mechanics. Computational Fluid Dynamics (CFD) is a subject of constant development in the long-term practice of fluid movement by means of numerical and discrete research, which has made great success in the study of complex fluid movement, including multi-phase flow. However, because the multi-phase flow often presents a very complex geometric interface, and with the severe interface topology deformation (such as the polymerization and splitting of the droplets, etc.), the conventional CFD method will encounter the bottleneck of the further study of the multi-phase flow, that is, the Navier-Stokes equations under the complex geometric boundary are not easy to solve, It is also very difficult to trace the interface with violent topological deformation. Lattice Boltzmann method (LBM), based on the molecular dynamics, is a special discrete form of the continuous Boltzmann equation, and belongs to the new mesoscopic method. In particular, it has outstanding performance in the research of multi-phase flow, and has been highly accepted by people. Compared with the traditional CFD method, at least the following advantages are:1. The algorithm is simple, and the complex Navier-Stokes equations need not be solved directly, but only a simple lattice Boltzmann equation is needed. It is easy to handle complex geometric boundary conditions, and does not need to track the interface explicitly, and the change of the interface is naturally contained in the simple evolution process;3. The evolution of the LBM is local, and is very suitable for high-performance parallel computing and the like. After nearly 30 years of development and improvement, the LBM has become a new and irreplaceable computational fluid dynamic method, which has taken an important position in the research of multi-phase flow and has become one of the main research methods. So far, the LBM multi-phase flow model, which has been widely accepted and widely popular and successfully applied, has a pseudo-potential model and a free-energy model, however, The two models and their subsequent improvements can not meet the Galileo invariance and the thermodynamic consistency. The pseudo-potential model does not have the thermodynamic consistency, and the free energy model can not satisfy the Galileo invariance. The model that does not have the thermodynamic consistency will not be able to accurately describe the thermodynamic behavior of the system, and the model that does not meet the Galileo invariance can not accurately describe the characteristics of the moving system. On the basis of calculating the non-ideal force with the aid of the free energy and the pressure tensor, a lattice Boltzmann multi-phase flow model based on the pressure tensor is proposed, which is called the pressure tensor model, EPL,112 (2015)44002). From the theoretical and numerical experiments, the new model is proved to have both thermodynamic consistency and Galileo invariance. The algorithm is simple and easy to realize, and the two-phase co-existence curve obtained by the simulation of one-stage phase change is better with the theory, and is expected to be further promoted and applied. Although the pressure tensor model has obvious advantages in both the theory and the numerical value, it has a good application prospect. However, this paper has found that the model has further improved and improved space in the in-depth study. First, through the pressure tensor may not be the best, more than the only effective way to calculate the non-ideal force, the free energy, chemical potential and entropy of the system can describe the macroscopic quantity of the thermodynamic behavior of the system, especially the chemical potential has a unique advantage when describing the phase equilibrium and the chemical balance; On the other hand, the fluid-solid wetting boundary condition of the constrained multi-phase flow system is difficult to express directly by the pressure tensor, and the effective density expression also has a certain complexity, and the chemical potential is used to describe the interaction between the solid phase and the liquid phase in the wetting. In this paper, the original pressure tensor model is explored and improved from the chemical potential, and a chemical potential-based lattice Boltzmann multi-phase flow model (the chemical potential model) is constructed by the derivation of a chemical potential-based non-ideal force calculation formula, which is also based on the chemical potential. A set of flow-solid wetting boundary conditions based on chemical potential is developed (for short, chemical potential wetting boundary conditions). Based on the theoretical and numerical experiments, the new model and the wetting boundary condition have the following advantages and characteristics:1. because of the improvement and perfection of the original pressure tensor model, the chemical potential model still has both the thermodynamic consistency and the Galileo invariance, and the chemical potential model and the wetting boundary condition are in a unified and self-consistent theory through the chemical potential, In that numerical calculation, the mutual coordination and share are achieved. The chemical potential model and the wetting boundary condition are more concise than the pressure tensor model algorithm, and through a typical van der waals fluid-level phase change simulation experiment, the new chemical potential model has different degrees of improvement in the calculation accuracy, the calculation efficiency and the stability, It fully shows that it also has a systematic and comprehensive advantage in the field of numerical value. Several commonly used non-ideal fluids (including van der waals, Peng-Robinson, Redlich-Kwang Soave and Carnahan-Starling fluid) and van der Waals droplet deformation simulation with different speeds show that the chemical potential model can well describe the two-phase co-existence of the non-ideal fluid, Galileo invariance is also exactly satisfied. The examples of the wetting phenomenon of the van der Waals droplet on the surface of the solid wall show that the realization and application of the chemical potential model and the wetting boundary condition are convenient and feasible. in that numerical experiment, it is found that the wetting contact angle is almost linear with the change of the chemical potential of the specified solid wall surface, so that the required contact angle is very simple by adjusting the surface chemical potential in the practical application, Therefore, the application of the chemical potential model and the wetting boundary condition to the surface wetting phenomenon has a sufficient advantage. Since the chemical potential is an important and universal macroscopic quantity for describing the thermodynamic system, the chemical potential model and the wetting boundary condition can be directly applied to the research of a multi-phase flow system with an electromagnetic field environment or a chemical reaction. The above advantages and characteristics show that the chemical potential model and the wetting boundary condition have a solid theoretical foundation and excellent numerical performance, and are expected to be widely promoted and applied in the field of multi-phase flow.
【学位授予单位】：广西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O641

【相似文献】