The density profile for the Klein-Kramers equation near an absorbing wall

We derive asymptotic series for the expansion coefficients of a function in terms of the Pagani functions, which occur in the boundary layer solutions of the Klein-Kramers equation. The results enable us to determine the density profile in the stationary solution of this equation near an absorbing wall from the numerically determined velocity distribution at the wall, with an accuracy of about 2%. We also obtain information about the analytic behavior of the density profile: this profile increases near the wall with the square root of the distance to the wall. Finally, the asymptotic analysis leads to an understanding of the slow convergence of variational approximations to the solution of the absorbing-wall problem and of the exponents that occur when one studies the variational approximations to various quantities of interest as functions of the number of terms in the variational ansatz. This is used to obtain a better variational estimate for the density at the wall.     

温度场内可吸入颗粒物运动特性的实验研究

对温度场内可吸入颗粒物的运动特性进行了实验研究,使用PDA测量了场内可吸入颗粒物的速度和浓度分布等参数,研究了实验段入口速度和温度等操作参数对温度场内颗粒相运动特性的影响.结果表明,在近冷壁区边界层内,PM2.5的轴向速度和脉动速度变化很大,颗粒因热泳力及扩散作用会向冷壁面运动并产生沉积.在实验研究的基础上,提出了计算温度场内PM2.5沉积效率的经验公式.     

Distribution of mean velocity in turbulent boundary layer over permeable surface with air blowing

In the present article, we investigate the possibility of using simple physical models for predicting properties of incompressible turbulent boundary layer on permeable wall at various values of air-microblowing mass flow rate. It is shown that the velocity scaling U _??*/?? ₉₉ can be successfully used to approximate the distribution of mean velocity in the outer region of the boundary layer. The use of this scaling makes the velocity profiles invariant with respect to Reynolds-number variation; this circumstance largely facilitates the analysis of experimental data, making it independent of upstream flow conditions. The distribution of mean velocity in the logarithmic flow region of the boundary layer over permeable surface can be described with a modified law of the wall involving a constant C ₀ equal to the same constant for canonical boundary layer, and a quantity K being a weak function of blowing ratio.     

The kinetic boundary layer for the Klein-Kramers equation; A new numerical approach

We explore a numerical technique for determining the structure of the kinetic boundary layer of the Klein-Kramers equation for noninteracting Brownian particles in a fluid near a wall that absorbs the Brownian particles. The equation is of interest in the theory of diffusion-controlled reactions and of the coagulation of colloidal suspensions. By numerical simulation of the Langevin equation equivalent to the Klein-Kramers equation we amass statistics of the velocities at the first return to the wall and of the return times for particles injected into the fluid at the wall with given velocities. The data can be used to construct the solutions of the standard problems at an absorbing wall, the Milne and the albedo problem. We confirm and extend earlier results by Burschka and Titulaer, obtained by a variational method vexed by the slow convergence of the underlying eigenfunction expansion. We briefly discuss some further boundary layer problems that can be attacked by exploiting the results reported here.     

微通道疏水表面滑移的耗散粒子动力学研究

了解疏水表面的滑移规律对其在流动减阻方面的应用至关重要.利用耗散粒子动力学(dissipative particle dynamics, DPD)方法研究了微通道疏水表面的滑移现象.采用固定住的粒子并配合修正的向前反弹机制,构建了DPD固体壁面边界模型,利用该边界模型模拟了平板间的Couette流动.研究结果表明,通过调整壁面与流体间排斥作用强度,壁面能实现从无滑移到滑移的转变,壁面与流体间排斥作用越强,即疏水性越强,壁面滑移越明显,并且滑移长度与接触角之间存在近似的二次函数关系.无滑移时壁面附近密度分布均匀,有滑移时壁面附近存在低密度区域,低密度区域阻碍了动量传递,致使壁面产生滑移.     

Investigation of scaling laws in a turbulent boundary layer flow with adverse pressure gradient using PIV

We present an experimental investigation and data analysis of a turbulent boundary layer flow at a significant adverse pressure gradient at Reynolds number up to Re_θ = 10, 000. We combine large-scale particle image velocimetry (PIV) with microscopic PIV for measuring the near wall region including the viscous sublayer. We investigate scaling laws for the mean velocity and for the total shear stress in the inner part of the boundary layer. In the inner part the mean velocity can be fitted by a log-law. In the outer part of the inner layer the log-law ceases to be valid. Instead, a modified log-law provides a good fit, which is given in terms of the pressure gradient parameter and a parameter for the mean inertial effects. Finally we describe and assess a simple quantitative model for the total shear stress distribution which is local in wall-normal direction without streamwise history effects.     

SPH方法气-液界面边界条件研究

针对界面附近粒子光滑函数截断和非物理穿透问题,提出一种气-液界面边界条件的处理方法.当界面附近支持域出现不同材料粒子,每步计算可在支持域设置虚粒子,按照密度分配方法给虚粒子物理量赋值,并对界面附近粒子引入气-液两相阻力.采用SPH方法和Level-Set方法,计算运动激波对气-液界面作用问题,两者计算结果一致,初步验证了气-液界面边界条件处理的适用性.用SPH方法分别计算超声速气流中的圆截面液柱绕流和下落问题,界面两侧粒子压力和法向速度连续,给出弓形激波、回流区和下游回流区等定性合理结果.表明本文方法可适度避免界面附近流体粒子光滑截断和粒子非物理穿透现象、界面附近流场数值振荡.     

纳米通道粗糙内壁对流体流动行为的影响

纳米流动系统具有高效、经济等优势,在众多领域具有广泛的应用前景.因该类系统具有极高的表面积体积比,致使界面滑移效应对流动具有显著影响.本文采用分子动力学方法以两无限大平行非对称壁面组成的Poiseuille流动为对象,分析了壁面粗糙度与润湿性变化对通道内流体流动的影响.对于不同结构类型的壁面,需要通过水动力位置来确定固液界面位置,准确计算固液界面位置有助于更好地分析界面滑移效应.研究结果表明,上下壁面不对称会引起通道内流场参数分布的不对称,壁面粗糙度及润湿性的变化会影响近壁面附近流体原子的流动特性,由于壁面凹槽的存在,粗糙壁面附近的数密度分布低于光滑壁面一侧.壁面粗糙度及润湿性的变化会影响固液界面位置,肋高变化及壁面润湿性对通道中速度分布影响较大,界面滑移速度及滑移长度随肋高和润湿性的增大而减小;肋间距变化对通道内流体流动影响较小,界面滑移速度和滑移长度基本保持恒定.     

Distribution of Orientations in Fibre Suspension Flowing in a Turbulent Boundary Layer

The equation of probability distribution function for mean fibre orientation in a turbulent boundary layer is derived, in which the correlation terms of the fluctuating velocity, fluctuating angular velocity with the fluctuating probability distribution function are related to the gradient of mean probability distribution function and the dispersion coefficients in order to make the equation be solvable. The finite-difference method is used to solve the equation numerically. The results show that the fibres tend to align with the streamline, which is in agreement qualitatively with the experimental result given by visualization. The fibre aspect-ratio has a significant effect on the orientation distribution of fibres, while the effect of the distance from the wall is negligible.     

The kinetic boundary layer around an absorbing sphere and the growth of small droplets

Deviations from the classical Smoluchowski expression for the growth rate of a droplet in a supersaturated vapor can be expected when the droplet radius is not large compared to the mean free path of a vapor molecule. The growth rate then depends significantly on the structure of the kinetic boundary layer around a sphere. We consider this kinetic boundary layer for a dilute system of Brownian particles. For this system a large class of boundary layer problems for a planar wall have been solved. We show how the spherical boundary layer can be treated by a perturbation expansion in the reciprocal droplet radius. In each order one has to solve a finite number ofplanar boundary layer problems. The first two corrections to the planar problem are calculated explicitly. For radii down to about two velocity persistence lengths (the analog of the mean free path for a Brownian particle) the successive approximations for the growth rate agree to within a few percent. A reasonable estimate of the growth rate for all radii can be obtained by extrapolating toward the exactly known value at zero radius. Kinetic boundary layer effects increase the time needed for growth from 0 to 10 (or 2 1/2) velocity persistence lengths by roughly 35% (or 175%).     

Investigation of electrostatic charge distribution within the reactor wall fouling and bulk regions of a gas–solid fluidized bed

The distribution of charge within the wall fouling region and bulk of a fluidized bed reactor was investigated. Experiments were conducted in a 0.1 m in diameter carbon steel fluidization column under atmospheric conditions. Polyethylene particles were fluidized with extra dry air at 1.5 the minimum fluidization velocity (bubbling flow regime) for 1 h. Using an online Faraday cup measurement technique, the net charge-to-mass ratio (q/m), as well as the size distribution of all particles adhered to the column wall and those in the bulk of the bed was determined. The wall particles were found to be predominantly negatively charged while those which did not adhere to the wall were predominantly positively charged. The charge distribution within each region was then investigated by a custom made charged particle separator that separated the particles according to their charge magnitude and polarity. It was determined that although the net charge of the wall layer particles was negative, a significant amount of positively charged particles existed within each sample and therefore the entire wall particle layer. This suggests that the wall layer was formed through layering between positively and negatively charged particles. Particles in the bulk of the bed also consisted of bipolarly charged particles.     

The kinetic boundary layer for the Fokker-Planck equation with absorbing boundary

The Fokker-Planck equation for the distribution of position and velocity of a Brownian particle is a particularly simple linear transport equation. Its normal solutions and an apparently complete set of stationary boundary layer solutions can be determined explicitly. By a numerical algorithm we select linear combinations of them that approximately fulfill the boundary condition for a completely absorbing plane wall, and that approach a linearly increasing position space density far from the wall. Various aspects of these approximate solutions are discussed. In particular we find that the extrapolated asymptotic density reaches zero at a distance x_M beyond the wall. We find x_M=1.46 in units of the velocity persistence length of the Brownian particle. This study was motivated by certain problems in the theory of diffusion-controlled reactions, and the results might be used to test approximate theories employed in that field.     

沟槽壁面减阻机理实验研究

利用IFA300型热线风速仪,测量了光滑壁面和沟槽减阻壁面湍流边界层内的瞬时速度,利用自行设计的阻力天平仪测量了壁面摩擦力。得到了边界层无量纲速度分布和平均湍动能分布。对测得的脉动速度信号,利用离散正交小波变换按时间和尺度分解,得到各尺度分量的湍动能,并且发现其分布在湍流惯性区具有极大值。分析表明,当沟槽有减阻效果时,边界层内的平均湍动能减小,湍流惯性区各分量的湍动能极大值亦减小。     

沉降分布孔隙率多孔介质模型及数值研究

研究沉降分布孔隙率多孔介质流动和传热,根据"O"形圈理论和现场测定确定孔隙率系数,建立坐标方向孔隙率分布函数;考虑流体密度变化,并引入Brinkman-Forchheimer的扩展Darcy模型,能量方程采用界面连续条件,建立沉降分布孔隙率多孔介质流动和传热求解模型.采用差分法对模型进行离散化,应用高斯-赛德尔方法迭代求解.数值分析表明:沉降分布孔隙率条件下多孔介质内流体流动速度在壁面附近较大,中心部位较小,壁面附近孔隙率的增大使得低流速区域减小,较高流速区域增大;当孔隙率小值时,温度按线性减小;当孔隙率大值时,温度在高低温壁面附近迅速减小,在中部减小较缓,热量按导热和对流共同传递;孔隙率增大能使平均怒谢尔数增大,对流换热作用增强.     

基于涡流发生器的风洞试验段附面层控制数值模拟

沿试验段侧壁发展的附面层是影响飞行器半模型实验数据精准度的主要因素之一.利用数值模拟方法验证了涡流发生器减小附面层影响的可行性,重点分析了安装角度、结构尺寸、安装位置及个数等设计参数对附面层内速度分布的影响规律,对涡流发生器尾涡强度以及沿流向的发展规律进行了初步探讨.结果表明,涡流发生器产生的尾涡能够有效改善附面层内的速度分布,进而减小附面层厚度,降低附面层影响;涡流发生器的后缘应略高于当地附面层厚度,安装角度、位置、个数等参数必须合理设计以减小涡流发生器对试验段主气流的影响.基于计算结果初步设计了可用于2.4 m跨声速风洞半模试验段的涡流发生器,在亚声速范围内能够减小模型区侧壁附面层厚度66%左右,对核心流Mach数影响小于0.003,为涡流发生器的实际应用提供了依据.      

Influence of wall motion on particle sedimentation using hybrid LB-IBM scheme

We integrate the lattice Boltzmann method (LBM) and immersed boundary method (IBM) to capture the coupling between a rigid boundary surface and the hydrodynamic response of an enclosed particle laden fluid. We focus on a rigid box filled with a Newtonian fluid where the drag force based on the slip velocity at the wall and settling particles induces the interaction. We impose an external harmonic oscillation on the system boundary and found interesting results in the sedimentation behavior. Our results reveal that the sedimentation and particle locations are sensitive to the boundary walls oscillation amplitude and the subsequent changes on the enclosed flow field. Two different particle distribution analyses were performed and showed the presence of an agglomerate structure of particles. Despite the increase in the amplitude of wall motion, the turbulence level of the flow field and distribution of particles are found to be less in quantity compared to the stationary walls. The integrated LBM-IBM methodology promised the prospect of an efficient and accurate dynamic coupling between a non-compliant bounding surface and flow field in a wide-range of systems. Understanding the dynamics of the fluid-filled box can be particularly important in a simulation of particle deposition within biological systems and other engineering applications.     

Wind-tunnel simulation of thick turbulent boundary layer

An experimental study aimed at revealing the possibility of simulation, in a subsonic wind tunnel, of enhanced Reynolds numbers Re^** via modeling a thick flat-plate boundary layer possessing the properties of a Clauser-equilibrium shear flow is reported. We show that turbulators prepared in the form of variable-height cylinders of height h and diameter d = 3 mm and installed in two rows along the normal to the streamlined wall offer rather an efficient means for modification of turbulent boundary layer in solving the problem. In the majority of cases, mean and fluctuating characteristics of the boundary layer exhibit values typical of naturally developing turbulent boundary layers at a distance of 530 cylinder diameters. The profiles of mean velocity with artificially enhanced boundary-layer thickness can be well approximated, in the law-of-the-wall variables, with the well-known distribution of velocities for canonical boundary layer.     

Velocity statistics in excited granular media

We present an experimental study of velocity statistics for a partial layer of inelastic colliding beads driven by a vertically oscillating boundary. Over a wide range of parameters (accelerations 3-8 times the gravitational acceleration), the probability distribution P(v) deviates measurably from a Gaussian for the two horizontal velocity components. It can be described by P(v) approximately exp(-mid R:v/v(c)mid R:(1.5)), in agreement with a recent theory. The characteristic velocity v(c) is proportional to the peak velocity of the boundary. The granular temperature, defined as the mean square particle velocity, varies with particle density and exhibits a maximum at intermediate densities. On the other hand, for free cooling in the absence of excitation, we find an exponential velocity distribution. Finally, we examine the sharing of energy between particles of different mass. The more massive particles are found to have greater kinetic energy. (c) 1999 American Institute of Physics.     

基于拟颗粒的气固两相曳力模型研究

为了研究气固两相流动大涡模拟中合适的曳力计算模型,本文引入拟颗粒和拟颗粒表面能的概念,通过拟颗粒表面能与外界输入能量之间的平衡关系来确定拟颗粒的粒径。根据拟颗粒粒径,得到运算量较小且考虑颗粒团聚效应的曳力计算模型。应用本文的曳力计算模型对二维竖直槽道内稠密气固两相流动进行了大涡模拟,结果表明颗粒的浓度分布具有上稀下浓,壁面附近浓中心稀及颗粒聚集等特点。这与实验结果在定性上是一致的。对气相和颗粒相的瞬时速度场进行了分析,发现气相和颗粒相速度场分布的非对称性是形成颗粒浓度分布壁面附近浓中心稀的重要原因之一。