【作者】 荣伏梅；

【导师】 施保昌； 郭照立；

【作者基本信息】 华中科技大学 ， 热能工程， 2011， 博士

【摘要】 多孔介质内的流动和传热是自然界中十分常见的一种现象,其应用涉及化学工程,石油开采,农田水利工程,生物组织内液体的复杂流动等等。控制流体’流动状态和强化传热是流动和传热领域内非常关键的两类问题。有研究表明,利用多孔介质可以达到减阻及强化传热的目的,但是对如何有效利用多孔介质及其物理机理并没有系统的研究。随着计算机技术的迅猛发展,数值模拟法因成本低、试验周期短、参数选择具有可控性和灵活性等优点日益受到人们的重视。目前多孔介质流动和传热问题的数值模拟研究主要分为表征体元(REV)尺度和孔隙尺度两类。孔隙尺度上的研究需要知道复杂的介质边界,计算量巨大,难以应用于实际,因此工程计算多采用REV尺度。鉴于此,本文的工作主要是基于REV尺度进行的。作为一种新兴的数值研究方法,格子Boltzmann方法(Lattice Boltzmann Method,LBM)由于其具有许多独特的优势已被证实非常适合于用来处理多孔介质内的流动和传热问题。但是,如同其他数值方法一样,LBM的理论也存在一些不足,现有的LB模型一般针对性都很强,比较适合于一些特定的物理问题。比如,针对工程中常见的多孔介质圆管内传热问题,并没有完善的LB模型来进行有效模拟。正是基于这一考虑,本文构造了一类REV尺度轴对称热LB模型,在此基础上,利用本文发展的模型对圆管内强化传热进行了研究,并对如何利用多孔介质对流动进行控制等前沿问题也进行了初步的探索。本文的工作主要包括以下几点：首先,在格子Boltzmann方法的相关理论方面：(1)提出了一类适合于多孔介质的弱可压轴对称热LB模型,该模型形式简单,不含复杂外力梯度项,计算稳定。解决了现有模型的局限性,完善了LBM在轴对称领域的理论。(2)进一步提出了一类适合于多孔介质的不可压轴对称LB模型。该模型可以有效克服压差较大所产生的问题,采用外力部分矫正的方法可以避免压力和速度的耦合求解,使得计算更加简单。这些理论的完善和发展为推动LBM在多孔介质圆管内传热的应用奠定了必要的基础。其次,在非线性渗流的数值研究方面：(1)研究了覆盖多孔介质的方柱绕流问题,分析了多孔介质厚度等重要参数对流场变化的影响,发现了这些参数中Darcy(Da)数的影响最为明显,找到了阻力系数(Cd)和升力系数(Cl)存在最大值的Da数变化范围,为利用多孔介质降低绕流柱体表面阻力提供了一定的理论依据。(2)研究了充满多孔介质的变粘性Rayleigh-Benard对流问题,分析了Prandtl (Pr)数、粘性随温度变化时流场和温度场呈现出的不同变化规律。数值结果表明粘性随温度变化对传热所产生的影响不容忽略；进一步提出了一个等价的Rayleigh (Ra)数关系式,可以将考虑粘性变化和不考虑粘性变化两种情况得到的结果统一起来,避免重新计算。这些结果对实际中的工程问题具有理论指导意义。(3)为了研究圆管内插入多孔介质对强化传热的影响,前面发展的轴对称热LB模型刚好为模拟这类问题提供了很好的计算方法。由于在模拟这类问题时一般计算量都很大,单个CPU计算效率很低,本文采用了具有超强数据处理能力并支持复杂计算的先进计算设备GPU(图形处理器)。研究结果表明：圆管内插入多孔介质在强化传热的同时也增加了流动阻力。在工程实际中,需要平衡这两者之间的关系,以到达最优的换热效果。总之,本文利用格子Boltzmann方法研究了REV尺度多孔介质内的流动和传热问题,为推动该方法在渗流领域中的应用作出了许多有益的尝试。针对多孔介质圆管内的轴对称流动分别提出了两类新的模型。此外,还对格子Boltzmann方法进行了大量的数值实验,发现了一些新现象,并分析了这些现象背后的物理机制,得到了一些有意义的结论。这些工作为后续研究的开展奠定了必要的基础。更多还原

【Abstract】 The flow and heat transfer in porous media is a common natural phenomenon, application of which is related to many domains such as chemical engineering, oil ex-ploitation, irrigation and water conservation project and so on. The fluid flow control and heat transfer enhancement are two key questions in the field of flow and heat trans-fer. It is well documented that the porous media can be used in fluid flow control and heat transfer strengthen. However, few systematic research has been carried out on its physical mechanism. With the rapid development of the computer technology, the advantages of numerical simulation become more prominent and receive increasing at-tentions. The numerical study on the fluid flow and heat transfer in porous media can be classified into two classes:the pore scale type and the REV (Representative Elementary Volume) scale one. The main works of this thesis are based on REV scale simulation.As a new numerical method, LBM (Lattice Boltzmann Method) is very suitable for studying flow and heat transfer in porous media. However, the exiting models still have some insufficiencies and the improvement are still needed. For example, no axisymmetric LBE mode for flow and heat transfer in porous media can be found. The aim of this thesis is to develop some new LB models for flow and heat transfer in porous media, and then applied them to study the flow control and heat transfer in porous media.Theory of the LB models:(1) This paper presents a kind of of axisymmetric thermal LBE model for flows through porous media. The model is similar to the standard LBE model and has a simple structure. Another advantage of the present model is that the simple force term in evolution equations makes the computation more effective and stable.(2) This paper presents a kind of axisymmetric LBE model for incompressible flows through porous media. In the model, distribution function is constructed based on the pressure instead of the fluid density, so that the compressibility is reduced ef-fectively. A improved method is proposed to deal with the external forces, which can overcome the difficulty of calculate the the fluid velocity and pressure. Applications of the models to flow in porous media:(1) The flow around a porous covering square cylinder in a channel has been stud-ied. The effects of several parameters on flow field are discussed. The numerical results show that the influence of porosity on the flow field, drag and lift coefficient is neglectable, whereas the effect of Darcy(Da) number is dominant.(2) Rayleigh-Benard convection with temperature-dependent viscosity in a porous cavity has been studied. The effects of several parameters on flow and heat transfer are studied, the results show that the influence of viscosity is very important. A new reference temperature based on linear fitting function is proposed, which is proved to be more efficient in the average Nusselt numbers computations.(3)The effect of heat transfer in a pipe partially filled with porous media is inves-tigated using our proposed axisymmetric thermal LBE model for flows through porous media. A Graphic Processing Unit(GPU) is applied to overcome the poor computa-tional efficiency of CPU. The numerical results show that filling porous media in the center of pipe can enhance the heat transfer while increase flow resistance. A balance between heat transfer and flow resistance reduction should be emphasized in practice.In conclusion, the fluid flow and heat transfer in porous media at REV scale is investigated via LBM, and many valuable efforts are made. Two kinds of lattice Boltzmann models are proposed to solve the axisymmetric flow in porous media. In addition, a large number of numerical simulations are conducted to study flow and heat transfer in porous media and a series of significative conclusions are gained through the analyses. These works can be viewed as a necessary basis for future studies.更多还原