Lattice-Boltzmann Simulations of Particle-Fluid Suspensions

This paper reviews applications of the lattice-Boltzmann method to simulations of particle-fluid suspensions. We first summarize the available simulation methods for colloidal suspensions together with some of the important applications of these methods, and then describe results from lattice-gas and lattice-Boltzmann simulations in more detail. The remainder of the paper is an update of previously published work,^{(69, 70)} taking into account recent research by ourselves and other groups. We describe a lattice-Boltzmann model that can take proper account of density fluctuations in the fluid, which may be important in describing the short-time dynamics of colloidal particles. We then derive macro-dynamical equations for a collision operator with separate shear and bulk viscosities, via the usual multi-time-scale expansion. A careful examination of the second-order equations shows that inclusion of an external force, such as a pressure gradient, requires terms that depend on the eigenvalues of the collision operator. Alternatively, the momentum density must be redefined to include a contribution from the external force. Next, we summarize recent innovations and give a few numerical examples to illustrate critical issues. Finally, we derive the equations for a lattice-Boltzmann model that includes transverse and longitudinal fluctuations in momentum. The model leads to a discrete version of the Green–Kubo relations for the shear and bulk viscosity, which agree with the viscosities obtained from the macro-dynamical analysis. We believe that inclusion of longitudinal fluctuations will improve the equipartition of energy in lattice-Boltzmann simulations of colloidal suspensions.     

Deformations of Dispersionless KdV Hierarchies

The obstructions to the existence of a hierarchy of hydrodynamic conservation laws are studied for a multicomponent dispersionless KdV system. It is proved that if the lowest order obstruction vanishes then all higher obstructions automatically vanish, if and only the underlying algebra is a Jordan algebra. Deformations of these multicomponent dispersionless KdV-type equations are also studied. It is shown that no new obstructions appear and, hence, that the existence of a fully deformed hierarchy depends only on the existence of a single purely hydrodynamic conservation law.     

Rigorous Derivation and Analysis of Coupling of Kinetic Equations and Their Hydrodynamic Limits for a Simplified Boltzmann Model

In this paper we derive rigorously the coupling of kinetic equations and their hydrodynamic limits for a simplified kinetic model. We prove the global convergence of the Chapman–Enskog expansion for this model. We then study the existence theory and asymptotic behaviour of the coupled systems. To solve the coupled problems we propose to use the transmission time marching algorithm. We then develop a convergence theory for the resulting algorithms.     

碳纤维增强铜基复合材料自润滑轴承的设计准则

根据均匀设计原理,对碳纤维增强铜基复合材料的磨损试验参数予以科学排列,不仅减少了试验次数,而且提高了试验数据统计结果的可靠性,同时,引入可靠性技术,建立了自润滑轴承在不同临界磨损率下材料的可靠度-压强-速度曲线及其计算方法,为碳纤维增强铜基复合材料自润滑轴承的设计提供依据。     

基于Poincare变换的滑动轴承非线性油膜力数据库方法

运用状态空间Poincare变换使径向滑动轴承动力系统的部分状态变量由无限区间变换到有限区间,在经过变换的状态空间中求解Reynolds方程,建立了径向滑动轴承非线性油膜力数据库及相应的插值拟合程序,实现了非线性油膜力的快速准确获得。通过滑动轴承,转子系统运动瞬态分析和Poincare映射方法验证了数据库及拟合程序的精度。     

SOME PROGRESS IN THE LATTICE BOLTZMANN MODEL

A lattice Boltzmann equation model has been developed by using the equilibrium distribution function of the Maxwell－Boltzmann-like form, which is third order in fluid velocity u_α. The criteria of energy conservation between the macroscopic physical quantities and the microscopic particles are introduced into the model, thus the thermal hydrodynamic equations containing the effect of buoyancy force can be recovered in terms of the Taylor and Chapman－Enskog asymptotic expansion methods. The two-dimensional thermal convection phenomena in a square cavity and between two concentric cylinders have been calculated by implementing a heat flux boundary condition. Both numerical results are in good agreement with the conventional numerical results.     

LATTICE BOLTZMANN EQUATION MODEL IN THE CORIOLIS FIELD

In a large-scale field of rotational fluid, various unintelligible and surprising dynamic phenomena are produced due to the effect of the Coriolis force. The lattice Boltzmann equation (LBE) model in the Coriolis field is developed based on previous works.^[1-4] Geophysical fluid dynamics equations are derived from the model. Numerical simulations have been made on an ideal atmospheric circulation of the Northern Hemisphere by using the model and they reproduce the Rossby wave motion well. Hence the applicability of the model is verified in both theory and experiment.     

Describing Hydrodynamic Particle Removal from Surfaces Using the Particle Reynolds Number

The fundamental processes related to the removal of fine particles from surfaces in a hydrodynamic flow field are not adequately understood. A critical particle Reynolds number approach is proposed to assess these mechanisms for fine particles when surface roughness is small compared to particle diameter. At and above the critical particle Reynolds number, particle removal occurs, while below the critical value, particles remain attached to a surface. The system under consideration consists of glass particles adhering to a glass surface in laminar channel flow. Our results indicate rolling is the removal mechanism, which is in agreement with the literature. Theoretical results of the critical particle Reynolds number model for rolling removal are in general agreement with experimental data when particle size distribution, particle and surface roughness, and system Hamaker constant are taken into account.     

Intelligent Fault Diagnosis of Rolling-Element Bearings Using a Self-Adaptive Hierarchical Multiscale Fuzzy Entropy

The fuzzy-entropy-based complexity metric approach has achieved fruitful results in bearing fault diagnosis. However, traditional hierarchical fuzzy entropy (HFE) and multiscale fuzzy entropy (MFE) only excavate bearing fault information on different levels or scales, but do not consider bearing fault information on both multiple layers and multiple scales at the same time, thus easily resulting in incomplete fault information extraction and low-rise identification accuracy. Besides, the key parameters of most existing entropy-based complexity metric methods are selected based on specialist experience, which indicates that they lack self-adaptation. To address these problems, this paper proposes a new intelligent bearing fault diagnosis method based on self-adaptive hierarchical multiscale fuzzy entropy. On the one hand, by integrating the merits of HFE and MFE, a novel complexity metric method, named hierarchical multiscale fuzzy entropy (HMFE), is presented to extract a multidimensional feature matrix of the original bearing vibration signal, where the important parameters of HMFE are automatically determined by using the bird swarm algorithm (BSA). On the other hand, a nonlinear feature matrix classifier with strong robustness, known as support matrix machine (SMM), is introduced for learning the discriminant fault information directly from the extracted multidimensional feature matrix and automatically identifying different bearing health conditions. Two experimental results on bearing fault diagnosis show that the proposed method can obtain average identification accuracies of 99.92% and 99.83%, respectively, which are higher those of several representative entropies reported by this paper. Moreover, in the two experiments, the standard deviations of identification accuracy of the proposed method were, respectively, 0.1687 and 0.2705, which are also greater than those of the comparison methods mentioned in this paper. The effectiveness and superiority of the proposed method are verified by the experimental results.