Eulerian Multiphase Flow Model Research Articles

A numerical study of heterogeneous nucleation of ice crystals and frost layer growth on horizontal cold surfaces

In engineering applications, the formation and growth of frost layers can significantly affect the normal operation of equipment, leading to undesirable influences. Therefore, it is imperative to understand the frost formation mechanisms as a basis for developing effective anti-frosting and defrosting methodologies. This study proposes a model for the growth of horizontal cold surface frost layers using the classical nucleation theory and the Eulerian multiphase flow model. Compared to numerous models that investigate the frost formation issues using the computational fluid dynamics (CFD) method, our proposed model takes into account the crystal growth period (the heterogeneous nucleation process of ice). The predicted results of the proposed model were found to be in good agreement with the data collected from five related experimental studies. In this regard, the maximum frost layer thickness error was 23.9 % with a mean error of 5.1 %, and the maximum density error was 22.8 % with a mean error of 8.1 %. Compared to existing models in the literature, the proposed model can reduce the maximum thickness and density uncertainties by 17.4 % and 10.2 %, respectively. Additionally, the effects of the surface contact angle and environmental parameters on the nucleation process were analyzed using the established model. It was found that a larger contact angle, higher cold surface temperature, and lower air temperature, humidity, and velocity were unfavorable conditions for supporting the formation and growth of ice crystals. Moreover, the nucleation completion time was shortened with the increase in the moist air supersaturation degree, varying as an exponential function. The findings of this study provide an important theoretical basis for the development of optimizing strategies for anti-frosting and defrosting.

Numerical Study of the Influence of the Type of Gas on Drag Reduction by Microbubble Injection

In this work, a novel numerical method for studying the influence of gas types on drag reduction by microbubble injection is presented. Aimed at the microbubble drag reduction (MBDR) process for different types of gases, the mass transfer velocity of different types of gases in the gas–liquid phase is defined by writing a user-defined function (UDF), which reflected the influence of gas solubility on the drag reduction rate. An Eulerian multiphase flow model and the Realizable k−ε turbulence model are used for numerical calculation. The population balance model is used to describe the coalescence and breakup phenomena of the microbubble groups. Henry’s theorem is used to calculate the equilibrium concentration of the microbubble mixed flow. The interphase mass transfer rate of the microbubble injection process for different types of gases is studied by using permeation theory. The local mass fraction of the mixed flow is solved by the component transport equation. It is found that the larger the solubility of the gas, the lower the efficiency of MBDR. When the volume flow rate of the same type of gas is the same but the injection speed is different, the larger the solubility of the gas is, the greater the difference in the drag reduction ratio.

Computational fluid dynamics analysis of a novel continuous cementing slurry mixer

To improve the uniformity of continuous slurry mixing in well cementing, a novel continuous mixing system is proposed in this paper. The CFD model of the mixing system is established by employing the Eulerian multiphase flow model, k-ε model, and Multiple Reference Frames (MRF) method to simulate the flow of the two-phase fluids and the rotation of the agitator, respectively. A segmented control simulation method, which includes a dynamic “monitoring-assignment” approach capable of handling secondary mixing processes in engineering, is proposed to calculate the slurry mixing process in the continuous system. A comparative analysis of the control effectiveness is conducted to demonstrate the feasibility of this method. Using the validated model and method, the mixing process of the slurry in the system is investigated. The obtained data is analyzed based on four indicators: uniformity calculation, power, velocity component, and solid volume fraction, to evaluate the effects of impeller diameter and rotational speed on slurry uniformity. The data shows that both impeller diameter and rotational speed significantly affect the slurry uniformity in the continuous mixing system, while only impeller diameter has a greater impact on the flow field and flow pattern inside the stirred tank. It is observed that increasing the impeller diameter and rotational speed beyond a certain point does not further improve slurry uniformity, and excessive impeller diameter and rotational speed may lead to a decrease in uniformity due to stratification in the tank, along with a significant increase in power consumption. The proposed novel structure and method can provide valuable references for the industry, and the research findings can offer scientific guidance for achieving efficient well cementing operations in engineering.

Effect of Blade Twist on The Flow Characteristics of Gas-Liquid Two-Phase Flow in a Spiral Axial Flow Pump

The mixing of oil and gas forms the foundation of deep-sea oil and gas extraction and transportation. However, traditional conveying equipment has low efficiency and high failure rates. In this study, a spiral axial flow gas and liquid multiphase pump was used as the base model. The Eulerian multiphase flow model and RNG turbulence model were used for numerical simulations to analyze the internal flow field of the multiphase pump. A modification scheme was proposed to twist the airfoil shape and create a twisted vane. The twisted blade with the center of the hub-side flange chord length as the twisting center was twisted in the counterclockwise direction to help reduce the relative volume of gas in the flow channel. When the twisted vane with the hub-side airfoil type trailing edge point as the twisting center was twisted in the suction side direction, it helped to accelerate the movement of the gas-liquid mixture at the trailing edge of the back of the vane and further reduced the low velocity zone at the back of the vane. When the twist center is located at the hub side wing type trailing edge point of the twist vane, the twist degree is 0.214. This results in the maximum head and efficiency of the pump, improves gas phase aggregation phenomenon, and enhances the performance of the multiphase pump.

Numerical simulation of proppant transport from a horizontal well into a perforation using computational fluid dynamics

With the increasing global demand for oil and gas, the development of unconventional resources such as shale gas is becoming ever more important. The key to developing unconventional oil and gas resources lies in horizontal wells with multistage fracturing technology. In the process of horizontal well segmentation fracturing, the distribution of the proppant among multiple clusters has a significant influence on the fracturing effect. However, the influence of various factors on the entry of proppant into the perforation and then into the fracture along the wellbore is unclear. In this paper, based on the flow characteristics of proppants in fracturing fluids, we investigate the wellbore–perforation proppant transport using a Eulerian multiphase flow model. The effect of different factors on proppant entry into the perforation in horizontal wells is studied. We first verify that the computational fluid dynamics model satisfies the accuracy requirements for studying the sand-carrying efficiency of proppants in a perforation cluster. Second, the effects of the proppant size, proppant density, fracturing fluid viscosity, perforation diameter, and fracturing fluid flow rate on the proppant transport efficiency are investigated. Finally, a mathematical model of the sand-carrying efficiency is established by multivariate nonlinear fitting. The results show that the proppant size has a more significant effect on proppant settling at low wellbore flow rates. Increasing the diameter of the proppant particles can accelerate proppant settling. Higher wellbore flow rates tend to reduce the sand-carrying efficiency, although using a low-density proppant can mitigate the effect of the wellbore flow rate. At low wellbore flow rates, increasing the perforation size makes it easier for the proppant to enter bottom perforations. Increasing the fluid viscosity helps to distribute the proppant evenly between perforations in different directions, but this effect diminishes as the flow rate increases. Finally, a formula for the wellbore sand-carrying efficiency is obtained and validated, providing a basis for optimizing the distribution of the proppant in the perforation. The results from this paper enhance our understanding of the sand and fluid feeding patterns of each perforation cluster and provide direction for improving the construction process and enhancing the fracture inflow capacity.

Numerical study on effects of nozzle hole spacing distance on steam submerged jet condensation from triangular holes spray nozzle

Steam-water direct contact condensation (DCC) is a phenomenon which is frequently found in the industrial sector due to its rapid and efficient heat and mass exchange rates. In this work, three dimensional numerical study of steam injection from triangular hole nozzles (with different holes pitch circle diameter, PCD = 6, 8,10 and 12 mm) into subcooled water tank has been carried out using Eulerian multiphase flow model along with realizable k-epsilon turbulence model. The thermal phase change model as User Defined Function (UDF) was employed in Fluent software for capturing submerged steam jet condensation. The simulation results were validated using experimental results as well as previously published numerical study and a fairly good agreement was observed. The effects of nozzle hole spacing distance on distributions of various thermal hydraulics parameters including velocity, pressure, temperature, heat and transfer characteristics have been studied. The axial distribution of the velocity, temperature, heat transfer coefficient and mass transfer computed at the centerline of the nozzle was found weaker than observed at the centerline of the nozzle holes. However, these distributions were not weak at nozzle centerline for nozzle with PCD 6 mm. The heat transfer coefficient has been found in the ranges of 1.75–2.3 MW/m2 K. The results reveal that the heat transfer coefficient for nozzle PCD 8 mm is higher than rate obtained for other nozzles. The rate of mass transfer at the holes centerlines has been found increasing with the holes PCD. The axial distribution of the mass transfer curve shifts downstream for nozzle with smaller PCD. Additionally, the mutual shielding effect of the jets weakens as holes PCD increases.

Numerical and experimental study of the effects of tangential to axial velocity ratio and structural parameters inside the nozzle on spray characteristics

Pressure swirl nozzles are widely applied in spray cooling, dust removal, and fuel injection. To better connect the nozzle structure with the internal flow to analyze their influence on spray parameters, this paper designs a nozzle structure and uses experimental measurement and computational fluid dynamics simulation methods to investigate the influence of the nozzle's tangential velocity to axial velocity ratio (vτin/vzin) and the swirl diversion channel eccentric distance (dl) on the spray parameters. A phase Doppler particle analyzer was used in the experiment study to determine the spray axial velocity (vz) and sault mean diameter (D32). In the simulation investigation, the Eulerian multiphase flow model was used to calculate the multiphase flow field of the spray. The results showed that dl and vτin/vzin both have an obviously linear relationship to the peak location (rpeak) of each spray parameter. It means that dl plays similar roles as the vτin/vzin, which can enhance the swirl strength inside the nozzle and increase the spray cone angle. The rpeak of liquid phase volume fraction (αw) and D32 of the droplet particle are always greater than the rpeak of vz. The analysis of the flow field inside the spray orifice indicates that as the vτin/vzin rises, the liquid in the nozzle orifice tends to move farther from the central axis, causing atomization to occur more upstream. This study serves as a reference for the flow analysis and structure design of the pressure swirl nozzle.

Numerical Study on Wind-Driven Thin Water Film Runback on an Airfoil

A method that combines the Eulerian multiphase flow (EMF) model with the Eulerian wall film (EWF) model is proposed to study the transportation of a wind-driven thin film caused by the impingement of water droplets. The external flow of air and droplets is simulated using the EMF model, while the wind-driven film is simulated with the EWF model. The effects of convection, shear stress, gravity, surface tension, and contact angle on the runback film flow are examined. The results show that shear stress from the air and capillary force due to the contact angle at the contact line are the two dominant influences on transportation, with the former acting as the driving force, while the capillary force at the contact line holds back the film and can cause a drastic increase in thickness at the contact line. With increased contact angle, the coverage of the film retracts, but film thickness upstream is not affected. A model for the film velocity containing the effects of shear stress and contact angle was proposed based on the analysis, which can be simplified to Newton’s shear law when the incoming velocity is large or the contact angle is small.

Computational fluid dynamics approach to study methane hydrate formation in stirred reactor

Hydrate formation management in oil and gas industries needs a detailed understanding of hydrate formation phenomena in terms of dynamics and kinetics aspects. Stirred reactors are one of the popular experimental systems to study hydrate formation/dissociation in terms of kinetics and thermodynamics mechanisms. Various processes/systems such as gas hydrate formation and decomposition phenomena in oil and gas facilities are simulated using computational fluid dynamics (CFD). This research examines the hydrate formation in a stirred reactor for a water-methane system using the Eulerian multiphase flow model by employing CFD software (STAR CCM +). The developed numerical model incorporates the conservation equations of momentum, mass, and energy, where the hydrate equations, including mass transfer, hydrate kinetics, and heat of hydrate formation, are included in the governing equations. In this paper, the methane hydrate formation in the stirred reactor for the stirring rate of 300 RPM and volume fraction of 0.04 with a pressure of 5,500 kPa is simulated. Then, the simulation results are validated using the experimental data collected from the literature, resulting in an overall absolute average deviation percentage (AAD%) of 15.6 %. The influences of stirring rate (300 to 500 RPM), methane volume fraction (0.04 to 0.4), pressure (3,500 to 7,500 kPa), and subcooling (1.96 to 9.23 °C) are studied on the hydrate formation in the agitated reactor. The results reveal that the developed CFD model can predict the methane hydrate formation in the stirred reactor with acceptable precision. According to the simulation runs, methane hydrate is formed mainly near the walls and around the stirrer blades. In addition, an increase in subcooling, gas volume fraction, pressure, and stirring rate leads to more hydrate formation in the reactor with a constant temperature of 274.3 K. The maximum mass fraction of hydrate is observed for the case when the gas volume fraction and stirring rates are 0.4 and 900 RPM, respectively. However, the minimum value of methane hydrate is 0.092 g, where the volume fraction and impeller speed are 0.04 and 300 RPM.The findings of this study can help to further understand hydrate formation phenomena in oil and gas facilities. This model can provide oil and gas engineering sectors with effective strategies to control and manage gas hydrates. In addition, the proposed CFD model can be helpful for engineers and researchers in the petroleum industry to simulate hydrate formation in other complicated geometries in petroleum facilities.

Study on a Circular Cylindrical Floating Device and Its Motion Response Characteristics

In this paper, a circular cylindrical floating device design is proposed by combining the structural features of the cylindrical Floating Production Storage and Offloading (FPSO) and the deep-sea Spar platform. It is suitable for deep-water oil and gas field development environment in the South China Sea. This floating device adds six floats with a Spar platform hard tank role based on the cylindrical FPSO to improve the buoyant center. This paper analyzes the motion response characteristics of the circular cylindrical floating device in waves by the Eulerian multi-phase flow model of STAR-CCM+. The results show that the pitch motion characteristics of the circular cylindrical floating device are better than those of the cylindrical FPSO and ship-type FPSO in the reference [8]. In addition, the paper also investigates the motion response of the circular cylindrical floating device with different directions of the incoming flow. The analysis shows that this floating device has the lowest motion response at 30° direction incoming flow. And the Response Amplitude Operator (RAO) of pitch motion shows a negative correlation with the incoming flow direction. The research results of this paper can provide a reference for the future development of marine resources, and have a certain practical significance.

CFD modeling of drill cuttings transport efficiency in annular bends: Effect of hole eccentricity and rotation

Increasing the cuttings transport efficiency in deviated wells is difficult due to the rolling transport and cuttings settling on the low side of the annulus. Advancing flow rates and improving mud properties may not be applicable for proper hole cleaning because of the hydraulic and mechanical limitations. Under these situations, the major contribution to cuttings transport is provided by drill-pipe rotation for different eccentricities. This project describes the relationship between hole eccentricity and rotation during cuttings transport through annular bends. The present study focused on developing a computational fluid dynamics model by using Ansys fluent 2021 R1 to predict these parameters conveniently. Two phases were considered: liquid (water) and cuttings (sulfur solid), the Eulerian multiphase flow model was used in Fluent for the present study. The inlet boundary conditions specified the inlet velocities and volume fraction of involved phases. The stationary surfaces of the flow channels were hydrodynamically considered smooth walls and the outlets were regarded as being open to the atmosphere. The pressure gradient is used as the primary output parameter to analyze the flow. The simulated pressure losses are found to be logical at different conditions, thus showing the characteristics of the flow.

Numerical Simulation of Conical and Linear-Shaped Charges Using an Eulerian Elasto-Plastic Multi-Material Multi-Phase Flow Model with Detonation.

This study developed a hydrocode to numerically simulate both conical and linear-shaped charges using an Eulerian multi-material and multi-phase flow model. Elasto-plastic solids and the detonation of a high explosive charge were modeled using a Johnson–Cook material model and the programmed burn model, respectively. Further, the plasticity of the solids was calculated using a radial return mapping algorithm. The model was solved using a high-resolution computational fluid dynamics (CFD) technique on Cartesian grids. Material interfaces were tracked using the level-set method, and the boundary conditions were imposed using the ghost fluid method. The developed hydrocode was validated using high-speed impact problems. Consequently, the developed hydrocode was used to successfully simulate the evolution and penetration of metal jets in shaped charges after a detonation.

첨가물이 존재하는 CO₂ Hydrate 형성의 CFD 모델링

CO₂ hydrate formation with additives in the pipeline was simulated by the CFD tool of the COMSOL Multiphysics. The length and diameter of the pipeline for the hydrate formation simulation were 1 m and 0.0347 m, respectively. The 3D axis-symmetric geometric structure was implemented. The Eulerian multiphase flow model was introduced for the modelling of the hydrate formation processes composed of complex multi-physical phenomena such as mass transfer, heat transfer, and phase change. The validity of the simulation results was proved by comparing them with previous experimental data in terms of hydrate formation rate. As a result, hydrate velocity and volume fraction along length direction were calculated. The average hydrate mass fraction increased from 8% to 12% by additive.

Computational fluid dynamic modeling of methane hydrate formation in a subsea jumper

Gas hydrate in subsea pipelines is a serious flow assurance issue that may impose operational challenges to offshore petroleum production and transportation. The effects of fluid properties on hydrate formation in complex geometries such as jumpers are not fully understood. This study aims to assess hydrate formation in the jumper for the water-methane system using the Eulerian multiphase flow model through employing computational fluid dynamic (CFD) software (STAR CCM+). The numerical model is developed through consideration of transport phenomena equations, including conservation of mass, momentum, and energy in which mass transfer, hydrate reaction kinetics model, and heat of hydrate formation are incorporated in the multiphase flow equations in the form of source terms in the CFD software. In this study, first, the hydrate mass fraction for the fluid velocity of 5 m/s with an inlet temperature of 7 °C and a gas volume fraction of 0.2 is calculated. The sensitivity analysis is then performed considering the influences of changes in the inlet fluid velocity, gas volume fraction, inlet temperature, and subcooling on the hydrate formation. The results reveal that the developed CFD model is capable of predicting hydrate formation behaviors in the jumper with acceptable precision. An increase in the liquid inlet velocity and gas inlet temperature lowers the amount of hydrate formed in the jumper. In contrast, an increase in the subcooling and gas volume fraction leads to more hydrate formation. The proposed CFD model can be successfully used to simulate hydrate formation in pipelines under various process and thermodynamic conditions so that it can help to find reliable/effective methods for hydrate management.

Numerical simulation of the effects of sandy water on regulator labyrinth channel in micro-sprinkler systems

Abstract The effects of sandy water on the W-shaped labyrinth channel of micro-sprinkler irrigation systems with large flowrate were investigated using Computational Fluid Dynamics (CFD). Using ANSYS FLUENT software and different inflow conditions (e.g., pressure, velocity, sediment concentration, and sand particle diameter), internal turbulent multiphase flow and sand deposition were simulated by the Eulerian multiphase flow model. Particle erosion in the labyrinth channel was calculated by the Discrete Phase Model (DPM). The results show that vortex movements and shear actions at the boundary layer cause self-flushing in the channel. The location of sand particle deposits and the turbulent dissipation rate are related to the operating pressure, which is optimal at 300 kPa. The erosion rate of the channel wall is proportional to the inflow sediment concentration but has no obvious relationship with inflow velocity. Based on the movement regulation of sand particles in the labyrinth channel, recommendations on filtration requirements and operating pressure of irrigation systems are proposed.

Experimental and simulation study on mixing time and suspension quality of liquid-solid flow field in stirred reactor with draft tube

Abstract The solid-liquid flow field is established in the stirred reactor with baffles and draft tube. Mixing time and suspension quality of the flow field are studied. Based on the Eulerian multiphase flow model and RNG k−ε turbulence model, the CFD model is established for the simulation research. By comparing the experimental data of solid concentration distribution and mixing time with the simulated values, it is proved that the CFD model established can be used to study the flow field in the stirred reactor. The effects of stirring speed, liquid viscosity and solid particle size on mixing time and suspension quality are considered. With the increase of stirring speed, mixing time decreases, mixing uniformity is improved. Mixing time decreases first, then increases slightly with the increase of liquid viscosity, and the suspension quality is improved. When the solid particle size increases, mixing time increases rapidly, but the mixing uniformity becomes worse.

Research on dust control of mobile straw granulator

High particle concentrations, large sizes and coupled flows areproduced in mobile straw granulators during operation. To control the dust emissions and reduce the mass ratio of the dust into the press device of the granulator, an Eulerian multiphase flow model was first used to analyze the effects of the storage cage structure, flow velocity at the duct outlet, ambient wind speed and particle size on dust emissions. The flow characteristics of the particle distribution, particle trajectory and particle concentration were studied and verified by experiments. Second, a diversion duct was designed to reduce the phenomenon of dust emission and sedimentation by using the principle of gravity settlement. The results showed that the structure of the diversion duct and dense storage cage could improve the flow characteristics at the outlet, change the coupled effect between flow and particles, and play a key role in reducing dust concentration. The diffusion distance of dust emission could be restrained, and the mass ratio of dust entering the press device could be increased by reducing the outlet wind speed. When the air flow velocity at the duct outlet was reduced from 7.5 to 2.9 m∙s−1, the horizontal dispersion distance of dust was reduced to 4.33 m, and the mass of dust entering the press device accounted for approximately 60%. The difference in diffusion distance between particles with diameters of 30 and 5 μm was only 0.47 m, and the particle size had little effect on the dust emission distance. The spread of dust emissions could be inhibited in breezy and calm weather. The results provide a reference for the modification of farm equipment.

Pyrolysis Preparation Process of CeO2 with the Addition of Citric Acid: A Fundamental Study

CeO2 is an important energy storage material that can be used in solid fuel cells. Adding citric acid can improve the particle distribution of the pyrolytic preparation of CeO2 inside the reactor. Through Fluent, this paper investigated the pyrolysis preparation of CeO2 with the addition of citric acid by adopting the Eulerian multiphase flow model, component transportation model, and standard k-ε turbulence model. The experimental and simulation results suggest that the addition of citric acid can alter the pressure, temperature, and component distributions inside the reactor. When the mass fraction of O2 is 0.3, the concentration distribution effect of the CeO2 component is optimal and its conversation rate is the highest. When the mass fraction of citric acid is 0.04, the concentration distribution effect of the CeO2 component is the best, as witnessed by the high CeO2 concentration at the exit. It was found that an O2 content of 30 wt % and citric acid content of 4 wt % were optimal operating conditions for this technology.

Evolution and Physical Characteristics of a Raceway Based on a Transient Eulerian Multiphase Flow Model

In industrial processes, a semi-cavity area formed by airflow wherein the particles circulate is called a “raceway”. In a blast furnace, the role of the raceway is particularly important. To understand and predict the evolution and physical characteristics of the raceway, a three-dimensional transient Eulerian multiphase flow model in a packed particle bed was developed. In the model, it was assumed that the gas and solid (particle) phases constitute an interpenetrating continuum. The gas-phase turbulence was described as a k–ε dispersed model. The gas-phase stress was considered in terms of the effective viscosity of the gas. The solid-phase constitutive relationship was expressed in terms of solid stress. It was found that the evolution process of the raceway can be divided into three stages: (1) rapid expansion, (2) slow contraction, and (3) gradual stabilization. When the blast velocity was increased from 150 m/s to 300 m/s, the surface area of the raceway increased from 0.194 m2 to 1.644 m2. The depth and height of the raceway increased considerably with velocity, while the width slightly increased.

Dissociation equilibrium height and friction coefficient in pipeline transportation of gas hydrate-bearing sediment particles

Compared with traditional fossil fuels, gas hydrates have vast reserves, cause little pollution, and are an essential strategic energy resource. Pipeline transportation is critical to realize the development and utilization of natural gas hydrate resources. The Eulerian multiphase flow model within the computational fluid dynamics software FLUENT was employed to calculate gas–liquid–solid flow, taking into account phase interactions, heat transfer, and collision among particles. Pipeline transportation of gas hydrate-bearing sediment (GHBS) particles was studied based on dimensional analysis and numerical simulation. First, the essential dimensionless numbers controlling multiphase flow and hydrate dissociation were deduced. Further, the obtained simulation results clearly indicate that when the system was in a stable state, there was a dissociation equilibrium height above which hydrate dissociated completely. The influences of the dimensionless numbers on the dissociation equilibrium height and friction coefficient in the pipe were determined, and power-law correlations for the dissociation equilibrium height and friction coefficient were obtained from the numerical data. Finally, an analytical expression of dissociation equilibrium height was derived by decoupling the solid–liquid flow and gas hydrate dissociation, and the validity of the power-law correlation for the dissociation equilibrium height was verified by the analytical expression.