不可压流动的离散统一气体动理学方法及应用

发布时间：2018-03-12 12:06

本文选题：介观方法　切入点：不可压流动　出处：《华中科技大学》2016年博士论文　论文类型：学位论文

【摘要】：CO2埋存与驱油、清洁燃烧、可吸收颗粒物的排放和控制等诸多能源、化工、环境领域所涉及到的流动都属于不可压流动。因此对于不可压流动的研究在工程实际中有重要的意义。介观方法是目前研究不可压流动的一种有效方法,且理论和应用方面都已经取得了重大进展。然而,介观方法中还存在一些未解决的问题。Guo等人提出的离散统一动理学方法(DUGKS)从理论上可以克服目前介观方法中存在的问题,但是还缺乏相应的数值实验研究；此外,作为一种新型的介观方法,DUGKS在不可压流动中的表现依然缺乏系统性研究,且局限于不可压等温流动。本文正是基于这样的研究现状,开展了以下工作：首先,分析了DUGKS中通量构造时引入的数值误差和渐进保持性质,并从理论上对比了其与统一动理学格式(UGKS)和有限体积形式的LBE方法的异同。分析结果表明,界面分布函数构造时,粒子自由迁移和碰撞效应的耦合保证了DUGKS具有较小的数值耗散和良好的渐进保持性质；对比结果表明了其相对于目前类似介观方法的优势。其次,研究了DUGKS和标准LBE方法的异同,并通过数值实验从精度、数值稳定性和计算效率三个方面比较两种模型。研究结果表明,DUGKS和LBE两种方法的精度类似,但是前者的数值稳定性要远优于后者,且前者可以结合其模型的特点采用非均匀网格提高计算效率。再次,采用DUGKS对三维衰减均匀各项同性湍流直接数值模拟,研究了湍动能及其耗散率、湍动能及其耗散谱、Kolmogrov尺度长度、Taylor微尺度长度、速度梯度的平坦度和偏斜度等低阶和高阶统计量,并将其结果与LBE方法和拟谱方法的结果进行对比,验证了DUGKS研究湍流的可行性,为壁面湍流的研究奠定了基础。最后,提出了耦合离散统一动理学方法(CDUGKS)和相应的动理学边界条件,将DUGKS扩展到不可压非等温流动。验证发现,与以往类似的介观方法相比,所提出的模型具有更好的数值稳定性,且更容易采用非均匀网格。此外,我们还使用提出的模型,系统的研究了二维和三维方腔内层流和湍流自然对流问题(Ra=103—1010)。尤其是,我们首次系统研究了Ra高达1010的三维自然对流的流动特征和传热状态分布,并首次给出了三维自然对流中Rayleigh数(Ra)和Nusselt数(Nu)的指数依赖关系,且所给出的预测值与已有的数值和实验结果非常吻合。总之,本文对DUGKS的建模特点进行了细致的分析,研究了DUGKS在模拟不可压流动时的表现,并通过数值实验证明了DUGKS能够有效的克服目前介观方法中存在的稳定性和非均匀网格问题,拓宽了介观方法的应用范围：此外,本文还提出了耦合DUGKS模型,将DUGKS拓展到非等温不可压流动,并结合所提出模型的优势,系统的研究了高Rayleigh数二维和三维自然对流问题。本文的工作为以后的相关研究奠定了基础。
[Abstract]:CO2 can store and drive oil, clean combustion, absorb particulate emissions and control, and many other energy, chemical, The flow involved in the field of environment belongs to incompressible flow, so the study of incompressible flow is of great significance in engineering practice. Mesoscopic method is an effective method for studying incompressible flow at present. Great progress has been made in both theory and application. However, there are still some unsolved problems in mesoscopic methods. The discrete Unified Kinetic method (DUGKS) put forward by Guo et al can theoretically overcome the problems existing in mesoscopic methods. In addition, as a new mesoscopic method, the performance of DUGKS in incompressible flow is still lack of systematic study and confined to incompressible isothermal flow. The following works have been done: firstly, the numerical error and asymptotic preserving properties introduced in the flux construction of DUGKS are analyzed, and the similarities and differences between them with UGKS and the LBE method in finite volume form are compared theoretically. When the interface distribution function is constructed, the coupling of particle free migration and collision effect ensures that the DUGKS has small numerical dissipation and good asymptotic retention, and the comparison results show its advantages over the current similar mesoscopic methods. The similarities and differences between DUGKS and standard LBE methods are studied, and the two models are compared in terms of accuracy, numerical stability and computational efficiency through numerical experiments. The results show that the accuracy of the two methods is similar to that of LBE. However, the numerical stability of the former is much better than that of the latter, and the former can combine the characteristics of the model with non-uniform meshes to improve the computational efficiency. Thirdly, DUGKS is used to simulate the three-dimensional attenuation homogeneous turbulence directly. The turbulent kinetic energy and its dissipation rate, the turbulent kinetic energy and its dissipation spectrum are studied. The length of the Kolmogrov scale and the Taylor microscale length, the flatness and skewness of the velocity gradient are studied. The results are compared with those obtained by the LBE method and the pseudo-spectral method. The feasibility of DUGKS to study turbulence is verified, which lays a foundation for the study of wall turbulence. Finally, the coupled discrete unified kinetic method (CDUGKS) and the corresponding kinetic boundary conditions are proposed to extend DUGKS to incompressible non-isothermal flow. Compared with the previous mesoscopic methods, the proposed model has better numerical stability and is easier to use non-uniform mesoscopic grids. In addition, we also use the proposed model. The problems of laminar and turbulent natural convection in two and three dimensional square cavities have been studied systematically. In particular, the flow characteristics and heat transfer state distribution of Ra up to 1010 have been systematically studied for the first time. For the first time, the exponential dependence of Rayleigh numbers Raand Nusselt numbers in 3D natural convection is given, and the predicted values are in good agreement with the existing numerical and experimental results. In a word, the modeling characteristics of DUGKS are analyzed in detail. The performance of DUGKS in simulating incompressible flow is studied. Numerical experiments show that DUGKS can effectively overcome the stability and non-uniform mesh problems existing in mesoscopic methods and broaden the scope of application of mesoscopic methods. The coupled DUGKS model is also proposed in this paper, which extends DUGKS to non-isothermal incompressible flow and combines the advantages of the proposed model. The 2D and 3D natural convection problems with high Rayleigh number are studied systematically. The work of this paper lays a foundation for the related research in the future.
【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O357

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