A boundary-Integral Equation for Two-Dimensional Oscillatory Stokes Flow Past an Arbitrary Body

The fundamental singular velocity and pressure fields generated by the presence of an isolated line force acting at a point in a two-dimensional unbounded viscous incompressible medium executing oscillatory motions are used to formulate an integral equation which governs the flow past an arbitrarily shaped body. The Fredholm integral equation of the first kind is then solved by means of a boundary-element method, for the translational oscillatory flow past circular, elliptic and orthogonally intersecting cylinders. The asymptotic behaviour of the force on the cylinder for large values of the frequency parameter is obtained.     

Slip Correction Measurements of Certified PSL Nanoparticles Using a Nanometer Differential Mobility Analyzer (Nano-DMA) for Knudsen Number From 0.5 to 83

The slip correction factor has been investigated at reduced pressures and high Knudsen number using polystyrene latex (PSL) particles. Nano-differential mobility analyzers (NDMA) were used in determining the slip correction factor by measuring the electrical mobility of 100.7 nm, 269 nm, and 19.90 nm particles as a function of pressure. The aerosol was generated via electrospray to avoid multiplets for the 19.90 nm particles and to reduce the contaminant residue on the particle surface. System pressure was varied down to 8.27 kPa, enabling slip correction measurements for Knudsen numbers as large as 83. A condensation particle counter was modified for low pressure application. The slip correction factor obtained for the three particle sizes is fitted well by the equation: C = 1 + Kn (α + β exp(−γ/Kn)), with α = 1.165, β = 0.483, and γ = 0.997. The first quantitative uncertainty analysis for slip correction measurements was carried out. The expanded relative uncertainty (95 % confidence interval) in measuring slip correction factor was about 2 % for the 100.7 nm SRM particles, about 3 % for the 19.90 nm PSL particles, and about 2.5 % for the 269 nm SRM particles. The major sources of uncertainty are the diameter of particles, the geometric constant associated with NDMA, and the voltage.     

贝克利数对圆管流道交变流动传热的影响分析

从可压缩黏性流体的一般控制方程出发,通过数值模拟,研究管内可压缩层流交变流动传热现象,重点关注贝克利数对于传热的影响.采用离散傅立叶级数的形式表征管内交变流动传热特性,研究表明采用五阶级数拟合值与原始数据的相对误差可小于10%.给出了贝克利数为2和300时,一个周期内交变流动传热过程的计算结果,并进行了对比分析.根据模...     

Benchmark problems in rarefied gas dynamics

In order to identify the most efficient and reliable methods and solvers for modeling of rarefied gas flows, it is proposed to choose few benchmark problems to be solved by different methods. The main requirements to such problems, such as geometrical simplicity and small number of determining parameters, are formulated in the present work. Two benchmark problems are proposed. A comparison between numerical and experimental data of these problems available in the open literature is performed.     

Effect of surface slip on Stokes flow past a spherical particle in infinite fluid and near a plane wall

The motion of a spherical particle in infinite linear flow and near a plane wall, subject to the slip boundary condition on both the particle surface and the wall, is studied in the limit of zero Reynolds number. In the case of infinite flow, an exact solution is derived using the singularity representation, and analytical expressions for the force, torque, and stresslet are derived in terms of slip coefficients generalizing the Stokes–Basset–Einstein law. The slip velocity reduces the drag force, torque, and the effective viscosity of a dilute suspension. In the case of wall-bounded flow, advantage is taken of the axial symmetry of the boundaries of the flow with respect to the axis that is normal to the wall and passes through the particle center to formulate the problem in terms of a system of one-dimensional integral equations for the first sine and cosine Fourier coefficients of the unknown traction and velocity along the boundary contour in a meridional plane. Numerical solutions furnish accurate predictions for (a) the force and torque exerted on a particle translating parallel to the wall in a quiescent fluid, (b) the force and torque exerted on a particle rotating about an axis that is parallel to the wall in a quiescent fluid, and (c) the translational and angular velocities of a freely suspended particle in simple shear flow parallel to the wall. For certain combinations of the wall and particle slip coefficients, a particle moving under the influence of a tangential force translates parallel to the wall without rotation, and a particle moving under the influence of a tangential torque rotates about an axis that is parallel to the wall without translation. For a particle convected in simple shear flow, minimum translational velocity is observed for no-slip surfaces. However, allowing for slip may either increase or decrease the particle angular velocity, and the dependence on the wall and particle slip coefficients is not necessarily monotonic.     

Isothermal slip flow over curved surfaces

It has long been recognised that the no-slip-boundary condition employed in the Navier-Stokes equations can only be applied when the Knudsen number, Kn?10⁻³. If the Knudsen number is increased beyond this value, rarefaction effects start to influence the flow and the molecular collision frequency per unit area becomes too small to maintain the no-slip-boundary condition. Unfortunately, Maxwell's famous slip equation describing the velocity discontinuity at the wall is often misapplied when analysing flows over curved or rotating boundaries. In the present study, a generalised version of Maxwell's slip equation is used to investigate low Knudsen number isothermal flow over walls with substantial curvature. The generalised slip equation is written in terms of the tangential shear stress to overcome the limitations of the conventional slip-boundary treatment. The study considers a number of fundamental, but challenging, rarefied flow problems and demonstrates that Maxwell's conventional slip equation is unable to capture important flow phenomena over curved or rotating surfaces.     

Rarefied gas flow through channels of finite length at various pressure ratios

A rarefied gas flow through channels (i.e. flow through parallel plates) of finite length has been modeled based on the direct simulation Monte Carlo method. The reduced flow rate and the flow field have been calculated as function of the gas rarefaction, the length-to-height ratio and the pressure ratio upstream and downstream of the channel. The whole range of the gas rarefaction including the free-molecular, transitional and hydrodynamic regimes and a wide range of the length-to-height ratio representing both short and long channels have been considered. Several values of the pressure ratio between 0 and 0.5 have been used in the calculations. It is shown that the rarefaction parameter has the most significant effect on the flow field characteristics and patterns, followed by the pressure ratio, while the length-to-height ratio has a rather modest impact. The Mach belt phenomenon is discussed in detail.     

A parametric study of dispersed laminar gas-particle flows through vertical and horizontal channels

Particle diameter, particle phase material density and inlet particle volume fraction are three important parameters governing the flow physics of dispersed gas-particle flows. In this work, an inhouse numerical solver is developed to investigate the effects of particle diameter (Stokes number), particle phase material density, inlet particle volume fraction and inlet phase velocities in the flow characteristics of gas-particle flows through vertical and horizontal channels and also in open domains. It is found that, for a constant inlet particle volume fraction, lower diameter particles attain a higher steady state velocity at any section inside the channel than the higher diameter particles; while the corresponding steady state gas velocity at any section increases with increase in particle diameter. On the other hand, for a constant particle diameter, the steady state gas phase velocity at any section decreases with increase in inlet particle volume fraction. Significant changes in both gas and particle velocity and volume fraction profiles have also been observed with inlet slip, i.e., when the velocities of both the phases at inlet are distinct as opposed to being equal, keeping all other flow and physical parameters invariant.     

A-posteriori compression of wavelet-BEM matrices

The success of the wavelet boundary element method (BEM) depends on its matrix compression capability. The wavelet Galerkin BEM (WGBEM) based on non-standard form (NS-form) in Tausch (J Numer Math 12(3): 233–254, 2004) has almost linear memory and time complexity. Recently, wavelets with the quasi-vanishing moments (QVMs) have been used to decrease the constant factors involved in the complexity estimates (Xiao in Comput Methods Appl Mech Eng 197:4000–4006, 2008). However, the representations of layer potentials in QVM bases still have much more negligible entries than predicted by a-priori estimates, which are based on the separation of the supports of the source- and test-wavelets. In this paper, we introduce an a-posteriori compression strategy, which is designed to preserve the convergence properties of the underlying Galerkin discretization scheme. We summarize the different compression schemes for the WGBEM and demonstrate their performances on practical problems including Stokes flow, acoustic scattering and capacitance extraction. Numerical results show that memory allocation and CPU time can be reduced several times. Thus the storage for the NS-form is typically less than what is required to store the near-field interactions in the well-known fast multipole method.     

Fundamental solutions for micropolar fluids

New fundamental solutions for micropolar fluids are derived in explicit form for two- and three-dimensional steady unbounded Stokes and Oseen flows due to a point force and a point couple, including the two-dimensional micropolar Stokeslet, the two- and three-dimensional micropolar Stokes couplet, the three-dimensional micropolar Oseenlet, and the three-dimensional micropolar Oseen couplet. These fundamental solutions do not exist in Newtonian flow due to the absence of microrotation velocity field. The flow due to these singularities is useful for understanding and studying microscale flows. As an application, the drag coefficients for a solid sphere or a circular cylinder that translates in a low-Reynolds-number micropolar flow are determined and compared with those corresponding to Newtonian flow. The drag coefficients in a micropolar fluid are greater than those in a Newtonian fluid.     

导叶式旋风管内短路流颗粒夹带的研究

采用数值模拟方法,结合试验与理论分析,研究Shell型导叶式旋风管内短路流颗粒夹带问题。结果表明:Shell型旋风管直筒芯管下口存在短路流现象,计算得知短路流量占进口总流量的39.3%。理论分析发现,短路流主要夹带粒径小于9μm的颗粒,短路流夹带颗粒临界粒径为9μm。另外,数值模拟跟踪颗粒逃逸的轨迹证明,Shell型旋风管能将粒径大于9μm的颗粒全部除尽;粒径小于9μm的颗粒既有经排尘口返混逃逸,又有短路流夹带逃逸,其中短路流夹带逃逸占主要部分,且随着粒径的增加,经芯管下口短路夹带逃逸的数目减小。     

Simulations of Vortex Evolution and Phase Slip in Oscillatory Potential Flow of the Superfluid Component of 4He Through an Aperture

The evolution of semicircular quantum vortex loops in oscillating potential flow emerging from an aperture is simulated in some highly symmetrical cases. As the frequency of potential flow oscillation increases, vortex loops that are evolving so as eventually to cross all of the streamlines of potential flow are drawn back toward the aperture when the flow reverses. As a result, the escape size of the vortex loops, and hence the net energy transferred from potential flow to vortex flow in such 2π phase-slip events, decreases as the oscillation frequency increases. Above some aperture-dependent and flow-dependent threshold frequency, vortex loops are drawn back into the aperture. Simulations are performed using both radial potential flow and oblate-spheroidal potential flow.     

不同粗糙表面的圆柱风压分布试验研究

通过风洞试验研究了不同表面粗糙度、不同雷诺数条件下二维圆柱的压力分布和阻力特性。结果表明:通过合理地增大表面粗糙度,在相对较低的风速下有效地模拟了圆柱的超临界绕流特性,满足了工程应用对超临界雷诺数的要求。