Eulerian-Eulerian Method Research Articles

Numerical modelling on dispersion behavior of particulate contamination induced by a moving operator in a semiconductor cleanroom: A eulerian-eulerian method

Contamination control in cleanrooms is crucial across various industries. In semiconductor manufacturing, operator-induced contamination presents a significant challenge, as it reduces the critical dimension. In this research, one comprehensive model describing contamination behaviour induced by operator motion was proposed, considering the moving operator as both a flow pattern changer and a contaminant source, combined with the number of particles accumulated (NPA) on the process instruments. To quantitatively characterise the transient contaminant dispersion behaviour caused by the operator, a Eulerian-Eulerian-based particle number density equation, integrated with overset mesh technology was employed. Our findings reveal that contamination dispersion behaviour is governed by convection and diffusion. The NPA on the side instruments at operator moving speeds at 0.5, 1, and 1.5 m/s were 4404.33, 8241.26, and 9384.41, respectively. And those of central instruments are 28463.75, 35848.60, and 43680.74 in corresponding cases. The largest reduction in influence on both the central and side instruments was found between cases with a maximum operator speed of 0.5 and 1.5 m/s, with NPA reaching reductions of 53.08 % and 34.84 % respectively. This indicates that the moving speed significantly affects contaminant dispersion.

Design and optimization of slot number in supercooled vapor suction in steam turbine blades for reducing the wetness

An enormous amount of the world's electricity is produced by steam power plants. The existence of a liquid phase in the steam turbine results in an efficiency drop and mechanical losses, which are very expensive due to its high price. Creating a suction slot in the stationary blade of the steam turbine for sucking the supercooled vapor and wetness fraction in the low-pressure stages of the turbine is one of the most effective methods of preserving the rotor blades against corrosion and erosion. The Eulerian-Eulerian method is employed for modeling the condensing flow. In the current research, the impact of the suction slot location and number on the surfaces of the turbine blades is investigated on condensation, total suction ratio, liquid suction ratio, average droplet radius, and condensation losses. Optimization is performed by the TOPSIS algorithm. Based on the results, the location and number of the suction slots affect the flow pattern in the turbine blade. Creating a suction slot in the optimal case has a total suction ratio of 4.1 %, which decreases the liquid suction ratio, condensation losses, and average droplet radius, respectively, by 5.28 %, 6 %, and 25 % compared to the original case.

Numerical study of raceway behaviours of a slow-moving packed bed solid fuel gasifier

The moving-bed gasifier of solid fuels (e.g., coal or biomass) is a key chemical reactor to convert coal or biomass to clean fuel, where the profile of the raceway cavity and its flow-thermal-chemical behaviours can affect the performance of the gasifier, however, they are not well understood because of the process complexity and modelling challenge. In this study, an advanced 3D multi-fluid model, based on the Eulerian-Eulerian method, coupled with heat transfer and heterogenous reactions, is developed to describe the reacting flow behaviours inside and around the raceways. It is found that raceways inside the slow-moving packed bed gasifier are of balloon-like shapes; they are built in just a few seconds after issuing the jet from gas entry, and then both the average velocity for gas and particle are relatively stable. The gauge pressure conditions are not isobaric, and high temperatures, small gas densities and high reaction rates are observed near the raceway “shell”. Besides, it is found the raceway behaviours on horizontal cross-section feature more symmetry compared to those on other directions. In addition, probability theory and statistics are used to analyse the quantitative raceway results, and possibilities related to the distributions of gas properties, momentum and species are discussed. This model provides an effective tool to systematically study and optimise raceway behaviours inside a slow-moving packed bed solid fuel gasifier.

Effects of tube configurations on the heat transfer and hydrodynamic behavior in a gas-solid fluidized bed

The study of surface-to-bed heat transfer and flow characteristics in a gas-solid fluidized bed with different immersed tube configurations were investigated using the Eulerian-Eulerian method coupled with the kinetic theory of granular flow (KTGF) computationally. Compared with cases of in-line configurations, the staggered configurations increased the heat transfer coefficients (HTC) of the center-immersed heating tube. Moreover, it was found that with an increase in the rows and columns of the configurations, the HTCs increased and decreased respectively. The surface-to-bed heat transfer process was investigated combined with the particle renewal mechanism, and it was demonstrated that the HTCs were significantly affected by the surrounding packet fraction distribution and the packet residence time on the immersed heating surface. The results could be quantitatively employed to aid the heating tube configuration in designing the external heat exchanger (EHE) of a circulating fluidized bed (CFB) boiler for the treatment of municipal solid waste (MSW).

Effects of Brownian Motions and Fractal Structure of Nanoparticles on Natural Convection

The study simulated heat transfer in alumina-water nanofluid in a natural convection flow and Rayleigh-Benard configuration considering the Brownian motions and fractal structure of the nanofluids. The simulations were based on a two-dimensional, Eulerian-Eulerian method. Many simulations have been performed to examine the effect of aspect ratio, heat flux, and para-meters related to the structure of the nanoclusters including size, fractal dimension, and volume fraction on the natural convective heat transfer coefficient. The comparison between the simulation results and the experimental data of heat transfer coefficient indicates a good agreement. The simulation results indicated that the enhancement of aspect ratio, heat flux, and fractal dimension increases the heat transfer coefficient. On the other hand, the reduction of nanoclusters and nanoparticle size decreased this coefficient. Moreover, the simulation results showed that in high heat transfer fluxes, the heat transfer coefficient first increases by increasing the nanoparticles solid volume fraction and then decreases. However, heat transfer coefficient decreased steadily with the increase in the nanoparticles solid volume fraction in low heat transfer fluxes. The results suggested that using the nanoparticles Brownian motion mechanism along with their fractal structure can be well-applied in natural-convection heat transfer modelling of nanofluids.

Classification of Ultrafine Particles Using a Novel 3D-Printed Hydrocyclone with an Arc Inlet: Experiment and CFD Modeling.

Ultrafine particle classification can be realized using hydrocyclones with novel structures to overcome the limitations of conventional hydrocyclones with tangential inlets or cone structures. Herein, the hydrocyclones with different inlet structures and cone angles were investigated for classifying ultrafine particles. Computational fluid dynamics (CFD) simulations were performed using the Eulerian-Eulerian method, and ultrafine MnO2 powder was used as a case study. The simulation results show a fine particle (≤5 μm) removal efficiency of 0.89 and coarse particle (>5 μm) recovery efficiency of 0.99 for a hydrocyclone design combining an arc inlet and a 30° cone angle under a solid concentration of 2.5 wt %. Dynamic analysis indicated that the novel arc inlet provided a preclassification effect to reduce the misplacement of fine/coarse particles, which cannot be provided by conventional tangential or involute inlets. Furthermore, the proposed design afforded comprehensive improvement in the flow field by regulating the residence time and radial acceleration. Subsequently, a novel hydrocyclone with an arc inlet and 30° cone angle was manufactured using the three-dimensional (3D) printing technology. Experiments were conducted for classifying ultrafine MnO2 particles using the novel 3D-printed hydrocyclone and conventional hydrocyclone. The results demonstrate that the classification performance of the 3D-printed hydrocyclone was superior to that of the conventional one, in particular, the removal efficiency of fine particles from 0.719 to 0.930 using a 10 wt % feed slurry.

Numerical simulation of herringbone gear abrasive flow machining

The Eulerian-Eulerian method is used to numerically simulate herringbone teeth using the precision machining technique of abrasive flow. The effects of inlet velocity and abrasive concentration factors on abrasive flow machining are investigated separately for numerical analysis to reveal the effects of dynamic pressure and wall shear on abrasive flow machining under different machining parameters. The simulation results show that increasing the inlet velocity can improve the processing efficiency and the processing effect of abrasive flow processing. Increasing the abrasive concentration increases the processing cost and predicts a weakening of the abrasive flow, allowing for the use of lower concentrations of abrasive flow for actual processing.

Forced ignition and oscillating flame propagation in fine ethanol sprays

The present work investigates forced ignition and oscillating propagation of spray flame in a mixture of fine ethanol droplets and air. The Eulerian-Eulerian method with two-way coupling is used and a detailed chemical mechanism is considered. Different droplet diameters and liquid fuel equivalence ratios (ER) are studied. The evaporation completion front (ECF) is defined to study the interactions between the evaporation zone and flame front. The gas composition at the flame front is quantified through an effective ER. The results show that the kernel trajectory is considerably affected by droplet size and liquid ER. Generally, the flame ER reaches the maximum when the ECF starts to move from the spherical center. It gradually decreases and reaches a constant value when the flame freely propagates. Quasi-stationary spherical flame is observed when the liquid ER is low, whilst kernel extinction/re-ignition appears when liquid ER is high. These flame behaviors are essentially affected by the heat conduction and species diffusion timescales between the droplet evaporation zone and flame front. The dependence of the minimum ignition energy (MIE) on liquid ER is U-shaped and there is an optimal liquid equivalence ratio range (ERo) with the smallest MIE. Long and short ignition failure modes are observed, respectively for small and large liquid ERs. When liquid ER is less than ERo (long failure mode), larger energy is required to initiate the kernel due to very lean composition near the spark. For liquid ER larger than ERo (short mode), ignition failure is caused by strong evaporative heat loss and rich gas composition due to heavy droplet loading. Flame speed oscillation is seen when the initial droplet size is above 10 μm. The oscillation frequency linearly increases with the liquid ER. Meanwhile, larger droplets lead to smaller oscillation frequencies.

Investigation of liquid n-heptane/air spray detonation with an Eulerian-Eulerian model

A two-dimensional numerical simulation of detonation in a reactive dispersed liquid droplet cloud is performed with an Eulerian-Eulerian method. This study aims to investigate the model and the effects of two-phase sub-models on the propagation of a detonation through an n-heptane spray. Firstly, the simulations are compared to the experiments conducted in the thesis of Mohamed El-Amine Benmahammed [1]. Three simulations are carried out for a mono-dispersed/one sample cloud of droplets with a mass corresponding to equivalence ratios of 0.8, 1.0, and 1.3. The Eulerian-Eulerian method predicted the experimental detonation velocity and gaseous phase thermodynamic properties with reasonable accuracy. Secondly, an investigation of the effects of the mobilization of the droplet size poly-dispersity on the detonation properties was carried out. For a droplet Sauter mean diameter of 30 µm, the effect of the number of droplet samples used for modeling the poly-dispersity modifies the front structure and detonation properties. For instance, comparing 15 samples of droplet size to a unique sample, the detonation velocity decreases by 2.0 %, and the mean detonation cell width increases by 10 %.

Investigation of the mixing characteristics of industrial flotation columns using computational fluid dynamics

The mixing characteristics of industrial flotation columns were investigated using computational fluid dynamics (CFD). Particular emphasis was placed on the clarification of the relationship between the liquid and solids mixing parameters such as the mean residence time and axial dispersion coefficients. The effects of particle size and bubble size on liquid dispersion in the column were also studied. An Eulerian-Eulerian method was applied to simulate the multiphase flow, while additional scalar transport equations were introduced to predict the liquid residence time distribution (RTD) and particle age distribution inside the column. The results obtained show that particle residence time decreases with increasing particle size. The residence time of the coarser particles (112.5 pm) was found to be at least 60% of the liquid residence time, while the finer particles (19 pm) had a residence time similar to the liquid. The results also show that an increase in the particle size of the solids results in a decrease in the liquid vessel dispersion number, while a decrease in the bubble size increases liquid axial mixing. Finally, the simulated axial velocity profiles confirm the similarity between the liquid and solids axial dispersion coefficients in column flotation.

Intrinsic insight of energy-efficiency optimization for CO2 capture by amine-based solvent: effect of mass transfer and solvent regeneration

Here the energy-efficiency performance of CO2 capture is investigated based on the combination of bench-scale experiments and simulated calculation. A comprehensive evaluation is performed by L25(56) orthogonal tests to analyze the effect of crucial operating conditions on CO2 capture. Experiments reveal desorption temperature and flue gas flow play a major role for CO2 capture efficiency. Rising flue gas flow could promote interfacial area, but decreases contact time, overally, net CO2 flow approximately determines the linear relationship of capture efficiency and absorption rate. With combination of Eulerian-Eulerian method with the population balance model, we predict the dynamics evolution process of dispersed bubble, in order to provide the detailed information of interphase contact area and multiphase flow for modelling complete mass transfer parameters. Meanwhile, rigorous process simulation is developed to analyze the energy consumption of carbon capture. Higher desorption temperature provides much leaner solvent, which is beneficial to CO2 absorption, but consumes greater energy penalty.

Numerical modeling of droplets injection in the secondary flow of the wet steam ejector in the refrigeration cycle

Steam ejector plays a key role in the refrigeration system. The water has been used as a working fluid because water is more economical and non-toxic. The operating fluid often enters the evaporator as a water liquid and droplets evaporate by absorbing heat. Cooling load changing causes the vapor in the outlet of the evaporator to be accompanied by droplets. Therefore, there are droplets at the inlet of secondary nozzle and flow should be simulated as a wet steam flow with injection droplets at the secondary flow. In this paper, the effects of droplets injection at secondary flow have been investigated on the performance of the refrigeration cycle. For this purpose, the Eulerian-Eulerian method has been used and the results have been validated with experimental data. Six cases are considered with different wetness and number of droplets in the secondary flow. The results of case 6 show COP, T¯outlet, and ER decrease about 22.93%, 15.66%, and 22.93%, respectively. In addition, the steam accompanies by droplets at the outlet of ejector. Therefore, it is essential for designers and operators to model and consider the effects of the droplets on the wall erosion to optimize the wet steam ejector and refrigeration cycle performance.

CFD-PBM Simulation on Bubble Size Distribution in a Gas-Liquid-Solid Flow Three-Phase Flow Stirred Tank.

The bubble size distribution, location distribution, and gas holdup in a gas–liquid–solid flow three-phase stirred tank were numerically simulated by the Eulerian–Eulerian method and the population balance model (PBM). The Euler–Euler method combined with the PBM model included the influence of bubble aggregation and fragmentation on the interfacial force, which can better predict the bubble size distribution and phase holdups. The simulation results show that there are some differences in the fluid morphology and gas dispersion characteristics in the stirred tank under different rotating speeds. With the increase of rotating speed, the content of small-diameter bubbles increases obviously, and they are mainly concentrated in areas with higher speeds. The higher the rotational speed, the more the bubbles with small diameters, but the content of bubbles with large diameters is less affected by the rotational speed. Small-size bubbles mainly exist in the region of high fluid velocity, while large-size bubbles mainly exist in the region of low hydrostatic pressure. Compared with the change of the bubble content at different speeds, the content of bubbles with diameters of 0.50–1.90 mm is largest at 2000 rpm, while the content of bubbles with diameters of 2.65–10.09 mm is largest at 1500 rpm. The simulation work has certain guiding significance for the research and development of the forced mineralization device and the understanding of the dispersion characteristics of bubbles in the stirred tank.

CFD modelling and simulation of drill cuttings transport efficiency in annular bends: Effect of particle size polydispersity

This study analyses the impact of particle polydispersity using the Eulerian-Eulerian (EE) and Lagrangian-Eulerian (LE) modelling approaches in the context of wellbore cleaning operations in the drilling industry. Spherical particles of sizes 0.5 mm, 0.75 mm and 1 mm are considered, whereas a Power Law rheological model is used for the fluid phase description. The EE approach implemented herein applies the Kinetic Theory of Granular Flow (KTGF) in ANSYS Fluent® and accounts for the particle size differences by representing them as different phases within the computational domain. With the LE approach, we employ the Dense Discrete Phase Model (DDPM) and capture this difference with the aid of a size distribution model (the Rosin-Rammler model). The findings of our computational experiments show considerable differences in key variables (the pressure drop, and particle deposition tendencies) between monodispersed and polydispersed transport scenarios. • A comparison between monodispersed and polydispersed transport is presented. • Considerable differences in cuttings transport velocity exist between the LE & EE method. • Increased particle deposition is observed with monodispersed transport in this study. • The pressure drop is overpredicted when monodispersity is assumed.

Numerical Study of Water-air Ejector using Mixture and Two-phase Models

In this research, steady-state Mixture and Eulerian-Eulerian method for liquid-gas parallel flow ejector were examined. The simulation demonstrated that the Mixture model simulation represents better and efficient. The Eulerian-Eulerian model needed longer computational time and had a complexity to achieve the optimal convergence. However, both methods' performances were shown slightly similar. The models indicated a difference of about 6% in the flow rate ratio, their pressure diagrams nearly coincide, and their velocity parameter varies by 7% by comparing to the existing experimental data. Additionally, the Mixture model results appropriately conformed much better to the experimental data. So, the Mixture model was chosen for futher parametric study. Simulation results indicated that the flow rate ratio decreases by increasing the throat's cross-sectional area, and the flow rate ratio increases by increasing the nozzle's cross-sectional area. In this regard, e.g., the flow rate ratio of ejector by increasing pressure from 70 to 80 kPa, the air inlet increases up to 94%, and by increasing ejector outlet pressure, the flow rate ratio reduces such that no suction can be observed at 160 kPa. Consequently, at 150 kPa pressure ratio, the flow rate ratio was reduced by almost 100%.

Migration and Distribution Characteristics of Proppant at the Corner of Horizontal Fracture Network in Coal Seam

A complex fracture network is composed of many similar structures. The migration law of proppant at each structure is the core and basic content of the migration law of proppant in complex fracture network, and there is little research. In this study, the EulerianEulerian method (TEM) is used to analyze the migration and distribution characteristics of solid–liquid two phases at the fracture corner according to different corner types of the fracture network. The results show that the migration characteristics of proppant in the corner area can be divided into the corner anomaly area, buffer area, and stability area; the influence of the turning angle on proppant migration is mainly concentrated at the corner and in the range of 4 times the fracture width after turning. The probability of sand plugging at the corner of the “Y → T” fracture is lower than that of “L → l”, higher than that of the “X → +” wing branch fracture, and lower than that of the main fracture. At the corner of the fracture network, after the solid flow turns, the proppant will form a high sand area on the side of the impact fracture surface, then rebound back to the fracture, form a sand-free area on the other side, and form a high-velocity core in the refraction interval. At the corner of the “L → l” fracture, there are one high sand area, one non-sand area, two low-velocity areas, and one high-velocity area; there are three low-velocity areas, two sand-free areas, and one high sand area at the corner of the “Y → T” fracture; at the corner of the “X → +” fracture, there is a high sand area and no sand-free area, and the flow velocity of the main fracture is much greater than that of the wing branch fracture.

Evaluation of the Erosion Characteristics for a Marine Pump Using 3D RANS Simulations

In the present study, an erosion analysis of an industrial pump’s casing and impeller blades has been performed computationally. Effects of various critical parameters, i.e., the concentration and size of solid particles, exit pressure head, and cavitation on the erosion rate density of the casing and blade have been investigated. Commercial codes CFX, ICEM-CFD, and ANSYS Turbogrid are employed to solve the model, mesh generation for the casing, and mesh generation of the impeller, respectively. The Eulerian-Eulerian method is employed to model the pump domain’s flow to solve the two phases (water and solid particles) and the interaction between the phases. Published experimental data was utilized to validate the employed computational model. Later, a parametric study was conducted to evaluate the effects of the parameters mentioned above on the erosion characteristics of the pump’s casing and impeller’s blade. The results show that the concentration of the solid particles significantly affects the pump’s erosion characteristics, followed by the particle size and distribution of the particle size. On the other hand, the exit pressure head and cavitation do not affect the erosion rates considerably but significantly influence the regions of high erosion rate densities.

A hybrid Eulerian-Eulerian/Eulerian-Lagrangian method for dense-to-dilute dispersed phase flows

Problems involving a transition between dense and dilute dispersed phase regimes often require hybridization of Eulerian-Eulerian (EE) and Eulerian-Lagrangian (EL) methods for accurate and efficient computational modeling. A hybrid EE-EL formulation is developed in this work from first principles, which asymptotes to well-established EE and EL methods in limiting conditions. A smooth and dynamic transition criterion and a corresponding algorithm for conversion between the two representations of the dispersed phase are developed. To use EE and EL in their respective regions of effectiveness, the transition criterion is designed as a function of local volume fraction and local kinetic energy of random uncorrelated motion of particles. Several one-dimensional numerical tests are conducted to analyze limits of the hybrid EE-EL method in dense (up to 65% volume loading) and dilute conditions, at first, without any conversion between EE and EL, and then the ability of the conversion algorithm to smoothly transition from EE to EL and vice versa is evaluated using prespecified and dynamically computed transition criteria for one- and two-dimensional tests. Particle evolution in two-dimensional frozen turbulence is simulated to evaluate the method's ability to dynamically transition from EE to EL and vice versa in regions of particle trajectory crossing. Finally, the hybrid method is used for simulating dispersion of an initially dense particle cloud in a three-dimensional spherical sector blast.

Numerical simulation of trickle bed reactors for biological methanation

Biological methanation in trickle bed reactors is an auspicious approach to convert hydrogen and carbon dioxide into methane. In order to analyze this process, a comprehensive CFD model was implemented including multiphase flow, absorption, and reaction phenomena. The model is based on the Eulerian-Eulerian method. Experimental investigations and literature data serve as its validation. The experiments focused on the hydrodynamics of a trickle bed composed of clay granulate and the applied reactor enabled detailed measurements of radial liquid flow profiles and liquid holdup dependent on the overall volume flow rate. The simulation of liquid dispersion confirms the experimental results regarding averaged macroscopic fluid flow. However, liquid holdup is slightly underestimated by the computational model. In addition to the hydrodynamic investigation, simulation of biological methanation provide insight into mutual interactions between multiphase flow and biochemical conversion and present a methane production rate on the same order of magnitude as literature values.

Effect of U-shaped absorber tube on thermal-hydraulic performance and efficiency of two-fluid parabolic solar collector containing two-phase hybrid non-Newtonian nanofluids

In the present paper, the effect of U-shaped absorber tube on the performance of parabolic solar collector containing two-phase non-Newtonian nanofluids is studied numerically. The present study aims to obtain an optimal geometry for parabolic solar collectors based on energy efficiency. In this study, the effect of using nanofluid on parabolic solar collectors is investigated using two-phase simulation. The effect of Re number (2500<Re<5000), nanoparticle diameter (20<dnp<50), volume fraction (1%<φ<4%) are investigated. The control volume method based on the SIMPLE algorithm is used to solve the governing equations. The Eulerian-Eulerian method is employed to simulate two-phase nanofluid flow. Surface-to-surface (S2S) is used for the simulation of the radiation and standard k-ε turbulence model is employed for modeling the turbulent equations. According to the results of the present work, the energy efficiency is always increasing with the Reynolds number for single-pass and dual-pass pipes. Hence, the optimal Reynolds number is 5000 where the highest energy efficiency occurs. It was also found that at all Reynolds numbers, the energy efficiency for the dual-pass pipe is higher than that of single-pass one. According to the results, in the case of the U-shaped system, the diameter of the pipe (assuming the hydraulic diameters are the same) is reduced, leading to an increase in the permeation of heat inside the passing flow, which is the reason for the enhancement of the efficiency.