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Coiled tubing (CT) drilling technology offers significant advantages in terms of cost and efficiency for exploitations of unconventional oil and gas resources. However, the development of CT drilling technology is restricted by cuttings accumulation in the wellbore due to non-rotation of the drill string and limited circulating capacity. Cuttings cleaning becomes more difficult with the wall resistance of pipe-wellbore annulus on the cutting transport. Accurate description of particle transport process in the pipe-wellbore annulus is, therefore, important for improving the wellbore cleanliness. In this study, high-speed camera is used to record and analyze the settling process of particles in the transparent annulus filled with power-law fluids. A total of 540 tests were carried out, involving dimensionless diameters of 0.10–0.95 and particle Reynolds Numbers of 0.01–12.97, revealing the effect of the dimensionless diameter and particle Reynolds number on the annulus wall effect, and the wall factor model with an average relative error of 2.75% was established. In addition, a dimensionless parameter, Archimedes number, independent of the settling velocity, was introduced to establish an explicit model of the settling velocity of spherical particles in the vertical annulus, with the average relative error of 7.89%. Finally, a calculation example was provided to show how to use the explicit model of settling velocity in annulus. The results of this study are expected to provide guidance for field engineers to improve the wellbore cleanliness of coiled tubing drilling. more...

Empirical correlations and experimental works relating the drag coefficient (CD) of spheres to the Reynolds number (Re) and Re to the Archimedes number (Ar) were reviewed with a focus on the correlations applicable to the entire Re range. In addition, experiments with various spherical particles and fluids for the entire range of Re were conducted using high-speed video and added to the literature data. One of the correlations from the literature for Re-Ar and a modified correlation for CD–Re were found to best fit the experimental results. The analysis also established new correlations for Re–Ha (a non-dimensional number for velocity not including particle size) and CD–Ar. The latter is easier to use than the common CD–Re curve. more...

The hindrance of boundary to particle transport exists widely in various industrial applications. In this study, the wall drag force of parallel plates on settling particles was revealed through settling experiment. High-speed camera was used to record and analyze the settling process of particles in parallel plates that are filled with Newtonian fluids. A total of 600 experiments were carried out, involving the range of relative diameter and particle Reynolds number of 0.01–0.95 and 0.004–14.30, respectively. The wall drag coefficient was defined to quantitatively analyze the wall drag force of the parallel plates. The influence of relative diameter, particle properties, rheological properties, and the settling dynamic process on the wall drag coefficient was revealed, and the wall drag coefficient model with mean relative error of 5.90% was established. Furthermore, an explicit settling velocity model with mean relative error of 8.96% for the particle in parallel plates was developed by introducing a dimensionless variable independent of settling velocity, the Archimedes number. Finally, a calculation example was provided to clarify the using process of the explicit model. This research is expected to provide guidance for optimizing water hydraulic fracturing in the oil and gas industry. more...

In the current study, the settling, interaction, drafting, kissing, and tumbling of two identical and non-identical circular particles were simulated in a two-dimensional box in shear-thinning, Newtonian, and shear-thickening fluids by using the combined lattice Boltzmann-smoothed profile methods. Furthermore, the drag coefficient of one particle settling for different power-law indexes and Archimedes numbers was calculated. Also, the effect of the diameter ratio of the two particle pairs was considered during settling. The developed method was validated by simulating the settling of one particle and two identical particles in a Newtonian fluid. To consider two non-identical particles, two cases were examined. In Case A, the larger particle was above the smaller one and in the Case B, the smaller particle was above the larger one. The results showed that the two non-identical particles were separated more easily than the identical ones. In the settling of two particles under the same Archimedes number, the drafting and kissing time considerably increased by changing the non-Newtonian fluid behavior from a shear-thinning one to a shear-thickening one. Also, when the larger particle was above the smaller one, the time duration of the kissing stage increased with the decrease in the diameter ratio. more...

The modeling of the fluidization or sedimentation velocity of a suspension of solid particles is revisited by examining experiments conducted in either a liquid or a gas. A general expression is found in the case of negligible fluid inertia, i.e. at low Reynolds or Archimedes number. It is built as the product of the velocity of an isolated particle by three non-dimensional corrections that each takes into account a specific physical mechanism. The first correction reflects the variation of the buoyancy with the particle concentration. The second correction describes how the drag force increases with the concentration in case of negligible particle inertia. The third one accounts for the further increase of the drag when the particle inertia is increased. Remarkably, each correction only relies on a single of the three independent non-dimensional groups that control the problem: (1) the particle volume fraction Φs; (2) the ratio Φs/Φpack where Φpack is the bed packing concentration; (3) the Stokes number S t 0 , which characterizes the inertia of the particles and controls their agitation. Moreover, the onset of the instability that separates the homogeneous regime from the heterogeneous one is found to be controlled similarly by the Stokes number. Empirical expressions of the corrections are given, which provide a reliable tool to predict fluidization and sedimentation velocities for all values of the three non-dimensional numbers. The present results emphasize the crucial role of particle inertia, which is often disregarded in previous modeling approaches, such as that of Richardson and Zaki. more...

Cooling of electronic equipments is playing an important role in the last decades as a world experiences a technological boom in all fields. In this study, a numerical study for mixed convection cooling of microprocessor is investigated by the use of pure water and CuO-water nanofluid at six different volume concentrations. The model is built, meshed and simulated by Ansys Fluent Package 16.0 and a mesh independence test is carried out. The study is performed by changing heat load (115W, 130W), inlet velocity, at different concentrations of nanofluids (Pure water, 0.5%, 0.86%, 1.5%, 2.25%, 3.5%, 5%). The present results showed that using CuO-water nanofluids over pure water provides an enhancement in heat transfer characteristics. The dimensionless parameters such as Nusselt number, Archimedes number, Prandtl number, friction factor and dimensionless temperature are studied and correlated. An enhancement of 36.5% in thermal hydraulic performance is found at 0.50% volume fraction at Re = 1679.212. The data are correlated with maximum error of 4.1%. more...

The solid circulation rate is essential for design of pressurized circulating fluidized beds (PCFBs). With increasing pressure from atmospheric pressure to a few bars, the gas density linearly increases with the pressure, which affects the gas–solid flow characteristics. In this work, experiments were performed at room temperature in a cold PCFB apparatus with a riser of 3.3 m in height and 0.05 m in diameter. The solid circulation rate was studied from 20 to 80 kg/(m2·s) under various conditions with increasing pressure from 0.1 to 0.6 MPa and fluidizing gas velocity from around 1.5 to 8.0 m/s for different Geldart B group particles. Most of the conditions were in the flow regimes of core-annulus flow (CAF) only and CAF with a turbulent fluidized bed at the bottom. The trend of the apparent slip factor with the dimensionless slip velocity was similar at different pressures and for different average particle sizes, and it converged to an exponential function. An empirical equation was obtained by fitting the solid circulation rate with the operating parameters (particle transport velocity, particle volume fraction, Archimedes number, and Froude number), which is helpful for design and operation of PCFBs. more...

This paper presents an analysis of all forces affecting the void fraction (VF) and density of a particulate bed. The bulk density of many materials, both spherical and non-spherical, with a variety of properties, including particle size and density, were measured in air and various liquids. The Archimedes number (Ar) was found to be an appropriate representation of the particle behavior that considered the van der Waals forces. The effects of buoyancy and viscous forces, as components of Ar, on the VF were shown by experiments in various liquids. Additional forces, such as friction, impact, and tapping were discussed quantitatively and qualitatively. Furthermore, the effect of the particle shape on the VF was considered. Finally, general equations for VF and density were developed for practical use. The major effects of the moisture content and compression pressure on the VF will be discussed in a following paper. more...

Current investigation presents the heat and mass transfer analysis for steady flow Oldroyd-B fluid induced by isothermally and exothermally stretching disks. The novel features of Joule heating, chemical reaction and Ohmic dissipations are also utilized in the energy and concentration equations. A non-dimensional set of transformations are introduced to convert the coupled partial differential system into a system of ordinary differential equations. The analytical solution of formulated dimensionless equations is obtained by using homotopy analysis method. The solution convergence is ensured carefully. The physical exploration of various dimensionless parameters on pressure, velocity, temperature and concentration profiles is presented. It is observed that heat transfer at lower disk increases with increment of Deborah number, Archimedes number and distance parameter. The rate of mass transfer at both surfaces of disk is enhanced for larger values of activation energy parameter and Deborah number. more...

The difference between homogeneous and bubbling fluidization behaviors has been studied for the past 70 years, where several researchers have reported on the influence of interparticle forces in fluidization. Although interparticle forces such as van der Waals forces are evident in a real system, these forces are not the determinant in homogeneous fluidization, which can be simulated without any interparticle forces. In our previous study, the difference in fundamental mechanisms of the two fluidization states was analytically determined with a dimensionless gravity term, comprising the Reynolds number, Archimedes number, and density ratio. Nevertheless, some researchers insist that interparticle forces are dominant and a hydrodynamic force is not dominant. In this study, a dimensional analysis was applied to obtain a dominant parameter for distinguishing two fluidizations. Furthermore, some parameters were examined by comparing the experimental data in previous studies. The results indicated that hydrodynamic force is the dominant factor and the dimensionless gravity term is the dominant parameter in differentiating the two fluidized states. more...

The supercritical-water fluidized bed (SCWFB) is a reactor for coal and biomass gasification without pollutant emission. We carried out a series of experiments in a SCWFB, and a dual-capacitance probe measurement system was applied to measure the hydrodynamics of slugs, such as the slug frequency, chord length, and rising velocity. Four groups of Geldart-B particles with different mean diameters were fluidized by supercritical water with a system pressure of 20–27 MPa and at 410–570 °C. The minimum slugging Reynolds number increases logarithmically with Archimedes number and a predicting correlation of the minimum slugging fluidization velocity in the SCWFB is presented: R e ms = 32908 .84 ln A r 0 .55 + 260376 .65 − 410361 .90 . The relative error of the above correlation was within ±15% and the averaged relative error was 7.5%. The effect of operating conditions on the minimum slugging fluidization velocity is discussed. This research provides useful guidance for scaling-up design and for determining the optimum range of operating conditions in the SCWFB. more...

Any scientific behavior is best represented by nondimensional numbers. However, in many cases, for pneumatic conveying systems, dimensional equations are developed and used. In some cases, many of the nondimensional equations include Reynolds (Re) and Froude (Fr) numbers; they are usually defined for a limited range of materials and operating conditions. This study demonstrates that most of the relevant flow types, whether in horizontal or vertical pipes, can be better described by Re and Archimedes (Ar) numbers. Ar can also be used in hydraulic conveying systems. This paper presents many threshold velocities that are accurately defined by Re as a simple power function of Ar. Many particulate materials are considered by Ar, thereby linking them to a common behavior. Using various threshold velocities, a flow regime chart for horizontal conveying is presented in this paper. more...

Knowledge on regime transition from conventional to circulating fluidization is important to scale-up and operation of liquid-solid fluidized systems in industrial applications. Previous experimental studies reported that the onset velocity measured by bed empty time test is pertinent to the physical properties of particle and liquid, and independent of solid inventory, bed geometry, and configuration. The effect of liquid properties is, however, not clear yet since tap water is usually used as the working fluid in laboratory test for convenience. To address this problem, a Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) model is applied to numerically measure the onset velocity of particles in different liquid media. The model is first validated in terms of the experimental data of bed expansion in literature. Then several kinds of particles and three kinds of liquid media of different densities and viscosities are further simulated. We find that the Reynolds number based on onset velocity and Archimedes number follows a power-law relationship. With the decrease of Archimedes number, the discrepancy of Reynolds number based on onset velocity and that on particle terminal velocity becomes highly significant. The ratio of the onset velocity to particle terminal velocity for various particles in one liquid medium is not a constant, and instead dependent on both the particle and liquid properties. more...

In this contribution, a three-dimensional prismatic spouted bed for coating and granulation purposes is investigated. To determine the influence of a particle size distribution on the spouting behavior, binary and ternary mixtures of different particle sizes (γ-Al2O3 particles) are used. The stability is quantified using the Fourier transforms of the pressure drop signals. The stability range of binary and ternary systems differs from the monodisperse systems. Both the lower and the upper velocity limits of stable spouting can be described by a power function dependent on the Reynolds number and the Archimedes number. A larger Archimedes number results in an increased Reynolds interval size of stable spouting, which refers to a larger size of the velocity interval. This correlation was found to be not valid for the mass equivalent mixture of three particle fractions where no stable spouting state was obtained. In addition, clustering and segregation effects were observed: Coarse particles accumulate in the spout and fine particles in the annulus region of the regarded prismatic spouted bed in case of the instable spouting regime. This is problematic for granulation and coating processes as a homogeneous droplet distribution and a proper mixing between spraying and drying zones is disabled if some particle fractions are inhibited to pass the spray zone. more...

Using the Eulerian-Eulerian two-fluid model (TFM) the hydrodynamics and heat transfer around different immersed bodies in a fluidized bed were analyzed. The kinetic theory of granular flow (KTGF) was used to simulate the solid phase. For hydrodynamic simulations, 3D, 2D Cartesian and 2D axisymmetric frameworks were examined and the differences in the results of these simulations were discussed. For the heat transfer analysis, due to the high computational demand of 3D simulations, the analyses were performed using 2D Cartesian and axisymmetric frameworks. For studying the effect of shape on the CFD results, two cases of spherical and cylindrical immersed bodies were simulated. In addition, two methods for calculating the surface-to-bed heat transfer coefficient (HTC) for 2D Cartesian and axisymmetric models were examined. The first (method I) is based on constant heat flux boundary condition, while the second one (method II) is based on the isothermal wall boundary condition. It was found that method I outperforms the second one for both 2D Cartesian and axisymmetric configurations in prediction of average HTC. It was shown that the simulation results were in closed agreement with the corresponding measured data. The findings revealed that the spherical immersed body, which has a better aerodynamic shape, produced higher HTC in bubbling fluidized bed with Geldart B particles. Finally, the impact of Archimedes number (Ar) on the surface-to-bed HTC was studied. more...

Experimental measurements of the force and torque on freely settling fibres are compared with predictions of the slender-body theory of Khayat & Cox (J. Fluid Mech., vol. 209, 1989, pp. 435–462). Although the flow is viscous dominated at the scale of the fibre diameter, fluid inertia is important on the scale of the fibre length, leading to inertial torques which tend to rotate symmetric fibres toward horizontal orientations. Experimentally, the torque on symmetric fibres is inferred from the measured rate of rotation of the fibres using a quasi-steady torque balance. It is shown theoretically that fibres with an asymmetric radius or mass density distribution undergo a supercritical pitch-fork bifurcation from vertical to oblique settling with increasing Archimedes number, increasing Reynolds number or decreasing asymmetry. This transition is observed in experiments with asymmetric mass density and we find good agreement with the predicted symmetry breaking transition. In these experiments, the steady orientation of the oblique settling fibres provides a means to measure the inertial torque in the absence of transient effects since it is balanced by the known gravitational torque. more...

Supercritical water fluidized bed (SCWFB) is a newly developed reactor for coal and biomass gasification without releasing pollutants. The knowledge of two-phase flow properties in SCWFB is still lacked so far in literatures due to the extreme operating condition of high-pressure and high-temperature supercritical water. In this paper, a special dual-capacitance probe measurement system is developed for the extreme flow environment in SCWFB. It is found that the linear relationship is more precise in converting the capacitance of the probe sensor into local volume fraction of solids in SCWFB than Bottcher relationship. With the help of the newly-developed dual-capacitance probe measurement system, an experimental study on the bubbling fluidization in a SCWFB is carried out when the system pressure is in the range of 20–27 MPa and the system temperature is in the range of 410–570 °C. Four groups of quartz sands with different mean diameters which belong to Geldart type B classification are fluidized. It is found that the bed expansion method which was used in literatures to identify the onset of bubbling fluidization in supercritical carbon dioxide fluidized bed doesn’t have enough precision in a SCWFB. To solve this problem, a new method of identifying the onset of bubbling fluidization in SCWFB is proposed. The minimum bubbling Reynolds number increases with the Archimedes number in a logarithmic relationship in SCWFB. At last, a new predicting correlation of the minimum bubbling fluidization velocity in SCWFB is proposed: R e mb = 26.709 ln ( A r + 10253.88 ) - 247.339 , 1900 A r 180000 The relative error of the new predicting correlation is within ±20% and the averaged relative error is 7.5%. The research work in this paper provides useful guidance for the optimization and operation of SCWFB reactor. more...

Temperature measurements combined with Particle Image Velocimetry (PIV) were performed in a cuboidal convection sample with a square cross section (width / height). The objective of the study is to analyze the influence of the aspect ratio Γ x z = L / H and the Archimedes number Ar on the large-scale coherent structures in mixed convection. Air at ambient pressure was used as working fluid ( P r = 0.7 ). The aspect ratio was varied between 1 ≤ Γxz ≤ 4 (length / height) and the variation of the Archimedes number was achieved by prescribing the inflow velocity of an air jet, which was superimposed on the thermally induced flow via an inlet and outlet channel. The Rayleigh number was kept constant at R a = 2.0 × 10 8 . A model, adopted from pure thermal convection, was used to extract the number of convection rolls from the circumferential temperature distribution measured along the sidewalls of the convection sample. For a fixed Archimedes number (Ar ≈ 4), the number of thermally induced large-scale circulations (LSCTC) increased with the aspect ratio of the sample. Specifically, starting with Γ = 2 , a linear dependence with unity slope was found. A decrease of the Archimedes number led to a transition from the single LSCTC structures to FC-dominated LSCs (LSCFC) for Γ = 1 and Γ = 2 , whereas the multi-roll structures found for Γ = 3 and Γ = 4 were more stable even for higher inflow velocities. more...

The amount of particulate matter (PM) in the environment has been confirmed to be health risks on human bodies[1, 2], and therefore removing suspended particles has become the research goal of many studies. Electrostatic precipitator (ESP) is one of the high-efficiency particle collection technologies[3-7]. Particle Image Velocimetry (PIV) has been an effective tool for visualizing the flow patterns in experimental fluid mechanics, and many studies adopted this technique to study flows in ESP[8-10]. However, particles charged by the electric field can cause deviation in measurement results since it does not follow the ionized air flow which can be charged differently from the tracer particles. In this study, the observation of the effects of different particle properties on flow field in a two-stage ESP is the objectives of this study. A two-stage ESP was built and four different seeding particles, aluminum oxide (Al2O3) particle, oil droplet particle, sodium chloride (NaCl) particle, and titanium dioxide (TiO2) particle, are tested in the current study. In this study, the streamwise velocity of the flows ranges from 2.36 m/s to 4.18 m/s, the voltage of the corona electrode varies from 8 kV to 12 kV with a positive polarity, and the voltage of the collector electrode is fixed at 16 kV. To investigate the 3-D flow patterns inside the channel, data at different planes were taken for comparison. The results show that by increasing charge voltage from 8 kV to 12 kV with a streamwise flow velocity the 2.36 m/s, the y-component velocity for Al2O3 particle, oil droplet particle, NaCl particle and TiO2 particle increased by 50.6%, 76.0%, 33.5% and 51.9%, respectively. Moreover, for the case of the 4.18 m/s primary flow, the y-component velocity for Al2O3 particle, oil droplet particle, NaCl particle and TiO2 particle increase by 52.7%, 59.2%, 59.4% and 65.9% after the voltages increase from 8 kV to 12 kV. PIV results for oil droplet particle shows slower y-component velocities, which can be due to the lower Archimedes number of 3.12E-06 and the mobility number that is larger than 3. On the contrary, in most of results from TiO2 particles show high y-component velocity, which is due to the highest Archimedes number of 1.15E-03 of the seeding particles tested in this study. This result shows that the particle is less affected by buoyancy effect. The PIV results of the middle plane also shows that the ycomponent of velocity from -2.6 m/s to -0.5 m/s, in contrast to -1.0 m/s to 1.0 m/s from the near wall observation plane. These results are consistent to simulation results of the electric field distribution, whichshows unequal electric field strengths between the middle and near wall regions of the test section. Only half of the cage shape distribution of the electric field can be observed, and primary flow influences the ionic wind to move to the downstream area. Based on the results, the oil droplet and TiO2 particles are more suitable for the role of tracer particles compared to aluminum oxide and sodium chloride particles. more...

The objective of this work is to study the two-dimensional mixed convection flow and heat transfer over an isoflux step projecting from the floor of an enclosure. The inflow into the enclosure takes place through two inlets placed at either end of the floor and the outflow occurs through an outlet provided in the ceiling of the enclosure. The walls of the enclosure are insulated. Convective heat transfer from the step surfaces to the fluid occurs due to the combined action of forced and free convection effects. The heat transferred to the fluid is carried away by the fluid leaving the enclosure. A mathematical formulation is developed by setting up the conservation equations for mass, momentum and energy, and the initial and boundary conditions. The density variation is taken into account only in so far as it gives rise to a buoyancy force. The equations are non-dimensionalised so that the results will have applicability to wide-ranging practical conditions. A numerical formulation is developed by discretising the primitive variable equations on a staggered mesh, using the ultra-sharp strategy for convection terms with donor-cell differencing scheme option, the modified strongly implicit procedure (MSIP) as the equation solver and the Simplified Marker and Cell (SMAC) method as the pressure-velocity coupling algorithm. Parametric studies are performed by varying the Archimedes number Ar and Reynolds number Re (while Prandtl number Pr is chosen as 0.71 corresponding to air as the working medium), and results are presented in the form of streamline and isotherm maps, graphs, and tables. more...

We study the effects of fluid-particle and particle-particle interactions in a three-dimensional monodispersed reactor with unstable fluidization. Simulations were conducted using the Immersed Boundary Method (IBM) for particle Reynolds numbers of 20-70 with an Archimedes number of 23600. Two different flow regimes were identified as a function of the particle Reynolds number. For low particle Reynolds numbers ($20 < Re_p < 40$), the porosity is relatively low and the particle dynamics are dominated by interparticle collisions that produce anisotropic particle velocity fluctuations. The relative importance of hydrodynamic effects increases with increasing particle Reynolds number, leading to a minimized anisotropy in the particle velocity fluctuations at an intermediate particle Reynolds number. For high particle Reynolds numbers ($Re_p > 40$), the particle dynamics are dominated by hydrodynamic effects, leading to decreasing and more anisotropic particle velocity fluctuations. A sharp increase in the anisotropy occurs when the particle Reynolds number increases from 40 to 50, corresponding to a transition from a regime in which collision and hydrodynamic effects are equally important (Regime 1) to a hydrodynamic-dominated regime (Regime 2). The results imply an optimum particle Reynolds number of roughly 40 for the investigated Archimedes number of 23600 at which mixing in the reactor is expected to peak, which is consistent with reactor studies showing peak performance at a similar particle Reynolds number and with a similar Archimedes number. Results also show that maximum effective collisions are attained at intermediate particle Reynolds number. Future work is required to relate optimum particle Reynolds number to Archimedes number., 28 pages, 17 figures more...

Minimum fluidization velocity is one of the most important fluidization characteristics when applying an Air Dense Medium Fluidized Bed to dry coal beneficiation. Measurements were carried out for magnetite particles (150–300 μm) and the binary mixtures of magnetite mixed with sand/gangue/coal particles (300–425 μm) to determine the influence of bed inventory on the characteristics at incipient fluidization state. The experimental results demonstrate that the minimum fluidization velocities of both single and binary mixtures of solid particles increase with increasing bed mass, which has not properly accomplished by the existing equations. The correlation proposed by Wen and Yu has been modified to predict the minimum fluidization velocity as a function of bed inventory. It only requires the knowledge of Archimedes number and the pressure drop of fluidized bed. This correlation is in reasonable agreement with almost all available data in the literature and the present work. more...

A method for estimating minimum fluidisation velocities in a well-mixed, bidisperse fluidised bed of spherical particles is described where a drag model iscombined with a particle packing model. The method described does not require empirical input about a specific particle mixture, and so these minimum fluidisation velocities can be estimated over wide ranges of size and densityratios. The treatment is fully non-dimensionalised. It is shown that two minimum fluidisation velocities may be defined for a well mixed bi-disperse bed:the gas speed at which fluidisation initiates determined from considering the bed as a whole, and a higher one corresponding to the balance of forces onan individual particle. The differences between bi- and mono-disperse beds arethe change in particle volume fraction owing to packing, the difference in dragaround individual particles compared with the average drag, and the action ofthe hydrostatic pressure gradient. The latter two effects tend to increase thedifference between the two limits of minimum fluidisation velocity, while packing decreases it and intensifies the dependence on mass fraction of the minimumfluidisation velocities. The influence of inertia is determined from particle properties through an Archimedes number. Though the inertial effects are not large for a wide range of particles, they can start to dominate other influences on the minimum fluidisation velocities as particle diameter increases. more...

The characteristic features of the motion of single particles in a swirled gas flow are considered. A dependence has been obtained for calculating the maximum height of particle ascent. An extreme dependence of the time taken by the particle to reach the chamber walls on its diameter has been established. more...

International audience; An experimental investigation of gas-liquid mass transfer in the wake of a confined air bubble sliding under an inclined wall in a 2D Hele-Shaw cell is reported. A colorimetric technique based on an oxygen-sensitive dye was used to visualize the oxygen transfer. Bubble velocities, shape eccentricities, interfacial areas and, for the first time, the instantaneous spatio-temporal distribution of oxygen concentration fields in the bubble wake, have been investigated for upper wall inclination angles of 10° ≤ α ≤ 60° and Archimedes numbers of 783 ≤ Ar ≤ 3221. Image processing has allowed, through a specific approach, a quantification of mass transfer. The calculation of the mass flux allowed the deduction of the liquid-side mass transfer coefficient kL. Experiments reveals that, at low angles of inclination, bubble velocities decelerates, shape eccentricities increased, and the instantaneous spatial and temporal distribution of oxygen concentration fields illustrated two distinct regions underneath the sliding bubble: a single vortex loop enclosing the near wake where oxygen is transferred, and a far wake containing oxygen in the form of a single long strip. When inclination angles and bubble sizes were increasing, velocities were increasing, the vortex elongated gradually until it disappears at high angles where total mass fluxes increased. This increase of bubble velocities has increased liquid-side mass transfer coefficient kL allowing a scaling law between the Sherwood number and the modified Archimedes number Ar.sin(α) to be proposed. more...

Particle and slip velocity evaluations are essential for the design of dilute phase pneumatic conveying systems in which the particles are fully suspended in the pipe, transportet at high velocities and low pressures with solid loading ratios that do not exceed 15. Although the subject was widely researched, it lacks a consistent correlation over various operating conditions and wide range of particle properties. Moreover, investigating the three dimensional velocity distribution in a cross section of a pipe may further contribute to the understanding of the phenomenon. In this study, we present a thorough experimental investigation of particle velocity obtained from 3“, 2“ and 1“ horizontal, dilute phase pneumatic conveying systems with various operating conditions and conveyed material with the following property ranges: 0.06 mm 940 kg m 3 ρ p 5800 kg m 3 ; 14 m s U g 28 m s ; 2.4 . · 10 4 Re g 1.4 · 10 5 ; 26 mm D 76 mm; 0.3 η 3 . The velocity was obtained using a high speed video camera combined with image processing. Data was obtained in all three dimensions for each particle allowing an investigation of the velocity distribution and the effect each component has on the equivalent velocity. The velocities of the non-axial directions were found to be considerably low in relative to the axial velocity. Therefore, in terms of the kinetic energy (e.g.), the non-axial velocities have negligible contribution; however, they have a major effect on the flow and acceleration mechanism. A correlation is presented for the axial particle velocity evaluation in the range of the tested operating conditions, which is mainly affected by the Archimedes number of the particle, with a good fit of our data and various data points from previous publications. more...

This paper presents a series of numerical simulation on solid-liquid two-phase flow in cross fractures based on the Two-Fluid Model and the kinetic theory of granular flow (KTGF). First, the model is validated by previous experimental data. Second, the dimensionless controlling parameters are derived to describe the particle-laden flow in cross fractures, including the angle between the main and branch slots (bypass angle) theta, inlet particle volume fraction alpha(s0), the ratio of particle size to branch slot width d(s)/w(b), the Archimedes number Ar and the Reynolds number Re. Third, the effects of the dimensionless parameters are investigated. The results show that particles tend to accumulate at the intersection between the main slot and the branch slot. Larger bypass angle between the main slot and branch slot leads to less particle's flow into the branch slot. The distance of the branch fracture from the inlet of the main fracture induces different particle-flow characteristics into the branch slot. Particle volume fraction at the stable stage increases with the decrease of d(s)/w(b). The deposition thickness of particles increases with the increase of the inlet volume fraction and Ar number, while decreases with the increase of Re number. (C) 2018 Elsevier Ltd. All rights reserved. more...

Many parameters need to be investigated in order to reduce power consumption, product degradation and flawless operation of pneumatic conveying systems. Particle velocity in vertical conveying is one such parameter that we are focussing on in this study. Many correlations were developed to predict particle velocity in steady state zone. Still, they lacked in consistency for finding any correlation that would explain particle velocity in acceleration zone as well as in fully developed flow. In this study, an experimental system was developed with 5 m vertical test section having 50 mm ID of pipe. Materials selected were representing a large range of Archimedes number (102–107). Very small quantities (Diluted) of various materials were manually fed into the upward conveying airflow using a piston forced particle feeder. Particle velocities were measured in acceleration as well as in fully developed region. Visuals of particle flow were recorded using high-speed camera and analyzed by a Matlab programme, specially developed for this analysis. Terminal velocity analysis (up-ss = ua–uT) has been used to predict steady state velocity. Terminal velocity analysis was found to have good agreement with previously published data by using its (terminal velocity) true value. Correlation of particle velocity and acceleration length was developed based on the investigation of statistical velocity distribution at different locations in vertical test section. The developed parameters of vertical conveying in this study have been compared with horizontal conveying results of [1]. Different relative curves (horizontal and vertical) were developed and a new threshold velocity (VH-identical velocity) was added to the master curve developed by [2]. These developed correlations and curves will help in designing and operation of pneumatic conveying systems. more...

In recent years, non-isothermal jets have received much attention due to their wide range of applications in the industry. The present work concentrates on comparing the buoyancy mediating effects on the performance and oscillating behavior of horizontal and vertical self-excited jets. To this aim, the oscillating behavior and performance characteristics of self-excited jets in horizontal and vertical directions have been simulated and compared under different thermal boundary conditions (e.g., heated, cooled, and adiabatic wall cavities). Computational solutions were obtained using unsteady Reynolds averaged Navier-Stokes (URANS) and energy equations for an incompressible flow. Investigations have been performed for different nozzle thicknesses/widths (0.5–2 cm) at a constant flow rate and inlet temperature of 300 K. The results showed that non-isothermal conditions did not significantly affect the oscillating behavior of horizontal jets, while this could be much more dramatic in vertical jets. In vertical jets with a nozzle thickness of 2 cm, under non-isothermal conditions, the oscillation frequency and the average Nusselt number are about 17% and 40% different from those of the isothermal jet, respectively. The results also indicated that when the Archimedes number exceeds 0.1, the effect of the jet orientation on its performance and oscillating behavior will be more pronounced. more...

Efforts are made to delineate the dynamics of entrained gaseous cusps and flow of liquid films wrapped around a horizontal partially submerged rotating roller numerically. The solid roller is allowed to rotate across the gas–liquid interface with a fixed submergence ratio of 0.5 (equally immersed in both gaseous and liquid phases) and the gaseous phase is subjected to horizontal crossflow. The finite volume-based solver Gerris has been employed to track the interfacial configuration by using the volume of fluid (VOF) method. The combined influence of roller rotation (ω) and strength of crossflow (Reflow) on the wrapped film thickness and the structure of entrained cusp is demonstrated thoroughly for different gas–liquid pairs in order to understand the underlying physics. This study also includes the transient dynamics of liquid tip movement from the receding to advancing junction for various Reflow and gas–liquid pairs. Subsequently, the structure and rate of entrainment are also estimated, where the collapsible gaseous jet breaks into circular gaseous bubbles. Predictions are also made in order to establish the dependence of interfacial configuration on the Archimedes number (Ar). Finally, a theoretical model has been developed to elucidate both entrainment and wrapped film dynamics, which shows excellent agreement with the numerical results. more...

This study aims to understand the effect of supply momentum and heat generation density on the cooling and ventilation effectiveness in a room with an impinging jet ventilation system (IJV). A parametric study was conducted by CFD analysis, and the number of supply terminals and occupants were varied as parameters. CFD validation was conducted before the parametric study by comparing the experimental and analytical results. RNG k-e and SST k-ω model showed almost the same accuracy for simulating, and SST k-ω model was chosen to be used for the parametric study. It is shown that the larger number of terminals and/or occupants leads to the air distribution to be displacement flow, whereas the smaller number leads to that of mixed condition. The ventilation effectiveness and cooling effectiveness within the room could be kept higher by locating the supply terminal at the centre of the walls than at the corner of the room. When the supply velocity was smaller than 0.833 m/s, the draught rate (DR) at ankle level in the central cross-section could keep lower than: 20% in the region farther than 0.5 m horizontally away from the terminals, and 15% in the region farther than 1.0 m away from the terminals. Finally, the cooling and ventilation effectiveness is expressed as the function of Archimedes number (the balance between supply momentum and buoyancy) in the specific studied cases. The asymptotic values for both large and small Archimedes numbers are obtained for each index expressing cooling and ventilation effectiveness. more...

In this study, we performed numerical simulations of three-dimensional turbulent flows over an isolated building with a door-type opening by using a CFD model in order to investigate the combined effect of wind and buoyancy on windward single-sided ventilation. Positive and negative temperature differences between the inside and outside of the building were considered. The Archimedes number ( A r ) was introduced as an index for evaluating the interaction between buoyancy and wind effects. The interaction between the two opposing forces under a positive temperature difference was found to be destructive, resulting in the combined effect reducing the volume flow rate. Furthermore, the wind effect was found to be dominant for A r 0.5 0.45 , with the buoyancy effect beginning to increase at A r 0.5 = 0.2 , and tending to be dominant for A r 0.5 > 0.45 . The two effects were found to be fairly comparable at A r 0.5 = 0.45 . The interaction between the two assisted forces under a negative temperature difference was always constructive, resulting in the combined effect reinforcing the ventilation for all the Archimedes numbers. more...

Prediction of horizontal pressure drop in dilute phase pneumatic conveying or slurry transport is among the fundamental issues of designing these systems. In this work a thorough literature survey demonstrates that there is no consensus on an integrative solution for conveying pressure drop, therefore a large data base of conveying systems' operating points at dilute phase is established and analyzed. It includes measurements taken at our 52 mm bore laboratory pneumatic conveying line, as well as thousands of data points collected from the literature. Two modelling approaches are attempted – the first is frictional representation based on dimensional analysis, which presents linear dependency between the pressure drop and the superficial fluid velocity normalized by the minimum pressure velocity of the transport curve. It had also been found that the pressure drop increase rate has a strong dependency on the Archimedes number. The second approach is an energy balance between the power of the drag force applied to the particles and the additional power required to drive the fluid due to particle presence. Unlike the common expressions, a modification to the drag coefficient is suggested, which takes into account pipe turbulence and particle acceleration. The two presented models do not require pilot plant calibration, and an applicability of one of them to slurry transport is demonstrated. Some future research routes are offered. more...

Shaul & Kalman (2014–2015) defined three different types of plugs (Plug-I, II and III) of different particulate materials for dense phase pneumatic conveying. The Present experimental study is undertaken to determine the borderline between Plug-I and the other type of plugs. The borderline is established by using the concept of detachment velocity of the particles from the front of the plug. For the current study, thirty three particulate materials have been tested having the Archimedes number (Ar) in the range of 10− 3 to106. The experiments conducted in three transparent Plexiglas pipes of diameters 1 in., 2 in. and 3 in. For each experiment, a single artificial plug of type I of varying length in the range of 10–100 cm was inserted into the test section of 1.5 m length. Further, as the plug flow is a low velocity phenomenon, the Reynolds number (Re) during experimentation, is varied in the range of 10− 3 to 102. The results of the experiments show that for the particulate materials with Ar > 102, first the phenomenon of detachment occurs at a corresponding velocity and on further increasing the flow rates the plug dissembled. The variation of the detachment velocity is found to be a power function of the Ar number (for Ar > 102), whereas, the detachment velocity is found to be independent of the pipe diameter and plug length. For materials with Ar more...

In this paper a two-phase Lattice Boltzmann model, capable of handling large density jumps, is used to simulate the vapor filmwise condensation and dew drop sprinkling, outside different horizontal geometries. These geometries include circle, rectangle, square, and a bank of circular and rectangular tubes. In order to calculate the temperature field a passive scalar approach is combined with the Lattice Boltzmann framework and the flow field is assumed to be affected by temperature under the hypothesis of Boussinesq. Additionally, the effect of phase-change on velocity field is taken into account by adding a suitable source term to the pressure-momentum distribution equation. To simplify the model, it is assumed that the vapor remains at the saturation temperature and the amount of heat transferred through the interface is the only driving force for condensation. To demonstrate the validity of the model, the results are compared with a variety of analytical, numerical and experimental data. The validated model then is employed to study the influence of different parameters such as vapor temperature, Stefan number and Archimedes number on vapor condensation outside multiple cross sections. Finally, the condensate inundation and mean heat transfer coefficients are analyzed in horizontal tube banks. more...

Campos-Diaz, K. E., & Alvarez-Cruz, J. L. (May-June, 2017). A proposal of a hydrodynamic model to low Reynolds numbers in a liquid-solid inverse fluidized bed reactor. Water Technology and Sciences (in Spanish), 8(3), 143-150. This paper examines the fundamental characteristics of an inverse liquid- solid inverse fluidized bed reactor. In this reactor, many experiments were performed using three sizes of polypropylene spherical solids, lighter than water, with different diameters (4.00, 4.16 and 4.18 mm) and of densities ranging from 808 to 867 kg/m3 , these were fluidized by continuous liquid phase flow. Various bed heights were obtained at different flowrates from 0.95 to 9.5 (L min-1). A predictive model is developed for the hydrodynamic behavior, such as height and solid holdups (bed porosity), this model was derived from the balance of forces acting on a single particle and the set of particles found in the fluidized bed; uses process parameters, such as reactor dimensions, particle properties, and liquid flowrates as input variables, this model also includes the inertial drag coefficient which allow extended a non-spherical particles. This model has several advantages when compared with previously reported. Among them, advantages such as standard deviation values ≤0.9% between experimental and calculated bed porosity, the bed porosity can be expressed in terms of the Reynolds and Archimedes numbers and this model estimate bed porosity in a range of Reynolds number from 5.5 to 200 which has not been studied in an inverse fluidized bed reactors. more...

Sedimentation of a particle pair in a shear-thinning fluid is studied for varying generalized Archimedes number. Unlike in the Newtonian fluid, one more group of multiple stable states is identified, and the drafting-kissing-tumbling state disappears when the shear-thinning effect is strong enough. more...

In this work, the dispersion of diesel fuel in water in a baffled tank stirred by a Rushton turbine is investigated. The impeller speeds corresponding to the initial drawdown, the just dispersed regime and the completely dispersed regime are identified by suitable variables obtained by means of the Electrical Resistance Tomography technique. The effect of the dispersed phase volume fraction and of the impeller off-bottom clearance on the different dispersion regimes is considered. The impeller Froude number, the Archimedes number and a dimensionless distance between the liquid-liquid interface position and the impeller elevation are adopted for the data interpretation. For the investigated system, the local volume fraction profiles show that the completely dispersed condition is practically achieved above the just dispersed impeller speed, with negligible gradients of the local volume fraction distribution in the axial direction. more...

In this work, we perform simulations of particle laden flow in a wide and long narrow channel in a Newtonian fluid. Simulations are performed for mono-sized and equal density spheres with varying Archimedes and Reynolds number. In the simulations, different phases of particle transport - rolling, saltation and suspension are observed. During simulations the average bed height is monitored and its steady state value is used for proposing a correlation between solids volume fraction (ϕ), shear Reynolds number (Res) and Archimedes number (Ar). This correlation is used to predict the critical shear Reynolds number for particle lift-off and a condition at which particles would occupy the whole channel at a given Archimedes number. The value of this critical Reynolds number is compared with the critical Reynolds number for single particle lift-off. more...

Column attached ventilation (CAV) is a new form of air distribution based on pillars widely distributed in buildings. Due to thermal buoyancy in the room, the airflow mechanism and performance of CAV is uncertain when it is applied for winter heating, especially in buildings with large space. In this study, a simplified three-dimensional model was established based on a shopping mall. A Computational Fluid Dynamics (CFD) method was employed to simulate the airflow in the room. Archimedes number (Ar) was used to study air distribution and ventilation performance. Results indicated that CAV could be used for room heating, and inertia force was the main driving force of the airflow. In the occupied zone, air velocity and temperature could be controlled by supply air velocity and temperature. Ar was related to air distribution and ventilation effect. In selected cases, Ar less than 2.241 × 10−3 was the prerequisite for effective air distribution. Heat removal effectiveness was linearly related to Ar, and it increased by about 0.01 when Ar reduced by 0.1. CAV saved more energy than mixing ventilation to achieve the same parameters of the occupied zone. These results provide a theoretical basis for the application of CAV in winter conditions. more...

The terminal settling velocity (TSV) of solid particles is experimentally determined in fluidizing columns. In monodispersed (single component) systems, the bed expansion behavior has been experimented with using pseudoplastic liquids. The terminal velocity is calculated from the plot of bed voidage (e) vs. liquid velocity and extrapolating to e = 1.0. An empirical correlation is developed for determining the TVS with acceptable statistical accuracy. Successful applicability of ANN modeling has been reported. After comparing with existing literature, it was found that the present work yielded better results (based on the statistical error parameters) than the previous literature. more...

A mass-conserving finite element lattice Boltzmann equation (FE-LBE) method for the simulation of a bubble rising in viscous fluid at high Reynolds number with large material property contrast is presented in this work. The presented model consists of the conservative phase-field equation for interface capturing and the pressure-velocity formulation of lattice Boltzmann equation (LBE) for recovering the hydrodynamic properties. In this computational framework, LBE is regarded as a special space time discretization of the discrete Boltzmann equation in the characteristic direction and the streaming step is carried out by solving a linear advection equation in an Eulerian framework. We conduct extensive investigations for numerical accuracy and stability through performing multiple benchmark simulations for single bubble rising in a viscous fluid in different flow regimes. The complex dynamics of a high Reynolds number bubble rising with path and shape oscillations are studied and compared to available experimental results. The simulated evolution of the bubble mean shape with Archimedes number, path and shape oscillations in different oscillation regimes, and wake dynamics of the bubble show a good agreement with available experimental data. The current model offers a remarkable improvement in mass conservation compared to the Cahn-Hilliard based FE-LBE model. more...

Computational Fluid Dynamics simulations of a typical occupied office were performed to study the effects of ventilation parameters (supply momentum and heat gain intensity) and inlet geometry (height and area of the supply) on the temperature profile of the air in the space. A knowledge of this profile is critical to ensure that the occupants are comfortable according to commonly used standards. Different room configurations were characterized in terms of their Archimedes number, which compares the effects of buoyancy and supply momentum, and dimensionless geometric variables. A high Archimedes space was found to be divided into a warm region of uniform temperature above the occupants and a zone where the temperature increases approximately linearly with height. In a low Archimedes space the air is mixed by the supply jet in the lower part of the room, especially near the outlet, resulting in this area having uniform temperature. However, the supply jet was found to be less efficient at mixing the air near the ceiling, resulting in higher temperatures in this zone than with higher Archimedes numbers. For a given Archimedes number, as the supply area increased, the air temperature was found to decrease in the lower part of the room but to increase near the ceiling. A high inlet increased the vertical mixing in the room. Correlations were proposed to establish the temperature profile within 5% of the temperature rise of the room. The inputs of the correlations are readily available in multi-zone software, facilitating their integration in this kind of software. The proposed correlations will allow the user of the multi-zone software to evaluate comfort conditions more accurately, while maintaining the high speed, simplicity and design flexibility of the multi-zone models. more...

A fluidization reactor was designed to study the possibility of performing circulating turbulent fluidized bed (CTFB) by using only single feed gas injection. The effect of the design parameters was studied based on the Geldart classification and Archimedes number. Two sizes of sand particles represented Geldart group B, whereas a polyvinyl chloride particle represented the Geldart group A. The effect of the operating parameters was studied by manipulating the solid recirculation rates. Interpretation of the solid fraction profile along riser height could be used to determine the bed front. The appearance of CTFB in the system was indicated by the disappearance of the bed front along the riser height. A suitable riser height was lower than the maximum solid particle bed expansion; this is a crucial design parameter to support the action of CTFB. more...

Severe reactor core damage may occur from fuel channel failure as a consequence of excessive heat emitted from calandria tubes (CTs) in a pressurised heavy water (D 2 O) reactor (CANDU). The heating of the CTs is caused by creep deformation of the pressure tubes (PTs), which may be ballooning or sagging depending on the internal pressure of the PTs. The deformation of the pressure tube is due to overheating as a result of a loss-of-coolant accident (LOCA) and emergency core cooling system (ECCS) failure. To prevent the exacerbation of the LOCA, circulating D 2 O in the moderator tank may be utilized by forming a secondary jet that externally cools the individual CTs. The buoyant plume develops around the CTs and interacts with the secondary jet at a certain oblique angle with respect to the gravitational axis, depending on the spatial location of the hot calandria tubes (or the hot reactor core region). This study reports on how the local and overall heat transfer characteristics on a calandria tube where the buoyant plume develops, are altered by the obliqueness of the external secondary jet (from a co-current jet to a counter-current jet) in a simplified configuration at the jet Reynolds number of Re j = 1500 for the Archimedes number of Ar D = 0.11 and Rayleigh number of Ra D = 1.6 × 10 6 (modified Rayleigh number of 3.0 × 10 7 ). more...

Particle image velocimetry (PIV) measurements of the flow patterns in a pressurized heavy water reactor (PHWR) were made in a 1/4 scaled-down model of the Canadian deuterium uranium (CANDU) reactor. Archimedes’ number (Ar) was introduced to evaluate the dynamic similarities between the isothermal (Ar = 0) and heating conditions. Small and large PIV fields of view were used to measure the overall flow field. Flow patterns were analyzed by measuring the spatial velocity distributions and the impingement positions of the inlet jet. The momentum-dominated flow patterns were measured under isothermal conditions (Ar = 0). The impingement position bias increased as Ar increased due to buoyancy effects. The overall moderator circulation characteristics were explored for various Ar values up to 0.157. more...

Three-dimensional direct numerical simulations are presented of the flow of fluid containing heavy spherical particles in a channel. The simulations resolve the motion of individual particles and the details of the flow at the particle level. They are based on the finite element method and the Distributed Lagrange Multiplier/ Fictitious Domain Method. The problem is characterized by four parameters, namely a Reynolds and an Archimedes number, a density ratio and a dimensionless particle size. The last three are fixed and the effects of the Reynolds number are studied over a range covering the onset of particle resuspension and the transition of flow to significant unsteadiness. Encouraging estimates for the onset of resuspension and the particle flux as a function of the excess Shields number are found. The results are analyzed in terms of the vertical distribution of horizontally averaged macroscopic quantities, obtained by applying integral momentum balances. On the basis of such balances, particle stresses and interfacial forces between the fluid and particle phases are estimated and compared to existing models, developed mainly for Stokes flow conditions. The qualitative agreement is encouraging but points to the need for taking into account several effects, notwithstanding those of finite particle Reynolds numbers. Provided that such information becomes available the set of four equations derived from the suspension and particle phase momentum equations could describe the average equilibrium distribution, the flow of both phases and the pressure in the fluid. more...

The rotary chamber technique allows extended observation times of rising bubbles up into the 10-mm range. After establishing the technique in combination with optical sizing in previous publications, this work completes the case of nitrogen bubbles in tap water. The rise velocity and the mass transfer are measured for five degrees of water saturation. A one-parameter model equation involving the Archimedes number is offered for calculation. The limit of the analytical boundary layer model is depicted. more...

A mixture of 85% nitrogen and 15% carbon dioxide (N2/CO2) is separable at ambient temperature on a continuous basis. A high-pressure, density-driven separator (HDS) was designed and fabricated to explore the process. The effect of the fluid variables, including pressure and mixture flow rate, was assessed on a separation efficiency metric. An important design parameter, the length of the HDS, was also evaluated in the experimental design. Essentially perfect separation is observed over a wide-range of conditions. Separation efficiency is correlated with two dimensionless groups. The first is the Archimedes number. It is a ratio of buoyant force to viscous force. The second dimensionless group is defined in this work. The Espanani number is the ratio of the pressure force to the viscous force. Excellent correlation between separation efficiency and the product of the Archimedes number and the Espanani number is observed. This observation informs both process and equipment design. more...

The unsteady laminar flow of an inverse fluidized bed reactor was addressed in this study using computational fluid dynamics (CFD). Three-dimensional (3D) and two-dimensional (2D) simulations were carried out using the Eulerian-Eulerian approach with the Syamlal O'Brien and Gidaspow models for modeling the drag between the solid and liquid phases. Reported data of solids expansion and bed porosity were used to validate the simulations. Results show that 2D simulations can satisfactorily reproduce experimental data of fluidized bed reactors, which are essentially equal to those obtained on 3D simulations. The model of Syamlal O'Brien was found to be in better agreement with experiments than that of Gidaspow. It is shown that commonly used correlations for predicting bed porosity fail to provide a reasonable overall description of the evaluated operating conditions. The flow patterns for both phases in the bed section exhibit chaotic recirculation zones with high values of shear stress, and after this, the flow quickly becomes fully developed. The effect of biofilm thickness increase on bed porosity, under similar apparent densities of colonized particles reported for this system, is analyzed. Biofilm growth generates a decrease in the Archimedes number (i.e., decreases the buoyancy of particles) and an increase in the particle Reynolds numbers (Rep), affecting significantly the final porosity of the bed. However, this effect vanishes for Rep more...