Operating range of magnetic stabilization flow regime for magnetized fluidized bed with Geldart-B magnetizable and nonmagnetizable particles

The magnetic stabilization flow regime could also be created for Geldart-B nonmagnetizable particles provided some magnetizable particles are introduced and the magnetic field is applied. This study aimed to explore the size (d_pM) and density (Ͽ_pM) effects of magnetizable particles on its operating range. The upper limit (U_mbH) could not be determined from the οP_b⿿U_g⿿ curve but could from analyzing the variation of οP_b-fluctuation with increasing U_g. Due to the variation of U_mfH (lower limit) with d_pM and Ͽ_pM, both U_mbH⿿U_mfH and (U_mbH⿿U_mfH)/U_mfH were used to quantify the operating range of magnetic stabilization. U_mbH⿿U_mfH varied hardly with d_pM but increased significantly with decreasing Ͽ_pM. (U_mbH⿿U_mfH)/U_mfH increased as d_pM or Ͽ_pM decreased. It was more difficult for the nonmagnetizable particles to escape from the network formed by the smaller/lighter magnetizable particles. For the same magnitude of change, d_pM had a stronger effect than Ͽ_pM on (U_mbH⿿U_mfH)/U_mfH. Neither U_mbH⿿U_mfH nor (U_mbH⿿U_mfH)/U_mfH varied monotonously with the minimum fluidization velocity of the magnetizable particles, indicating that no straightforward criterion for matching the magnetizable particles to the given nonmagnetizable particles could be established based on their minimum fluidization velocities to maximize the operating range of magnetic stabilization.     

Hydrodynamic behaviour of Cellets™ (Ph.Eur./USP) in a spouted bed using image processing method

The hydrodynamic behaviour of the spouted bed in the pharmaceutical industries has been found to be less addressed. The present paper has focused on the hydrodynamic characteristics of a spouted bed where the Cellets™ (Ph.Eur./USP) is adopted as the bed material. Experiments are carried out with three different static bed heights (H₀) of shallow depth (2D_i ≤ H₀ < 3D_i) using two different particle sizes. The spouted bed employed with D_i/D₀ of 5 has given the experimental information on external spouting (U_es) by mapping the pressure drop, and fountain height (H_f) against the superficial gas velocity (U_g) is represented with the image contours, which show the intrinsic behaviour. All the 1000 μm and 700 μm particles have been found to exhibit symmetric and asymmetric spouting. With increasing U_g, the fully suspended particles are limited to a certain height in the freeboard region due to the gas-solid cross-flow, which implies the clusters have identified with the image processing method.     

Solids behavior in dilute zone of a CFB riser under turbulent conditions

The behavior of the solid phase in the upper zone of a circulating fluidized bed riser was studied using a phase Doppler anemometer. Glass particles of mean diameter 107 μm and superficial gas velocities U_g covering the turbulent and the beginning of the fast fluidization regime were investigated. Three static bed heights were tested. Ascending and descending particles were found co-existing under all operating conditions tested, and at all measurement locations. Superficial gas velocity proved/happened to have a larger effect on descending particles at the wall and on ascending particles in the central region. Transversal particle velocities in both directions (toward the center and toward the wall) behaved relatively equivalently, with only slight difference observed at the wall. However, observation of the number of particles moving in either transversal direction showed a change in bed structure when increasing U_g. Furthermore, a balance was constantly observed between the core zone and the annulus zone where the mutual mass transfer between these two zones occurred continuously. Transition from a slow to a fast particle motion was accompanied by a transition to high levels of velocity fluctuations, and was found corresponding to the appearance of significant solid particle flow rate.     

Bifurcations in the wake of a thick circular disk

Using DNS, we investigate the dynamics in the wake of a circular disk of aspect ratio χ = d/w = 3 (where d is the diameter and w the thickness) embedded in a uniform flow of magnitude U ₀ perpendicular to its symmetry axis. As the Reynolds number Re = U ₀ d/ν is increased, the flow is shown to experience an original series of bifurcations leading to chaos. The range Re ${\in}$ [150, 218] is analysed in detail. In this range, five different non-axisymmetric regimes are successively encountered, including states similar to those previously identified in the flow past a sphere or an infinitely thin disk, as well as a new regime characterised by the presence of two distinct frequencies. A theoretical model based on the theory of mode interaction with symmetries, previously introduced to explain the bifurcations in the flow past a sphere or an infinitely thin disk (Fabre et al. in Phys Fluids 20:051702, 2008), is shown to explain correctly all these results. Higher values of the Reynolds number, up to 270, are also considered. Results indicate that the flow encounters at least four additional bifurcations before reaching a chaotic state.     

Bifurcation and chaos of a flag in an inviscid flow

A two-dimensional model is developed to study the flutter instability of a flag immersed in an inviscid flow. Two dimensionless parameters governing the system are the structure-to-fluid mass ratio M^⁎ and the dimensionless incoming flow velocity U^⁎. A transition from a static steady state to a chaotic state is investigated at a fixed M^⁎=1 with increasing U^⁎. Five single-frequency periodic flapping states are identified along the route, including four symmetrical oscillation states and one asymmetrical oscillation state. For the symmetrical states, the oscillation frequency increases with the increase of U^⁎, and the drag force on the flag changes linearly with the Strouhal number. Chaotic states are observed when U^⁎ is relatively large. Three chaotic windows are observed along the route. In addition, the system transitions from one periodic state to another through either period-doubling bifurcations or quasi-periodic bifurcations, and it transitions from a periodic state to a chaotic state through quasi-periodic bifurcations.     

Hydrodynamic behavior of magnetized fluidized beds with admixtures of Geldart-B magnetizable and nonmagnetizable particles

This work focuses on the hydrodynamic behavior of admixtures of Geldart-B magnetizable and nonmagnetizable particles in a magnetized fluidized bed. The applied magnetic field was axial, uniform, and steady. In operating the beds, the magnetization-LAST mode was adopted under which four distinct flow regimes exist: fixed, magnetized-bubbling, partial segregation-bubbling, and total segregation-bubbling. The operational phase diagram was drawn to display the transitions between flow regimes in an intuitive manner. Only in the magnetized-bubbling regime could the magnetic field reduce the bubble size and improve fluidization quality. In the segregation-bubbling regimes, fluidization quality deteriorated as segregation developed. The segregation of the binary mixture was quantitatively studied by observing pressure drops in the local bed. Reasons for the improvement in fluidization quality as well as the occurrence of segregation were analyzed. Furthermore, the flow regime transition under magnetization-LAST operation mode was different from that under magnetization-FIRST mode. The magnetically stabilized bed (MSB) flow regime, which could be easily created under magnetization-FIRST mode, could no longer be achieved under magnetization-LAST mode. With the admixture, the MSB was proved to be a metastable equilibrium state. Under the magnetization-LAST mode, the admixture bed reached directly the stable equilibrium state—bubbling with segregation.     

Passive Scalar Transport in a Turbulent Cylinder Wake in the Presence of a Downstream Cylinder

This work aims to investigate how the presence of a downstream cylinder affects the passive scalar transport in a cylinder wake. The wake was generated by two tandem brass circular cylinders of the same diameter (d). The cylinder centre-to-centre spacing L/d was 1.3, 2.5 and 4.0, respectively, covering the three typical flow regimes of this flow. The upstream cylinder was slightly heated. Measurements were conducted at x/d= 10 and Re (≡ dU _∞/ν, where U _∞ is the free-stream velocity and ν is the kinematic viscosity of fluid) = 7000. A three-wire probe consisting of an X-wire and a cold wire was used to measure the velocity and temperature fluctuations, while an X-wire provided a phase reference. The phase-averaged velocity vectors and vorticity display single vortex street behind the downstream cylinder, irrespective of the flow regimes. However, the detailed flow structure exhibits strong dependence on L/d in terms of the Strouhal number, the vortex strength and its downstream evolution. This naturally affects passive scalar transport. The coherent and incoherent heat flux vectors show significant variation for different L/d.     

Unsteady separated and reattaching turbulent flow over a two-dimensional square rib

The spatio-temporal characteristics of the separated and reattaching turbulent flow over a two-dimensional square rib were studied experimentally. Synchronized measurements of wall-pressure fluctuations and velocity fluctuations were made using a microphone array and a split-fiber film, respectively. Profiles of time-averaged streamwise velocity and wall-pressure fluctuations showed that the shear layer separated from the leading edge of the rib sweeps past the rib and directly reattaches on the bottom wall (x/H=9.75) downstream of the rib. A thin region of reverse flow was formed above the rib. The shedding large-scale vortical structures (fH/U₀=0.03) and the flapping separation bubble (fH/U₀=0.0075) could be discerned in the wall-pressure spectra. A multi-resolution analysis based on the maximum overlap discrete wavelet transform (MODWT) was performed to extract the intermittent events associated with the shedding large-scale vortical structures and the flapping separation bubble. The convective dynamics of the large-scale vortical structures were analyzed in terms of the autocorrelation of the continuous wavelet-transformed wall pressure, cross-correlation of the wall-pressure fluctuations, and the cross-correlation between the wall pressure at the time-averaged reattachment point and the streamwise velocity field. The convection speeds of the large-scale vortical structures before and after the reattachment point were U_c=0.35U₀ and 0.45U₀, respectively. The flapping motion of the separation bubble was analyzed in terms of the conditionally averaged reverse-flow intermittency near the wall region. The instantaneous reattachment point in response to the flapping motion was obtained; these findings established that the reattachment zone was a 1.2H-long region centered at x/H=9.75. The reverse-flow intermittency in one period of the flapping motion demonstrated that the thin reverse flow above the rib is influenced by the flapping motion of the separation bubble behind the rib.     

Flow regime development analysis in adiabatic upward two-phase flow in a vertical annulus

In this work radial and axial flow regime development in adiabatic upward air-water two-phase flow in a vertical annulus has been investigated. Local flow regimes have been identified using conductivity probes and neural networks techniques. The inner and outer diameters of the annulus are 19.1 mm and 38.1 mm, respectively. The equivalent hydraulic diameter of the flow channel, D_H, is 19.0 mm and the total length is 4.37 m. The flow regime map includes 1080 local flow regimes identifications in 72 flow conditions within a range of 0.01 m/s < 〈j_g〉 < 30 m/s and 0.2 m/s < 〈j_f〉 < 3.5 m/s where 〈j_g〉 and 〈j_f〉 are, respectively, superficial gas and liquid velocities. The local flow regime has been classified into four categories: bubbly, cap-slug, churn-turbulent and annular flows. In order to study the radial and axial development of flow regime the measurements have been performed at five radial locations. The three axial positions correspond to z/D_H = 52, 149 and 230, where z represents the axial position. The flow regime indicator has been chosen as some statistical parameters of local bubble chord length distributions and self-organized neural networks have been used as mapping system. This information has been also used to compare the results given by the existing flow regime transition models. The local flow regime is characterized basically by the void fraction and bubble chord length. The radial development of flow regime shows partial and complete local flow regime combinations. The radial development is controlled by axial location and superficial liquid velocity. The radial flow regime transition is always initiated in the center of the flow channel and it is propagated towards the channel boundaries. The axial development of flow regime is observed in all the flow maps and it is governed by superficial liquid velocity and radial location. The prediction results of the models are compared for each flow regime transition.     

Cross-flow past a pair of nearly in-line cylinders with the upstream cylinder subjected to a transverse harmonic oscillation

An experimental investigation is presented for the cross-flow past a pair of staggered circular cylinders, with the upstream cylinder subject to forced harmonic oscillation transverse to the flow direction. Experiments were conducted in a water tunnel with Reynolds numbers, based on upstream velocity, U, and cylinder diameter, D, in the range 1440⩽Re⩽1680. The longitudinal separation between cylinder centres is L/D=2.0, with a transverse separation (for the mean position of the upstream cylinder) of T/D=0.17; the magnitude of the harmonic oscillation is 0.44D peak-to-peak and the nondimensional frequency range of the excitation is 0.05⩽f_eD/U⩽0.44. Flow visualization of the wake-formation region and hot-film measurements of the wake spectra are used to investigate the wake-formation process. An earlier study showed that stationary cylinders in this nearly in-line configuration straddle two very different flow regimes, the so-called shear-layer reattachment (SLR) and induced separation (IS) regimes. The present study, demonstrates that oscillation of the upstream cylinder causes considerable modification of the flow patterns around the cylinders. In particular, the wake experiences strong periodicities at the frequency of the oscillating cylinder; in addition to the usual fundamental lock-in, both sub- and superharmonic resonances are obtained. It is also observed that, although the flow exhibits regions of SLR and IS for excitation frequencies below the fundamental lock-in, for frequencies above the lock-in range the flow no longer resembles either of these flow regimes and vortices are formed in the gap between the cylinders.     

Modified correlation for minimum fluidization velocity of low-density particles in inverse liquid–solid fluidized beds

The minimum fluidization velocity (U_mf) is a key parameter for the scale-up of inverse liquid–solid fluidized beds. Theoretical predictions using common correlations were compared against experimental minimum fluidization velocity measurements of low density (28–638 kg/m³), 0.80–1.13 mm Styrofoam particles in a fluidized bed with a height of 4.5 m and 0.2 m diameter. The average absolute relative deviation for the predicted minimum fluidization velocity for particles below 300 kg/m³ was above 40% using the studied common correlations. A modified Wen and Yu correlation was thus proposed based on novel and past measurements with low-density and small-diameter particles, expanding the range for predicting U_mf. The new correlation predicted U_mf with deviations below 15% for ST028, ST122 and ST300. This modified correlation also improved U_mf predictions for comparable particles from a previous study, demonstrating its validity for a larger range of low-density particles.     

Flow evolution of a turbulent submerged two-dimensional rectangular free jet of air. Average Particle Image Velocimetry (PIV) visualizations and measurements

The paper presents average flow visualizations and measurements, obtained with the Particle Image Velocimetry (PIV) technique, of a submerged rectangular free jet of air in the range of Reynolds numbers from Re = 35,300 to Re = 2200, where the Reynolds number is defined according to the hydraulic diameter of a rectangular slot of height H. According to the literature, just after the exit of the jet there is a zone of flow, called zone of flow establishment, containing the region of mixing fluid, at the border with the stagnant fluid, and the potential core, where velocity on the centerline maintains a value almost equal to the exit one. After this zone is present the zone of established flow or fully developed region. The goal of the paper is to show, with average PIV visualizations and measurements, that, before the zone of flow establishment is present a region of flow, never mentioned by the literature and called undisturbed region of flow, with a length, L_U, which decreases with the increase of the Reynolds number. The main characteristics of the undisturbed region is the fact that the velocity profile maintains almost equal to the exit one, and can also be identified by a constant height of the average PIV visualizations, with length, L_CH, or by a constant turbulence on the centerline, with length L_CT. The average PIV velocity and turbulence measurements are compared to those performed with the Hot Film Anemometry (HFA) technique. The average PIV visualizations show that the region of constant height has a length L_CH which increases from L_CH = H at Re = 35,300 to L_CH = 4–5H at Re = 2200. The PIV measurements on the centerline of the jet show that turbulence remains constant at the level of the exit for a length, L_CT, which increases from L_CT = H at Re = 35,300 to L_CT = 4–5H at Re = 2200. The PIV measurements show that velocity remains constant at the exit level for a length, L_U, which increases from L_U = H at Re = 35,300 to L_U = 6H at Re = 2200 and is called undisturbed region of flow. In turbulent flow the length L_U is almost equal to the lengths of the regions of constant height, L_CH, and constant turbulence, L_CT. In laminar flow, Re = 2200, the length of the undisturbed region of flow, L_U, is greater than the lengths of the regions of constant height and turbulence, L_CT = L_CH = 4–5H. The average PIV and HFA velocity measurements confirm that the length of potential core, L_P, increases from L_P = 4–5H at Re = 35,300 to L_P = 7–8H at Re = 2200, and are compared to the previous experimental and theoretical results of the literature in the zone of mixing fluid and in the fully developed region with a good agreement.     

Effects of aspect ratio on the drag of a wall-mounted finite-length cylinder in subcritical and critical regimes

The effect of cylinder aspect ratio (??H/d, where H is the cylinder height or length, and d is the cylinder diameter) on the drag of a wall-mounted finite-length circular cylinder in both subcritical and critical regimes is experimentally investigated. Two cases are considered: a smooth cylinder submerged in a turbulent boundary layer and a roughened cylinder immersed in a laminar uniform flow. In the former case, the Reynolds number Re _d (??U _?? d/??, with U _?? being the free-stream velocity and ?? the fluid viscosity) was varied from 2.61?×?10⁴ to 2.87?×?10⁵, and two values of H/d (2.65 and 5) were examined; in the latter case, Re _d ?=?1.24?×?10⁴?C1.73?×?10⁵ and H/d?=?3, 5 and 7. In the subcritical regime, both the drag coefficient C _D and the Strouhal number St are smaller than their counterparts for a two-dimensional cylinder and reduce monotonously with decreasing H/d. The presence of a turbulent boundary layer causes an early transition from the subcritical to critical regime and considerably enlarges the Re _d range of the critical regime. No laminar separation bubble occurs on the finite-length cylinder immersed in the turbulent boundary layer, and consequently, the discontinuity is not observed in the C _D?CRe _d and St?CRe _d curves. In the roughened cylinder case, the Re _d range of the critical regime grows gradually with decreasing H/d, while the C _D crisis becomes less obvious. In both cases, H/d has a negligible effect on the critical value of Re _d at which transition occurs from the subcritical to critical regime.     

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.     

Numerical simulation (DNS and LES) of manipulated turbulent boundary layer flow over a surface-mounted fence

Results from numerical simulations are presented for manipulated turbulent boundary layer flow over a surface-mounted fence, for a Reynolds number of Re_h=3000 (based on fence height, h , and maximum inflow velocity, U_∞ ). First, a reference data set was provided from a Direct Numerical Simulation (DNS) using 51.6 million grid points to resolve all the relevant spatial scales of the flow. A Large-Eddy Simulation (LES), using 1.67 million grid points, was validated with this reference solution and compared with experimental data for the same Reynolds number. Then, manipulated flow cases were investigated applying time-periodic forcing through a narrow slot upstream of the flow obstacle. High-frequency forcing, with Str₁=f₁h/U_∞=0.60 , leads to about 10% reduction of the mean re-attachment length. A much stronger reduction of about 36% could be achieved by low-frequency forcing with Str₂=f₂h/U_∞=0.08 . In the latter case, large-scale coherent structures are created between the location of the disturbance and the fence, they roll over the flow obstacle (nearly unaffected) and in rolling downstream they still grow in size until they fill out the entire height of the separation zone behind the fence. In agreement with corresponding experiments of Siller and Fernholz in 1997 for a higher Reynolds number ( Re_h=10500 ) the optimum forcing Strouhal number seems to be related to the low-frequency movement of the entire separation bubble and not to the instability mode of the separating shear layer.©2000 Éditions scientifiques et médicales Elsevier SAS     

Effect of spanwise-varying local forcing on turbulent separated flow over a backward-facing step

An experimental study was made of turbulent separated flows over a backward-facing step. A local forcing was given to the separated flow by means of a sinusoidally oscillating jet issuing from a thin slit near the separation line. To produce a spanwise-varying local forcing at the separation edge, a banded thin tape covered the slit. Effects of the spanwise-varying local forcings on the separated flow were scrutinized by altering the spatially banded blocking width (w) and the open slit distance (g). An optimal value of w/g was sought, which led to the minimum reattachment length (x _R ). The effect of spanwise-varying local forcing on x _R was found to be slight compared to the case of two-dimensional forcing (w=0). The experiment was made at Re _H =33000 and A ₀=0.018 by changing the forcing frequency (0?St _H ?1.0).     

Analytical and level-set method based numerical study on oil-water smooth/wavy stratified-flow in an inclined plane-channel

Level-set method based transient 2D simulation of developing oil-water smooth-stratified (SS) and wavy-stratified (WS) flow in a horizontal and inclined plane-channel is done; for various inlet-velocity (u_in), inlet-interface-height (H_in), inclination-angle (θ), reduced surface-tension (σ ? σ_ow) and reduced gravity (g ? g_e). At the certain critical value of the governing parameters, SS to WS flow transition is captured, analyzed and reasoned. Increase in u_in, H_in and θ and a decrease in σ_ow and g_e are found to destabilize the SS flow. For fully-developed SS flow, a detailed analytical solution of interface-height, maximum axial-velocity, its transverse location, pressure-gradient and wall-shear stress is proposed for an inclined channel; an excellent agreement between the present analytical and numerical results is also reported. The SS flow analytical-results are also compared with the time-averaged WS flow numerical-results (near the channel-outlet), to understand the reasons for flow-transition. Flow development is studied with the help of axial variation of interface-height and maximum (over the cross-section of the channel) axial velocity; time-averaged for WS flow. Furthermore, the variation of development-length for SS flow and WS flow is studied. Finally, stretching of interface-area due to onset of WS flow is presented with the help of interfacial-area-concentration. Its calculation directly from the Dirac-delta function of the level set method is a novel-contribution.     

Determination of the aerodynamic droplet breakup boundaries based on a total force approach

The determination of the critical We_g number separating the different breakup regimes has been extensively studied in several experimental and numerical works, while empirical and semi-analytical approaches have been proposed to relate the critical We_g number with the Oh_l number. Nevertheless, under certain conditions, the Re_g number and the density ratio ε may become important. The present work provides a simple but reliable enough methodology to determine the critical We_g number as a function of the aforementioned parameters in an effort to fill this gap in knowledge. It considers the main forces acting on the droplet (aerodynamic, surface tension and viscous) and provides a general criterion for breakup to occur but also for the transition among the different breakup regimes. In this light, the present work proposes the introduction of a new set of parameters named as We_g,eff and Ca_l monitored in a new breakup plane. This plane provides a direct relation between gas inertia and liquid viscosity forces, while the secondary effects of Re_g number and density ratio have been embedded inside the effective We_g number (We_g,eff)     

Modeling of the phase lag causing fluidelastic instability in a parallel triangular tube array

Fluidelastic instability is considered a critical flow induced vibration mechanism in tube and shell heat exchangers. It is believed that a finite time lag between tube vibration and fluid response is essential to predict the phenomenon. However, the physical nature of this time lag is not fully understood. This paper presents a fundamental study of this time delay using a parallel triangular tube array with a pitch ratio of 1.54. A computational fluid dynamics (CFD) model was developed and validated experimentally in an attempt to investigate the interaction between tube vibrations and flow perturbations at lower reduced velocities U_r=1–6 and Reynolds numbers Re=2000–12 000. The numerical predictions of the phase lag are in reasonable agreement with the experimental measurements for the range of reduced velocities U_g/fd=6–7. It was found that there are two propagation mechanisms; the first is associated with the acoustic wave propagation at low reduced velocities, U_r<2, and the second mechanism for higher reduced velocities is associated with the vorticity shedding and convection. An empirical model of the two mechanisms is developed and the phase lag predictions are in reasonable agreement with the experimental and numerical measurements. The developed phase lag model is then coupled with the semi-analytical model of Lever and Weaver to predict the fluidelastic stability threshold. Improved predictions of the stability boundaries for the parallel triangular array were achieved. In addition, the present study has explained why fluidelastic instability does not occur below some threshold reduced velocity.