摘要
多相流系统是典型的非线性、非平衡、多尺度、复杂系统。基于非平衡统计物理的格子玻尔兹曼(lattice Boltzmann, LB)方法对该类系统的建模与模拟具有天然的自适应性。本论文从物理建模、数值算法和数据后处理三个方面发展LB方法并将其用于多相流系统的研究。主要研究内容为：(1)基于傅里叶变换(FFT)和逆变换构造了含温度场的可压FFT-TLB多相流模型。该模型能够有效抑制界面处的虚假速度,更好地保持系统总能量的数值守恒；(2)将FFT-TLB模型用于等温和非等温气液对称相分离的研究。为了实现复杂物理场信息的有效提取,将形态分析技术用于相变所形成的斑图的数据处理中,澄清了非等温相变的温度场效应；(3)利用FFT-TLB模型和形态分析技术定量研究了相分离过程中的热传导、粘性和Prandtl数效应；(4)构造了一个适用于可压流体系统的D2V19-LB模型,该模型在连续极限下给出与Euler方程一致的结果,利用该模型研究了可压开尔文-赫姆霍兹不稳定性,着重研究了速度和密度梯度效应；(5)在D2V65-LB模型的基础上,通过修改LB方程中的BGK碰撞项构造了适用于任意比热比、任意Prandtl数可压流体系统的通量限制LB模型。上述工作推进了多相流和可压流体系统介观模拟方法的发展,获得一系列新的规律和认识,为相关的工程应用提供物理支持。
Multiphase flows are typical nonlinear, nonequilibrium, multiscale complex systems. The lattice Boltzmann method (LBM), based on nonequilibrium statistical physics, is particularly suitable for modeling and simulating such systems. This paper aims to develop LBM from the following three aspects:physical modeling, numerical scheme and data analysis method, and applies it to investigate behaviors of multiphase flows. The main contents are as below:(i) Based on the fast Fourier transform (FFT) and its inverse, we propose the FFT-TLB model for compressible thermal multiphase flows. With this new model, artificial velocities near interfaces decrease to negligible scale and the numerical total energy is better conserved;(ii) Investigate thermal and isothermal symmetric liquid-vapor separations via the FFT-TLB model. To effectively characterize and pick up information from such a complex system. Minkowski functionals are employed to characterize the density fields, as well as to understand the configurations and the kinetic processes;(iii) Via the FFT-TLB model, we study the effects of heat conduction, viscosity and Prandtl number on thermal liquid-vapor separation quantitatively:(iv) Propose a D2V19-LB model for compressible fluids. Via this model, we investigate the Kelvin-Helmholtz instability, specially examine the velocity and density gradient effects;(v) Based on the original D2V65-LB model, by modifying the BGK collision operator, we propose a flux-limiter-LB model for compressible flows with flexible specific-heat ratio and Prandtl number. The above-mentioned works help to extend the LBM to study multiphase and compressible flows, and provide physical supports for related engineering applications.
引文
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