CFD-DEM方法分析颗粒流体系统的非平衡特性

颗粒流体系统在自然界中是一种普遍的现象，并且在工业中具有重要的应用。尽管对颗粒流体系统研究了很多年，但是我们对于颗粒流体系统复杂性的认识还不够全面。近些年来，计算流体力学方法被广泛应用于研究颗粒流体系统的物理特性。目前已经建立了双流体模型、颗粒轨道模型、直接数值模拟等方法。 双流体模型在工业规模的模拟中具有较为广泛的应用。它将气相和固相看作是可以相互渗透的连续相，通过平均化的连续微元得到质量、动量、能量守恒方程并且固相应力的本构关系通常由颗粒动理论来封闭。从热力学的角度来看，Navier-Stokes 阶的连续介质模型是建立在局域热力学平衡假设的基础上，如果局域系统状态远离平衡态，那么局域热力学平衡假设就不成立，或者说NS阶的连续介质模型不成立。 颗粒轨道模型仅对气相做连续模型假设处理，对颗粒通过牛顿第二定律分别追踪其运动轨迹，这个模型只需要相间耦合作用力来封闭方程，如果不考虑曳力模型的选择对模拟结果的影响，那么可以通过颗粒轨道模型来研究两相流中颗粒相连续化处理的可行性。为了探讨NS 阶的连续介质模型或局域热力学平衡假设成立的条件，本论文的主要工作是通过颗粒轨道模型计算熵判据、努森数和分析颗粒速度分布函数来量化非均匀气固两相流中的非平衡特性。 因此本论文第一章简要介绍双流体模型，并系统归纳了判断局域非平衡假设的参数包括努森数和熵判据的研究进展。论文第二章简要介绍颗粒轨道模型并应用颗粒轨道模型统计出颗粒流体系统中每个位置的熵判据努森数等判断参数的数值，探讨了A、B、D类颗粒在鼓泡、湍动和循环流态化下熵判据和努森数的数值分布进而系统地分析局域平衡假设成立的判断依据。得到的结论如下：（i）不论哪种判据准则，局域平衡假设在鼓泡流态化中基本成立，除了气泡中心颗粒浓度很低的情况下局域平衡假设失效。（ii）对于湍动和循环流态化，局域平衡假设成立取决于使用的判断标准。熵判据描述了颗粒速度梯度、颗粒温度梯度和颗粒非弹性碰撞在流动过程中的非平衡特性，通过对熵判据的量化，我们发现由熵判据判断的局域平衡假设适用于所有测试的颗粒流体系统，说明颗粒相的连续化假设并不是导致连续模型失效的主要原因。 根据动理论可知，系统在平衡状态下颗粒的速度分布满足麦克斯韦分布，而在局域平衡假设下通过Chapman-Enskog方法引入小扰动函数后得到修正后的麦克斯韦分布可以用来描述这种状态下的颗粒速度分布，通常情况下系统处在非平衡态，颗粒速度分布函数呈现出具有“长拖尾”特征或者双峰分布的非麦克斯韦分布，因此论文第三章探讨颗粒速度分布函数在气固两相流中的形式，通过麦克斯韦分布、指数分布、t-分布和双峰分布这几种函数形式回归DEM模拟得到的颗粒分布，我们发现在水平方向上颗粒速度分布满足指数分布或t-分布，而在气流方向基于EMMS思想的双峰分布相对而言更贴近模拟得到的颗粒速度分布。第四章是本论文的总结和概括，总结了本论文的主要结论和创新点并对研究方向提出了展望。;Granular fluid systems are common in nature and have important applications in industry. Although granular fluid systems have been studied for many years, the understanding of its complexity is not much comprehensive. In recent years, computational fluid dynamics has been widely used to study the hydrodynamics of granular fluid systems. Two-fluid model, discrete particle method and direct numerical simulation are the most popular methods. Two-fluid model has a more extensive application especially in the industrial-scale simulation. It treats the gas phase and the solid phase as continuous phases and these two phases can be mixed with each other. The mass, momentum and energy conservation equations are obtained via proper averaging. The constitutive relation of the solid-phase stress is usually closed by kinetic theory. From the thermodynamic point of view, the continuum model under Navier-Stokes order is based on the assumption of local thermodynamic equilibrium(LTE). If the state of the system is far from the equilibrium, the local thermodynamic equilibrium hypothesis does not valid, that is to say, the NS order continuum model does not valid anymore. Discrete particle model (DPM) only treats the gas phase as a continuous flow. The motion of the particles is tracked by Newton's second law. The model only needs the interphase coupling force to close the governing equation. Under the same drag model, the feasibility of the continuous assumption of solid phase in two-flow model can be studied by discrete particle model. In order to find out under what conditions the NS order continuum model or the local thermodynamic equilibrium hypothesis is valid, the main work of this thesis is to quantify the non-equilibrium gas-solid flow by using discrete particle model. The first chapter of this thesis introduces the TFM model and reviews the state-of-the-art in using the Knudsen numbers and the entropy criterion to judge the local non-equilibrium hypothesis. In the second chapter, the discrete particle model is elaborated to calculate the entropy criterion and the Knudsen numbers in the bubbling, turbulent and circulating fluidization of Geldart A, B and D particles. The conclusions obtained are as follows: (i) The local equilibrium hypothesis is valid in most region under bubbling fluidization no matter which criterion is chose while the local equilibrium hypothesis fails with low solid concentrations in bubble center. (ii) For turbulent and circulate fluidization, the validity of the local equilibrium hypothesis depends on the criteria used. The entropy criterion describes the non-equilibrium characteristics with particle velocity gradient, particle temperature gradient and particle inelastic collision. By quantifying the entropy criterion, we find that the local equilibrium hypothesis applies to all tested particle-fluid system, so the assumption of continuous process for solid phase is not the major reason for the inaccuracy of continuum model. According to the kinetic theory, the particle velocity distribution in the equilibrium state can be described as the Maxwellian distribution. However, when the system is in the non-equilibrium state which is far from the thermodynamic equilibrium, the particle velocity distribution exhibits a non-Maxwellian with an overpopulated high-energy tail or the bimodal distribution. Therefore, the third chapter discusses the form of the particle velocity distribution function (PVDF) in the gas-solid flow. The statistic results of PVDF calculated by DPM is regressed by the functions of Maxwell distribution, exponential distribution, t-distribution and bimodal distribution. It is found that the exponential or t-distribution fits the numerical results well in the horizontal direction, while the bimodal distribution based on EMMS is much closer to the statistic results in the gas-flow direction. The forth chapter summarizes the main conclusions and innovations of this thesis, and puts forward the prospect of this research.