Local Slip Velocity Research Articles

Experimental Characterization of Bimodal Granular Flow

Solid–liquid flows are encountered in various industrial and natural environments. The internal structure of such flows is highly sensitive to the grading of the solid particles present. In this experimental study, an extended stereometric method is employed to assess the distributions of velocity of particles of different fractions, distinguished by different colors, in vertical and nearly horizontal granular flows. In the vertical flow experiments, mixtures comprising three fractions of lightweight particles, characterized by a very similar density, size, and shape, were tested. The results affirmed the method’s ability to discern particle velocity differences on the order of millimeters per second, establishing its suitability for characterizing nearly horizontal open-channel flows with bimodal mixtures that are stratified and exhibit more complex velocity distributions. Tilting flume experiments, incorporating additional measurements of water velocity distribution, allowed for the evaluation of local slip between water and particles, as well as between particles of the two fractions in the flow. The results indicated that, although the local slip velocity was relatively small, the average slip velocity between the carrying water and transported particles was significantly larger. This factor must be taken into consideration when evaluating bed friction or bed erosion for granular flow in a channel with an erodible bed.

Experimental Study of an upflow Fluidized Bed: Identification of Fluidization Regimes

The concept of solar receiver using fluidized particles as heat transfer fluid is attractive from the point of view of its performance but also of the material used. In this concept, the receiver is composed of tubes subjected to concentrated solar radiation in which the fluidized particles circulate vertically. Circulation in the tubes, immersed in a “nurse” fluidized bed, is ensured thanks to a controlled pressure difference imposed on the latter and secondary aeration. This ventilation located at the bottom of the absorber tubes makes it possible to control the fluidization regimes. The latter strongly influence the parietal heat transfers and therefore the performance of the receiver. In order to better understand the conditions of appearance of these regimes and to better identify them, a study at room temperature was carried out with a tube 45 mm in internal diameter and 3.63 m in height. The tube is instrumented with several pressure sensors distributed over its height. More than 170 experiments have been performed exploring wide ranges of particle and aeration flow rates, with and without particle circulation. Signal processing methods, classically used in the scientific literature of fluidized beds, are applied. Combined together, these methods have enabled the identification of bubbling, pistoning (of the wall and axisymmetric), turbulent fluidization and rapid fluidization regimes. The pooling of all this information allows the establishment of a diagram of the fluidization regimes and their transition, showing that the local slip velocity is the key parameter governing the structure of the flow.

Fluidization regimes of dense suspensions of Geldart group A fluidized particles in a high aspect ratio column

Fluidization regimes were studied in numerous papers with applications in risers in which gas velocity is the main driving force. The situation is different when a tube is immersed in a fluidized bed vessel in which a pressure is imposed to move the particle upward. The particle-in-tube solar receiver concept is based on this latter operation mode with the aim to heat particles at high temperature with concentrated solar energy. This study identifies the fluidization regimes in a pressure-driven system that includes a secondary aeration to control the air velocity in the tube. Bubbling, slugging, turbulent and fast fluidization regimes are determined thanks to temporal pressure signal processing methods and a regime map is plotted. The transition velocities are significantly lower than in classical risers. The local slip velocity is defined as the governing parameter of the flow structure and the variation of the local particle volume fraction is discussed.

CFD modelling of the flow of ice slurry in a vertical slit channel

In this article, the Euler-Euler method was applied to CFD modelling of adiabatic ice slurry flow, for different flow directions in a vertical slit channel. The mean relative accuracy of determining pressure drops compared to experimental studies was 5.6%. Calculations showed that the relative slip velocity and the effect of flow direction on slip velocity increase with decreasing carrier fluid concentration, decreasing mean flow velocity, and decreasing mean solid particles volume fraction. The mean particle slip velocity does not exceed 4%, and local slip velocity values can be 58% of the mean suspended solids flow velocity. For heterogeneous flow, the highest slip velocities occur at a distance of 15% of the channel width from the channel sidewalls. The shape of the solid particles distribution profile is determined by the mean flow velocity and the mean solid particles volume fraction. Excluding the area at a distance of 8% of the channel width from the sidewall where local maximum (for low velocities) and minimum (for higher velocities) values may occur, the profile is stabilised in the central part of the channel. In this study, the boundary curves between heterogeneous and homogeneous flow were determined for ice slurry flow in a vertical slit channel.

Three-dimensional modelling of the multiphase hydrodynamics in a separated-gasification chemical looping combustion unit during full-loop operation

Separated-gasification chemical looping combustion (SG-CLC) is a clean utilization technology for fossil fuels, which can separate CO2 during high-performance combustion process with low degradation of oxygen carrier and zero-energy penalty. As an important part of the optimization, modelling and prediction of the multiphase hydrodynamics in the SG-CLC unit were conducted in this work. This unit consists of a gasifier (GR), a reduction reactor (RR) and an air reactor (AR). For thorough understanding of the flow behaviors of three phases (gas, oxygen carrier and sand phases), a three-dimensional computational fluid dynamics (CFD) model for SG-CLC system was first implemented. The main purpose is to predict multiphase hydrodynamics at the fuel side of this SG-CLC system due to its significant effects on combustion efficiency. The axial pressure profile predicted by the CFD model was validated by experimental data to demonstrate its feasibility. Then, based on this model, the hydrodynamics of different phases at fuel side (GR and RR) were investigated under fundamental condition, which indicated the gas-solid flow mechanism in circulation establishment process. Furthermore, effects of the operation condition on the hydrodynamics properties were investigated. The local gas-solid slip velocity in RR was fitted as the function of superficial fluidizing number Nr and axial position, which showed high accuracy for the prediction in this system.

Compaction Dynamics during Progenitor Cell Self-Assembly Reveal Granular Mechanics

Summary We study the self-assembly dynamics of human progenitor cells in agarose microwells that are used for production of chondrogenic organoids. Using image analysis on time-lapse microscopy, we estimate the aggregate area in function of time for a large number of aggregates. In control conditions, the aggregate radius follows an exponential relaxation that is consistent with the dewetting dynamics of a liquid film. Upon introducing Y-27632 Rho kinase inhibitor, the compatibility with the liquid model is lost, and slowed-down relaxation dynamics are observed. We demonstrate that these aggregates behave as granular piles undergoing compaction, with density relaxation that follows a stretched exponential. Using simulations with an individual cell-based model, we construct a phase diagram of cell aggregates that suggests that the aggregate in presence of Rho kinase inhibitor approaches glass transition.

The local slip length and flow fields over nanostructured superhydrophobic surfaces

The local slip behavior and flow fields near the gas-liquid interface (GLI) of a Newtonian liquid flowing past a superhydrophobic surface with periodic rectangular grooves are investigated using molecular dynamics (MD) simulations. The saturated vapor of the liquid fills the groove to form the GLI. A flat GLI is introduced by carefully adjusting the channel height to make the liquid bulk pressure equal to the coexistence pressure. The setup with the flat GLI allows for an accurate determination of the local slip velocity, shear rate and slip length. We find that the local slip velocity and shear rate at the GLI are well described by the elliptical and exponential functions, respectively. By directly computing the local slip length from the local flow fields, we propose a novel distribution function for the slip length along the GLI for both transverse and longitudinal flows. Moreover, we demonstrate that the relationship between the local and the effective slip lengths in the transverse and longitudinal cases deviates from the continuum assumptions as the groove width is reduced to the nanoscale dimensions. The functional form for the local slip length can be potentially used as a boundary condition in the continuum analysis without considering the explicitly gas flow in the grooves of superhydrophobic surfaces.

Local bubble slip velocity in a downward laminar tube flow

The paper presents a study of the slip velocity for almost spherical bubbles in a downward laminar tube flow. The local slip velocity is defined as a difference between the mean liquid velocity (measured with electrodiffusional method) and the mean bubble velocity (measured with a modified LDA tool with a small size of measurement volume). The law for slip velocity for downward flow is significantly different from a similar law for upward flow. This reveals that the bubble flow motion is rather random than structured in the upward flow.

Sound and turbulence modulation by particles in high-speed shear flows

High-speed free-shear-flow turbulence, laden with droplets or particles, can radiate weaker pressure fluctuations than its unladen counterpart. In this study, Eulerian–Lagrangian simulations of high-speed temporally evolving shear layers laden with monodisperse, adiabatic, inertial particles are used to examine particle–turbulence interactions and their effect on radiated pressure fluctuations. An evolution equation for gas-phase pressure intensity is formulated for particle-laden flows, and local mechanisms of pressure changes are quantified over a range of Mach numbers and particle mass loadings. Particle–turbulence interactions alter the local pressure intensity directly via volume displacement (due to the flow of finite-size particles) and drag coupling (due to local slip velocity between phases), and indirectly through significant turbulence changes. The sound radiation intensity near subsonic mixing layers increases with mass loading, consistent with existing low Mach number theory. For supersonic flows, sound levels decrease with mass loading, consistent with trends observed in previous experiments. Particle-laden cases exhibit reduced turbulent kinetic energy compared to single-phase flow, providing one source of their sound changes; however, the subsonic flow does not support such an obvious source-to-sound decomposition to explain its sound intensity increase. Despite its decrease in turbulence intensity, the louder particle-laden subsonic flows show an increase in the magnitude and time-rate-of-change of fluid dilatation, providing a mechanism for its increased sound radiation. Contrasting this, the quieter supersonic particle-laden flows exhibit decreased gas-phase dilatation yet its time-rate-of-change is relatively insensitive to mass loading, supporting such a connection.

The effect of an unsteady flow incident on an array of circular cylinders

In this paper we investigate the effect of an inhomogeneous and unsteady velocity field incident on an array of rigid circular cylinders arranged within a circular perimeter (diameter $D_{G}$) of varying solid fraction $\unicode[STIX]{x1D719}$, where the unsteady flow is generated by placing a cylinder (diameter $D_{G}$) upwind of the array. Unsteady two-dimensional viscous simulations at a moderate Reynolds number ($Re=2100$) and also, as a means of extrapolating to a flow with a very high Reynolds number, inviscid rapid distortion theory (RDT) calculations were carried out. These novel RDT calculations required the circulation around each cylinder to be zero which was enforced using an iterative method. The two main differences which were highlighted was that the RDT calculations indicated that the tangential velocity component is amplified, both, at the front and sides of the array. For the unsteady viscous simulations this result did not occur as the two-dimensional vortices (of similar size to the array) are deflected away from the boundary and do not penetrate into the boundary layer. Secondly, the amplification is greater for the RDT calculations as for the unsteady finite Reynolds number calculations. For the two highest solid fraction arrays, the mean flow field has two recirculation regions in the near wake of the array, with closed streamlines that penetrate into the array which will have important implications for scalar transport. The increased bleed through the array at the lower solid fraction results in this recirculation region being displaced further downstream. The effect of inviscid blocking and viscous drag on the upstream streamwise velocity and strain field is investigated as it directly influences the ability of the large coherent structures to penetrate into the array and the subsequent forces exerted on the cylinders in the array. The average total force on the array was found to increase monotonically with increasing solid fraction. For high solid fraction $\unicode[STIX]{x1D719}$, although the fluctuating forces on the individual cylinders is lower than for low $\unicode[STIX]{x1D719}$, these forces are more correlated due to the proximity of the cylinders. The result is that for mid to high solid fraction arrays the fluctuating force on the array is insensitive to $\unicode[STIX]{x1D719}$. For low $\unicode[STIX]{x1D719}$, where the interaction of the cylinders is weak, the force statistics on the individual cylinders can be accurately estimated from the local slip velocity that occurs if the cylinders were removed.

Fast imaging of the velocity profile of the conducting continuous phase in multiphase flows using an electromagnetic flowmeter

This paper describes a novel dual-frequency inductive flow tomography (IFT) system, which relies on the use of a multi-electrode electromagnetic flow meter (EMFM). This flow meter is currently capable of imaging the velocity profile of the conducting continuous phase of both single phase and highly asymmetric multiphase flows ten times every second. Uniform and anti-Helmholtz magnetic fields are simultaneously applied to the cross section of the flow tube of the EMFM. This enables flow induced potentials to be measured, at an array of electrodes, flush mounted on the inner wall of the EMFM, ten times every second using a multi-channel analogue signal conditioning system. These measured flow induced potentials are then used in an image reconstruction algorithm to reconstruct the water velocity profile in the flow cross section at 0.1 s time intervals.A series of experiments were carried out in water continuous, upward, air-water flows inclined at 15° to the vertical to measure the water velocity profile using the IFT system. The water velocity profiles were compared with air velocity profiles previously obtained for inclined air-water flows at similar flow conditions using local probing techniques. For all of the flow conditions investigated it was found that both the local axial water and air velocities were significantly greater at the upper side of the inclined pipe than at the lower side. The high local water velocities were probably due to upward momentum of the air bubbles being locally transferred to the water at the upper side of the inclined pipe. A comparison of the local axial air velocity distribution and the local axial water velocity distribution also showed that the local slip velocity between the phases varied markedly in the flow cross section – indicating that previous assumptions that the local slip velocity is constant in the flow cross section are clearly incorrect.

A grid-independent EMMS/bubbling drag model for bubbling and turbulent fluidization

The EMMS/bubbling drag model takes the effects of meso-scale structures (i.e. bubbles) into modeling of drag coefficient and thus improves coarse-grid simulation of bubbling and turbulent fluidized beds. However, its dependence on grid size has not been fully investigated. In this article, we adopt a two-step scheme to extend the EMMS/bubbling model to the sub-grid level. Thus the heterogeneity index, HD, which accounts for the hydrodynamic disparity between homogeneous and heterogeneous fluidization, can be correlated as a function of both local voidage and slip velocity. Simulations over a periodic domain show the new drag model is less sensitive to grid size because of the additional dependence on local slip velocity. When applying the new drag model to simulations of realistic bubbling and turbulent fluidized beds, we find grid-independent results are easier to obtain for high-velocity turbulent fluidized bed cases. The simulation results indicate that the extended EMMS/bubbling drag model is a potential method for coarse-grid simulations of large-scale fluidized beds.

Study of the Falling Friction Effect on Rolling Contact Parameters

The existence of a wheel–rail friction coefficient that depends on the slip velocity has been associated in the literature with important railway problems like the curving squeal and certain corrugation problems in rails. Rolling contact models that take into account this effect were carried out through the so-called Exact Theories adopting an exact elastic model of the solids in contact, and Simplified Theories which assume simplified elastic models such as Winkler. The former ones, based on Kalker’s Variational Theory, give rise to numerical problems; the latter ones need to adopt hypotheses that significantly deviate from actual conditions, leading to unrealistic solutions of the contact problem. In this paper, a methodology based on Kalker’s Variational Theory is presented, in which a local slip velocity-dependent friction law is considered. A formulation to get steady-state conditions of rolling contact by means of regularisation of the Coulomb’s law is proposed. The model allows establishing relationships in order to estimate the global properties (creepage velocities vs. total longitudinal forces) through local properties (local slip velocity vs. coefficient of friction) or vice versa. The proposed model shows a good agreement with experimental tests while solving the numerical problems previously mentioned.

Numerical modeling of measured railway creep versus creep-force curves with CONTACT

Numerical simulation of the behavior of rail vehicles requires a frictional contact model for the wheel–rail contact forces that must be fast and detailed. A comment on Kalker's original theories is that they describe well only the situation for scrupulously clean surfaces. Measured creep versus creep force curves show two important deviations: a reduced initial slope of the traction curve, i.e. smaller stiffness of the contact interface, and falling friction, decreasing traction forces at higher creepages after attaining a maximum.This paper describes extensions of the numerical model CONTACT by which these two effects are incorporated. The reduced initial slope is attributed to effects of roughness and contamination, which are modeled by introducing an interfacial layer in which auxiliary displacements occur. Falling friction is implemented via a friction coefficient dependent on the local slip velocity. By itself this gives irregular results, therefore a further change concerns the introduction of so-called friction memory. All together these extensions yield the much improved capability to reproduce measured creep-force curves in a wide range of practically relevant circumstances.

Momentum transfer in a turbulent, particle-laden Couette flow

A point-force model is used to study turbulent momentum transfer in the presence of moderate mass loadings of small (relative to Kolmogorov scales), dense (relative to the carrier phase density) particles. Turbulent Couette flow is simulated via direct numerical simulation, while individual particles are tracked as Lagrangian elements interacting with the carrier phase through a momentum coupling force. This force is computed based on the bulk drag of each particle, computed from its local slip velocity. By inspecting a parameter space consisting of particle Stokes number and mass loading, a general picture of how and under what conditions particles can alter near-wall turbulent flow is developed. In general, it is found that particles which adhere to the requirements for the point-particle approximation attenuate small-scale turbulence levels, as measured by wall-normal and spanwise velocity fluctuations, and decrease turbulent fluxes. Particles tend to weaken near-wall vortical activity, which in turn, through changes in burst/sweep intensities, weakens the ability of the turbulent carrier-phase motion to transfer momentum in the wall-normal direction. Compensating this effect is the often-ignored capacity of the dispersed phase to carry stress, resulting in a total momentum transfer which remains nearly unchanged. The results of this study can be used to interpret physical processes above the ocean surface, where sea spray potentially plays an important role in vertical momentum transfer.

A microgrooved membrane based gas–liquid contactor

This research presents an approach for applying microgrooved membranes for improved gas–liquid contacting. The study involves analysis of the performance of the microdevice by quantifying the flux enhancement for different membrane configurations. Two kinds of configurations, continuous and non-continuous grooves, were investigated. The microgrooves provide shear-free gas–liquid interfaces, which result in local slip velocity at the gas–liquid interface. Exploiting this physical phenomenon, it is possible to reduce mass transport limitations in gas–liquid contacting. An experimental study using grooved membranes suggests enhancement in flux up to 20–30 %. The flux enhancement at higher liquid flow rates is observed due to a partial shear-free gas–liquid interface. The performance of the membrane devices decreased with wetted microgrooves due to the mass transport limitations. The flow visualization experiments reveal wetting of the microgrooves at higher liquid flow rates. According to the numerical and experimental study, we have shown that microgrooved membranes can be employed to improve gas–liquid contacting processes.

Lateral migration of a small spherical buoyant particle in a wall-bounded linear shear flow

Lateral migration velocities of solid spherical particles suspended in a linear wall-bounded shear flow are measured for Reynolds number, Re<2 (Re=2RU/ν, where R is the particle radius, U is the local slip velocity between the particle and the fluid, and ν is the kinematic viscosity of the suspending fluid). The velocity parallel to the wall and the distance between the particle and the wall are measured as a function of time, allowing the lateral migration velocity and the slip velocity of the particle to be determined. The measured velocities are compared to the theoretical predictions of McLaughlin [“The lift on a small sphere in wall-bounded linear shear flows,” J. Fluid Mech. 246, 249 (1993)] and Magnaudet et al. [J. Fluid Mech. 476, 115 (2003)] corresponding to the situation where the wall lies in the Oseen region and in the Stokes region of the flow disturbance produced by the particle, respectively. A good agreement is observed in both regimes with the corresponding prediction. The measurements are used to build an empirical fit capable of predicting the migration velocity whatever the distance between the particle and the wall.

Fluctuating motion in a homogeneous liquid-liquid dispersed flow at high phase fraction

Velocity fluctuations in a dispersed liquid-liquid cocurrent upward flow, statistically homogeneous and gravity driven, have been characterized with the help of a particle image velocimetry technique in a matched refractive index medium. Results first show a strong anisotropy of the fluctuations field in the range of phase fraction investigated (from 0.01 to 0.4), the axial component of the kinetic energy of the continuous phase being 4–5 times larger than the transverse component. The axial component of the fluctuating energy of the continuous phase normalized by the square of the local slip velocity follows a 2∕3 power law as a function of the product of the phase fraction by the local drag coefficient, in the whole range of phase fraction investigated. This remarkable result agrees with the hypothesis of a local equilibrium between the dissipation of these fluctuations at a nonresolved length scale (0.12×drop diameter) and their production rate is induced by the mean drag force. Examination of the local structure of the instant fluctuating velocity field shows that the continuous phase instant fluctuations are locally correlated with the dispersed phase spatial distribution that is found to follow a Poisson law. The characteristic length of this distribution in the direction of the flow is of the order of several drop diameters and is comparable with the integral scale of the fluctuations of the continuous phase (correlation length). These results at high phase fraction are discussed and compared with experimental data and models available in the literature, for most of them in dilute systems.

A discrete particle model for particle–fluid flow with considerations of sub-grid structures

The effect of meso-scale structures on the hydrodynamic behaviors of particle–fluid systems is considered in an Eulerian–Lagrangian model utilizing the detailed particle distribution information provided by such models. The fluid flow is distributed within each computational cell from pressure balance considerations according to weighted local porosities, rather than by using traditional linear interpolations. The drag on each particle is then calculated with its local porosity and slip velocity, which shows significant difference to traditional methods. Simulations in this model have reproduced multi-scale flow behaviors in better agreement with experimental results, suggesting the validity of the model.

Analysis of the flow in inhomogeneous particle beds using the spatially averaged two-fluid equations

The drag force term appearing in two-fluid models for fluid–particle flows is commonly closed by expressing it as a function of the local quantities, such as the local particle volume fraction, the local slip velocity between the particle and fluid phases, and the local mean-squared fluctuating velocity of the particles. The adequacy of such closures for inhomogeneous suspensions has been debated in the literature and some researchers have suggested the need for additional terms involving spatial gradients in these quantities. To test this proposition, simulations of flow in inhomogeneous steady beds of particles have been performed using the lattice-Boltzmann method. The particle beds consisted of disordered assemblies with a density profile on a scale much larger than the particle radius. Inhomogeneous beds with a controlled density profile were generated in three different ways, (i) by inhomogeneous stretching of the particle bed in one direction, (ii) by applying an inhomogeneous force to the particle phase during random motion of the particles, and (iii) by taking snapshots of a direct simulation of a traveling wave in a fluidization simulation. The global structure of the three beds was comparable, while assessment of the radial distribution functions showed that the three beds exhibited clearly different microscopic structures. The force profiles along the inhomogeneous direction of the particle bed were obtained from the flow simulations. These were analyzed by applying spatial averaging in a manner identical to the averaging procedure that is used to derive the two-fluid model equations. The force profiles were compared to predictions based on flow simulations of homogeneous disordered particle beds over a range of volume fractions. To assess the role of the microstructure of the particle bed also simulations were executed where the homogeneous disordered bed was modified by either applying homogeneous stretching or by applying a lubrication force during generation of the particle bed. This study demonstrated that the microscopic structure of the particle bed has a severe impact on the closure of the drag force. Our computations did not reveal any evidence supporting the need for terms involving gradients in particle volume fraction in the drag force closure.