Vibration induced flow in hoppers: DEM 2D polygon model

A two-dimensional discrete element model (DEM) simulation of cohesive polygonal particles has been developed to assess the benefit of point source vibration to induce flow in wedge-shaped hoppers. The particle-particle interaction model used is based on a multi-contact principle.The first part of the study investigated particle discharge under gravity without vibration to determine the critical orifice size (Be) to just sustain flow as a function of particle shape. It is shown that polygonal-shaped particles need a larger orifice than circular particles. It is also shown that Be decreases as the number of particle vertices increases. Addition of circular particles promotes flow of polygons in a linear manner.The second part of the study showed that vibration could enhance flow, effectively reducing Be. The model demonstrated the importance of vibrator location (height), consistent with previous continuum model results, and vibration amplitude in enhancing flow.     

Bimodal model of slurry viscosity with application to coal-slurries. Part 2. High shear limit behavior

It is shown that in a truly bimodal coal-water slurry the hydrodynamic interactions between the coarse particles impose on the fine fraction a shear rate higher than that applied externally by the viscometer walls. A semi-empirical function of the coarse volume fraction is obtained for this correction factor to the applied shear rate. The derivation of this shear correction factor is based on lubrication concepts and introduces the maximum packing fraction,ø _m, at which flow can take place.ø _m is obtainable from a simple dry packing experiment. It is shown that the contribution of the coarse particles to the viscosity rise can be successfully described by a viscosity model employing the same concepts used to derive the shear correction factor. The bimodal model is applied in the high shear limit to polymodal coal slurries with a continuous particle size distribution. In the model, the contribution of the coarse particles to the viscosity rise is taken from separate viscosity measurements for the coarse coal particles, while the contribution to the viscosity of the fine coal particles is taken to be that given by the measured viscosity of colloidal suspensions of monomodal rigid spheres. It is shown that there is a ratio of coarse to fine fraction volumes in the continuous size distribution, corresponding to a specific separating particle size, for which the measured viscosities of the polymodal slurries match almost perfectly over the whole solids volume fraction range with the viscosity values obtained using the bimodal approach. The match is found to be relatively insensitive to the precise value of the separating particle size.     

Flow characteristics of gas-liquid-particle mixing in a gas-stirred ladle system with throughflow

An experimental study is performed on air-liquid-particle mixing, resulting from an air-particle mixture injected into a liquid flowing through a slender ladle. Flow visualization combined with image processing is employed to investigate the bubble and particle behavior at the nozzle outlet. Effort is directed to particle discrimination in both the liquid and the bubbles to determine particle distribution, which affects the mixing performance of gas bubbles, solid particles and liquid. A real-time movement of bubble and particle behavior can be visualized by means of image processing with the use of a slow-motion video recording. It is disclosed that the particles injected through the nozzle may stick on the inner surface of the gas bubble, break through the bubble surface, or mingle with the gas stream to form a two-phase jet, depending on the particle-to-gas mass flow rate ratio. It is observed that when a solid-gas two-phase jet penetrates deeper in the horizontal direction, the particles and bubbles rise along the vertical sidewall and simultaneously spread in the transverse direction, thus promoting a better liquid-particle mixing. The application of the slow-motion video recording results in quantitative evaluations of both the penetration depth of particles or of gas-particles from the injection nozzle and the velocity distribution along the sidewall.List of symbols B Width of water vessel, m - B _n Nozzle location on bottom surface of water vessel, m - d _o Diameter of a gas-particle injection nozzle, m - H Height of water vessel, m - H _n Nozzle location on vertical surface of water vessel, m - L Penetration length of particles or of particles and gas from the nozzle, m - Q _g Volumetric flow rate of gas, m³/s - Q _l Volumetric flow rate of water, m³/s - Q _s Volumetric flow rate of particle, m³/s - Re _g Gas Reynolds number based on inner diameter of the air-particle injection nozzle - t Time, sec. - W Thickness of water vessel, m - x Transverse coordinate, m - y Longitudinal coordinate, m - Mass flow rate ratio of particles to gas Visiting scholar on leave from the Mechanical Engineering Department, Kagoshima University, Kagoshima, JapanThe work reported was supported by the National Science Foundation under the Grant No. CTS-8921584     

Experimental study of the induced flow birefringence of a suspension of rigid particles at the transition from Couette flow to Taylor vortex flow

The flow birefringence induced in solutions of rigid particles is studied experimentally in the region of the axisymmetrical Taylor vortex flow which arises once the velocity gradient G in the annular gap of a conventional Couette cell reaches a critical value G _c .The measurements are performed for several values of G > G _c and for 10 radial observation points in the annular gap. Solutions of two types of rigid particles are investigated: the first is a suspension of flattened clay particles like bentonite, while the second contains rod-like particles of tobacco mosaic virus (TMV). The variations of the birefringence intensity n and of the extinction angle measured in the domain of the axisymmetrical flow show a different behavior according to the shape of the particle in solution. This fact is confirmed theoretically with a good agreement for the measurements performed with solutions of flat particles.     

A Summary of New Predictive High Frequency Thermo-Vibrational Models in Porous Media

In this paper, we consider the effect of mechanical vibration on the onset of convection in porous media. The porous medium is saturated either by a pure fluid or by a binary mixture. The importance of a transport model on stability diagrams is presented and discussed. The stability threshold for the Darcy–Brinkman case in the Ra _Tc -R and k _c -R diagrams is presented (where Ra _Tc , k _c and R are the critical Rayleigh number, the critical wave number and the vibration parameters, respectively). It is shown that there is a significant deviation from the Darcy model. In the thermo-solutal case with the Soret effect, the influence of vibration on the reduction of multi-cellular convection is emphasized. A new analytical relation for obtaining the threshold of mono-cellular convection is derived. This relation shows how the separation factor Ψ is related to the controlling parameters of the problem, Ψ = f (R, ε*, Le), when the wave number k → 0. The importance of vibrational parameter definition is highlighted and it is shown how, by using a proper definition for vibrational parameter, we may obtain compact relationship. It is also shown how this result may be used to increase component separation.     

Inertial-microfluidic radial migration in solid/liquid two-phase flow through a microcapillary: Particle equilibrium position

Although equilibrium of spherical particles under radial migration has been extensively investigated, mostly in macroscale flows with characteristic lengths on the order of centimeters, it is not fully characterized at relatively small Reynolds numbers, 1 ≤ Re ≤ 100. This paper experimentally studies “inertial microfluidic” radial migration of spherical particles in circular Poiseuille flow through a microcapillary. Microparticle tracking experiments are performed to obtain the spatial distribution of the particles by adopting a depth-resolved measurement technique. Through the analysis of the radial distribution of particles, inertial microfluidic circular Poiseuille flow is shown to induce a strong radial migration of particles at substantially small Re, which is quite in contrast to the pipe flows at large Re previously reported. This particle migration phenomenon is so prominent that particle equilibrium positions are formed even at small Re. However, it turns out that there exists a certain critical Re below which particle equilibrium position is almost fixed, but above which it seems to drift toward the channel wall.     

On Turbulent Jets Issuing from Notched-Rectangular and Circular Orifice Plates

This paper reports an experimental investigation of the near-field flow characteristics of two air/air turbulent jets issuing respectively from notched-rectangular and circular orifice plates with identical opening areas or equivalent diameters (D _e ). Planar particle image velocimetry (PIV) was used to measure the velocity field at the same Reynolds number, based on D _e , of Re = 72,000. Consistent with previous work on other noncircular jets, the present study finds that the notched jet has a higher rate of mixing than does the circular counterpart. In particular, this jet in the very near field transfers its momentum to the surroundings at a greater rate, evidenced by a notably shorter unmixed core and faster turbulence intensity growth. The higher rates of overall decay and spread of the notched jet are maintained over the entire measurement region and likely beyond. In addition, the phenomenon of axis switching is also found to occur in this jet.     

A new method to measure particle turbulent dispersion using laser doppler anemometer

A laser doppler anemometer (LDA) was used to measure local dispersion coefficients of particles in turbulent flow. The experimental set-up is described along with the data acquisition equipment and processing procedures. Results for 5 particles dispersing from a point source in pipe flow are shown. A second estimate for the diffusivity was obtained from mean square dispersion measurements.List of symbols A projected area of LDA measuring volume, normal to pipe axis - B ₀ – B ₂ coefficients used in concentration curve fits - C particle number density, concentration - d _f fringe spacing - f _B Bragg cell frequency shift - f _D frequency of Doppler signal - H LDA measuring volume dimension in pipe axial direction - h random variation in H - J particle flux - J ₀, J ₁ bessel function of zeroth and first order - r radial location - t time - U axial velocity - u fluctuating component of axial velocity - v_p average particle radial velocity - x axial coordinate - y position of particle in the direction normal to the mean flow relative to the centerline - mean square dispersion Greek Symbols _2,3 roots of Bessel functions - _p turbulent diffusivity of particles - laser wave length - laser beam intersection angle     

Self-sustained oscillations between two tandem cylinders at Reynolds number 1,000

This study focuses on the self-sustained oscillatory flow characteristics between two tandem circular cylinders of equal diameter placed in a uniform inflow. The Reynolds number (Re _D ), based on the cylinder diameter, was around 1,000 and all experiments were performed in a recirculating water channel. The streamwise distance between two tandem cylinders ranged within 1.5 ≤ X _c/D ≤ 7.0. Here X _c denotes the center-to-center distance between two tandem cylinders. For all experiments studied herein, quantitative velocity measurements were performed using hot-film anemometer and the LDV system. The laser sheet technique was employed for qualitative flow visualization. The wavelet transform was applied to elucidate the temporal variation and phase difference between two spectral components of the velocity signals detected in the flow field. The remarkable finding was that when two tandem circular cylinders were spaced at a distance within 4.5 ≤ X _c/D ≤ 5.5, two symmetrical unstable shear layers with a certain wavelength were observed to impinge onto the downstream cylinder. The responding frequency (f _u ), measured between these two cylinders, was much higher than the natural shedding frequency behind a single isolated cylinder at the same Re _D . This responding frequency decreased as the distance X _c/D increased. Not until X _c/D ≥ 6.0, did it recover to the natural shedding frequency behind a single isolated cylinder. Between two tandem cylinders, the Strouhal numbers (St _c = f _u X _c/U_c) maintained a nearly constant value of 3, indicating the self-sustained oscillating flow characteristics with a wavelength X _c/3. Here U _c is the convection speed of the unstable shear layers between two tandem cylinders. At Re _D = 1,000, the self-sustained oscillating characteristics between two tandem circular cylinders were proven to exhibit a sustained flow pattern, not just a sporadic phenomenon.     

Finite Element Solution of Laminar Flow through Square-Edged Orifice with a Variable Thickness

A numerical analysis of laminar flow through square-edged orifice has been studied for Reynolds number in the range 0 < Re₀ < 2000 with β values varying from 0.2 to 0.8 and with l* values varying from 1/16 to 1. It is shown thai the flow discharge coefficient gradually decreases when the orifice thickness/diameter ratio increases for a high porosity.     

Flow fields and packing states in the discharge flow of noncircular particles—A SIPHPM simulation

Although the discharge flow of spherical materials has been extensively explored, the effect of particle shape on discharge is still poorly understood. The present work explores the two-dimensional discharge flow fields of noncircular particles using the soft-sphere-imbedded pseudo-hard particle model method. Rectangular particles having different aspect ratios (R_a = 1, 1.5, 2–5) and regular polygonal particles having different numbers of sides (N_s = 3–8, 10) are discharged through hopper beds having different orifice widths (D_i = 40, 70.77, 99.13, 125.74, 151.13 mm). The discharge rates of differently shaped particles in different beds are consistent with Beverloo’s relation. Moreover, the flow fields are computed and evaluated to study the effects of R_a, N_s, and D_i on particle discharge. The characteristics of particle–particle connections in the discharge process are evaluated according to the temporal evolution and spatial distribution of the contact points. Additionally, the effect of the initial packing on the discharge profile is investigated. The findings help clarify the discharge of noncircular particles.     

The stability of low Reynolds number round jets

Multigrid cross-correlation digital particle image velocimetry (MCCDPIV) is used to investigate the stability and structure of low Reynolds number axisymmetric jets. The in-plane velocities, out-of-plane vorticity and some of the components of the Reynolds stress tensor are measured. Two Reynolds numbers based on the orifice outlet diameter are examined (680 and 1,030) at two different positions: one close to the orifice, ranging from 2D ₀ to 5D ₀ (D ₀ is the orifice diameter); and the other further from the orifice, ranging from 10D ₀ to 14.4D ₀. The results show that the lower Reynolds number jet (Re=680) is marginally unstable in the near-orifice region and is best described as laminar. Further downstream some intermittent structures are observed in the jet, and the growth in integrated turbulent kinetic energy with axial position indicates that the jet is also unstable in this region. For the higher Reynolds number jet (Re=1,030) the increasing size and intensity of vortical structures in the jet in the near-orifice region observed from the MCCDPIV data and the growth in integrated turbulent kinetic energy indicate that the jet is unstable. Further downstream this jet is best described as transitional or turbulent. From flow visualisation images in the near-orifice region it seems that, for both Reynolds numbers, shear layer roll-up occurs when the jet exits the orifice and enters the quiescent fluid in the tank, resulting in vortical structures that appear to grow as the jet proceeds. This is indicative of instability in both cases and is consistent with previous flow visualisation studies of low Reynolds number round jets. Discrepancies observed between the flow visualisation results and the MCCDPIV data is addressed. On the basis of flow visualisation results it is generally assumed that round jets are unstable at very low Reynolds number, however the present work shows that this assertion may be incorrect.     

Application of an electrodynamic balance to the study of particle-fluid interactions

An electrodynamic balance was used to study the aerodynamics and mass transfer characteristics of spherical and nonspherical particles up to 200 m in size. The balance uses an electric field established by a DC potential to a pair of end electrodes and an AC potential to the central electrode to suspend single changed particles. The suspended particle is then subjected to a steady and/or oscillating air jet. Results from this study indicate that the drag coefficient of irregular-shaped particles was greater than that for spheres, and was unaffected by rotation. Measured mass transfer rates for irregular-shaped naphthalene particles were consistently higher than values predicted for equivalent spheres. These results suggest a strong influence of mass transfer on particle shape and particle Reynolds number.List of symbols A project area - d diameter - d _e area equivalent diameter - F _D drag force - F _E electrostatic force - g gravitational constant - K _B, K _B balance constants - k ₁, k ₂ calibration constants - m mass - P pixel count - q charge - Re Reynolds number - U jet velocity - V _DC balance DC voltage - V _DC,O balance DC voltage without air flow - particle density - _a density of air - v viscosity of air     

Particle response in a planar sudden expansion flow

Particle velocity and concentration statistics were measured in a vertically downward planar sudden expansion flow for large-eddy particle Stokes numbers (τ_pU_o/5H) ranging from 0.5 to 7.4. Particles with Stokes numbers greater than 3 did not enter the recirculation zone, exhibited substantial attenuation of cross-stream velocity fluctuations, and had large streamwise velocity fluctuations in regions of strong velocity gradient. The smallest particles filled the recirculation zone and showed strong response to the large eddies in the flow. Phase-locked particle concentration measurements showed that these particles were centrifuged away from vortex cores and concentrated between vortices. Intermediate-size particles with Stokes numbers of 1.4 were injected intermittently into the recirculation zone as tongues of particles moving down between vortices. Particle Reynolds number was found to have negligible effect on the particle velocity statistics.     

Analysis of fluid–structure interaction by an arbitrary Lagrangian–Eulerian finite element formulation

In this paper, the interaction fluid–rigid body is analysed by a finite element procedure that incorporates the arbitrary Lagrangian–Eulerian (ALE) method into a well‐known two‐step projection scheme. The flow is assumed to be two‐dimensional, incompressible and viscous, with no turbulence models being included. The flow past a circular cylinder at ℛℯ=200 is first analysed, for fixed and oscillating conditions. The dependence of lock‐in upon the shift between the mechanical and the Strouhal frequencies, for a given amplitude of forced vibration, is illustrated. The aerodynamic forces and the wake geometry are compared for locked‐in conditions with different driving frequencies. The behaviour of a rectangular cylinder (B/D=4) at ℛℯ=500 (based on height D) is also analysed. The flutter derivatives associated with aerodynamic damping (H₁* and A₂* in Scanlan's notation) are evaluated by the free oscillation method for several values of reduced flow speed above the Strouhal one (namely for 3≤U*≤8). Torsional flutter was attained at U*≥5, with all the other situations showing stable characteristics. Copyright © 1999 John Wiley & Sons, Ltd.     

Nonlinear rheology of concentrated spherical silica suspensions: 3. Concentration dependence

Nonlinear rheology was examined for concentrated suspensions of spherical silica particles (with radius of 40 nm) in viscous media, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture and pure ethylene glycol. The particles were randomly and isotropically dispersed in the media in the quiescent state, and their effective volume fraction φ_eff ranged from 0.36 to 0.59. For small strains, the particles exhibited linear relaxation of the Brownian stress σ_B due to their diffusion. For large step strains γ, the nonlinear relaxation modulus G(t,γ) exhibited strong damping and obeyed the time-strain separability. This damping was related to γ-insensitivity of strain-induced anisotropy in the particle distribution that resulted in decreases of σ_B/γ. The damping became stronger for larger φ_eff. This φ_eff dependence was related to a hard-core volume effect, i.e., strain-induced collision of the particles that is enhanced for larger φ_eff. Under steady/transient shear flow, the particles exhibited thinning and thickening at low and high γ˙, respectively. The thinning behavior was well described by a BKZ constitutive equation using the G(t,γ) data and attributable to decreases of a Brownian contribution, σ_B/γ˙. The thickening behavior, not described by this equation, was related to dynamic clustering of the particles and corresponding enhancement of the hydrodynamic stress at high γ˙. In this thickening regime, the viscosity growth η₊ after start-up of flow was scaled with a strain γ˙t. Specifically, critical strains γ_d and γ_s for the onset of thickening and achievement of the steadily thickened state were independent of γ˙ but decreased with increasing φ_eff. This φ_eff dependence was again related to the hard-core volume effect, flow-induced collision of the particles enhanced for larger φ_eff. Received: 26 June 1998 Accepted: 9 December 1998     

Numerical and experimental investigation of thermal convection for a thermodependent Herschel-Bulkley fluid in an annular duct with rotating inner cylinder

Thermal convection for an incompressible Herschel-Bulkley fluid along an annular duct, whose inner cylinder is rotating and outer is at rest, is analyzed numerically and experimentally. The outer cylinder is heated at constant heat flux density and the inner one is assumed adiabatic. The first part of this study deals with the effect of the rheological behavior of the fluid and that of the rotation of the inner cylinder on the flow field and heat transfer coefficient. All the physical properties are assumed constant and the flow is assumed fully developed. The critical Rossby number Ro_c = (R₁Ω/U_d)_c, for which the dimension of the plug flow is reduced to zero is determined with respect to the flow behavior index, the radius ratio and the Herschel-Bulkley number for axial flow. The rotation of the inner cylinder induces a decrease of the axial velocity gradient at the outer cylinder thereby reducing the heat transfer between the heated wall and the fluid. The second part of this study introduces the variation of the consistency K with temperature and analyzes the evolution of the flow pattern and heat transfer coefficient along the heating zone. Two cases are distinguished depending on the Rossby number: (i) Ro < Ro_c, the plug flow dimension increases along the heating zone; (ii) Ro < Ro_c, the decrease of K with temperature leads to the reappearance of the plug flow. For high angular velocities, it is possible to have a plug zone attached to the outer cylinder. Finally, a correlation is proposed for the Nusselt number. It shows clearly that the effect of thermodependency of K on the heat transfer becomes more important with increasing rotational velocity of the inner cylinder.     

On the Chebyshev collocation spectral approach to stability of fluid flow in a porous medium

In this paper, the temporal development of small disturbances in a pressure‐driven fluid flow through a channel filled with a saturated porous medium is investigated. The Brinkman flow model is employed in order to obtain the basic flow velocity distribution. Under normal mode assumption, the linearized governing equations for disturbances yield a fourth‐order eigenvalue problem, which reduces to the well‐known Orr–Sommerfeld equation in some limiting cases solved numerically by a spectral collocation technique with expansions in Chebyshev polynomials. The critical Reynolds number Re_c, the critical wave number α_c, and the critical wave speed c_c are obtained for a wide range of the porous medium shape factor parameter S. It is found that a decrease in porous medium permeability has a stabilizing effect on the fluid flow. Copyright © 2008 John Wiley & Sons, Ltd.