Large aerodynamic forces on a sweeping wing at low Reynolds number

The aerodynamic forces and flow structure of a model insect wing is studied by solving the Navier-Stokes equations numerically. After an initial start from rest, the wing is made to execute an azimuthal rotation (sweeping) at a large angle of attack and constant angular velocity. The Reynolds number (Re) considered in the present note is 480 (Re is based on the mean chord length of the wing and the speed at 60% wing length from the wing root). During the constant-speed sweeping motion, the stall is absent and large and approximately constant lift and drag coefficients can be maintained. The mechanism for the absence of the stall or the maintenance of large aerodynamic force coefficients is as follows. Soon after the initial start, a vortex ring, which consists of the leading-edge vortex (LEV), the starting vortex, and the two wing-tip vortices, is formed in the wake of the wing. During the subsequent motion of the wing, a base-to-tip spanwise flow converts the vorticity in the LEV to the wing tip and the LEV keeps an approximately constant strength. This prevents the LEV from shedding. As a result, the size of the vortex ring increases approximately linearly with time, resulting in an approximately constant time rate of the first moment of vorticity, or approximately constant lift and drag coefficients. The variation of the relative velocity along the wing span causes a pressure gradient along the wingspan. The base-to-tip spanwise flow is mainly maintained by the pressure-gradient force. The project supported by the National Natural Science Foundation of China (10232010)     

Hydrodynamic force and torque models for a particle moving near a wall at finite particle Reynolds numbers

This research work is aimed at proposing models for the hydrodynamic force and torque experienced by a spherical particle moving near a solid wall in a viscous fluid at finite particle Reynolds numbers. Conventional lubrication theory was developed based on the theory of Stokes flow around the particle at vanishing particle Reynolds number. In order to account for the effects of finite particle Reynolds number on the models for hydrodynamic force and torque near a wall, we use four types of simple motions at different particle Reynolds numbers. Using the lattice Boltzmann method and considering the moving boundary conditions, we fully resolve the flow field near the particle and obtain the models for hydrodynamic force and torque as functions of particle Reynolds number and the dimensionless gap between the particle and the wall. The resolution is up to 50 grids per particle diameter. After comparing numerical results of the coefficients with conventional results based on Stokes flow, we propose new models for hydrodynamic force and torque at different particle Reynolds numbers. It is shown that the particle Reynolds number has a significant impact on the models for hydrodynamic force and torque. Furthermore, the models are validated against general motions of a particle and available modeling results from literature. The proposed models could be used as sub-grid scale models where the flows between particle and wall can not be fully resolved, or be used in Lagrangian simulations of particle-laden flows when particles are close to a wall instead of the currently used models for an isolated particle.     

Slow motions of a circular cylinder experiencing slip near a plane wall

A theoretical study is presented for the two-dimensional creeping flow caused by a long circular cylindrical particle translating and rotating in a viscous fluid near a large plane wall parallel to its axis. The fluid is allowed to slip at the surface of the particle. The Stokes equations for the fluid velocity field are solved in the quasi-steady limit using cylindrical bipolar coordinates. Semi-analytical solutions for the drag force and torque acting on the particle by the fluid are obtained for various values of the slip coefficient associated with the particle surface and of the relative separation distance between the particle and the wall. The results indicate that the translation and rotation of the confined cylinder are not coupled with each other. For the motion of a no-slip cylinder near a plane wall, our hydrodynamic drag force and torque results reduce to the closed-form solutions available in the literature. The boundary-corrected drag force and torque acting on the particle decrease with an increase in the slip coefficient for an otherwise specified condition. The plane wall exerts the greatest drag on the particle when its migration occurs normal to it, and the least in the case of motion parallel to it. The enhancement in the hydrodynamic drag force and torque on a translating and rotating particle caused by a nearby plane wall is much more significant for a cylinder than for a sphere.     

双柱状颗粒在线性剪切流场中的动力学分析

为研究柱状颗粒在线性剪切流场中的运动状态和受力情况,本文以颗粒长径比为2,颗粒之间的初始距离ΔS_Py=4D为例,基于直接力浸入边界法数值模拟了双柱状颗粒在三维线性剪切流场中的运动过程。根据模拟结果分析了柱状颗粒周围流场参数分布,在考虑壁面对颗粒的影响和颗粒之间相互影响的条件下,研究了颗粒的受力和运动的变化,探索了流体曳力导致柱状颗粒迁移和转动的规律。研究结果表明,双柱状颗粒在线性剪切流场中易向速度大的流体区域运动;前后两颗粒运动状态和轨迹不同,颗粒之间距离较近时,曳力会产生较大的波动;只有当颗粒在壁面附近时,滞后颗粒才能追上领先颗粒,两颗粒发生牵引、翻滚和分离过程。     

Shock-induced Near-wall Two-phase Flow Structure Over a Micron-sized Particles Bed

The present paper studies numerical modelling of near-wall two-phase flows induced by a normal shock wave moving at a constant speed, over a micron-sized particles bed. In this two-fluid model, the possibility of particle trajectory intersection is considered and a full Lagrangian formulation of the dispersed phase is introduced. The finiteness of the Reynolds and Mach numbers of the flow around a particle as well as the fineness of the particle sizes are taken into account in describing the interactions between the carrier- and dispersed-phases. For the small mass-loading ratio case, the numerical simulation of flow structure of the two phases is implemented and the profiles of the particle number density are obtained under the constant-flux condition on the wall. The effects of the shock Mach number and the particle size and material density on particle entrainment motion are discussed in detail. The obtained results indicate that interphase non-equilibrium in the velocity and temperature is a common feature for this type of flows and a local particle accumulation zone may form near the envelope of the particle trajectory family.     

Rolling/sliding of a particle on a flat wall in a linear shear flow at finite Re

Recently Lee and Balachandar proposed analytically-based expressions for drag and lift coefficients for a spherical particle moving on a flat wall in a linear shear flow at finite Reynolds number. In order to evaluate the accuracy of these expressions, we have conducted direct numerical simulations of a rolling particle for shear Reynolds number up to 100. We assume that the particle rolls on a horizontal flat wall with a small gap separating the particle from the wall (L = 0.505) and thus avoiding the logarithmic singularity. The influence of the shear Reynolds number and the translational velocity of the particle on the hydrodynamic forces of the particle was investigated under both transient and the final drag-free and torque-free steady state. It is observed that the quasi-steady drag and lift expressions of Lee and Balachandar provide good approximation for the terminal state of the particle motion ranging from perfect sliding to perfect rolling. With regards to transient particle motion in a wall-bounded shear flow it is observed that the above validated quasi-steady drag and lift forces must be supplemented with appropriate wall-corrected added-mass and history forces in order to accurately predict the time-dependent approach to the terminal steady state. Quantitative comparison with the actual particle motion computed in the numerical simulations shows that the theoretical models quite effective in predicting rolling/sliding motion of a particle in a wall-bounded shear flow at moderate Re.     

Aerosol Aspiration into a Slot Sampler for Two Angles of Orientation

The problem of aerosol aspiration into a slot between two plates (slot intake model) is studied for two angles between the slot and the free-stream velocity. Within the incompressible potential separationless approximation for the flow field, an analytical solution is obtained which is used for integrating the particle trajectory equations. Using the limiting trajectory method, the aspiration coefficients are calculated for variable Stokes number and ratio of the free-stream and aspiration velocities. The calculated aspiration coefficient is compared with the known results obtained from approximate theories.     

Statics and kinematics of discrete Cosserat-type granular materials

A theoretical framework is presented for the statics and kinematics of discrete Cosserat-type granular materials. In analogy to the force and moment equilibrium equations for particles, compatibility equations for closed loops are formulated in the two-dimensional case for relative displacements and relative rotations at contacts. By taking moments of the equilibrium equations, micromechanical expressions are obtained for the static quantities average Cauchy stress tensor and average couple stress tensor. In analogy, by taking moments of the compatibility equations, micromechanical expressions are obtained for the (infinitesimal) kinematic quantities average rotation gradient tensor and average Cosserat strain tensor in the two-dimensional case. Alternatively, these expressions for the average Cauchy stress tensor and the average couple stress tensor are obtained from considerations of the equivalence of the continuum force and couple traction vectors acting on a plane and the resultant of the discrete forces and couples acting on this plane. In analogy, the expressions for the average rotation gradient tensor and the average Cosserat strain tensor are obtained from considerations of the change of length and change of rotation of a line element in the two-dimensional case. It is shown that the average particle stress tensor is always symmetrical, contrary to the average stress tensor of an equivalent homogenized continuum. Finally, discrete analogues of the virtual work and complementary virtual work principles from continuum mechanics are derived.     

Creeping motion of a slip spherical particle in a circular cylindrical pore

A combined analytical–numerical study for the creeping flow caused by a spherical fluid or solid particle with a slip-flow surface translating in a viscous fluid along the centerline of a circular cylindrical pore is presented. To solve the axisymmetric Stokes equations for the fluid velocity field, a general solution is constructed from the superposition of the fundamental solutions in both cylindrical and spherical coordinate systems. The boundary conditions are enforced first at the pore wall by the Fourier transforms and then on the particle surface by a collocation technique. Numerical results for the hydrodynamic drag force acting on the particle are obtained with good convergence for various values of the relative viscosity or slip coefficient of the particle, the slip parameter of the pore wall, and the ratio of radii of the particle and pore. For the motion of a fluid sphere along the axis of a cylindrical pore, our drag results are in good agreement with the available solutions in the literature. As expected, the boundary-corrected drag force for all cases is a monotonic increasing function of the ratio of particle-to-pore radii, and approaches infinity in the limit. Except for the case that the cylindrical pore is hardly slip and the value of the ratio of particle-to-pore radii is close to unity, the drag force exerted on the particle increases monotonically with an increase in its relative viscosity or with a decrease in its slip coefficient for a constant ratio of radii. In a comparison for the pore shape effect on the axial translation of a slip sphere, it is found that the particle in a circular cylindrical pore in general acquires a lower hydrodynamic drag than in a spherical cavity, but this trend can be reversed for the case of highly slippery particles and pore walls.     

Analytic solution of the problem of rotation of a sphere in a rarefied molecular gas with allowance for the accommodation coefficients

In the case of the slip flow regime expressions both for the mass velocity of a rarefied molecular gas entrained by a rotating sphere and for the moment of the friction forces exerted on the sphere by the gas are obtained with allowance for the second-order correction with respect to the Knudsen number. It is demonstrated that these quantities depend on the Prandtl number and the accommodation coefficients of the tangential impulse of the gas molecules and its flux toward the sphere surface. The results are compared with analogous results obtained in the case of diffuse reflection of the gas molecules by the sphere surface.     

一种摩擦学状态在线监测系统的研究

研制了一种用于船用柴油机的摩擦学状态在线监测系统。它集磨粒监测，润滑油质量监测，柴油机扭矩及时转速监测于一体，利用在线铁谱技术监测润滑油中的铁磁性磨粒，利用容栅型电容传感器在线监测污染物引起的润滑油介电常数的变化，利用光电传感器和随轴转动齿盘产生的脉冲及相位差在线测量柴油机输出轴的扭矩及瞬时转速。此外，该监测系统还可将柴油机的磨损状态与动力状态相关联，监测由于各缸爆排压力变化造成的瞬时转速变化，从     

干气密封旋转流场的宏观特性与介观速度场的逻辑关系研究

旋转流场中的流体流动比较复杂,特别是在高转速、微尺度工况时,流场中的流体流态及其判断方法缺乏完备的理论模型. 选择干气密封作为高速旋转流场的研究对象,以开启力和泄漏量作为宏观特性表征指标参数,选择剪切(周向)、径向及轴向速度分量对速度流场进行介观表述,通过Fluent软件仿真计算大跨距转速(低转速至超高转速)时的宏观、介观指标参数,研究密封性能指标参数与速度场间的内在逻辑关系. 结果表明:低速旋转流场中的轴向速度分量较小,可忽略不计,转速升高会促使轴向速度分量持续增大,当转速持续增大并超过某一临界值时,轴向速度分量会出现迅速升高的情形;轴向速度分量的变化情形与微尺度流场(开启力和泄漏量)波动密切相关,是影响旋转流场流态的关键性指标参数,也是引起宏观流场特性变化的主要因素;径向速度分量的变化情形与微尺度流场泄漏量的变化规律基本一致,随着转速的增大,泄漏量的宏观性能反馈要早于开启力波动的出现. 基于以上研究,同时根据管道雷诺数、流量因子判定模型及流体力学基本理论,尝试提出了基于三维速度分量的针对旋转流场流态的椭球判定模型.      

Behavior of a small single bubble rising in a rotating flow field

A small single bubble was generated with a single-hole nozzle facing upward in a water bath contained in a rotating cylindrical vessel. The bubble size falls in the surface tension force dominant regime. The vertical, radial, and tangential migration velocities of the bubble were measured with two CCD cameras and a high-speed video camera. The tangential velocity component of water flow was measured with particle image velocimetry. A helical motion of the bubble was observed under every experimental condition. The direction of the helical motion was the same as that of the tangential velocity component. This helical motion is associated with the large initial shape deformation of the bubble near the nozzle exit and the subsequent regular shedding of vortices behind it. The period and amplitude of the helical motion were obtained by analyzing the trajectory of the bubble. These quantities were non-dimensionalized by the volume equivalent bubble diameter and the terminal bubble velocity in the vertical direction and correlated as functions of the Eotvos number. Empirical equations were proposed for the period and amplitude. Originally published in the Journal of JSEM, Vol. 4, No. 2, pp. 38–45 (2004).     

Heat transfer and flow temperature measurements in a rotating triangular channel with various rib arrangements

In the present study, the regionally-averaged heat transfer coefficients and flow temperature distributions were measured in an equilateral triangular channel with three different rib arrangements (α = 45, 90 and 135°). To measure regionally-averaged heat transfer coefficients in the channel, two rows of copper blocks and a single heater were installed on two ribbed walls. The fluid temperature distributions were obtained using a thermocouple-array. The rotation number ranged from 0.0 to 0.1 with a fixed Reynolds number of 10,000. For the 90° ribs, the heat transfer coefficients on the pressure side surface were increased significantly with rotation, while the suction side surface had lower heat transfer coefficients than the stationary channel. For the angled ribs, rib-induced secondary flow dominated the heat transfer characteristics and high heat transfer rates were observed on the regions near the inner wall for the 45° angled ribs and near the leading edge for the 135° angled ribs.     

Effects of vibrations on particle motion near a wall: Existence of attraction force

The effects of small vibrations on a particle oscillating near a solid wall in a fluid cell, relevant to material processing such as crystal growth in space, have been investigated experimentally and theoretically. Assuming the boundary layer around the particle to be thin compared to the particle radius at high vibration frequencies, an inviscid fluid model was developed to predict the motion of a spherical particle placed near a wall of a rectangular liquid-filled cell subjected to a sinusoidal vibration. Under these conditions, a non-uniform pressure distribution around the particle results in an average pressure that gives rise to an attraction force. Theoretical expressions for the attraction force are derived for the particle vibrating normal to and parallel with the nearest cell wall. The magnitude of this attractive force has been verified experimentally by measuring the motion of a steel particle suspended in the fluid cell by a thin wire. Experiments performed at high frequencies showed that the mean particle position, when the particle is brought near a cell wall, shifts towards the same wall, and is dependent on the cell amplitude and frequency, particle and fluid densities.     

Dynamics of a spherical particle in a laminar boundary layer

The problem of the motion of an individual spherical particle in a laminar boundary layer is considered for small Reynolds numbers determined from the relative velocity and the transverse velocity gradient of the flow undisturbed by the particle. The dependence of the transverse force acting on the particle, which results from the nonuniformity of the free stream, on the distance of the particle from the surface of a flat plate is calculated. It is shown that the direction of the transverse force changes with the distance of the particle from the plate: near the surface the force is positive, i.e., directed away from the plate, and at greater distances negative.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 91–96, November–December, 1990.The author wishes to thank M. N. Kogan and N. K. Makashev for useful discussions.     

Material force for dynamic crack propagation in multiphase micromorphic materials

Micromorphic theory, which considers material body as a continuous collection of deformable particles of finite size and inner structure; each has nine independent degrees of freedom describing the stretches and rotations of the particle in addition to the three classical translational degrees of freedom of its center, is briefly introduced in this work. The concept of material forces, which may also be referred as Eshelbian mechanics, is extended to micromorphic theory. The balance law of pseudo-momentum is formulated. The detailed expressions of Eshelby stress tensor, pseudo-momentum, and material forces are derived for thermoelastic micromorphic solid. It is found that the material forces are due to (1) body force and body moment, (2) temperature gradient and (3) material inhomogeneities in density, microinertia, and elastic coefficients. The general expression of material forces due to the presence of dynamically propagating crack front has also been derived. It is found that, at the crack front, material force is reduced to the J-integral in a very special and restrictive case.     

The flow of a non-Newtonian liquid near a rotating disk

Synopsis The flow of non-Newtonian liquid near a rotating disk has been discussed by using second order stress strain velocity relations of classical hydrodynamics. It is found that the effect of cross-viscosity depends on a non-dimensional number R _c. The boundary layer thickness decreases and the dimensionless moment coefficient increases with the increase of R _c.     

The viscosity of a plasma in a strong magnetic field

The viscosity of a plasma is studied under conditions in which a magnetic field influences particle collisions. The expressions obtained for the viscosity coefficients differ significantly from those obtained in the normal theory. It is shown that in sufficiently strong magnetic fields a temperature difference arises between the electron and ion plasma components which is proportional to the drift velocity and depends logarithmically on the magnetic field strength.