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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

An extended classification of powders based on their fluidization behavior is proposed for describing their fluidization behavior. This classification takes into account the interparticle forces acting on particles. A diagram is generated, using existing data in the literature, in which the dimensionless interparticle force is plotted against the Archimedes number. At a specific Archimedes number (fixed solid and liquid), type D behavior is expected when dimensionless interparticle force is extremely low. Increasing the interparticle force can change the type of powder to B, then A and finally type C behavior would be encountered at high enough value of dimensionless interparticle force. Clear boundaries were detected between different fluidization behaviors in the proposed diagram. Geldart boundaries, which can be used in the absence of interparticle forces, coincide with the newly proposed boundaries. The absence of an apparent interparticle force can be interpreted as the presence of van der Waals force among particles while no other type of interparticle force is induced on particles. The advantage of considering the boundaries presented in this work is that they can identify the type of fluidization when interparticle forces are significant, which cannot be detected with the extended classifications already available in the literature.

This investigation explored the significances of heterogeneous and homogeneous reactions on magneto hydrodynamic Maxell fluid flow induced by radially stretching disks under influence of buoyancy driven force. The steady state system is examined for the specific case in which the coefficient of diffusion of the reactants and auto catalytic agent are identical. The mathematical formulation for present flow problem is developed by using flow assumptions. The analytical solution for formulated flow problem is determined analytically by using homotopy analysis method (HAM) by using MATHEMATICA software. It is noticed that presence of Deborah number and thermal Biot number enhances the temperature profile. The homogeneous and heterogeneous parameter and Deborah number decays the concentration profile effectively. Further, an improved concentration distribution is noted for Archimedes number.

The moderator system in a CANDU reactor provides the unique ability to provide emergency cooling to the fuel in postulated severe accidents during the early phases of the transient. A key criteria which dictates the effectiveness of heat removal during these events is the integrity of the fuel channel assembly. This in turn relies on the prevention of dryout on the calandria tube. The main tool used to demonstrate adequate margins to dryout on the calandria tubes is Computational Fluid Dynamics (CFD). While several experimental datasets are available for validation of these tools, the historical facilities lack the specific geometrical features present in some of the older CANDU designs. The historic tests were typically scaled based on the so-called Archimedes number and non-dimensional heat flux. To extend the validation database two unique 1/16th scale (based on vessel diameter) experiments are performed which include features found in the moderator systems of two operating CANDU designs. The primary goal of these new experiments was to generate thermalhydraulic data for validation of CFD codes, but several additional tests were performed to examine the potential impact of scaling on the results. This paper demonstrates a consistent conservative bias in the CFD predictions with respect to maximum temperature in the experiments over the range of conditions tested. The combination of CFD and experimental observations concludes that the likely cause of the bias is due to CFD’s over prediction of inlet jet dissipation leading to less cold fluid penetration in the heated core of the test section. In terms of scaling, a combination of experimental evidence and supporting CFD simulations indicate that the historical scaling parameters do provide some level of qualitative similarity in the mixed-convection regimes in the vessel, but some revision to account for geometrical and flow pattern deviations may be necessary.

Stratum ventilation (SV) is feasible for heating applications. Owing to the downward supply vane angle and positive thermal buoyancy, the airflow characteristics of SV for winter heating can be distinct from those for summer cooling. This study aimed to investigate the airflow pattern and turbulence characteristics in a field environment chamber heated by SV experimentally. Twelve cases were studied with the room air temperature controlled between 19.9 and 24.3 °C. Air velocities and temperatures in the occupied zone were measured. Based on the measurements, draft risk (DR) and vertical air temperature difference between head and ankle levels (ΔT) were evaluated. The results show that the warm supply air jets were initially delivered to the zone below 1.1 m, but gradually ascended to the upper zone owing to the effect of positive thermal buoyancy. Consequently, the heights where the highest air velocity and temperature were measured varied with the distance from the supply inlets. As a result of the airflow pattern, the re-separation phenomenon of velocity spectra at different heights was observed at the far field from the inlets. These characteristics were different from those of SV for summer cooling. The airflow pattern illustrated that SV could warm the occupied zone efficiently, especially when the Archimedes number was less than 0.045. An appropriate reduction in the supply air temperature is recommended to achieve satisfactory local thermal comfort with ΔT and DR values conforming to the comfortable ranges as stipulated in ISO 7730–2005.

The movement and distribution of methane in coalmine roadways are major issues relating to coalmine safety. Once high concentrations of methane accumulate in downward ventilated tilted roadways, the movement of methane can be very special. A 1/50 experimental model was constructed for the study on high concentrations of methane behavior in downward ventilated parallel roadways. This experiment measured gas concentrations in the upper and lower parts of the methane accumulating roadway and the wind speeds both in the methane accumulating roadway and in its parallel roadway The experimental results indicate that the methane draft pressure (the additional natural draft pressure due to the density difference of methane and air when high concentrations of methane accumulate in tilted roadways) could lead to airflow reversion in a downward ventilated roadway; methane may flow with the reversed airflow into the parallel roadway. The reversed methane that flows into the parallel roadway could generate a new methane draft pressure, which would oscillate airflow under certain conditions. According to the experimental results with parallel roadways of different windage, a larger windage of the parallel branch could ensure a relatively stable airflow, and a smooth methane discharge process. Through analysis by oscillation theory and the Archimedes number, it is concluded that the parallel roadway windage affects the methane draft pressure-caused airflow disorder by two aspects: (1) a larger windage deceases the amplitude of airflow oscillation and (2) a larger windage decreases the methane flown into the parallel branch, which, in turn, decreases the critical wind velocity for airflow reversion in the parallel roadway. The effect of windage is proved by a numerical simulation of Jiulishan Mine at the end of this paper.

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.

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.

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.

This paper presents a numerical simulation of a liquid droplet evaporation during penetration in a porous medium based on lattice Boltzmann method. The binary-fluid model of Lee, which is applicable to high density ratio, is combined with a passive scalar LB thermal model to simulate two-phase flow. A proper source term is incorporated at the phase interface, and the classical convective Cahn–Hilliard equation in the presence of phase change is employed in the multiphase LB framework of Lee. Effects of different non-dimensional parameters including the Archimedes number, the Bond number, the Stefan number, the Prandtl number, the porosity, contact angle and density ratio on the penetration of liquid inside the porous media and the droplet evaporation are investigated and temperature profiles, flow fields, mass source contours are analyzed. Increasing the Bond number, the Archimedes number and density ratio will decrease the penetration rate, and accelerates the evaporation. Also, increasing the Stefan number and porosity accelerate the evaporation, while increasing the Prandtl number leads reduction in evaporation rate.

The aim of present analysis is to investigate the effects of heat source/sink, chemical and material composition on steady MHD mixed convection axisymmetric flow of an incompressible Maxwell fluid between two infinite stretching disks in the presence of viscous dissipation and Joule heating. The lower disk is subjected to an exothermic surface reaction, while an upper disk is maintained at uniform temperature and concentration. Also an exothermal surface reaction modeled by Arrhenius kinetics supplied heat to the Maxwell fluid. Similarity transformations are used for simplifying equations governing the flow, thermal fields, material and chemical composition fields. The analytic solution of dimensionless governing ordinary differential equations is successfully obtained using homotopy analysis method (HAM). Here, convergence of the derived series solution is ensured. We mainly focus on the effects of Hartmann number, Archimedes number, Eckert number, Prandtl number, heat generation or absorption parameter, activation energy parameter, chemical reaction parameter on dimensionless velocity, pressure, temperature and concentration distribution. The results with several values of the problem parameters are expressed graphically. To understand the behavior of flow between stretching isothermal and exothermal disks, the values of skin friction coefficient, Nusselt number and Sherwood number are tabulated for both lower and upper disks. Further, the critical value of Frank-Kamenetskii are presented through graphs and tables and discussed for different values of parameters involved in problem.

We report experimental results on the injection of a heavy fluid into a light one in a closed-end pipe, inclined at intermediate angles. The injection of the heavy fluid is made using an inner duct with a smaller diameter than that of the pipe in which the light fluid is placed. The fluids used are miscible and Newtonian, and they have the same viscosity. Our observation shows that, during the removal/replacement of the light fluid by the heavy fluid, at least four distinct flow stages can be identified: (i) initial buoyant jet of the heavy fluid, (ii) development of a mixing region, (iii) slumping flow of the heavy fluid, and (iv) heavy fluid front reaching the pipe end and returning toward the mixing region. Using high-speed camera images along with the ultrasound Doppler velocimetry and laser induced fluorescence data, the flow characteristics in these flow stages are quantified, and they are described in detail vs the dimensionless groups that govern the flow dynamics, namely, the Froude number (Fr), the Reynolds number (Re), the Archimedes number (Ar), and the pipe inclination angle (β). While our findings are of fundamental importance, they can also be used to provide a fluid mechanics understanding of the dump bailing method in the plug and abandonment (P&A) of oil and gas wells.

We study the sedimentation of finite-size particles in quiescent wall-bounded Newtonian and shear-thinning fluids by interface resolved numerical simulations. The suspended phase consists of Non-Brownian rigid spherical particles with particle to fluid density ratio ρ p / ρ f = 1.5 at three different solid volume fractions Φ = 1 % , 5% and 20%. Firstly, to focus on the effect of shear-thinning on the particle dynamics and interactions, the Archimedes number is increased for a single particle to have the same settling speed in the Newtonian fluid as in the shear-thinning fluid. Secondly, we consider fixed Archimedes and vary the shear-thinning properties of the fluid. Overall, we report a twofold effect of shear thinning. First and more important, the substantial increase of the particle sedimentation velocity in the shear-thinning case due to the increase of the shear rate around the particles, which reduces the local viscosity leading to a reduced particle drag. Secondly, the shear-thinning fluid reduces the level of particle interactions, causing a reduction of velocity fluctuations and resulting in particles sedimenting at approximately the same speed. Moreover, the mean settling velocities decrease with the particle concentration as a consequence of the hindering effect. Particles tend to sediment in the middle of the channel, preferentially positioning in the wake of neighbouring particles or aside them, resulting in lower levels of fluid velocity fluctuations in the gravity direction in the shear-thinning fluid.

Dense phase pneumatic conveying is preferred by industry over dilute phase flow due to its advantages. Models enabling to calculate pressure drop are worthless for a designer if he is unable to predict in advance the mode of conveying. Therefore, this research is focused on developing a new flow regime chart. Based on hundreds of experiments all required threshold velocities are defined by Reynolds number as a simple power function of Archimedes number. This work, revealed two new kind of plugs unknown before. Using the threshold functions a new flow regime chart was plotted By comparing the results to previously published models characterizing only the material properties revealed that the feeder is probably have a major role controlling the final mode of flow. Taking into account the findings in this paper, one might have ideas of how to improve the feeders in order to fully fulfill the flow potential.

The critical deposition velocity in horizontal pipe flow of liquid-solid slurries separates bed-forming and fully suspended flows. A compilation of critical deposition velocity data is presented using new experimental data (for particles ranging from 9 to 690 µm in diameter) along with data from the literature, and a close correlation between the particle Reynolds number and the Archimedes number (which describe the properties of the flow and the liquid and solid phases) is found. The role of solid particle packing is discussed and suggestions are made for the incorporation of solid-phase material properties – specifically particle shape and angularity, and surface forces – into an empirical parameter, the volume factor, α, to account for the deviation of particle behaviour from ideal, non-interacting, hard-sphere behaviour.

The aim of this current contribution is to examine the rheological significance of Maxwell fluid configured between two isothermal stretching disks. The energy equation is also extended by evaluating the heat source and sink features. The governing partial differential equations (PDEs) are converted into the ordinary differential equations (ODEs) by using appropriate variables. An analytically-based technique is adopted to compute the series solution of the dimensionless flow problem. The convergence of this series solution is carefully ensured. The physical interpretation of important physical parameters like the Hartmann number, Prandtl number, Archimedes number, Eckert number, heat source/sink parameter and the activation energy parameter are presented for velocity, pressure and temperature profiles. The numerical values of different involved parameters for skin friction coefficient and local Nusselt number are expressed in tabular and graphical forms. Moreover, the significance of an important parameter, namely Frank-Kamenetskii, is presented both in tabular and graphical form. This particular study reveals that both axial and radial velocity components decrease by increasing the Frank–Kamenetskii number and stretching the ratio parameter. The pressure distribution is enhanced with an increasing Frank–Kamenetskii number and stretching ratio parameter. It is also observed that thetemperature distribution increases with the increasing Hartmann number, Eckert number and Archimedes number.

The use of a scale-model is an effective technique to predict the performance of ventilation in full-scale prototypes. Many criteria have been proposed to simulate the behavior of airflow between scale-model and prototype. Because of the inconsistent results of past proposed similarity criteria, more validation work is needed to clarify the conflicts. Dimensional analysis using both the Buckingham Pi method and manipulating the governing differential equations was used to theoretically establish similarity parameters. Only partially similarity was reached since conflicts exist between proposed similarity parameters. Experiments of two scale models were conducted to study airflow similarity in ceiling slot-ventilated agricultural enclosures using different similarity criteria. The evaluation of similarity between scale-model and prototype included validation of penetration distance, airflow pattern, airspeed field, and temperature field using methods that included smoke visualization, airspeed field measurement, and temperature field measurement. The studies focused on the Reynolds number (Re) and inlet jet momentum ratio (Rm) as the similitude criteria for isothermal airflow, and Archimedes number (Ar) for nonisothermal airflow. The experimental results offer better agreement using Rm than using Re as the similitude criterion for isothermal airflow. Ar is an appropriate similitude criterion when the nonisothermal airflow pattern exhibits two-circulation airflow behavior. After the airflow is

Supercritical water fluidized bed (SCWFB) has been used to gasify biomass, coal and solid waste to produce gas fuel. Supercritical carbon dioxide fluidized bed (SCCO2FB) was applied in the coating industry. Both the two fluidized bed treats the supercritical fluids as fluidization medium. The fluidization behaviours of particles in the supercritical fluids are quite important issues for achieving the basic two phase flow pattern. Few research institutions have conducted experimental and numerical investigations on the fluidization in supercritical conditions. The authors try to establish a comprehensive insight of fluid dynamics of the supercritical fluidized bed. For the SCWFB, the fluidization transitions of fixed bed, homogeneous bed expansion and bubbling were demarcated by discrimination number Dn. A flow pattern map of Reynolds number vs. Archimedes number was available for describing the flow patterns and their boundaries of the SCCO2FB. Ergun equation was acceptable for calculating the fixed bed pressure drop for both SCWFB and SCCO2FB. Wei and Lu correlations of the minimum fluidization velocity, minimum bubbling velocity and homogeneous bed expansion rate are suggested to design the SCWFB. Wen and Yu equation of the minimum fluidization velocity, Vogt et al. correlation of the homogeneous bed expansion rate and their method for determining the minimum bubbling velocity, Nakajima et al. equation of transition velocity, and Bi and Fan correlation of turbulent velocity were recommended to calculate SSCO2FB.

This paper dealt with simulating a typical occupied office equipped with displacement ventilation using CFD method. The STAR-CCM+ commercial software was employed for performing the simulations in order to analyze the trend of the indoor air temperature profile in the office occupied space. Understanding this trend is a key parameter to ensure that the occupants are comfortable and thereby further conclusions on energy efficiency could be extracted. The simulations were carried out for incompressible, turbulent, and constant property air flow in the steady state condition. The results showed that increasing the number of occupants, while Archimedes number was constant, would increase the throw length of the incoming cold jet leading to an overall lower temperature profile for the case with five occupants. © 2018 The Authors. Published by Linköping University Electronic Press, Linköpings universitet. This is an open access article under the CC BY-NC 4.0 license (https://creativecommons.org/licenses/by-nc/4.0/)

Nanoscale droplets at a solid-liquid interface are of high relevance for many fundamental phenomena and applied processes. The solvent exchange process is a simple approach to produce, e.g., oil nanodroplets over a large surface area on a substrate, by exchange oil-saturated ethanol by oil-saturated water, which has a lower oil solubility than ethanol. In this process, the size of the nanodroplets is closely related to the flow conditions. To achieve control of the droplet size, it is essential to fully understand the nucleation and growth of nanodroplets under different flow conditions. In this work, we investigate the gravitational effect on the droplet formation by the solvent exchange. We compared the droplet size as the substrate was placed on the upper or lower wall in a horizontal fluid channel or on the sides of a vertical channel with an upward or downward flow. We found significant difference in the droplet size for the three substrate positions in a wide channel with height h = 0.21 mm. The difference of droplet size was eliminated in a narrow channel with height h = 0.07 mm. The relevant dimensional control parameter for the occurrence of the gravitational effects is the Archimedes number Ar and these two heights correspond to Ar = 10 and Ar = 0.35, respectively. The gravitational effects lead to a nonsymmetric parabolic profile of the mixing front, with the velocity maximum being off-center and thus with different distances α(Ar)h and (1 - α(Ar))h to the lower and upper wall, respectively. The ratio of the total droplet volume on the lower and upper wall is theoretically found to be (α(Ar)/(1 - α(Ar)))(3). This study thus improves our understanding of the mechanism of the solvent exchange process, providing guidelines for tailoring the volume of surface nanodroplets.

The phenomena of core debris heaping and self-levelling on the core catcher plate are important from cooling considerations and also from recriticality aspects to ensure the safety of the reactor main vessel after the accident. A series of experiments is conducted in water, with funnel guided pouring of lead spheres on to a flat collector plate to mimic the heaping behaviour of core debris in sodium on core catcher plate. The rationale behind the choice of Lead–water pair is that their density ratio is equal to that between the nuclear fuel and the coolant in the reactor. From dimensional analysis it is shown that that repose angle of the heap ( θ ) is a function of particle Reynold’s number ( Re ), Froude number ( Fr ) and Archimedes number ( Ar ) apart from density ratio and linear dimension ratios. Using the experimental data obtained from systematic parametric studies, the functional dependence of repose angle on Re , Fr and Ar is determined and the following empirical correlation is developed. θ = 26 Re - 0.38 Fr 0.15 Ar 0.20 In the nuclear reactor, the decay heat generated within the core debris leads to natural convection and then local boiling within the coolant because of which self-levelling of the heap is expected to occur. To understand the evolution of repose angle with time, experiments have been conducted with bottom heated lead spheres, in the second part of the study. About 25% reduction of repose angle is observed in the first half an hour of heating in the natural convective regime itself which serves to reduce the possibility of coolant dryout occurring within the debris bed. But perfect levelling leading to a plane level is not achieved in the experiments with lead spheres.

In this paper, the flow patterns observed in horizontal Couette-Taylor flow (CTF) were correlated using dimensionless numbers. The analysis of the results showed that the structure of the flow was an outcome of interaction between fluid inertia related to axial and rotational flows and gravitation. Therefore, the flow structures were correlated using axial and angular Reynolds numbers, and Archimedes number for the given value of gas-to-liquid flow ratio. Finally, the correlation for the prediction of the transition to the flow regime observed at high rotational speeds was proposed. The comparison with experiments carried out in the vertical CTF from the literature showed that this correlation can also be useful in the case of vertical flow.

Controlling airflow trajectory through slot-openings is important to induce an efficient thermal exchange in a broiler house, particularly in winter. A jet-drop-distance model was proposed to establish a plan for the control and management of a cold jet trajectory by Zhang & Strom (1999), Transactions of the ASAE, 42(4), 1121–1126. Jet-drop-distance is defined as the horizontal distance from a wall to an animal occupied zone where the incoming cold air first reaches at. Regression models employing jet-drop-factor and corrected Archimedes number variables were calculated based on experimental data. However, this approach was restricted, because of the small-scale model, the small number of slot-openings and difficulties in measuring invisible airflows being observed. Here, computational fluid dynamics (CFD) was adopted to overcome the experimental limitations and to analyse jet-drop-distances qualitatively and quantitatively in a commercial broiler house with multiple slot-openings. Predictions of jet-drop-distances were computed using the experimental conditions used by Zhang & Strom (1999) and compared with their regression models to validate the accuracy of developed method. In the validation test, the regression model using the corrected Archimedes number more accurately predicted the jet-drop-distance in the simulation model (R2 = 0.90). The validated method was subsequently applied to the analysis of the jet-drop-distance in a mechanically ventilated broiler house with multiple slot-openings. Trends of the CFD computed jet-drop-distance were analysed according to such variables as ventilation rate, initial angle of slot-openings and outdoor air temperature.

Three dimensional computational fluid dynamics (CFD) analysis has been performed for the moderator flow and temperature fields inside a vertical calandria vessel of nuclear reactor under normal operating condition using OpenFOAM CFD code. OpenFOAM is validated by comparing the predicted results with the experimental data available in literature. CFD model includes the calandria vessel, calandria tubes, inlet header and outlet header. Analysis has been performed for the cases of uniform and spatial distribution of volumetric heat generation. Studies show that the maximum temperature in moderator is lower in the case of spatial distribution of heat generation as compared to that in the uniform heat generation in calandria. In addition, the effect of Archimedes number on maximum and average moderator temperature was investigated.

This work presents a volume-filtered formulation for describing chemically reacting flows in the presence of solid catalytic particles. The equations are discretized in a Eulerian–Lagrangian framework and applied to flows of isothermal, heterogeneously reacting chemical species in fully developed three-dimensional risers. The aim of this study is to identify and quantify the influence of particle clusters on heterogenous reactions. The Archimedes number, Ar, is varied from 500 to 12,500, and the Damkohler number, Da, from 0.1 to 10. To assess the multiphase dynamic effects on the chemistry, conversion times from the three-dimensional simulations are compared to a zero-dimensional model that solves for the temporal evolution of the species mass fraction and ignores all spatial variations. The conversion process associated with the three-dimensional simulations is shown to be significantly longer compared to the zero-dimensional solution, with an increasing effect for larger values of Da. The discrepancies can be fully attributed to the presence of clusters, which are accounted for in the zero-order equations by an additional term that contains the covariance between species mass fraction and particle volume fraction fluctuations, which needs to be modeled. To this purpose, contributions to the fluctuating chemical source term are evaluated from the three-dimensional data and discussed, and a presumed-shape probability distribution function (PDF) approach is investigated. This PDF approach models the fluctuating chemical source term by a product of a beta distribution for the species mass fraction and a lognormal distribution for the particle concentration, and yields a mean species solution that agrees very well with the three-dimensional results for the range of Ar and Da considered in this study.

The effect of particle properties on gas solid flow in the whole circulating fluidized bed (CFB) system was investigated. Two Geldart-B particles with different sizes were used and the differences in pressure balance and material balance of the whole CFB system with a loop seal were described. The results show that coarse particles have a larger transport velocity U tr to fall into the fast bed regime, which means accumulation in the riser is easier for the coarse particles at the same fluidization velocity U r . The coarse particles also have a smaller solid saturation carrying rate G s , max and a lower height of the acceleration region in the fast fluidization regime. Considering the pressure balance of the system, a higher pressure head should be supplied by the standpipe at the aeration tap of the loop seal under the same G s when coarse particles are used. The pressure drop through the cyclone is lower for coarse particles under the same solid concentration at the entrance of it. In the loop seal, coarse particles need more aeration gas to reach the same G s because of its higher minimum fluidization velocity. Coarse particles show a higher pressure drop through the weir part and a lower pressure drop through the horizontal part of the loop seal. In the standpipe, coarse particles have a lower drag coefficient and need a higher gas solid slip velocity to build up the same pressure gradient, so fine particles suffer less bypassing gas into the cyclone and have higher material seal capability. However, because of the same density of the two particles, the maximum pressure gradient built up in the standpipe is similar.

This article is on the dimensional analysis and the classification of fluidization from the viewpoint of numerical analysis. At first, the governing equations used in the DEM (Discrete Element Method) and CFD (Computational Fluid Dynamics) coupling model was non-dimensionalized with the method of Hellums and Churchill (1964). From the resulting dimensionless equations, it was concluded that the five dimensionless numbers, i.e. Re: Reynolds number, Ar: Archimedes number, Ga: Galilei number, Fr: Froude number and i�²*: ratio of particle density divided by fluid density, can be derived and hydrodynamically dominant on the fluid behaviors. Further, these can illustrate the dimensionless numbers proposed in the previous studies. Secondary, a three-dimensional flow regime map of homogeneous, bubbling and turbulent fluidizations was proposed with these dimensionless numbers using the DEM-CFD simulations. Finally, the plane of the minimum bubbling fluidization velocity umb in the map can be proposed and expressed as,a��Rea��_mb=0.263I�^(*-0.553) a��Ara��^0.612. umb can be estimated using this equation for various conditions.

Hydrodynamic similarity in the liquid–solid circulating fluidized bed systems under different operating conditions was investigated. The experimental data obtained from this work and in the literature show that when the scaling parameter, Gs/(ρpjl), is modified as (ja/jl), ratio of auxiliary liquid velocity to total liquid velocity, a detailed hydrodynamic similitude of the liquid–solid circulating fluidized risers under different operating conditions can be achieved. Furthermore, the experimental results from different liquid–solid flow systems show that as long as (ja/jl)0.3 remains constant, the solid concentrations in the zone of CFB risers increase linearly. Archimedes number, Ar, Galileo number and Froude number, FrD were used to use the modified scaling parameter, (ja/jl), without power. Experimental results show that as long as Ar− 0.07(ja/jl), Ga− 0.07(ja/jl) and FrD− 0.07(ja/jl) is maintained, the similarity of the liquid–solid circulating fluidized bed riser is obtained using the new similarity parameter without using power. The empirical similarity parameter, (ja/jl), appears to have incorporated the effects of operating parameters (Gs and jl).

Rise and fall velocities of oil drops in water and water drops in oil, respectively, are measured in a liquid column. The main perspective is on the similarity of the flows in these largely different cases. When the experimental data are plotted as the normalized rise velocity, which is the Reynolds number, versus the Archimedes number a common curve appears. This proves that similarity exists at least with respect to the velocity. Larger drops deviate considerably from the spherical shape. Nevertheless the data set can be represented by a formula derived from data on hard spheres. In particular the Stokes limit for Re→0 is nicely confirmed by measuring down to 10− 4.

The complexity and diversity of airflow in buildings make the accurate definition of convective heat transfer coefficients (CHTCs) difficult. In a full-scale test facility, the convective heat transfer of two cooling systems (active chilled beam and radiant wall) has been investigated under steady-state and dynamic conditions. With the air-based cooling system, a dependency of the convective heat transfer on the air jet trajectory has been observed. New correlations have been developed, introducing a modified Archimedes number to account for the air flow pattern. The accuracy of the new correlations has been evaluated to±15%. Besides the study with an air-based cooling system, the convective heat transfer with a radiant cooling system has also been investigated. The convective flow at the activated surface is mainly driven by natural convection. For other surfaces, the complexity of the flow and the large uncertainty on the CHTCs make the validation of existing correlations difficult.

This paper aims at investigating the capability of numerical models to accurately capture the physical characteristics of particle clustering in vertical risers. Within the energy sector, particle clustering in vertical risers of circulating fluidized bed reactors are known to play a key role in the multiphase dynamics as well as secondary processes such as catalytic conversion and heat transfer. Recent experiments suggest that particle clustering is most significant in the fully developed flow region of the riser, hence this study focuses on this region. To explore such flows, a high-fidelity large-eddy simulation framework is combined with a Lagrangian particle tracking solver to simulate statistically stationary gravity-driven risers in vertical pipes for a large range of Archimedes numbers. The walls of the reactor are modeled using a conservative immersed boundary scheme integrated with the Lagrangian particle tracking framework. A structure tracking algorithm akin to particle image velocimetry is used to accumulate statistics on individual clusters. Cluster descent velocities display excellent agreement with experimental measurements for the range of flow conditions considered. Predicted volume fraction fluctuations and mean solid concentration within the clusters also match experimental correlations. The probability distribution function of solid concentration and radial distribution function provide insight on the degree of clustering and the characteristic cluster length scale. The degree of particle clustering is found to be independent of the Archimedes number, and models for the volume fraction distribution are discussed. Statistics on the solid concentration and phase velocities for two- and three-dimensional configurations are compared, and the ramifications of simulating risers in two dimensions are discussed.

Design specifications for solids suspension (just suspended speed-Njs) in stirred tanks are currently based on the original form of the Zwietering correlation. There are several limitations of this correlation which can lead to poor predictions. The limitations, however, are not clearly defined. In this paper we review the reported limitations of applicability of the Zwietering correlation in detail, and propose ways to predict Njs which extend some of these limits. New data is reported and a detailed analysis of the effects of off-bottom clearance and solids concentration is presented. These results show two things: first that the effect of off-bottom clearance cannot be explicitly accounted for using the Zwietering equation form. S values that exactly match the geometry of the system must be used. Second, the current exponent on solids concentration is applicable only up to 2 wt% solids (X = 2). Three new exponents are proposed based on the particle type: 0.17, 0.23, and 0.32. Using a modified exponent of 0.23, which represents the entire data set with some scatter, Njs can be predicted up to 35 wt% solids (X = 54). A new correlation that is a combination of Zwietering and Baldi, and is robust in scale-up based on constant power/mass is proposed.

The current work study the heat dissipation characteristics and airflow distribution in a power cabin. By simplifying the cable structure, a 1:5 reduced-scale model was constructed based on the Archimedes number. Computational fluid dynamics (CFD) simulations were applied to the prototype power cabin. The 3D steady-state Reynolds average Navier-Stokes (RANS) equation is used to solve the ventilation flow, where the turbulence model is realizable k–e. The CFD simulation of the prototype has been verified by the reduced-scale model. On this basis, several conclusions were drawn. The airflow distribution in the power cabin and cable arrangement cause a difference in the temperature distribution between the cables. The strong turbulence at the air inlet causes a significant temperature drop. The mechanical fan can effectively cool the cable to a certain extent, but cable temperature control should take into account the effects of ampacity and ventilation, as well as cable location.

On the basis of modelling with similarity theory and by using the Archimedes number, Ar, as the similitude parameter, this paper analyzes the air distribution of a busbar corridor in a hydropower station by using the Particle Image Velocimetry (PIV) measurement technique. The measurements were conducted in a 1:50 scale model for nine different operating conditions, including three air supply rates: 0.75G0, G0, 1.25 G0 and three heat release rates: 0.75Q0, Q0, 1.25 Q0 (G0 and Q0 are design values). The variation regularity of air distribution for the nine conditions were analyzed and evaluated based on the following aspects: the airflow pattern in the busbar corridor, the efficiency of energy utilization and the uniformity of air velocity and air temperature in the occupied zone. The experimental results show that the confluence of two air supply jets forms a cold airflow attached on the ground of the occupied zone, and that the attached distance increases with larger modified Archimedes number ArQ...

The axial dispersion coefficient of liquid in downflow slurry bubble column is estimated experimentally by the residence time distribution (RTD) technique. Its variation with superficial gas and slurry velocities, separator pressure, and slurry concentration is analyzed. The axial dispersion coefficient is correlated in terms of dispersion number with the velocity ratio of slurry to gas, Archimedes number, and Reynolds number by dimensional analysis. The mixing time is represented by the isotropic turbulence theory. We found that the axial dispersion coefficient in this present gas-liquid-solid three-phase downflow bubble column is an order of magnitude higher than that in upflow three-phase system. The dispersion coefficient of bubble motion (Db) and the velocity characteristic factor (k) are analyzed based on velocity distribution theory. The present study may be useful for further understanding and developing of specific multiphase reactor in industrial applications.

The rotary chamber technique is capable of observing small levitated bubbles in liquid for various research purposes. The present paper focuses on diffusion of a small spherical bubble into undersaturated water. The decaying bubble size is recorded in time by image processing. The results are plotted as Sherwood versus Reynolds number where the Schmidt number is of order 300. Similarity is found for each of four gases in water. The boundary layer prediction Sh is confirmed in general. A physically accountable model provides a good representation of results.

Fluidization of biomass particles is an important process in the gasification, pyrolysis and combustion of biomass for the extraction of energy. In this study, experiments were carried out in a 14.5 cm internal diameter cold flow fluidization bed to determine the minimum fluidization velocities with air as fluidizing medium. Studies on the fluidization of biomass particles (corn cobs and walnut shells), inert particles (sand, glass beads, and alumina), and biomass and sand mixtures were performed. Various weight percentages of biomass particles in the biomass and sand mixture were chosen in the range of 0–100%. On the of basis of experimental data from both present work and those found in the literature, new correlations were developed to predict the minimum fluidization velocity for inert particles, biomass particles, and biomass and sand mixtures in terms of biomass weight percentage. It was found that our results for the inert particles and biomass particles are in good agreements with those found in the literature. It was further found that the minimum fluidization velocity based Reynolds number for the mixture of biomass and inert particles depends on the weight percentage of biomass particles other than the Archimedes number. Based on our experiment results, we proposed a new correlation which includes the weight percentage as an additional variable for the mixture of biomass and sand particles. This new correlation can also be applied to inert particles or biomass particles by setting the weight percentage to be 0 or 100% accordingly.

In the current study, a direct-forcing immersed boundary–non-Newtonian lattice Boltzmann method (IB–NLBM) is developed to investigate the sedimentation and interaction of particles in shear-thinning and shear-thickening fluids. In the proposed IB–NLBM, the non-linear mechanics of non-Newtonian particulate flows is detected by combination of the most desirable features of immersed boundary and lattice Boltzmann methods. The noticeable roles of non-Newtonian behavior on particle motion, settling velocity and generalized Reynolds number are investigated by simulating benchmark problem of one-particle sedimentation under the same generalized Archimedes number. The effects of extra force due to added accelerated mass are analyzed on the particle motion which have a significant impact on shear-thinning fluids. For the first time, the phenomena of interaction among the particles, such as Drafting, Kissing, and Tumbling in non-Newtonian fluids are investigated by simulation of two-particle sedimentation and twelve-particle sedimentation. The results show that increasing the shear-thickening behavior of fluid leads to a significant increase in the kissing time. Moreover, the transverse position of particles for shear-thinning fluids during the tumbling interval is different from Newtonian and the shear-thickening fluids. The present non-Newtonian particulate study can be applied in several industrial and scientific applications, like the non-Newtonian sedimentation behavior of particles in food industrial and biological fluids.

This paper describes a comprehensive experimental analysis that reexamines Geldart's classification. Geldart's classification defines four types of materials which differ by the cohesion forces between particles. A system containing fluidized beds of four pipe diameters and fully controlled by LabVIEW was developed and constructed. A fluidization test was performed automatically by small increase of the air velocity and measuring the pressure drop over the bed. For each test the fluidization curve is recorded and minimum fluidization, bubbling and slugging velocities are defined. It is well established that cohesion and gravity forces affect the fluidization behavior of numerous materials. Based on our experimental and theoretical study, we show that group D particles for height to bed diameter ratios above four start to be fluidized by slugging. Group B particles, however, does not always start fluidization in the bubbling regime. Rather in height to bed diameter ratios above ten they behave like those of group D. Particles of group A start to fluidize first by increasing bed volume, and later by bubbling and finally slugging may be reached. We further found that the bed height to diameter ratio affect the minimum bubbling and slugging velocities. On this basis, we developed a generalized flow regime diagram of the Reynolds number as a function of the Archimedes number to describe the fluidization state. According to this diagram, various materials can be accurately classified by both the Archimedes number and the height to bed diameter ratio.

The present paper deals with CFD study of flow and thermal characteristics in air-conditioned rooms under turbulent mixed convection conditions. Air enters room from a sidewall slot flush with isothermal ceiling and leaves through a slot in opposite wall flush with floor. Velocity and temperature distributions are determined by a CFD model that has been previously validated by comparison with experimental data. Rigorous dimensional analysis shows that performance of the air-distribution system depends on: supply Reynolds number Red, Grashof number Grd (or Archimedes number Ard), room aspect ratio L/H, dimensionless heights of supply and return ports (d/H and t/H), where H is room height. For a room with fixed geometry, the effects of Red and Grd (or Ard) are investigated systematically by varying one parameter at a time. Results show that ceiling average Nusselt number (Nud,av) increases with Red and decreases with Grd (or Ard). For a given Grd, the heat removal index (HRI) increases with Red up to Red ≈ 9000, then stays practically constant thereafter. For a given Red, HRI decreases with increasing Grd (or Ard). A criterion for distinction between forced and mixed convection situations is developed, resulting in a critical Archimedes number of 0.11. Results further indicate that Ard alone, irrespective of the particular values of Red and Grd, determines to a reasonable extent Nud,av and HRI when Ard is above its critical value. Streamlines and temperature contours are found to be consistent with other results and helped explain them.

There had previously been many studies about displacement ventilation systems, but only a few cases mentioned mechanism of heat emitting. Therefore, this study presents the effects of adjusting heights and air volume of heat emitting to the indoor thermal environment by experiments of the model and the factory installed a displacement ventilation system. As results of them, adjusting heights and air volume of heat emitting avoids rise in temperature at the low level in the room. And it was suggested that a normalized temperature can be given as an unique function of the Archimedes number.

Experimental data available in the literature for bed voidage and bed expansion index of biofilm-coated particles in a fluidized bed was extracted, sorted and used to study the validation of the proposed bed expansion index equations in the literature. Drag coefficients of biofilm-coated particles for all the aforementioned data were calculated using a new proposed equation [1] that describes drag forces as a function of Archimedes numbers. Archimedes number was proposed to be superior to Reynolds number for bed expansion definition. New equations based on Archimedes number and physical properties of biofilm-coated particles were proposed to calculate the bed expansion index of fluidized biofilm-coated particles as well as bed voidage in fluidized bed bioreactors. The new equations predicted the existing experimental bed expansion index and voidage with less standard average error than all other literature equations that related bed expansion to Reynolds number.

Thus far, studies on the effects of the polydisperse size distribution on the minimum particle entrainment velocity (UPU) in horizontal pneumatic transport are limited to binary mixtures of sandlike particles. Herein we experimentally investigate UPU of ternary mixtures involving large (i.e., 400 and 170 μm) and fine particles (40 μm), where the roles of the fine particles in the entrainment of the large particles are elucidated. The presence of the 40 μm particles below ≈20% (w/w) enhances the entrainment of the 400 and 170 μm particles attributed to the high interstitial velocity of the conveying air because the fine particles occupy the interstitial spaces of the larger particles. Similar to monodisperse particles, a master curve of the particle Reynolds number versus Archimedes number is obtained for the ternary mixtures. From the master curve, a new empirical correlation for polydisperse UPU is derived using the Sauter mean diameter, where improved UPU predictions are demonstrated.

In the winter season, when the ventilation system is operating, the fresh cold air from the slot-type openings of broiler house which directly reached the animal zone can cause various problems such as thermal stress, decreasing of feed and water consumption, occurrence of respiratory disease, and etc. Therefore it is very important to control the trajectory of aero-flow from the slot openings to induce an efficient thermal heat change. Jet-drop distance model was proposed to predict and control the jet-trajectory. However their study was restricted due to the small scaled model and difficulties of measuring the Jet-drop distance. In this study, CFD was applied to analyze qualitatively and quantitatively the jet-drop distance in a real broiler house. The various variables were considered such as installed slot-angle, designed ventilation rate, and the outdoor ambient temperature. From the present study, two linear-regression models using the Jet-drop factor and corrected Archimedes number, and their R-squared values 0.744 and 0.736, respectively, were used. From this study, the applicability of CFD on the analysis of Jet-drop distance model was confirmed.