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Pore clogging and unclogging in porous media are ubiquitous in subsurface hydrologic processes, which have been studied extensively at various scales ranging from a single pore to porous‐medium samples. However, it remains unclear how fluid flow, particle rearrangement, and the arching effect typical of cone‐shaped pore geometry interact and how they are captured by a pressure drop model at the macroscopic scale. Here, we investigate the pore‐scale feedback mechanisms between fluid flow and pore clogging and unclogging using a fully resolved fluid‐particle coupling approach (lattice Boltzmann method‐discrete element method). We first propose to use a truncated‐cone pore to represent realistic pore geometries revealed by X‐ray images of prepared sand packing. Then, our simulations indicate that the pore cone angle significantly influences the pressure drop associated with the clogging process by enhancing particle contacts due to arching. A modified Ergun equation is developed to consider this geometric effect. At the microscale, clogging can be explained by the interparticle force statistics; a few particles in an arch (or a dome) take the majority of hydrodynamic pressure. The maximum interparticle force is positively proportional to the particle Reynolds number and negatively associated with the tangent of the pore cone angle. Finally, a formula is established utilizing fluid characteristics and pore cone angle to compute the maximal interparticle force. Our findings, especially a modified pressure drop model that accounts for pore geometry resistance, provide guidance for applying pore‐scale models of clogging and unclogging to large‐scale subsurface fines transportation issues, including seepage‐induced landslides, stream bank failure, and groundwater recharge. Plain Language Summary: Pore clogging and unclogging in porous materials are important in underground water movement processes. However, the interaction between fluid flow, particle rearrangement, and the arching effect in cone‐shaped pores remains unclear. The X‐ray images of sand packing were used to analyze realistic pore geometries. We simplified the three‐dimensional pores to a truncated cone shape and conducted numerical simulations to investigate how fluid flow and pore clogging‐unclogging mechanisms are connected. Our simulations revealed that the pore cone angle significantly affects fluid pressure drop by enhancing particle contacts through arching. We developed a modified equation to consider this geometric effect. At the microscale, clogging can be explained by interparticle force statistics, where a few particles in an arch bear most of the hydrodynamic pressure. The maximum interparticle force depends on the particle Reynolds number and is inversely related to the tangent of the pore cone angle. We established a formula to compute the maximal interparticle force using fluid characteristics and pore cone angle. Our findings, particularly the modified pressure drop model, provide valuable insights for applying pore‐scale models to understand large‐scale issues like landslides, stream bank failure, and groundwater recharge caused by fine particle transportation in subsurface systems. Key Points: This study explores the effect of fluid velocity and pore shape on pore clogging and unclogging by coupling lattice Boltzmann method and discrete element methodA modified Ergun equation considering pore cone angle improves the prediction of fluid pressure drop for imminent uncloggingAn empirical relationship of the maximum interparticle force for imminent unclogging is developed using pore geometry and fluid parameters as variables [ABSTRACT FROM AUTHOR]

A popular equation that is often employed to represent the relationship between the pressure loss and the fluid flow in fluidized or packed granular beds is the Ergun equation, which is an extension of Darcy's law. In this paper, the method of Smoothed Particle Hydrodynamics (SPH) is used to numerically study the flow field across a rectangular channel partially filled with a porous layer both at the Representative Elementary Volume (REV) scale using the Ergun equation and at the pore scale. Since the flow field can be estimated at the REV scale with a much lower cost compared to the pore scale, it is important to evaluate how accurately the pore-scale results can be reproduced at the REV scale. The comparison between both scales is made in terms of the velocity profiles at the outlet of the rectangular channel and the pressure losses across the clear and porous zones for three different arrays of solid grains at the pore scale. The results show that minimum differences in the flow structure and velocity profiles between the REV and the pore scale always occur at intermediate values of the porosity ( ϕ = 0.44 and 0.55). As the porosity increases, the differences between the REV and the pore scale also increase. The details of the pressure losses are affected by the geometry of the porous medium. In particular, we find that the pressure profiles at the REV scale match those at the pore scale almost independently of the porosity only when the grains are uniformly distributed in a non-staggered square array. [ABSTRACT FROM AUTHOR]

Accurately predicting gas pressure drop in packed beds is challenging in various industrial processes due to the size dispersity of bed particles. The original Ergun equation has been widely used for predicting gas pressure drop in packed beds of monosized spherical particles. Here, we aim to evaluate its prediction accuracy for non-monosized spherical particle beds and propose a modified Ergun-type correlation to consider involved particle-size-dispersity effects. Specifically, we focus on conditions where the tube-to-particle diameter ratio is larger than 14, and the particle Reynolds number, R e p , ranges from 26 to 561. An experimentally validated numerical approach that couples computational fluid dynamics and the discrete element method is used to obtain the gas pressure drop for various beds, showing that the original Ergun equation (with the Sauter mean diameter, d 32 , a common choice in both academia and industry, used as the average particle diameter) yields a predication discrepancy of up to 30%. Accordingly, we propose a novel correlation by using different particle sizes in different terms, revealing the distinct physics of the flow past a sphere in different regimes. In the inertial term, the use of d 32 is reasonable as it considers both volume and surface area of the particles, analogous to the corresponding body and surface forces on the sphere in this regime. In the viscous term, however, the surface-diameter mean, d 21 , which emphasizes particle surface area and geometric effect, is used because it describes the dominant skin frictional surface force in viscous flow. The modified Ergun equation demonstrates improved predictions for bidisperse packed beds by reducing the largest discrepancy to 4%, and can be applied to polydisperse beds as well. Moreover, the proposed correlation aligns well with the original Ergun equation, i.e., the monosized limit, in the investigated R e p range. [Display omitted] • Ergun equation shows limited prediction accuracy for non-monosized packed beds. • It overlooks dense packing (or low porosity) effects in non-monosized packings. • A modification is proposed by using different particle sizes in different terms. • The modified Ergun equation improves prediction, reducing discrepancy to under 4%. [ABSTRACT FROM AUTHOR]

A popular equation that is often employed to represent the relationship between the pressure loss and the fluid flow in fluidized or packed granular beds is the Ergun equation, which is an extension of Darcy’s law. In this paper, the method of Smoothed Particle Hydrodynamics (SPH) is used to numerically study the flow field across a rectangular channel partially filled with a porous layer both at the Representative Elementary Volume (REV) scale using the Ergun equation and at the pore scale. Since the flow field can be estimated at the REV scale with a much lower cost compared to the pore scale, it is important to evaluate how accurately the pore-scale results can be reproduced at the REV scale. The comparison between both scales is made in terms of the velocity profiles at the outlet of the rectangular channel and the pressure losses across the clear and porous zones for three different arrays of solid grains at the pore scale. The results show that minimum differences in the flow structure and velocity profiles between the REV and the pore scale always occur at intermediate values of the porosity (ϕ=0.44 and 0.55). As the porosity increases, the differences between the REV and the pore scale also increase. The details of the pressure losses are affected by the geometry of the porous medium. In particular, we find that the pressure profiles at the REV scale match those at the pore scale almost independently of the porosity only when the grains are uniformly distributed in a non-staggered square array.

The viscosity η m of dense fluid mixtures of carbon dioxide and ethanol was determined from the pressure drop between the inlet and outlet of a packed bed using the Ergun equation at temperatures from 313.2 K to 343.2 K and pressures from 15 MPa to 30 MPa over the entire range of ethanol composition. The η m values for the fluid mixtures decreased with increasing temperature and increased with increasing pressure under isocratic conditions. In addition, the values measured η m with Ergun eq. were correlated with the equation combining the Eyring theory and the perturbed chain statistical associating fluid theory equation of state (PC-SAFT EoS) and with that based on the rough hard-sphere (RHS) model proposed by Dymond and Assael. The accuracies of the Eyring + PC-SAFT EoS and the RHS model were 8.7% and 12%, respectively, in terms of average relative deviation for 80 conditions over the entire range of ethanol composition. [Display omitted] • Ergun equation described pressure drop of dense CO 2 +ethanol flowing in packed bed. • Constants in Ergun equation were modified as functions of temperature and pressure. • Viscosity of dense mixture was determined in packed bed by Ergun equation. • Combined method of Eyring theory+PC-SAFT EoS well expressed CO 2 +ethanol viscosity. [ABSTRACT FROM AUTHOR]

Structural parameters are critical for the final properties of fibrous materials. Three common parameters (i.e., porosity, thickness and average fiber diameter) of each fibrous material are simultaneously determined based on their air penetration behavior. The Ergun-type equation and the Kozeny-type equation, with the help of the optimization method, are applied to conduct the inverse characterization. The prediction performance of the equations is evaluated by comparing the given pressure drop and the values predicted by the Ergun-type and Kozeny-type equations. The inversely determined parameters are compared with the directly measured values. The results show that the Ergun-type equation and the Kozeny-type equation are suitable for various fibrous materials, including conventional nonwoven materials and nanofibrous membranes. The selection criteria of these two equations are provided based on the relation of pressure drop-airflow velocity and the prediction accuracy. The results also suggest that the Ergun-type equation's coefficients and the Blake–Kozeny–Carman constant of the Kozeny-type equation need to be determined for each material. The relative errors for most of the inversely determined parameters are reasonable. The findings indicate that the airflow-based method is feasible for fibrous materials.

Porous media combustion has significant advantages of high thermal efficiency and low pollution emissions. However, the flow state in the porous media will affect the reaction rate. In order to increase the rate of chemical reactions, the fluid flow resistance in the porous media must be reduced. The pressure drop test of SiC foam ceramics was carried out. By changing the pore density of the experimental materials, the pressure drop characteristics of SiC foam ceramic are tested and analyzed. Based on the classical Ergun equation, a semi-empirical formula for calculating the pressure drop gradient of SiC foam ceramics with the airflow velocity is proposed. The two constants in the formula are calculated by measurement, and the applicability of the formula is verified. This formula can quickly analyze the pressure drop characteristics of SiC foam ceramic materials. The accurate measurement of pressure drop is helpful to determine the rated pressure of the head of foam ceramic burner and reduce the investment of front-end fans in industrial burners. [ABSTRACT FROM AUTHOR]

[Display omitted] • Prediction of permeability based on zeolite diameter and porosity. • Experiments verified the accuracy of the calculation model. • Two new structural forms are proposed. • Optimized the parameters of the new structure. Silver zeolite filters have potential applications in nuclear power plant filtration and emission systems due to their high-efficiency adsorption properties for radioactive methyl iodide. The adsorption performance of the filter is closely related to the flow distribution characteristics. To analyze the flow distribution characteristics of the filter element, we established a reasonable numerical calculation model and verified the model through experiments. Then based on the model, the advantages and disadvantages of different filter unit structures are analyzed. We proposed two new structural forms of filters and evaluated the performance of the filters based on the pressure distribution and flow increment curve, considering the difficulty of processing and space utilization. Comparative analysis and characteristic research have been carried out under different sizes, from the cylindrical filter to the round table filter and, finally, to the square filter. Our results show that round table and square filters have significantly improved flow distribution compared to traditional cylindrical filters. However, the structure of the round table filter is irregular, and the space utilization rate is low. Finally, through optimization design, the square filter with channel spacing L of 250 mm has the best performance. Our research results have a certain guiding significance for the design of the silver zeolite filter prototype. [ABSTRACT FROM AUTHOR]

The gas flow distribution in the magnesite shaft furnace is relatively complicated. Obtaining the resistance characteristics in the magnesite pellets packed bed is the basis for the research on the gas flow and gas-solid heat transfer process. Starting from the gas dynamics of the gas-solid packed bed based on the Ergun equation, the key macroscopic properties of the magnesite pellets， including particle size distribution, density, sphericity and voidage, were systematically measured. The viscous resistance coefficient and the inertial resistance coefficient in the Ergun equation were corrected through cold experiments, and a relational equation suitable for describing the resistance characteristics of the magnesite pellet bed was obtained. The results showed that the sphericity and voidage increase with the increase of particle size. The pressure drop increases with the increase of gas flow rate, and the increasing trend gradually intensifies. On the contrary, it decreases with the increase of particle size. [ABSTRACT FROM AUTHOR]

The modeling of the minimum fluidization velocity (U0mf) and the incipient fluidization pressure drop (ΔPmf) is a valuable research topic in the fluidization field. In this paper, first, a series of experiments are carried out by changing the particle size and material mass to explore their effects on U0mf and ΔPmf. Then, an Ergun equation modifying method and the dimensional analysis method are used to obtain the modeling correlations of U0mf and ΔPmf by fitting the experimental data, and the advantages and disadvantages of the two methods are discussed. The experimental results show that U0mf increases significantly with increasing particle size but has little relationship with the material mass; ΔPmf increases significantly with increasing material mass but has little relationship with the particle size. Experiments with small particles show a significant increase at large superficial gas velocity; we propose a conjecture that the particles' collision with the fluidization chamber's top surface causes this phenomenon. The fitting accuracy of the modified Ergun equation is lower than that of the dimensionless model. When using the Ergun equation modifying method, it is deduced that the gas drag force is approximately 0.8995 times the material total weight at the incipient fluidized state. [ABSTRACT FROM AUTHOR]

Biomass grinds are typically non-spherical and are composed of particles with wide range of sizes that may vary up to 10× between the smallest and largest particle. Since fluidized bed system is often used to convert biomass into fuels, chemicals and products, the viscous and kinetic energy losses’ coefficients in the Ergun equation were determined to incorporate these unique characteristics of biomass grinds. The revised Ergun’s equation, validated using loblolly pine wood grinds, and data from other published work resulted in estimated Ergun’s K1 and K2 coefficients of 201 and 2.7 respectively. In addition, the relative mean deviation between experimental and predicted pressure drop was in general better with the modified Ergun’s equation when compared to the original Ergun’s equation.

The Ergun equation is commonly used to predict velocity-pressure drop behaviour in packed beds. For many particular systems, the measurements deviate significantly from this relationship. Because of this, the equation is often treated as a purely empirical relationship, and its factors as fit parameters. This paper shows that the physics-based model underlying the Ergun equation should be treated by careful investigation of the included parameters. It is shown that discrepancies between experiment and theory for particle collectives in the millimetre range and above are caused by insufficient methods to determine the specific surface area. This effect is especially large for coarse particles with very rough surfaces. As a 2D measurement method, dynamic image analysis can not provide a good measure of specific surface area. It does not account for both macroscale particle shape and microscale surface roughness, which is confirmed by an analysis of 3D particle measurements from X-ray microscopy. Unlabelled Image • For use in Ergun's equation, specific surface area must be determined accurately. • Otherwise, pressure drop will not be predicted accurately from flow velocity. • Dynamic image analysis determines specific surface area insufficiently. • The circularity factor does not account for rough and concave surfaces. [ABSTRACT FROM AUTHOR]

In narrow fixed‐bed reactors the influence of the confining wall on pressure drop cannot be neglected. Here, the pressure drop in single pellet string reactors, a limiting case of fixed‐bed reactors with a cylinder‐to‐particle diameter ratio below 2, is studied using computational fluid dynamics simulations. Deviations to the Ergun, and more specifically Blake‐Kozeny equation are evident though the general trend is met. A geometry‐based weighting factor is introduced to scale the influence of the confining wall in an equivalent diameter expression. Agreement between numerical simulation and pressure drop predictions from correlation are thereby improved significantly. [ABSTRACT FROM AUTHOR]

• Water storage tanks for fire suppression can be utilized to fulfill the function of structure control as Tuned Liquid Damper (TLD) if properly designed. • A TLD is outfitted with a perforated floor to allow for water passage between compartments to meet both volume and flow rate fire code requirements. • A 2D macroscopic SPH model is employed to model the dual function rectangular tank with a perforated floor. • The model showed excellent agreement when compared with an explicit microscopic model (MM), with significant decrease in computational time. • For a structure-TLD system subjected to random excitation, the tank with a perforated floor was tested against tanks with a solid floor and a fire reserve. • The tank with a perforated floor enhanced the performance of the TLD compared to other tanks, while obtaining the required water volume for fire suppression. Exceeding serviceability limits due to wind-induced motions in tall buildings can cause discomfort for residents and adversely affect auxiliary building services, such as elevator operations. A tuned liquid damper (TLD) is an attractive type of dynamic absorber because of its simplicity and affordability. However, its dimensions and geometry can be limited by available floor space. Utilizing dual-purpose water tanks for both damping and fire suppression purposes can be a feasible resolution to fire code requirements and building motion control. Several design criteria need to be considered to accommodate the fire code requirements and the proper tuning of the TLD. Consequently, in this study, a TLD tank is fitted with a perforated floor to divide it into two compartments that allow water transmission to meet fire code requirements. However, the sloshing motion within the tank is complex and computationally expensive to capture when using traditional simulation models. This paper presents a 2D ISPH code equipped with a macro-level model to capture the effect of the perforated floor on the overall sloshing response of the tank. The model is first evaluated using existing results from previous studies on tanks with horizontal baffles. Next, the ISPH model is used to numerically model the perforated floor using the Ergun resistance (ER) macro-level model. In addition, the perforated floor is also explicitly micro-level modelled using rigid boundary particles to validate the proposed ER model. A numerical analysis is then conducted under different excitation amplitudes and frequencies, with both time history and frequency response results being presented. A structure-TLD model is subsequently used to capture the structure-TLD system response under random excitation. Results show that the ER model can efficiently model tanks with dual functions under both harmonic and random excitation and across a wide range of amplitudes and frequencies, with appreciable computational time savings. The proposed tank with a perforated floor is found to be effective in serving as a dual-purpose TLD and storage tank for fire suppression in buildings. [ABSTRACT FROM AUTHOR]

The small open area available at the slots of underdrains in pressurized granular bed filters for drip irrigation implies: (1) the existence of a region with non-uniform flow, and (2) local values of modified particle Reynolds number >500. These flow conditions may disagree with those accepted as valid for common pressure drop-flow rate correlations proposed for packed beds. Here, we carried out detailed computational fluid dynamics (CFD) simulations of a laboratory filter to analyze the results obtained with five different equations of head losses in porous media: (1) Ergun, (2) Darcy-Forchheimer, (3) Darcy, (4) Kozeny-Carman and (5) power function. Simulations were compared with experimental data at different superficial velocities obtained from previous studies. Results for two silica sand media indicated that all equations predicted total filter pressure drop values within the experimental uncertainty range when superficial velocities −1. At higher flow rates, Ergun equation approximated the best to the observed results for silica sand media, being the expression recommended. A simple analytical model of the pressure drop along flow streamlines that matched CFD simulation results was developed.

Effective characteristics, such as the effective particle diameter and hydraulic radius, are usually used to determine the pressure loss associated with single-phase flow through an isotropic, dense non-spherical granular packing. These quantities can be considered as those of an equivalent spherical particle system. This paper reviews different methods to select effective particle diameters taking into account the effect of particle shape. A new method is proposed to determine an equivalent spherical particle system with both the hydraulic radius and the pressure loss equivalent to those in the actual non-spherical particle packing. This equivalent system can be used to determine the characteristics of flow in the actual system. The analyses provide theoretical justification for adoption of proper effective particle diameters and porosity as well as the dependency of Ergun–Kozeny constant on the shape factor of particles. It is also shown theoretically that the critical Reynolds number for Darcian flow depends on the porosity and the shape factor of particles. [ABSTRACT FROM AUTHOR]

Biomass grinds are typically non-spherical and are composed of particles with wide range of sizes that may vary up to 10× between the smallest and largest particle. Since fluidized bed system is often used to convert biomass into fuels, chemicals and products, the viscous and kinetic energy losses' coefficients in the Ergun equation were determined to incorporate these unique characteristics of biomass grinds. The revised Ergun's equation, validated using loblolly pine wood grinds, and data from other published work resulted in estimated Ergun's K1 a nd K2 coefficients of 201 and 2.7 respectively. In addition, the relative mean deviation between experimental and predicted pressure drop was in general better with the modified Ergun's equation when compared to the original Ergun's equation. [ABSTRACT FROM AUTHOR]

The modeling of the minimum fluidization velocity (U0mf) and the incipient fluidization pressure drop (ΔPmf) is a valuable research topic in the fluidization field. In this paper, first, a series of experiments are carried out by changing the particle size and material mass to explore their effects on U0mf and ΔPmf. Then, an Ergun equation modifying method and the dimensional analysis method are used to obtain the modeling correlations of U0mf and ΔPmf by fitting the experimental data, and the advantages and disadvantages of the two methods are discussed. The experimental results show that U0mf increases significantly with increasing particle size but has little relationship with the material mass; ΔPmf increases significantly with increasing material mass but has little relationship with the particle size. Experiments with small particles show a significant increase at large superficial gas velocity; we propose a conjecture that the particles’ collision with the fluidization chamber’s top surface causes this phenomenon. The fitting accuracy of the modified Ergun equation is lower than that of the dimensionless model. When using the Ergun equation modifying method, it is deduced that the gas drag force is approximately 0.8995 times the material total weight at the incipient fluidized state.

• Monolithic porous materials based on Schwarz Diamond TPMS were 3D printed. • Printed parts were scanned using micro-CT. • Structures accurately reproduced the designed geometry, but with reduced porosity. • Pressure drop was measured for 1 < Re < 1000 for each part. • A correlation for pressure drop based on the Ergun equation is proposed. Additive manufacturing (3D printing) is enabling novel porous structures such as triply periodic minimal surfaces (TPMS) that may help improve the efficiency of various applications in chemical engineering. In this work, a range of Schwarz-Diamond TPMS structures were examined experimentally in terms of printability and pressure drop. X-ray computed tomography scans were used to show that the shape of the structures was accurately printed, however a systematic reduction in porosity was observed compared with each designed structure. The pressure drop through the printed structures was measured for Reynolds numbers between 1 and 1000. Pressure drop reduced with increasing porosity and hydraulic diameter but there was no effect of printer type or column diameter on the measured pressure drop. These measurements were used to propose a new pressure drop correlation that can be used to predict the pressure drop for Schwarz-Diamond TPMS structures over a range of porosities and hydraulic diameters. [ABSTRACT FROM AUTHOR]

The recycling and reutilization of powdery/dust waste are becoming increasingly important for ensuring a sustainable environment and decreasing the cost of waste disposal. In this regard, we examined component separation using a vibrating fluidized bed based on the differences in the agglomeration properties of the particles of each component. In the proposed separation method, the knowledge of agglomerate formation and destruction in a fluidized bed is essential. In this study, the effects of particle properties on agglomerate formation and destruction in a vibrating fluidized bed were investigated. Rutile and anatase titanium oxide and zinc oxide were used as test powders. The changes in the powder layer height and pressure drop were recorded. The results were utilized to compute the changes in the agglomerate size using the Ergun equation, and agglomerate formation and destruction were evaluated. Furthermore, the relationship between the equilibrium agglomerate size and vibration intensity was investigated. [Display omitted] • Behaviors of agglomerates in vibrating fluidized bed were examined. • Rutile and anatase TiO 2 and ZnO powders were used. • Formation and destruction behaviors were investigated. • Powder behaviors differed based on the powder type. • Apparent agglomerate size represented average degree of agglomeration progress. [ABSTRACT FROM AUTHOR]

The modelling of flow leaching solution through the porous media has been considered. The heap bioleaching process can be tested using the column experimental equipment. This equipment was employed to the hydrodynamic studies of copper ore bioleaching. The copper ore (black shale ore) with the support, inertial materials (glass small balls and polyethylene beads) was used to the bioleaching tests. The packed beds were various composition, the ore/support ratio was changed. The correlation between the bed porosity and bioleaching kinetics, and copper recovery was investigated.

The second law of thermodynamics is indispensable in engineering applications. It allows us to determine if a given process is feasible or not, and if the given process is feasible, how efficient or inefficient is the process. Thus, the second law plays a key role in the design and operation of engineering processes, such as steam power plants and refrigeration processes. Nevertheless students often find the second law and its applications most difficult to comprehend. The second law revolves around the concepts of entropy and entropy generation. The feasibility of a process and its efficiency are directly related to entropy generation in the process. As entropy generation occurs in all flow processes due to friction in fluids, fluid mechanics can be used as a tool to teach the second law of thermodynamics and related concepts to students. In this article, flow through packed beds and consolidated porous media is analyzed in terms of entropy generation. The link between entropy generation and mechanical energy dissipation is established in such flows in terms of the directly measurable quantities such as pressure drop. Equations are developed to predict the entropy generation rates in terms of superficial fluid velocity, porous medium characteristics, and fluid properties. The predictions of the proposed equations are presented and discussed. Factors affecting the rate of entropy generation in flow through packed beds and consolidated porous media are identified and explained.

• A new catalyst has been developed for an FCC process. • Catalyst is designed for producing diesel fuel from a waste crude oil. • A computational fluid dynamics model is used for designing the catalyst. • The newly designed catalyst is applied to our experimental setup and promising results are observed. • Detailed experimental results are planned for mapping purposes. Cyclone separators, which have an important role in the recovery of catalysts, constituted one of the aims of the study. In the work to be done, the pressure drop occurring during the fcc reaction is also calculated using the Ergun equation and it is aimed to provide the same value in a cyclone separator. In this study, which was presented for the first time in the literature, the best working conditions were determined by simulating the pressure drop in the cyclone separator modeled by using the various catalyst types namely NiMo/ASA–Al 2 O 3 , NiMo/p–Al 2 O 3 , NiMo/Y–Al 2 O 3 , Co-Mo, HZSM-5 zeolite, HY zeolite, pAl 2 O 3 , ASA-Al 2 O 3 , Y-Al 2 O 3 determined from the literature in the Ergun equation. Among them, NiMo/ASA Al 2 O 3 , Co-Mo, HY zeolite, and ASA-Al 2 O 3 were determined as the best catalyst for producing diesel from high oil fractions. Unlike previous studies, the condition that the cyclone separator modeled cleans the catalyst with maximum efficiency also determines the condition that provides low catalyst porosity in the determination of the catalyst type to be determined in diesel production. Due to the accuracy between the calculated and the predicted pressure drop results (about 1,8%), HY zeolite is the best catalyst for cyclone separator geometry. It is widely used to convert high molecular weight hydrocarbon fractions, the high boiling point of petroleum crude oils into olefinic gases, more valuable gasoline, and other products. The purpose of the FCC unit is to increase the refinery conversion and white product yield by converting heavy vacuum gas oil (HVGO) into light hydrocarbons at high temperatures with the aid of fluid catalysis. These two zones (reactor and regenerator) are placed as two different pressure vessels. For these two different systems to work in harmony with each other, unlike in previous studies, the "dense discreet phase-Eularian" approach was used in the modeling of the catalytic unit and the "discreet phase" approach was used in the modeling of the cyclone separator. The values required for both processes to work together have been determined approximately. [ABSTRACT FROM AUTHOR]

Experimental measurements of pressure drops through three biofilters filled with expanded schist for H 2 S degradation were used to determine the change in the porosity of packed beds over time, and to calculate the thickness of biofilms covering the material. Three mathematical models characterizing the fluid flow through porous media were used for this purpose, i.e. (i) the modified Ergun model, (ii) the model of Comiti & Renaud and (iii) the granular Representative Unit Cell (RUC) model. Porosity values calculated by these models were compared to the experimental porosity measurements. Results showed that the model of Comiti & Renaud cannot be used to predict the porosity of the packed bed, whereas the RUC model slightly underestimates the porosity values (discrepancy values from − 0.7 to − 21.2%). Conversely, the agreement between the experimental values and the values calculated by the modified Ergun model is remarkable for the three biofilters. From porosity values obtained by this model, it was calculated that biofilms grew to reach average thicknesses ranging from 0 to 140 μm. For the two biofilters inoculated with activated sludge, the development of biofilms slightly increased the tortuosity of the packed bed (from 1.9 to 2.2–2.4, according to the biofilter considered) and slightly decreased the specific surface area of the packed bed (− 5.2% and − 3% in comparison with the initial value, respectively). [ABSTRACT FROM AUTHOR]

Liquid sloshing inside a Tuned Liquid Damper (TLD) equipped with screens introduces significant numerical modelling challenges. A 2D Incompressible Smoothed Particle Hydrodynamics (ISPH) model employing a novel macroscopic screen model is presented to capture the complex flow associated with screens and significantly minimize the high computation cost of traditional microscopic screen models. The macroscopic screen model is based on Ergun's equation for pressure drop in porous media. The Sub-Particle Scale (SPS) turbulence model is added to the base code. The modified ISPH code is validated for a hydrostatic case and tank without screens scenario. The predicted sloshing forces and wave heights are validated against experimental data and are compared to numerical results of an existing macroscopic screen model. Findings indicate that the proposed model agrees with experimental results for different fluid depths and under a broad range of excitation amplitudes. The proposed macroscopic screen model and updated ISPH code can more accurately capture the response at small excitation amplitudes and requires less computation time than an existing macroscopic model. The proposed model can be an efficient tool for studying internal tank responses over various excitation amplitudes and frequencies without the need for experimental data to determine the drag coefficient for different screen geometries. • A Smoothed Particle Hydrodynamics (SPH) model employing a macroscopic screen model has been shown to perform well in capturing the complex flow associated with screens in sloshing tanks. • SPH models using a macroscopic screen model can significantly minimize the high computation cost of traditional microscopic screen models. • The presented macroscopic ER model showed excellent agreement against shake table test results for all excitation amplitudes and fluid fill ratios considered, with significantly decrease in computational time. [ABSTRACT FROM AUTHOR]

Sintered metal porous media currently play a significant role in a broad range of industrial equipments. The flow properties in porous media are generally approximated by Forchheimer regime or Ergun regime. In this study, a modified Ergun equation is developed to correlate the pressure drop with flow rate. Experimental and theoretical investigations on pressure drop are conducted with a series of metal-sintered porous media. A viscous drag region and a form drag region are defined with Reynolds number Re = 1 and Re = 10 as the boundary. The coefficient α and β in the equation are determined by, α first in the viscous drag region, then β in the form drag region. It is confirmed that theoretical pressure drop versus flow rate in terms of the modified Ergun equation provides close approximations to the experimental data. In addition, it is found that compressibility effect can aggravate the pressure drop. It is also concluded that there exists a range of transitional diameters, within which the wall effect on the pressure drop would become extraordinarily uncertain. [ABSTRACT FROM AUTHOR]

The dry pressure drops for 8 wire mesh pads were measured experimentally. The pads were of a spiral wound configuration and made of stainless steel wire. They ranged in porosities from 97.64% to 98.9% and with specific surface areas from 283 m 2 /m 3 to 593 m 2 /m 3 . The range of heights was 50–150 mm. A total of three fluid systems were used; One low pressure system using air at 1 bar and two high pressures systems, nitrogen and natural, gas at pressures of 20, 50 and 85 bars. The data were fitted to a modified Darcy–Hazen–Dupuit type equation, which included the specific surface area of the wire mesh pads, Δ P ϵ 2 / ( ρ g U g 2 ) = f ( SL ) + μ g ϵ S 2 L / ( ρ g U g ) , with a mean standard deviation of ±5.3%. In addition a correlation encompassing literature data was developed with standard deviation of ±13.4%. A discussion is provided on the impact of specific surface area on dry wire mesh pad operation. Two other correlations for predicting dry pressure drop in wire mesh pads were also examined. [ABSTRACT FROM AUTHOR]

Moist irregular wood chips or wood bark are used in packed beds for reducing odour and other gaseous emissions from waste gases. Moisture control of packing materials is essential for effective waste gas treatment. Therefore, simple experiments have been carried out to determine the influence of moisture content in a biofiltration bed made up of a mixture of irregular wood chips and wood bark in proportion 50:50 by mass on the pressure drop of air flowing through that bed. Nine moisture content levels varying from 8.1% to 64.5% (w.b.) were tested. The limiting empty bed residence time (EBRT) has been determined for each level. The influence of moisture content on true density, porosity and specific surface of the bed was determined. Above the moisture content of 28.3% (w.b.) there was a drastic change in the physical parameters of the biofilter packing. For moisture contents ≤28.3% (w.b.) the pressure drop increased slightly, while at values greater than 28.3% (w.b.) the opposite trend was observed. The Ergun equation was used to describe the relationship between the pressure drop through the bed and the superficial air velocity. For moisture contents ≤28.3% (w.b.) an approximate Ergun-type equation was proposed to describe pressure drop through the bed and the superficial air velocity. [ABSTRACT FROM AUTHOR]