Darcy–Brinkman Flow over a Grooved Surface

Uniform Darcy–Brinkman flow over a surface with periodic rectangular grooves is studied by domain decomposition and matching. It is found that the effect of corrugations is equivalent to replacing the rough surface with a smooth surface with an apparent slip for the bulk flow. Such equivalence would greatly simplify the boundary conditions for porous flow bounded by a rough surface. The slip velocity is larger along the grooves than transverse to the grooves, and is increased by the porous media parameter k.     

高压条件下界面滑移长度的定量测量

采用光干涉技术对高压条件下的界面滑移现象进行了试验研究.通过追踪冲击封油核心的运动位移,实现了对滑移长度的定量测量.结果表明:在纯滑条件下封油核心并不以卷吸速度运动,而是在盘纯滑时小于卷吸速度、球纯滑时大于卷吸速度,从而说明了滑移发生在玻璃盘表面.对封油核心的运动特征进行分析,得出了油膜界面滑移长度及剪应变率.试验分析表明滑移长度随油膜厚度、初始封油压力和润滑油黏度的增加而增加;随速度的增加而呈现减小趋势.     

Polymer Flow Through Porous Media: Numerical Prediction of the Contribution of Slip to the Apparent Viscosity

The flow of polymer solutions in porous media is often described using Darcy’s law with an apparent viscosity capturing the observed thinning or thickening effects. While the macroscale form is well accepted, the fundamentals of the pore-scale mechanisms, their link with the apparent viscosity, and their relative influence are still a matter of debate. Besides the complex effects associated with the rheology of the bulk fluid, the flow is also deeply influenced by the mechanisms occurring close to the solid/liquid interface, where polymer molecules can arrange and interact in a complex manner. In this paper, we focus on a repulsive mechanism, where polymer molecules are pushed away from the interface, yielding a so-called depletion layer in the vicinity of the wall. This depletion layer acts as a lubricating film that may be represented by an effective slip boundary condition. Here, our goal is to provide a simple mean to evaluate the contribution of this slip effect to the apparent viscosity. To do so, we solve the pore-scale flow numerically in idealized porous media with a slip length evaluated analytically in a tube. Besides its simplicity, the advantage of our approach is also that it captures relatively well the apparent viscosity obtained from core-flood experiments, using only a limited number of inputs. Therefore, it may be useful in many applications to rapidly estimate the influence of the depletion layer effect over the macroscale flow and its relative contribution compared to other phenomena, such as non-Newtonian effects.     

织构深度对不锈钢表面油润滑条件下摩擦学性能影响的试验和仿真研究

采用激光加工技术在不锈钢表面构造深度不同的沟槽型织构图案,通过UMT摩擦磨损试验机测试了不同织构深度的不锈钢表面在PAO6油润滑条件下的摩擦磨损性能,利用表面轮廓仪和扫描电镜(SEM)对摩擦前后的沟槽形貌进行表征分析,采用计算流体动力学(CFD)方法对试验进行模拟并计算,结合ANSYS Fluent软件模拟分析结果,探究了沟槽织构深度对不锈钢表面在油润滑条件下的摩擦学性能的影响机理. 研究结果表明:加工的沟槽织构及其织构深度显著影响不锈钢表面在PAO油润滑条件下的摩擦磨损行为,织构深度为10 μm的不锈钢表面获得最好的抗磨和减摩效果,与未织构表面相比,其摩擦系数与磨痕宽度降低了60%以上. 这主要是由于织构深度为10 μm的不锈钢表面在摩擦过程中,润滑油通过其收敛区域时产生了很好的楔效应,润滑油产生的升力较大,改善了该织构表面在摩擦过程的润滑状态,从而呈现很好的摩擦学性能.      

Evaluation of wall slip effects in the lubricating grease/air two-phase flow along pipelines

Evaluation of wall slip phenomena during the horizontal pipeline flow of air/lubricating grease mixtures was investigated. With this aim, pressure drop measurements have been carried out along pipelines with different diameter and roughness. A modified Jastrzebski's equation for the slip velocity, based on the introduction of the relative roughness, has been used to correct wall slip effects for a lithium lubricating grease/air system. This expression has been introduced in the classical Rabinowitsch–Mooney treatment and applied to the superficial liquid velocity instead of the single-phase average velocity following a single-phase treatment analogy. Thus, the non-slip flow curve data for the two-phase mixture were obtained from roughened pipes and compared with those obtained from pipes with smooth internal surfaces. The effect of air on the extension of wall slip has been established as a function of air flow rate. Thus, the consideration of the reduction of the wetted pipe surface as air is injected allows an adequate explanation of this phenomenon, confirmed by the reduction of the effective slip contribution on the observed apparent shear rate. A power-law relationship between the slip velocity and the wall shear stress has been deduced, although this tends asymptotically to linearity as air flow rate is increased.     

Interaction between slip and the high-frequency vibrations of a shaped surface in the working gap of a gas-lubricated bearing with inclined grooves

The article discusses a flat bearing with a gas lubricant, one of whose surfaces is shaped by inclined grooves and vibrates in accordance with a given harmonic law with a high frequency. The reaction of a thin layer of viscous compressible gas is formed as a result of interaction between the effects of slip and high-frequency vibrations. Asymptotic methods are used in the investigation of the reactions of the gaseous layer; the thermodynamic process in the lubricating layer is assumed to be isothermal, and in the equation of motion of the gas the effect of inertial and mass forces is not taken into consideration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 43–50, March–April, 1976.     

纳米薄膜润滑物理—数学模型及数值分析

基于润滑剂分子通常具有链状结构的事实，在分析润滑剂分子链长同膜厚关系的基础上，建立了纳米薄膜润滑物理模型，并利用含旋转量的流体力学运动方程得到了相应的Reynolds方程，同时对薄膜润滑Reynolds方程进行了数值计算，以考察特征长度对薄膜润滑状态参数的影响。结果表明，同相应的厚膜解相比，薄膜模型中润滑剂的粘度及承载能力均明显提高，且其提高幅度随着特征长度的增大而增大。根据润滑剂分子链长度确定的薄膜润滑区间以及膜厚－速度关系数值解同相应的试验结果一致。     

界面闪温对ZDDP反应膜生成特性的研究

二烷基二硫代磷酸锌(ZDDP)作为最常见的发动机润滑油添加剂,通常认为ZDDP摩擦膜在较高的宏观环境温度下产生,而忽视了局部区域的闪温变化对于膜生长的影响. 本文作者结合应力促进的热活化理论和润滑界面闪温计算模型,以球-盘滑滚摩擦试验研究为主,进行了界面闪温对ZDDP摩擦膜生成特性的分析. 在载荷和环境温度恒定的条件下,计算了不同界面滑滚比的闪温大小与分布,采用球-盘试验测得了常温下不同滑滚比的ZDDP润滑剂摩擦系数变化趋势,并与计算得到的闪温模型对照,得到闪温对ZDDP反应膜生长的影响规律;为了改善ZDDP薄膜导致的高摩擦,测试了硬脂酸钙与ZDDP的协同减摩效果. 结果表明:界面闪温的升高同样可以促进一定厚度的ZDDP摩擦膜生长;硬脂酸钙润滑剂与ZDDP共同生成的边界膜可以有效地降低ZDDP带来的高摩擦力,可以用于改善ZDDP摩擦膜的摩擦性能.      

Analysis of lubricated squeezing flow

A thin film of low-viscosity lubricating liquid between a solid wall and a viscous material reduces shear stress on the latter and tends to make it flow as though it were slipping along the wall. The result when the lubricated material is being squeezed out of the gap between approaching parallel plates is flow more nearly irrotational, or extensional, the more effective the lubricating film on the plates. Two Newtonian analyses of this flow situation are reported. One is an approximate, asymptotic analytical solution for Newtonian lubricating flow in the films and combined mixed flow, shear and extension, in the viscous layer. The second is a full two-dimensional axisymmetric solution of the momentum and continuity equations along with the kinematic condition which governs the motion of the interface. Both analyses indicate that there are two limiting flow regimes, depending on the ratio of the thickness of each of the two phases to radius and on the viscosity ratio of the two liquids. In one limit the flow is parallel squeezing and the lubricant layer slowly thins and persists a long time. In the other the lubricant is expelled preferentially. Implications of the results are discussed for rheological characterization of viscoelastic liquids and for prediction of lubricated or autolubricated flows in processing situations.     

Generation of Three-Dimensional Disturbances in a Boundary Layer on Strong Interaction with a Hypersonic Flow

Laminar boundary layer flow over an infinite-span, finite-length flat plate is investigated in the regime of strong interaction with a hypersonic gas flow. Under the assumption that an additional condition dependent on the transverse coordinate can be imposed on the trailing edge of the plate the flow functions are expanded in power series in the vicinity of the leading edge. It is shown that these expansions include an indefinite function dependent on the transverse coordinate. The corresponding boundary value problems are formulated and solved and the eigenvalues are determined. It is established that in this case the two-dimensional boundary layer can rearrange itself into a three-dimensional boundary layer.     

Peristaltic motion of third grade fluid in curved channel

＂ Analysis is performed to study the slip effects on the peristaltic flow of non-Newtonian fluid in a curved channel with wall properties. The resulting nonlinear partial differential equations are transformed to a single ordinary differential equation in a stream function by using the assumptions of long wavelength and low Reynolds number. This differential equation is solved numerically by employing the built-in routine for solving nonlinear boundary value problems （BVPs） through the software Mathematica. In addition, the analytic solutions for small Deborah number are computed with a regular perturbation technique. It is noticed that the symmetry of bolus is destroyed in a curved channel. An intensification in the slip effect results in a larger magnitude of axial velocity. Further, the size and circulation of the trapped boluses increase with an increase in the slip parameter. Different from the case of planar channel, the axial velocity profiles are tilted towards the lower part of the channel. A comparative study between analytic and numerical solutions shows excellent agreement.     

Exact solutions of incompressible Couette flow with porous walls for slightly rarefied gases

In this work, the transient incompressible Couette flow and steady-state temperature profiles between two porous parallel plates for slightly rarefied gases are solved exactly. The first-order approximation of slip velocity at the boundaries is used in the formulation. The solution is also applicable for Couette flow in micro-channels under certain circumstances. The influences of mass transfer and a nondimensional slip parameter on slip velocities are discussed. It is also found that the transient slip velocities at the walls are greatly different from the steady-state velocity slips. The influences of velocity slip and temperature slip parameters on the temperature distribution and heat transfer at the walls are analyzed and discussed. It is shown that the slip parameters can greatly change the temperature profiles and heat transfer characteristics at the walls.     

On the relationship between drag and vertical velocity fluctuations in flow over riblets and liquid infused surfaces

Direct numerical simulations (DNS) of flow over triangular and rectangular riblets in a wide range of size and Reynolds number have been carried out. The flow within the grooves is directly resolved by exploiting the immersed-boundary method. It is found that the drag reduction property is primarily associated with the capability of inhibiting vertical velocity fluctuations at the plane of the crests, as in liquid-infused surfaces (LIS) devices. This is mimicked in DNS through artificial suppression of the vertical velocity component, which yields large drag decrease, proportionate to the riblets size. A parametrization of the drag reduction effect in terms of the vertical velocity variance is found to be quite successful in accounting for variation of the controlling parameters. A Moody-like friction diagram is thus introduced which incorporates the effect of slip velocity and a single, geometry-dependent parameter. Reduced drag-reduction efficiency of LIS-like riblets is found as compared to cases with artificially imposed slip velocity. Last, we find that simple wall models of riblets and LIS-like devices are unlikely to provide accurate prediction of the flow phenomenon, and direct resolution of flow within the grooves in necessary.     

Effect of variable slip boundary conditions on flows of pressure driven non-Newtonian fluids

In microfluidic devices it has been suggested a scheme for enhancing the mixing of two fluids is to use patterned, slip boundary conditions. This has been shown to induce significant transverse flow for Newtonian fluids [S.C. Hendy, M. Jasperse, J. Burnell, Effect of patterned slip on micro- and nanofluidic flows, Phys. Rev. E 72 (2005) 016303]. Here we study the effect of patterned slip on non-Newtonian fluids. Using a power-law model it is shown for shear-thickening fluids patterned slip can induce significant transverse flows comparable in size to those produced for Newtonian fluids. However, for shear-thinning fluids this transverse flow is suppressed. We predict a convenient way to increase the transverse flow for shear-thinning fluids is to use a patterned slip boundary condition coupled to a sinusoidally time-varying pressure gradient. This system is studied using a simple linearized White–Metzner model which has a power-law viscosity function [R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics, John Wiley & Sons, New York, 1987]. In this case it is shown the two variations combine to produce transverse flow, which can be increased by increasing the frequency of the sinusoidal time-dependent fluctuation.     

Numerical simulation of laminar flow past a circular cylinder with slip conditions

The no‐slip condition is an assumption that cannot be derived from first principles and a growing number of literatures replace the no‐slip condition with partial‐slip condition, or Navier‐slip condition. In this study, the influence of partial‐slip boundary conditions on the laminar flow properties past a circular cylinder was examined. Shallow‐water equations are solved by using the finite element method accommodating SU/PG scheme. Four Reynolds numbers (20, 40, 80, and 100) and six slip lengths were considered in the numerical simulation to investigate the effects of slip length and Reynolds number on characteristic parameters such as wall vorticity, drag coefficient, separation angle, wake length, velocity distributions on and behind the cylinder, lift coefficient, and Strouhal number. The simulation results revealed that as the slip length increases, the drag coefficient decreases since the frictional component of drag is reduced, and the shear layer developed along the cylinder surface tends to push the separation point away toward the rear stagnation point so that it has larger separation angle than that of the no‐slip condition. The length of the wake bubble zone was shortened by the combined effects of the reduced wall vorticity and wall shear stress which caused a shift of the reattachment point closer to the cylinder. The frequency of the asymmetrical vortex formation with partial slip velocity was increased due to the intrinsic inertial effect of the Navier‐slip condition. Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of injection angle,density ratio,and viscosity on droplet formation in a microfluidic T-junction

The T-junction microchannel device makes available a sharp edge to form micro-droplets from biomaterial solutions. This article investigates the effects of injection angle, flow rate ratio, density ratio,viscosity ratio, contact angle, and slip length in the process of formation of uniform droplets in microfluidic T-junctions. The governing equations were solved by the commercial software. The results show that contact angle, slip length, and injection angles near the perpendicular and parallel conditions have an increasing effect on the diameter of generated droplets, while flow rate, density and viscosity ratios, and other injection angles had a decreasing effect on the diameter.     

Couette–Poiseuille flow of Bingham fluids between two porous parallel plates with slip conditions

Analytical solutions of Couette–Poiseuille flow of Bingham fluids between two porous parallel plates are derived. This study extends the work of Tsangaris et al. [S. Tsangaris, C. Nikas, G. Tsangaris, P. Neofytou, Couette flow of a Bingham plastic in a channel with equally porous parallel walls, J. Non-Newtonian Fluid Mech. 144 (2007) 42–48] to a general situation where the slip effect at the porous walls is considered. It is found that the form of the flow inside the channel depends not only on the Bingham number Bn, the Couette number Co (related to the moving wall) and the transverse Reynolds number Re, but also on the slip parameter Cs at the porous walls. In both the Co–Re diagram and the Co–Bn diagram, the region where plug flow appears enlarges as the slip effect increases, especially in the case where Co is negative. In the case where plug flow and double shear flow coexist, the transverse position of the plug flow and the shear rate at the boundaries exhibit two opposite behaviors when Cs increases, depending on the value of the other three dimensionless numbers. In other cases, slippage always weakens the shearing deformation of the flow.     

Stokes flow over a cavity on a superhydrophobic surface containing a gas bubble

Within the approximation of Stokes hydrodynamics, several problems of a steady-state flow over a two-dimensional cavity containing a gas bubble are solved using the method of boundary integral equations. In contrast to previous publications, the method developed makes it possible to study the situation in which the cavity is only partially filled with gas, and the edges of a curved phase interface do not coincide with the cavity corners. Using periodic boundary conditions for the velocity, the flows with pure-shear and parabolic velocity profiles, and also the flow over a group of cavities were considered. The aim of the study was to calculate the effective (average) slip velocity over a microcavity, as applied to flows near textured superhydrophobic surfaces. A parametric numerical study of the effective velocity slip as a function of the radius of curvature of the interface and the position of the interface relative to the cavity boundaries was performed. The accuracy of the method is validated by the calculations of a number of limiting flows over a cavity, for which a quantitative agreement with the results known in the literature is demonstrated.     

Effects of longitudinal grooves on the Couette–Poiseuille flow

The effects of longitudinal grooves on the flow resistance in a channel where the flow is driven by movement of one of the walls and modified by a streamwise pressure gradient have been studied. The reducedorder geometrymodel has been used to extract geometric features that are hydraulically relevant. Three distinct zones leading to the reduced resistance have been identified, depending on the flow pressure gradient and the groove wave number. Two of these zones correspond to grooves with long wavelengths and one to grooves with short wavelengths. Optimization has been used to determine shapes that provide the largest flow rate. In the case of the long-wavelength grooves, the optimal shapes depend on the constraints. These shapes are well approximated by a certain universal trapezoid for grooves that have the same height and depth. There exists an optimum depth which, combined with the corresponding shape, defines the optimal geometry in the case of the unequal-depth grooves; this shape is well approximated by a Gaussian function. No optimal shape exists for the short-wavelength grooves if the groove amplitude is sufficiently small; the shortest admissible wavelength dominates system performance under such conditions. The most effective groove wave number does exist for higher grooves, but the optimal shape cannot be determined due to numerical limitations.     

评价半流体润滑剂性能的齿轮台架

作者对全尺寸功率流封闭式齿轮试验台架成功地进行了改进和完善,发展了一种测试方法齐全、测量精度高的齿轮试验台架与测试系统,并以其进行了00~#半流体润滑脂、50~#机械油等润滑时啮合齿面间的油膜电压、齿轮传动效率、减速器的振动和噪声、润滑剂的温升和抗磨性能等多方面的对比分析和评价。结果表明,这种全尺寸齿轮试验台架与测试系统对半流体润滑剂性能的评价分析是可靠的,适合作为各种半流体润滑剂性能的全尺寸试验台架推广应用。