SUMMARYA three‐dimensional Cartesion cut cell method is presented for the simulations of incompressible viscous flows with irregular domains. A new model (referred to as ‘6+N’ model) is proposed to describe arbitrarily shaped cut cells and treat all the cells as polyhedrons with 6+N faces. The finite volume discretization of the Navier–Stokes equation is then implemented by using the ‘6+N’ model to separate the surface flux integrals into two parts, that is, the fluxes through the basic face of the hexahedron and those through the cutting surfaces. The previously proposed Kitta Cube algorithm and volume computer‐aided design platform (J. Comput. Aided. Des. 2005; 37(4): 1509–1520. Doi:10.1016/j.cad.2005.03.006) are adopted to generate cut cells and provide shape data and physical attributes for the numerical analysis. A modified SIMPLE‐based smoothing pressure correction scheme is applied to suppress checkerboard pressure oscillations caused by the collocated arrangement of velocities and pressure. The calculation accuracy of the numerical method expressed by L1 and L ∞ norm errors is first demonstrated by the simulation of a pipe flow. Then its feasibility, efficiency, and potential in engineering applications are verified by applying it to solve natural convections between concentric spheres and between eccentric spheres. The heat transfer patterns in eccentric spheres are also obtained by using the numerical method. Copyright © 2011 John Wiley & Sons, Ltd.

A physical model of the electric field induced by charged droplets taking account of the effect of space charged droplet emitted from the tip of cone–jet to the external electric field is proposed. Combining this model with the fluid flow equations and charge conservation equation, the evolution of the cone–jet is simulated. The diameter of droplets emitted from the cone–jet tip and current on cone–jet are predicted at various applied voltages and flow rates. The calculated droplet diameter agrees well with experimental measurement. For low conductivity liquid, the droplet diameter decreases with the increment of applied voltage, but decreases with the reduction of flow rate. The simulation result also indicates that the current on the cone–jet increases linearly with the applied voltage. The electric field induced by charged droplets results in the decrease of the cone angle and the presence of space charged droplets has a non-negligible effect on the operation parameters.

A Cartesian cut cell solver with solution‐based adaptive mesh refinement is developed for simulating viscous, incompressible flows with arbitrary complex geometries. The cut cells are automatically generated using Volume CAD (VCAD), a framework for storing geometric and material attribute data. Unlike earlier cut cell methods, this solver organizes the cutting patterns into only six categories and further subdivides the resulting pentagon into two quadrilaterals, such that mesh data can be stored by uniform data structure and the post‐processing of flow data can be handled conveniently. A novel method is proposed to treat minuscule cut cells without the process of cell merging. A collocated finite volume method, which can be used even when multiple cell shapes and orthogonal and non‐orthogonal grids exist in the decomposition, is employed to discretize the Navier–Stokes equations. A modified SIMPLE‐based smoothing pressure correction scheme is applied in this cut cell method to suppress checkerboard pressure oscillations caused by collocated arrangement. The solver is first used to simulate a channel flow to demonstrate its calculation accuracy expressed with L1 and L∞ norm errors and then the method is utilized to solve three benchmark problems of flow and heat transfer within irregular domains to verify its feasibility, efficiency, accuracy and potential in engineering applications. Copyright © 2010 John Wiley & Sons, Ltd.

A novel viscous micropump consisting of a cylindrical rotor eccentrically placed inside a microchannel is simulated by the two Volume-CAD (V-CAD) framework-based flow solvers, i.e., the direct simulation Monte Carlo (DSMC) package (named as V-DSMC) and the Navier-Stoke solver (named as V-Flow). V-DSMC is used in the case of the pump applied to gas, while V-Flow is applied to model the pump in the case of liquid working medium. The pumping performance curves under different liquid media with the variation of Reynolds number, as well as under different eccentricity factors are obtained. The performance and the flow filed characteristics are very sensitive to the tangential momentum accommodation coefficient in the case of gas medium. Three recirculations exist in the flow field, and the sizes of recirculation are different at the different operating points in a performance curve.

耦合大涡模拟与植被阻力、热源项模型,提出了城市灌木绿化街谷内风场和污染物浓度分布的热、动力数学模型.首先利用均匀植被层边界层湍流算例考核了模型的合理性以及程序的稳定性,表明本文模型能较好模拟植被层内部速度分布,并能对温度变化做出正确响应.对形状因子为0.5的理想绿化街谷,研究了街谷大气不同稳定度对街谷内风场和污染物浓度分布的影响.结果表明,相比于裸露街谷,植被层的引入减弱了街谷内环流风场强度,同时减小了街谷顶部污染物置换速率(pollutant exchange rate,PER),导致绿化街谷地面、背风面和迎风面附近污染物浓度增加.对于街谷大气稳定度对绿化街谷内风场和污染物浓度分布的影响,街谷大气强不稳定情形下,街谷顶部、地面、背风面和迎风面附近,风速比街谷大气中性层结时明显降低,污染物浓度相应增加;街谷大气弱不稳定情形下,街谷顶部和迎风面附近,风速有轻微减弱,同时,街谷地面和背风面附近,风速有加强趋势,导致绿化街谷内污染物浓度在迎风面和背风面比中性层结时减小,而在两排植被层之间有所加强.关于街谷大气稳定度对街谷顶部PER的影响,街谷大气弱不稳定情形街谷顶部PER要比街谷大气中性层结时小,而街谷大气强不稳定情形街谷顶部PER最小.

In this work, a large eddy simulation (LES) model, which includes momentum and heat source (or sink) inside the tree planting layer, is proposed for the simulation of flow in a street canyon with tree planting. Vegetation canopy layer simulation shows that this model can be used to simulate the velocity distribution and temperature variation inside the canopy layer. Effects of atmospheric instability on flow and pollutant distribution in a street canyon with tree planting of an aspect ratio of 0.5 are studied. Results show that compared with the canyon with no tree planting (or the exposed street canyon), the canyon with tree planting shows a reduced wind circulation and pollutant exchange rate (PER) at the top layer of the street canyon, which induces the increase in the pollutant concentrations near road surface, leeward wall and windward wall. When street canyon atmosphere is under a strongly unstable condition, wind velocity decreases while pollutant concentration is increased in the areas near the street canyon top, road surface, leeward and windward walls, compared with the wind velocity in the street canyon with the neutral stratification. When street canyon atmosphere is under a weakly unstable condition, wind velocity weakens near the street canyon top and windward wall, but strengthens near the road surface and leeward wall, and pollutant concentration is decreased near the leeward and windward walls and is increased between the two rows of trees. When the street canyon atmosphere is under an unstable condition, PER is lower than that under the neutral stratification.

As significant components of micromechanics, gas-lubricated microbearings are more prevalent for their special advantages than other types. The fluid dynamics of the microbearing is different from their larger cousins due to the noncontinuum effect and surface-dominated effect, which may make the Navier-Stokes equations invalid. In this paper, by considering the accommodation coefficients on journal (α i) and that on bearing (α o) separately, the microbearings with different bearing numbers under the assumption of large L/D (length to diameter) are simulated using direct simulation Monte Carlo (DSMC) program incorporated with a Volume-CAD software. The diffuse reflection model and Cercignani-Lampis-Lord (CLL) model are applied to model the molecule-surface interaction. The flow field characteristics, as well as the performances of gas-lubricated journal bearings including load-carrying capacity, attitude angle and bearing drag are obtained. The results reveal that αi and αo have different effects to flow field characteristics and bearing performances. The bearing number has significantly impact on the bearing performances. The method developed in this paper would be very useful for designing and evaluating the gas-lubricated journal microbearing.

A novel three-dimensional Cartesian cut cell algorithm,referred to as 6+N,is proposed to describe and treat arbitrary three-dimensional Kitta Cube.This method can avoid the enumeration for millions of cutting patterns and implement the discretization and solution of the N-S equations in a unified form.The present method is applied to simulate natural convection heat transfer in an annular tunnel between two concentric or eccentric spheres.The numerical results show that Kitta Cube can express curve surfaces accurately with an error of less than 1.0%.The accuracy of solutions obtained by the present method is approximately equivalent to that by the body-fitted method.In addition,higher overall heat transfer coefficients can be achieved by lowering the position of the inner sphere for eccentric arrangement.

Heat transfer in particulate systems plays an important role in a range of industrial processes, such as drying, heating, cooling, and so on. However, the inter-particle heat transfer mechanism is comparatively less understood. Due to the multi-scale complexity of the system and the limitations of measurement techniques, the details of the processes are difficult to investigate experimentally. DEM is a powerful tool for us to obtain insight into the dynamics of particulate system. To extend the classical DEM to the Thermal Discrete Element Method (TDEM) for particulate system with heat transfer, the effect of softening treatment for TDEM was analyzed, which results in the change of some important micro-behaviors of inter-particle, such as impact time and contact area etc, and the unrealistic heat transfer between particles. Two coefficients, time restoration coefficient C, and area restoration coefficient C, were derived to simulate the contact heat transfer between particles more realistically even if particle stiffness is artificially adjusted by several orders while a large time step is taken to save computational cost.

Algorithms for detecting particle collision play an important role in the discrete element method (DEM) for the simulation of granular flow systems since the time taken to detect the contact pairs usually occupies a considerable proportion of the total CPU time for the simulation. In this study, we developed a new octree algorithm called multi-octree algorithm, for detecting candidate contact pairs. The so-called multi-octree algorithm adopts the topology of octree for detecting possible contacts, in which the particles are managed by hierarchical classification according to particle size and then mapped to different level nodes of an octree, instead of mapping all particles into the leaf nodes of an octree in Vemuri-octree algorithm. The present algorithm speeds up the detecting process by reducing the number of candidate particles for possible contacts. A non-uniform size particulate system with three particle sizes was simulated by the multi-octree and the Vemuri-octree algorithms simultaneously. The simulation results showed that the multi-octree algorithm is relatively insensitive to the volumetric fraction of particles and particle shapes, and takes much shorter time to find candidate particles for possible contacts than the Vemuri-octree algorithm for non-uniform size particulate systems.

Many micromachines use rotating shafts and other moving parts which carry a load and need fluid bearings for support. Most of them operate with air or water as the lubricating fluid. The present study analyzes air microbearing represented as an eccentric cylinder rotating in a stationary housing. The fluid mechanics and operating characteristics of microbearing are different from their larger cousins. The small length-scale may invalidate the continuum approximation in Navier-Stokes equations, and slip flow, rarefaction, compressibility and other unconventional effects may have to be taken into account. Surface effects dominate in small devices due to a high surface-volume ratio. In this study, two-dimensional eccentric-shaft journal microbearings with different eccentricities are simulated by direct simulation Monte Carlo (DSMC) code incorporated with a Volume-CAD software. The diffuse reflection model and Cercignani-Lampis-Lord (CLL) model are applied to model the molecule-surface interaction by considering the accommodation coefficients of shaft wall and housing wall separately. The distribution of mean free path in the flow field indicates that the continuum model may break down and it is necessary to carry our molecular modeling. Calculation results show that at high eccentricity and high accommodation coefficient on the housing wall (ACO) the flow may develop a recirculation region. However, the accommodation coefficient on shaft wall (ACI) does not have any effect on the occurrence of recirculation and the size of recirculation zone. There is antisymmetry of the pressure about a vertical axis, which produces a pressure force on the shaft wall. The influence of ACI to isobars is larger than that of ACO. The shear stress profile on shaft wall is big at low ACI. At the region of short clearance between the shaft wall and housing wall, it is also influenced by the surface condition of housing wall and may even change its direction at low ACO. The pressure profile is reduced in amplitude as the ACI increases, but it is enhanced a little with the increase of ACO. The ACO has great impact on the viscous force in the case of big eccentricity. With the increase of ACI, the viscous force decreases. The pressure force is high at large eccentricity. The influence of ACO to pressure force is insignificant, but the pressure force fall is enormous when ACI increases, especially for large eccentricity. The total force decreases markedly at high eccentricity when ACI increases. The ACO almost has no impact on the total force. The torque increases with ACO, but decreases with ACI. The eccentricity also has great impact on the torque, and the microbeaing may have large torque at high eccentricity. The method developed in this paper would be very useful for designing and evaluating journal microbearing.

The thermal discrete element method (TDEM), a coupling of the discrete element model (DEM) with the inter-particle heat transfer models, has been applied to the simulation of the particulate systems with heat transfer. Additionally, small normal spring stiffness coefficient has often been adopted instead of the real value in the softening treatment to improve the calculation efficiency. However, present research has indicated that the heat transfer thus simulated is exaggerated even though such softening treatment has almost no effect on the movement of particles. In this letter, we propose a restoration method to restore the inter-particle contact time and contact area in the real heat transfer process even when particle stiffness is softened by several orders. This restoration method keeps the merit of the softening treatment in the DEM simulation of the particulate systems with heat transfer and avoids the unreasonable heat transfer calculations using the softening treatment method. Copyright (C) EPLA, 2009

The cylindrical Couette flow of a rarefied gas from macro- to micro-scales, in the case where the inner cylinder is rotating whereas the outer cylinder is at rest, is extensively investigated by direct simulation Monte Carlo (DSMC) code incorporated with a Volume-CAD software. The generalized soft sphere (GSS) model is applied to an intermolecular collision calculation. The diffuse reflection model and Cercignani-Lampis-Lord (CLL) model are used to model the molecule-surface interaction by considering the accommodation coefficients on inner cylinder (ACI hereafter) and outer cylinder (ACO hereafter) separately. The contents in this paper include following three aspects: I the flow field characteristics and force and torque on inner cylinder for eccentric Couette flow between different scales with same non-dimensional parameters (accommodation coefficients, eccentricity-clearance ratio, Knudsen number and Reynolds number) are compared; the flow field characteristics for different scales are same; with the increase of the scale, the total force on the inner cylinder increases slightly, while the torque is proportional to the scale; II the velocity profiles in concentric Couette flow under different non-dimensional parameters are studied; the result shows that the phenomenon of inverted velocity profile in the concentric Couette flow is only induced by a smooth outer cylinder; the non-dimensional tangential velocity, as well as its gradient is high at low Reynolds number; the Knudsen number has great impact on the tangential velocity profile, and the velocity profile may not be inverted in the case of low Knudsen number; III the flow field characteristics in eccentric Couette flow under different non-dimensional parameters are obtained; the recirculation zone may not appear when Knudsen number is high; the position of its center may be different depending on Reynolds number; with the increase of Reynolds number, the compressibility effect becomes important; stratified distribution of the density becomes obvious at low Knudsen number.

Based on VCAD system, a general DSMC (direct simulation Monte Carlo) program, named as V-DSMC, has been developed by the authors. Recently with the development and wide applications of MEMS (micro electromechanical systems), the numerical simulations of gas flow in MEMS have been an increasing demand. DSMC has particular advantage on modeling gas flow in MEMS due to the accurate simulations in slip, transitional and free-molecule flow regimes. In this paper, the strong potential applications of V-DSMC to MEMS are shown by taking one case of shear-driven flow (microbearing) and one case of pressure-driven flow (micronozzle) as examples.

An adaptive unstructured grid generation algorithm,which adopts Cartesian grid to decompose a background domain and adopts a cut cell approach to express curvilinear boundaries,is presented for solving steady incompressible Navier-Stokes equations. By using quadtree data structure to store mesh data,simplifying cut types into six schemes,and employing the curl and divergence of velocity as criteria of grid refinement,this approach can implement mesh generation and adaptive refinement for arbitrary complex geometries automatically. A solution of N-S equations via finite volume method for this mesh is derived. The SIMPLE based smoothing pressure correction is chosen to suppress the checkerboard pressure oscillation due to collocated variables arrangement. The present method is applied to two benchmark problems and is verified to be accurate and efficient.

以四叉树非结构化网格为基础,提出了背景区域采用正方形四叉树网格、边界区域采用切削网格的一种可以表达复杂几何形状的网格生成方法,该网格具有生成过程简单,正交性好等优点.在这种网格的基础上,采用非结构网格有限体积法进行离散得到了多种形状切削网格并存时Navier-stokes(N-S)方程的求解算法,并以顶盖驱动斜方腔流和方腔内热圆柱自然对流为例,应用上述算法实现了网格生成和流动数值模拟,与基准解进行了比较,一致性较好.计算结果表明这种切削网格方法及其N-S方程求解方法具有可靠性和应用前景.

Research on turbomolecular pumps (TMPs) based on the analysis of single blade row has been carried out by a number of investigators Kruger CH, Ph.D. Thesis, Massachusetts Institute of Technology; 1960: Katsimichas S, Goddard AJH, Lewington R, Oliveira de CRE. J Vac Sci Technol A 1995; 13:2954; Schneider TN, Katsimichas S, de Oliveira CRE, Goddard AJH. J Vac Sci Technol A 1998;16:175: De Simon M. Vacuum 1990;41:2021; Chu JG, Hua ZY. J Vac Sci Technol 1982;20:1101; Amoli A, Ebrahimi R, Hosseinalipour SM. Vacuum 2004:72:427; Sawada T. Bull Jpn Soc Mech Eng 1973:16:993; Joong-Sik Heo, Hwang Young-Kyu. Vacuum 2001:56:133: Sawada T. Bull Jpn Soc Mech Eng 1979;22:362; Amoli A, Hosseinalipour SM. Vacuum 2004;75:361; Sheng Wang, Hisashi Ninokata. Prog Nucl Energy 2005;47:664, but those calculations were either limited to free-molecule flow, or failed to obtain good results in the transition regime. Furthermore, they were usually focused on pumping performance and did not report detailed flow field characteristics. In this study, a three-dimensional direct simulation Monte Carlo (DSMC) code adopting an accurate intermolecular collision model, i.e., a generalized soft sphere (GSS) model, has been developed to simulate the single blade row of a one-stage TMP from free-molecule flow to transition flow without any geometrical simplification. Molecular velocities and position equations are deduced under a rotating frame with consideration for the Coriolis and centrifugal acceleration, and the number of sample molecules is tested for sensitivity. The validity of this study and its accuracy are verified through comparison with previous DSMC results and experimental data, and the deterioration of the maximum pressure ratio in the transition flow regime and the influence of the intermolecular collision model on the maximum pressure ratio calculation are analyzed with the aid of transmission probability. Pumping performance under differing geometrical parameters (clearance between the blade tip wall and the housing wall, and the spacing-chord ratio) is investigated, and detailed flow field characteristics, including the number of molecule-surface collisions, temperature and density distributions, particle traces of single gas components and gas mixtures are all obtained under zero pumping speed. (C) 2009 Elsevier Ltd. All rights reserved.

With the characteristic of the quadtree data structure, a new mesh generation method, which adopts square meshes to decompose a background domain and a cut cell approach to express arbitrary boundaries, is proposed to keep the grids generated with a good orthogonality easily. The solution of N-S equations via finite volume method for this kind of unstructured meshes is derived. The mesh generator and N-S solver are implemented to study two benchmark cases, i.e. a lid driven flow within an inclined square and a natural convection heat transfer flow in a square duct with an inner hot circular face. The simulation results are in agreement with the benchmark values, verifying that the present methodology is valid and will be a strong tool for two-dimensional flow and heat transfer simulations, especially in the case of complex boundaries.