Heat transfer and flow pattern in vertical liquid-solids flow

Wall-to-bed heat transfer in hydraulic transport of spherical glass particles of diameter 1.20, 1.94 and 2.98 mm and in single-phase flow regime was studied. Experiments were performed by transporting the spherical glass particles with water in a 25.4 mm I.D. copper tube equipped with a steam jacket.In the runs without particles, the tube Reynolds number varied between 2280 and 21,300, while in hydraulic transport runs, the tube Reynolds number varied between 3300 and 20,150. The loading ratio (G_p/G_f) was between 0.07 and 0.328, and the fluid superficial velocity was between 0.29·U_t and 2.86·U_t, where U_t represents the single particle terminal velocity. For these ratios, the voidage ranged from 0.715 to 0.895.The data for the heat transfer factor (j_H) in single-phase flow are correlated using a general form j_H=f(Re). The data for wall-to-bed heat transfer in the hydraulic transport of particles show that an analogy between heat and momentum transfer exists. The data were correlated by treating the flowing fluid-particle suspension as a pseudofluid, by introducing a modified suspension-wall friction coefficient (f_w) and a modified Reynolds number (Re_m).     

Heat transfer in a pulsed bubbling fluidized bed

Surface-to-bed heat transfer and pressure measurements were carried out in a 0.17 m ID pulsed bubbling fluidized bed with glass bead and silica sand particles having mean diameters ranging from 37 μm to 700 μm to investigate the effects of flow pulsation on heat transfer and bed hydrodynamics. A solenoid valve was used to supply pulsed air to the bed at 1 to 10 Hz. The bed surface was found to oscillate with the frequency of pulsation, the oscillation's amplitude decreasing with frequency. The standard deviation of the bed pressure drop in the pulsed bed was found to be larger than that in the conventional bed due to the acceleration force imposed by pulsation. For both Geldart B and A particles, high frequency pulsation (7, 10 Hz) enhances the heat transfer compared to continuous flow, the enhancement diminishing with superficial gas velocity and particle size. For Geldart B particles, the effect of pulsation on heat transfer ceases around U_o/U_mf = 3.5, whereas 24% improvement in heat transfer coefficient was obtained for 60 μm glass bead particles (Group A) at superficial gas velocities as high as U_o/U_mf = 27. Furthermore, in the fixed bed (U_o/U_mf < 1) for Geldart B particles, 1 Hz pulsation was found to be very effective resulting in two- to three-fold increase in heat transfer coefficient compared to continuous flow at the same superficial gas velocity. The flow pulsation loses its effect on heat transfer with increasing static bed height, i.e., when H_bed/D > 0.85.     

Orthogonal design process optimization and single factor analysis for bimodal acoustic agglomeration

Acoustic agglomeration is proved as a promising pretreatment to control the emission of fine particles. As to removal of coal-fired fly ash particles (first mode), this paper investigates the combination of acoustic agglomeration with the addition of lime seed particles (second mode). The bimodal acoustic agglomeration can improve agglomeration efficiency significantly. Orthogonal designs are carried out for the first time to optimize the agglomeration conditions. The factors range as follows: acoustic frequency, f = 1000-1800 Hz; sound pressure level, SPL = 135-150 dB; residence time, t = 3-7 s, lime seed particle mass fraction, m_lime% = 30%-90%. The results of difference analysis and analysis of variance reveal that frequency is the dominant factor and the optimal conditions are: f = 1400 Hz, SPL = 150 dB, t = 4 s, m_lime% = 30%. In addition, the detailed influences of single factor on agglomeration efficiency are investigated.     

Dependence of particle fluctuation velocity on gas flow, and particle diameter in gas fluidized beds for monodispersed spheres in the Geldart B and A fluidization regimes

In this paper we present new experimental data on the steady-state, mean squared, fluctuation velocity, or granular temperature, of Geldart B polymer, glass, nickel, and stainless steel monodispersed spheres averaged over the wall of a gas fluidized bed, as a function of gas flow and sphere diameter. The granular temperature is obtained by Acoustic Shot Noise technology—namely power spectral analysis of the steady state vibrational energy of the wall excited by random sphere impact, and calibrated by hammer excitation over the wall. The new data extends to polymer and metallic spheres the experimental discovery of a 1996 paper of Cody et al. that the fluctuation velocity of Geldart B glass spheres when scaled to the gas superficial velocity, U_s, is inversely proportional to sphere diameter, directly proportional to a fundamental length scale, D_o^B, and is a universal function of U = (U_s / U_mf). We also demonstrate that the new data is consistent with the diameter dependence of the fluctuation velocity that can be derived from both the 1997 paper of Menon and Durian, who measured random sphere motion near the wall through the spectroscopy of scattered laser light, and the 1992 paper of Rahman and Campbell, who measured the average granular pressure of random sphere impact on a porous steel membrane. While the inverse scaling of the fluctuation velocity with sphere diameter, and the existence of a fundamental length scale for gas fluidization, D_o^B, had not been a feature of any published fundamental model, or computer simulation, of the steady state granular temperature of spheres in gas fluidized beds, we show that it is a feature of two recent dense kinetic fluidization models published in 1999, by Buyevich and Kapbasov, and Koch and Sangani. Both theories implicitly define a fundamental length scale for the fluctuation velocity, D^? = (μ_f² / ρ_p²g)^1 / 3, where ρ_p is the sphere density, μ_f is the gas viscosity, and g is the laboratory gravitational field. The new data for polymer, glass, nickel and stainless steel spheres presented in this paper, defines D_o^B = (56 ± 2)D^?. We use the Anderson-Jackson stability model to show that the length scale D_o^B, also defines a stability length scale, such that for D < D_o^B(D > D_o^B), the uniform dense phase of the fluidized bed is stable (unstable), against one dimensional, first order fluctuations in sphere concentration. The length scale, D_o^B is thus the theoretical equivalent to the empirical scaling length introduced by Geldart, D_B/A, to distinguish spheres (D > D_B/A) that bubble at fluidization, from spheres (D < D_B/A) that fluidize before bubbling. Finally, we present new experimental data, on the remarkable changes in the granular temperature, bed expansion, and bed collapse time, between Geldart B and Geldart A monodispersed glass spheres, and compare that data to granular temperature, and bed expansion, for Geldart A rough, non-spherical, log-normal dispersed diameter catalytic particles.     

Electrodeposition from a fluidized bed electrolyte. II. Effects of bed porosity and particle size

Mass transfer from a fluidized bed electrolyte containing inert particles has been found to depend on bed porosity and particle size. The optimum porosity was found to vary from 0.52 – 0.57 with decreasing particle size but mass transport increased with particle size.A mass transfer entry length effect was observed on the cylindrical cathode but its position within the bulk of the bed was found not to be critical, thus indicating that the hydrodynamic entry length was small. The limiting current density was found to vary as (d _e/L _e)^0.15 whered _e is the annular equivalent diameter andL _e the electrode length.List of symbols Re_I modified Reynolds No. =U _o d _p /v(1–) - Re_II particle Reynolds No. =U _o d _p /v - Re_O sedimentation Reynolds No. =U _i d _p v (constant value) - Re_t terminal particle Reynolds No. =U _t d _p /v - Sc Schmidt No. =v/D - St_I modified Stanton No. =k _L /U _o - C _b bulk concentration, M cm^–3 - D diffusion coefficient, cm² s^–1 - d _t tube diameter, mm - d _e electrode equivalent diameter, mm - d _p particle diameter, mm - bed porosity - zF Faradaic equivalence - cd current density - i _L limiting current density, mA cm^–2 - i _LO limiting current density in the absence of particles - k _L mass transfer coefficient, cm s_–1 - L _e electrode length, mm - m, n constants or indices - v kinematic viscosity, cm² s^–1 - U _o superficial velocity, cm s^–1 - U _i sedimentation velocity, cm s^–1     

Dispersion polymerization of 2-hydroxyethyl methacrylate stabilized by a hydrophilic/CO2-philic poly(ethylene oxide)-b-poly(1,1,2,2-tetrahydroperfluorodecyl acrylate) (PEO-b-PFDA) diblock copolymer in supercritical carbon dioxide

Dispersion polymerization of 2-hydroxyethyl methacrylate (HEMA) has been successfully performed in supercritical carbon dioxide at P=370 bar and T=65 °C with azobis(isobutyronitrile) as initiator and a hydrophilic/CO₂-philic poly(ethylene oxide)-b-poly(1,1,2,2-tetrahydroperfluorodecyl acrylate) (PEO-b-PFDA) block copolymer as steric stabilizer. The PEO-b-PFDA (2K/21K) block copolymer was synthesized by reversible addition-fragmentation chain transfer (RAFT) polymerization. Spherical particles of poly(HEMA) were obtained in the range of 200-400 nm diameter size with a narrow particle size distribution (D_w/D_n<1.1). The effect of the stabilizer concentration on the dispersion polymerization was investigated from 20 w/w% down to 3.5 w/w% versus HEMA. Precipitation polymerization in the absence of stabilizer lead to the formation of large aggregates of partially coalesced particles whereas discrete spherical particles of poly(HEMA) were obtained by dispersion polymerization even at low concentration of PEO-b-PFDA (3.5 w/w% versus HEMA).     

Granular temperature in a liquid fluidized bed as revealed by diffusing wave spectroscopy

We report granular temperature and solid fraction fields for a thin rectangular bed (20×200 mm cross-section and 500 mm high) of glass particles (mean diameter of 165 μm and density of 2500 kg/m³) fluidized by water for superficial velocities ranging from 0.05U_t, which is approximately double the minimum fluidization velocity, to 0.49U_t, where U_t is the particle terminal velocity estimated by fitting the Richardson-Zaki correlation to the bed expansion data. At superficial velocities below 0.336U_t, the solid fraction and granular temperature are uniform throughout the bed. At higher superficial velocities, the solid fraction tends to decrease with height above the distributor, whilst the granular temperature first increases to a maximum before decaying towards the top of the bed. Correlation of the mean granular temperature with the mean solid fraction and the local granular temperature with the local solid fraction both suggest that the granular temperature in the liquid fluidized bed can be described solely in terms of the solid fraction. The granular temperature increases monotonically with solid fraction to a maximum at φ≈0.18 where it then decreases monotonically as φ approaches the close-packed limit.     

The solids flow in the riser of a Circulating Fluidised Bed (CFB) viewed by Positron Emission Particle Tracking (PEPT)

Circulating Fluidised Beds (CFB) are attracting increasing interest for both gas-solid and gas-catalytic reactions, although the operating modes in these two cases are completely different. In modelling CFBs as reactors, the solids residence time is an important parameter. Previous studies mostly assess operations at moderate values of the solids circulation rates (≤ 100 kg/m² s), whereas gas-catalytic reactions and e.g. biomass pyrolysis require completely different operating conditions. In the current work, Positron Emission Particle Tracking (PEPT) is used to study the movement and population density of particles in the CFB-riser.The PEPT results can be used to obtain: (i) the vertical particle movement and population density in a cross sectional area of the riser; (ii) the transport gas velocity (U_tr) required in order to operate in a fully established circulation mode; (iii) the overall particle movement mode (core flow versus core/annulus flow); and (iv) the particle slip velocity (U_s).Only in a core flow mode can the particle slip velocity be estimated from the difference between the superficial gas velocity (U) and the particle terminal velocity (U_t). The slip velocity is lower than U − U_t outside the core flow mode. To operate in core flow, the superficial gas velocity should exceed U_tr by approximately 1 m/s and the solids circulation rate should exceed 200 kg/m² s.     

Study of geometry and operational conditions on mixing time, gas hold up, mass transfer, flow regime and biomass production from natural gas in a horizontal tubular loop bioreactor

A horizontal tubular loop bioreactor (HTLB) was used for production of biomass from natural gas. Hydrodynamic characterizations (mixing time and gas hold up) and mass transfer coefficients were considered in the HTLB (L=2.2 m, H=0.4 m and D=0.03 m) as functions of design parameters, i.e., horizontal length to diameter ratio (L/D) and volume of gas-liquid separator (S) as well as operational parameters, i.e., superficial gas and liquid velocities (U_sG, U_sL). In addition, flow regime in different gas and liquid flow rates was investigated. It was observed from experimental results that U_sL has remarkable effects on gas hold up and k_La due to its influence on mixing time. The volumetric mass transfer coefficients for oxygen (k_La_O2) and methane (k_La_CH4) were determined at different geometrical and operational factors. In average, the amount of oxygen consumption for metabolism is approximately 1.4 times higher than that of methane. In bubble flow regime, the HTLB was used for biomass production, too. A gas mixture of 50% methane and 50% oxygen (based on results of dry cell weight, optical density and doubling time) was the best gas mixture inlet for biomass production. The empirical correlations for mixing time, gas hold up and k_La in terms of U_sG, U_sL, L/D and volume of gas-liquid separator were obtained and expressed separately.     

Solvent effect on the nucleation and growth mechanisms of poly(thiophene)

Applying the step potential method, the effect of parameters such as solvent, potential, electrolyte and monomer concentration on the nucleation and growth processes of poly(thiophene) on Pt electrode in tetrabuthylammonium hexafluorophosphate-acetonitrile or dichloromethane has been studied. The j/t transients were generally fitted by means of a mathematical equation that considers different contributions. In acetonitrile the j/t transient (0<t<30 s) present three contributions corresponding to the following mechanisms: two-dimensional instantaneous nucleation (IN2D), three-dimensional progressive nucleation (PN3D_CT) under charge transfer control and three-dimensional progressive nucleation (PN3D_dif) under diffusion control. Similar results were obtained in dichloromethane, but in this case the 3D_CT nucleus presented an instantaneous nucleation mechanism (IN3D_ct). A second wave has been observed in the j/t transients obtained in CH₃CN at t>30 s, which was fitted by a mathematical equation that included two contributions corresponding to a PN3D_CT and PN3D_dif mechanisms. In general, the charge associated to each contribution depended on the solvent, the monomer and electrolyte concentration and the applied potential. However, the PN3D_CT (CH₃CN) or IN3D_CT (CH₂Cl₂) mechanisms were always the more important contributions. The scanning electron microscopy (SEM) analysis of the deposits morphology are in agreement with the nucleation and growth models that are proposed by this method.     

Application of √t-type, logarithmic and half-time methods in desorptive measurements of diffusivity in narrow humidity ranges

This paper concerns the use of non-stationary desorptive measurement techniques for defining the mass diffusivity of cement based materials. Three different procedures are presented: √t-type calculation; logarithmic; and half-time procedures. Cement mortars of different water to cement ratios (w / c), equal to 0.50, 0.65 and 0.80 were selected as the model environment for testing the usability of the above-mentioned desorptive techniques. The study was carried out at the temperature (T) of 20 °C within narrow relative humidity (φ) ranges: from φ₁ = 30% to φ₂ = 12%, and 50% → 30%, 75% → 50%, 85% → 75%, 97% → 85%. The results obtained are used to evaluate the conformity of these methods. The conformity is analyzed with regard to each mortar in all the above humidity ranges Δφ. The values of diffusivity D_m, defined by means of the √t-type calculation and the logarithmic procedure, demonstrated rather high conformity, all relative differences between D_m(√t) and D_m(ln) did not exceeded 20%. However, the half-time procedure can be applied for rough estimation of the diffusivity only. That is because deviations between D_m(t_1 / 2) and the values found by means of the two other methods were too large.     

Diffusional mass transfer model for the adsorption of food dyes on chitosan films

The adsorption kinetics of erythrosine B and indigo carmine on chitosan films was studied by a diffusional mass transfer model. The experimental curves were obtained in batch system under different conditions of stirring rate (80–200 rpm) and initial dye concentration (20–100 mg L⁻¹). For the model development, external mass transfer and intraparticle diffusion steps were considered and the specific simplifications were based on the system characteristics. The proposed diffusional mass transfer model agreed very well with the experimental curves, indicating that the surface diffusion was the rate limiting step. The external mass transfer coefficient (k_f) was dependent of the operating conditions and ranged from 1.32 × 10⁻⁴ to 2.17 × 10⁻⁴ m s⁻¹. The values of surface diffusion coefficient (D_s) increased with the initial dye concentration and were in the range from 0.41 × 10⁻¹⁴ to 22.90 × 10⁻¹⁴ m² s⁻¹. The Biot number ranged from 17.0 to 478.5, confirming that the intraparticle diffusion due to surface diffusion was the rate limiting step in the adsorption of erythrosine B and indigo carmine on chitosan films.     

Particle motion in the CFB riser with special emphasis on PEPT-imaging of the bottom section

The riser is the key-part of a circulating fluidized bed (CFB) and its hydrodynamics are determined mainly by the combined operating superficial gas velocity, U, and solids circulation flux, G. The bottom part of the riser contributes to the total pressure drop of the riser and affects the solids residence time in the riser, due to the possible existence of a dense bed and to the presence of an acceleration zone. Positron Emission Particle Tracking (PEPT) is applied to study these phenomena by measuring the real-time particle motion in a riser of 0.09 m diameter, defining (i) the extent of the acceleration zone, including acceleration length and acceleration time; (ii) the occurrence of a bubbling/turbulent bed under specific conditions of U and G; (iii) the establishment of a fully developed flow immediately after the acceleration zone; (iv) the occurrence of core-annulus flow under specific combinations of U and G; and (v) the disappearance of the intermediate core-annulus region at high values of U and G, where riser hydrodynamics will be either dilute or dense solid up-flow.The particle upflow velocity, U_pf, after acceleration was measured and compared with the situation of dilute transport. When the solids circulation flux increases, the dilute transport mode no longer prevails, and U_pf should be calculated using an appropriate slip factor, itself a combined factor of U and G. The acceleration length and time are nearly constant, at an approximate average of 0.26 m and 0.21 s respectively, independent of U and G. The acceleration length can be modelled fairly accurately, using a C_D-factor of approximately 3.2, which is about half the value predicted by empirical equations established for dilute transport.Dense Suspension Upflow (DSU) is achieved when G exceeds ~ 130 kg m⁻ ² s^− 1.     

Numerical simulations of transfer and transport properties inside packed beds of spherical particles

In this study, we investigate the transport and transfer properties inside packed beds of spherical particles by means of CFD simulations. Heat and mass transfer properties have been computed in packing configurations of increasing complexity at low to moderate Reynolds numbers (1<R_e<80). Only liquid-phase flows are studied (300<S_c<1000). The problem of contact points between particles, which is inherent to finite-volume numerical methods, is solved by applying a contraction of 2% on all the particles of the bed. We show that this treatment has very little influence on the results when analyzed with dimensionless numbers as N_u=f(R_e, P_r) or S_h=f(R_e, S_c). Finally, a very dense packing of spheres was built using a Discrete Element Method and used to represent the real granular media. Transfer predictions by the model are very realistic. Longitudinal and transverse dispersion coefficients are determined inside geometries containing hundreds of particles. Predictions of dispersion coefficients are consistent with literature, but a correction is applied to improve results, because the bed contraction leads to the underestimation of the transverse dispersion coefficient. The model is found to be very promising to study the “near wall channelling” phenomena inside small packed columns induced by the heterogeneity of the porosity profile close to the wall.     

Effects of binary particle size distribution on minimum pick-up velocity in pneumatic conveying

Minimum pick-up velocities (U_pu) for entrainments of particle mixtures having binary particle size distributions (PSD) are measured in a horizontal pneumatic-conveying line using the weight-loss method. Geldart's groups A, B, and C glass beads having diameters of 400, 170, 40, and 5 μm are used. Variations in U_pu as a function of particle mass fraction (m) are examined. The capability of empirical correlations of monodisperse U_pu in predicting U_pu of binary mixtures is investigated. For group B particle mixtures (i.e. 400 & 170 μm), the particles are entrained separately resulting in linear U_pu variations with m, which is accurately predicted by the monodisperse U_pu correlation. For mixtures involving group A and B particles (i.e. 170 & 40, 400 & 40 μm), the two particles are collectively entrained resulting in U_pu that vary non-linearly with m and that cannot be predicted by the correlation. For mixtures involving group B and C particles (i.e. 400 & 5, 170 & 5 μm), U_pu are comparable to that of the monodisperse group B particles, therefore they are accurately predicted by the correlation. The significant impacts of binary PSD on U_pu found presently indicates that PSD effects on particle entrainment process warrants further investigations.     

A simplified correlation for fixed bed pressure drop

An experimental study was conducted on the pressure drop characteristics of a variety of vertical packed beds in turbulent flow of air. The materials of different particle diameter, D_p, with a range of sphericity Φ, 0.55 ≤ Φ ≤ 1.00 were used in random loose packing to produce beds of different lengths, L, with a range of porosity, ε, 0.36 ≤ ε ≤ 0.56. In the covered test cases the cross-sectional velocity distribution at the exit plane of the packed beds and the pressure drop ΔP_Bed were measured in a particle Reynolds number range of Re_p, 675 ≤ Re_p ≤ 7772. The particular emphasis of the study was given to determine the influence of ε, Φ, D_p, L, Re_p on ΔP_Bed. In this respect the measurements of ΔP_Bed were compared with the well-known Ergun's Equation and the data were expressed in terms of correlations through introduced dimensionless parameters of pressure coefficient, ΔP^? and exit Reynolds number Re_exit. The proposed correlations of ΔP^? = ΔP^?(εRe_pD_p / L) and Re_exit = Re_exit(Re_pD_p / L) are found to be appropriate for the determination of ΔP_Bed and mean exit velocity, U, respectively with an acceptable fit of experimental data in an error margin less than ± 20%. The methodology is presented in this paper as an alternative approach to the available literature on packed beds.     

Rational determination of exchange current density for hydrogen electrode reactions at carbon-supported Pt catalysts

The rotating disk electrode (RDE) is a useful technique for precise determination of exchange current density (j₀) in electrochemistry. For the study of powder catalysts, a common practice is to apply the powder onto an inert disk substrate (such as glassy carbon). However, this approach in its usual version will lead to wrong results for the exchange current density of hydrogen electrode reactions at carbon-supported Pt nanoparticles (Pt/C) because of the poor utilization of the loaded Pt nanoparticles. Our new approach is to dilute the Pt/C powder with a large amount of pristine carbon support to make the catalyst layer. In this way, all the catalyst particles in the catalyst layer have nearly the same and much enhanced mass transport so that rational exchange current density can be obtained. Using the new approach, the current density for hydrogen electrode reactions at Pt/C in 0.1 M perchloric acid at 25 °C is found to be 27.2 ± 3.5 mA/cm² with an apparent activation energy 43 kJ/mol. These results are in agreement with the j₀ estimation based on real fuel cell experiments.     

Simultaneous heat and mass transfer in spouted beds

The results of a fluid-particle heat and mass transfer study in air spouted beds of silica gel and activated coal particles, using a 9 cm I.D. column with a 30° and 90° conical base, are reported. The effects of gas velocity, particle size, bed depth and cone angle on the heat and mass transfer coefficients are discussed. Equations correlating heat and mass transfer coefficients have been established. The ratio (jn)_s/(j_D)₈ has been found to be dependent on the Reynolds number and the system of spouting.     

Characterisation of flow and heat transfer patterns in low aspect ratio packed beds by a 3D network-of-voids model

Using an illustrative sphere packing assembly, it is demonstrated that flow structure and wall heat transfer patterns in low aspect ratio fixed bed reactors are more realistically modelled by properly accounting for the discrete void fraction variations. A 3D network-of-voids (NoV) model has been devised to characterise and examine the discrete flow and heat transfer phenomena in a low aspect ratio packed bed with d_t/d_p = 1.93. The model as formulated is deliberately designed to be not too complicated so as not to place severe demands on computational resources. Hence, the model can potentially easily be applied to simulate the typically large sets of tubes (often comprising more than 10,000) in the case of industrial multi-tubular reactors, where every tube is different due to the random insertion of the packing particles. Because of its simplicity, the model offers an opportunity of coupling the individual catalyst pellet level transport with the complex interstitial flows at the reactor scale. Illustrative studies of this NoV model on a random packed bed of spheres predict large variations of discrete in-void angular velocities and consequently wall heat transfer coefficients within a single tube. The wide variations of wall heat transfer coefficients imply that the different angular sections of the tube will transfer heat at radically different rates resulting in potentially large temperature differences in different segments of the tube. This may possibly result in local temperature runaway and/or hot spot development leading to several potentially unanticipated consequences for safety and integrity of the tube and hence the reactor. The NoV model predictions of the overall pressure drop behaviour are shown to be consistent with the quantitative and qualitative features of correlations available in the literature.