Single-Fluid Model of a Mixture for Laminar Flows of Highly Concentrated Suspensions

A model of laminar flow of a highly concentrated suspension is proposed. The model includes the equation of motion for the mixture as a whole and the transport equation for the particle concentration, taking into account a phase slip velocity. The suspension is treated as a Newtonian fluid with an effective viscosity depending on the local particle concentration. The pressure of the solid phase induced by particle-particle interactions and the hydrodynamic drag force with account of the hindering effect are described using empirical formulas. The partial-slip boundary condition for the mixture velocity on the wall models the formation of a slip layer near the wall. The model is validated against experimental data for rotational Couette flow, a plane-channel flow with neutrally buoyant particles, and a fully developed flow with heavy particles in a horizontal pipe. Based on the comparison with the experimental data, it is shown that the model predicts well the dependence of the pressure difference on the mixture velocity and satisfactorily describes the dependence of the delivered particle concentration on the flow velocity.     

Free-surface flow of concentrated suspensions

Free-surface flows of concentrated suspensions exhibit many interesting phenomena such as particle segregation and surface corrugation. In this work the flow structures associated with free-surface has been studied experimentally. The free-surface velocity for neutrally buoyant suspension of uniform spheres in a gravity driven inclined channel flow was determined by particle imaging velocimetry (PIV) technique. Experiments were carried out for concentrated suspensions with particle fractions ? ranging from 0.40 to 0.50. The measured velocities show blunted profile in the channel. The blunting of the velocity profile increases with the particle concentration. The rms velocity fluctuations measured at the free-surface progressively increase with particle fraction ? and are linear in shear rate γ. The surface roughness were characterized by analyzing the power spectral density of the refracted light from the free-surface. The characteristics observed are in support of earlier findings.     

The effects of surface roughness geometry of flow undergoing Poiseuille flow by molecular dynamics simulation

Numerical simulation of Poiseuille flow of liquid Argon in a rough nano-channel using the non-equilibrium molecular dynamics simulation is performed. Density and velocity profiles across the channel are investigated in which roughness is implemented only on the lower wall. The Lennard–Jones potential is used to model the interactions between all particles. The effects of surface roughness geometry, gap between roughness elements (or roughness periodicity), surface roughness height and surface attraction energy on the behavior of the flow undergoing Poiseuille flow are presented. Results show that surface shape and roughness height have a decisive role on the flow behaviors. In fact, by increasing the roughness ratio (height to base ratio), the slip velocity and the maximum velocity in the channel cross section are reduced, and the density fluctuations near the wall increases. Results also show that the maximum density near the wall for a rough surface is less than a smooth wall. Moreover, the simulation results show that the effect of triangle roughness surface on the flow behavior is more than the cylindrical ones.     

Direct numerical simulation of particle-laden plane turbulent wall jet and the influence of Stokes number

The distribution and motion of inertial particles in plane turbulent wall jet are investigated using direct numerical simulation, under the assumption of one-way coupling. To our knowledge, this appears to be the first direct numerical simulation of a particle-laden plane turbulent wall jet. It is shown that, in outer part of the wall jet, the behaviour of particles closely resembles that of a free plane jet. Due to the streamwise decay of particle Stokes number, the particle streaks formed in the near wall region of the wall jet are characterized by their intensity variation, which differs significantly from those in the channel flow. The streamwise growth of the particle velocity half-width is approximately equal to that of the fluid velocity half-width and the maximum velocity of particles decays slower than that of fluid due to inertia. The outer scaling can collapse the mean particle velocity in both the inner and outer region for heavier particles. In the buffer region, the particle–fluid velocity difference can be negative or positive depending on the Stokes number since there are two competing effects, namely the memory effect and turbophoresis. In the viscous region, the larger particles are on average faster than fluid and the velocity difference is found to be self-similar depending on outer Stokes number. The near-wall distribution of velocity difference is significantly correlated with the presence of high-momentum particles which are entrained by vortical structures generated in the outer region of the wall jet. These results are useful for environmental and engineering applications.     

Experiments on the linear instability of flow in a wavy channel

The effects of wall corrugation on the stability of wall-bounded shear flows have been examined experimentally in plane channel flows. One of the channel walls has been modified by introduction of the wavy wall model with the amplitude of 4% of the channel half height and the wave number of 1.02. The experiment is focused on the two-dimensional travelling wave instability and the results are compared with the theory [J.M. Floryan, Two-dimensional instability of flow in a rough channel, Phys. Fluids 17 (2005) 044101 (also: Rept. ESFD-1/2003, Dept. of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada, 2003)]. It is shown that the flow is destabilized by the wall corrugation at subcritical Reynolds numbers below 5772, as predicted by the theory. For the present corrugation geometry, the critical Reynolds number is decreased down to about 4000. The spatial growth rates, the disturbance wave numbers and the distribution of disturbance amplitude measured over such wavy wall also agree well with the theoretical results.     

微纳结构超疏水表面的湍流减阻机理研究

超疏水表面的优异性质使其在现代生活和工业生产中具有十分广泛的潜在应用价值. 本文采用了碳纳米管缠绕技术和聚氟硅氧烷疏水化处理方法制备了具有二级微纳米结构的超疏水表面. 测量了由该超疏水表面构建的槽道中的流动压降,将其与普通表面构建的槽道内的流动压降进行比较,发现在层流情况下,流动阻力减小最多达到了22.8%. 在湍流的情况下,超疏水表面的减阻比例约为53.3%,减阻效果比层流更加明显.利用PIV (particle image velocimetry) 技术测量了具有超疏水表面的槽道内的速度场,通过超疏水表面速度滑移和湍动脉动场信息,分析了湍流减阻效果比层流更加明显的物理机制.     

Particle transport in Poiseuille flow in narrow channels

Particle-tracking experiments were performed to validate a model [Staben, M.E., Zinchenko, A.Z., Davis, R.H., 2003. Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow. Phys. Fluids 15, 1711–1733] for neutrally buoyant spherical particles convected by a Poiseuille flow in a thin microchannel for particles as large as d_p/H = 0.95, where d_p is the particle diameter and H is the channel width (narrow dimension). The measured and predicted velocities agree within experimental error and show that a particle’s velocity is more retarded when it is larger and/or closer to a channel wall. The particle distribution across the channel for a blunt entrance shows a focusing of small particles away from the walls and towards the center of the channel, whereas the particle distribution for an offset-angled entrance is slightly skewed towards the wall encountered first in the entrance region. As a result, the average particle velocities for the blunt entrance exceed those for the angled entrance. Moreover, due to the depletion of particles from the slow-moving region within one radius of the wall, the average particle velocity exceeds the average fluid velocity unless the particle diameter exceeds about 80% of the channel width.     

Molecular dynamics simulation of liquid argon flow at platinum surfaces

The micro Poiseuille flow for liquid argon flowing in a nanoscale channel formed by two solid walls was studied in the present paper. The solid wall material was selected as platinum, which has well established interaction potential. We consider the intermolecular force not only among the liquid argon molecules, but also between the liquid argon atoms and the solid wall particles, therefore three regions, i.e. the liquid argon computation domain, the top and bottom solid wall regions are included for the force interaction. The present MD (Molecular Dynamics) simulation was performed without any assumptions at the wall surface. The objective of the study is to find how the flow and the slip boundaries at the wall surface are affected by the applied gravity force, or the shear rate. The MD simulations are performed in a nondimensional unit system, with the periodic boundary conditions applied except in the channel height direction. Once the steady state is reached, the macroscopic parameters are evaluated using the statistical mechanics approach. For all the cases tested numerically in the present paper, slip boundaries occur, and such slip velocity at the stationary wall surface increases with increasing the applied gravity force, or the shear rate. The slip length, which is defined as the distance that the liquid particles shall travel beyond the wall surfaces to reach the same velocity as the wall surface, sharply decreases at small shear rate, then slightly decreases with increasing the applied shear rate. We observe that the liquid viscosity remains nearly constant at small shear rates, and the Newtonian flow occurs. However, with increasing the shear rate, the viscosity increases and the non-Newtonian flow appears.     

A plane turbulent wall jet on a fully rough surface

The mean velocity field and skin friction characteristics of a plane turbulent wall jet on a smooth and a fully rough surface were studied using Particle Image Velocimetry. The Reynolds number based on the slot height and the exit velocity of the jet was Re = 13,400 and the nominal size of the roughness was k = 0.44 mm. For this Reynolds number and size of roughness element, the flow was in the fully rough regime. The surface roughness results in a distinct change in the shape of the mean velocity profile when scaled in outer coordinates, i.e. using the maximum velocity and outer half-width as the relevant velocity and length scales, respectively. Using inner coordinates, the mean velocity in the lower region of the inner layer was consistent with a logarithmic profile which characterizes the overlap region of a turbulent boundary layer; for the rough wall case, the velocity profile was shifted downward due to the enhanced wall shear stress. For the fully rough flow, the decay rate of the maximum velocity of the wall jet is increased, and the skin friction coefficient is much larger than for the smooth wall case. The inner layer is also thicker for the rough wall case. The effects of surface roughness were observed to penetrate into the outer layer and slightly enhance the spread rate for the outer half-width, which was not observed in most other studies of transitionally rough wall jet flows.     

Experimental investigation of the unsteady structure of a transitional plane wall jet

 A laminar wall jet undergoing transition is investigated using the particle image velocimetry (PIV) technique. The plane wall jet is issued from a rectangular channel, with the jet-exit velocity profile being parabolic. The Reynolds number, based on the exit mean velocity and the channel width, is 1450. To aid the understanding of the global flow features, laser-sheet/smoke flow visualizations are performed along streamwise, spanwise, and cross-stream directions. Surface pressure measurements are made to correlate the instantaneous vorticity distribution with the surface pressure fluctuations. The instantaneous velocity and vorticity field measurements provide the basis for understanding the formation of the inner-region vortex and the subsequent interactions between the outer-region (free-shear-layer region) and inner-region (boundary-layer region) vortical structures. Results show that under the influence of the free-shear-layer vortex, the local boundary layer becomes detached from the surface and inviscidly unstable, and a vortex is formed in the inner region. Once this vortex has formed, the free-shear-layer vortex and the inner-region vortex form a vortex couple and convect downstream. The mutual interactions between these inner- and outer-region vortical structures dominate the transition process. Farther downstream, the emergence of the three-dimensional structure in the free shear layer initiates complete breakdown of the flow. Received: 8 November 1995/Accepted: 6 November 1996     

An experimental investigation of the flow structure over a corrugated waveform in a transpired air collector

An experimental investigation of the flow dynamics in a channel with a corrugated surface is presented. Particle image velocimetry was used to obtain two-dimensional velocity fields at three different locations along the channel length, over a range of Reynolds numbers. The results show a significant impact of the corrugation waveform on the mean and turbulent flow structure inside the channel. Strong bursting flow originating from the trough, sweeping flow from the bulk region and the vortex shedding off the crest were observed. Their interactions created a complex three-dimensional flow structure extended over almost the entire channel. The mean velocity profiles indicate a strong diffusion of shear. The profiles of various turbulent properties show the enhancement of turbulence in the vicinity of the waveform. It was found that the turbulence in the channel was almost entirely produced in this region above the corrugation trough. Significant momentum transfer from the corrugation wall by the turbulent velocity field was also observed. The mean and turbulent flow behaviour was found to be periodic with respect to the waveform over most of the channel length. The results show the presence of strong turbulence even at the Reynolds number that falls within the conventional laminar range.     

Numerical study of particle deposition in a turbulent channel flow with transverse roughness elements on one wall

A numerical study is presented for the effect of wall roughness on the deposition of solid spherical particles in a fully developed turbulent channel flow based on large eddy simulation combined with a Lagrangian particle-tracking scheme. The interest is focused on particles with response times in wall units in the range of 2.5 ≤ τ_p⁺ ≤ 600 depositing onto a vertical rough surface consisting of two-dimensional transverse square bars separated by a rectangular cavity. Predictions of particle deposition rates are obtained for several values of the cavity width to roughness element height ratio and particle response time. It is shown that the accumulation of particles in the near wall region and their preferential concentration in flow areas of low streamwise fluid velocity that occur in turbulent flows at flat channels are significantly affected by the roughness elements. Particle deposition onto the rough wall is considerably increased, exhibiting a subtle dependence on the particle inertia and the spacing between the bars. The observed augmentation of deposition coefficient can be attributed to the flow modifications induced by the roughness elements and to the inertial impaction of particles onto the frontal deposition area of the protruding square bars.     

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.     

Experimental studies on particle behaviour and turbulence modification in horizontal channel flow with different wall roughness

Detailed measurements in a developed particle-laden horizontal channel flow (length 6 m, height 35 mm, the length is about 170 channel heights) are presented using phase-Doppler anemometry for simultaneous determination of air and particle velocity. The particles were spherical glass beads with mean diameters in the range of 60 µm-1 mm. The conveying velocity could be varied between about 10 m/s and 25 m/s, and the particle mass loading could reach values of about 2 (the mass loading is defined as the ratio of particle to gas phase mass flow rates), depending on particle size. For the first time, the degree of wall roughness could be modified by exchanging the wall plates. The influence of these parameters and the effect of inter-particle collisions on the profiles of particle mean and fluctuating velocities and the normalised concentration in the developed flow were examined. It was shown that wall roughness decreases the particle mean velocity and enhances fluctuating velocities due to irregular wall bouncing and an increase in wall collision frequency, i.e. reduction in mean free path. Thereby, the larger particles are mainly more uniformly distributed across the channel, and gravitational settling is reduced. Both components of the particle velocity fluctuation were reduced with increasing mass loading due to inter-particle collisions and the momentum loss involved. Moreover, the effect of the particles on the air flow and the turbulent fluctuations was studied on the basis of profiles in the developed flow and turbulence spectra determined for the streamwise velocity component. In addition to the effect of particle size and mass loading on turbulence modulation, the influence of wall roughness was analysed. It was clearly shown that increasing wall roughness also results in a stronger turbulence dissipation due to two-way coupling.     

The effect of sphere–wall interactions on particle motion in a viscoelastic suspension of FENE dumbbells

A new method for simulating the motion of particles in viscoelastic Boger fluids is extended to problems with bounded geometries. Viscoelasticity is incorporated into the Stokesian dynamics method by modeling a viscoelastic fluid as a suspension of finite-extension nonlinear-elastic (FENE) dumbbells. Wall–particle and wall–bead interactions are included by using the image system method of Blake; particle–particle and particle–bead interactions are also modified by the presence of the wall. The method of incorporating sphere–wall interactions is verified by doing calculations for several problems involving particle–wall interactions in Newtonian fluids. The method is then used to study particle–wall interactions in viscoelastic dumbbell suspensions by examining several problems of interest: the sedimentation of a spherical particle near vertical and tilted walls; the sedimentation of a nonspherical particle between two flat plates; and the migration of a neutrally buoyant sphere in plane Poiseuille flow. We find that a single sphere falling near a wall moves toward the wall and exhibits anomalous rotation. When the wall is tilted by an amount less than a few degrees, the sphere still moves toward the wall, but tilting the wall greater than an angle of approximately 1.5° results in the sphere falling away from the wall. A nonspherical particle settling in a channel exhibits an oscillatory motion, but ultimately becomes centered in the channel with its long axis parallel to gravity. Finally, it is shown that a neutrally buoyant sphere in plane Poiseuille flow migrates to the channel center in wide channels, but migrates to the walls when the sphere is sufficiently large relative to the channel width.     

Numerical study of concentrated fluid–particle suspension flow in a wavy channel

The particle migration effects and fluid–particle interactions occurring in the flow of highly concentrated fluid–particle suspension in a spatially modulated channel have been investigated numerically using a finite volume method. The mathematical model is based on the momentum and continuity equations for the suspension flow and a constitutive equation accounting for the effects of shear‐induced particle migration in concentrated suspensions. The model couples a Newtonian stress/shear rate relationship with a shear‐induced migration model of the suspended particles in which the local effective viscosity is dependent on the local volume fraction of solids. The numerical procedure employs finite volume method and the formulation is based on diffuse‐flux model. Semi‐implicit method for pressure linked equations has been used to solve the resulting governing equations along with appropriate boundary conditions. The numerical results are validated with the analytical expressions for concentrated suspension flow in a plane channel. The results demonstrate strong particle migration towards the centre of the channel and an increasing blunting of velocity profiles with increase in initial particle concentration. In the case of a stenosed channel, the particle concentration is lowest at the site of maximum constriction, whereas a strong accumulation of particles is observed in the recirculation zone downstream of the stenosis. The numerical procedure applied to investigate the effects of concentrated suspension flow in a wavy passage shows that the solid particles migrate from regions of high shear rate to low shear rate with low velocities and this phenomenon is strongly influenced by Reynolds numbers and initial particle concentration. Copyright © 2008 John Wiley & Sons, Ltd.     

Roughness effects on turbulent plane wall jets in an open channel

This paper reports the effects of surface roughness on the mean flow characteristics for a turbulent plane wall jet created in an open channel. The velocity measurements were obtained using a laser Doppler anemometer over smooth and transitionally rough surfaces. The power law proposed by George et al. (2000) was used to determine the friction velocity. Both conventional scaling and the momentum–viscosity scaling proposed by Narasimha et al. (1973) were used to analyze the streamwise evolution of the flow. The results show that surface roughness increases the skin friction coefficient and the inner layer thickness, but the jet half-width is nearly independent of surface roughness.     

Effect of surface roughness on a turbulent wall-attaching offset jet

The flow characteristics of a two-dimensional offset jet discharged parallel to a rough wall is experimentally investigated by using a split film probe. The distributions of the mean velocity and turbulent stresses in the flow field are obtained and compared with those of the wall attaching offset jet on a smooth wall. It is found that the wall-attaching region on the rough wall is longer than on the smooth wall for the same offset height and the jet speed. The normal distance of the maximum velocity point is farther away from the wall than that for the smooth wall case because of the thick wall boundary layer established by the surface roughness. It is also found that the roughness of the wall accelerates the relaxation process towards redeveloped plane wall jet and that it exhibits a quite different turbulent diffusion behavior especially near the wall from that in the wall jet over a smooth surface.