Eulerian Two-fluid Model Research Articles

Numerical investigation on boiling crisis characteristic of a 7-rod HCF assembly in hexagonal lattice

Helical cruciform fuel (HCF) has the advantages of larger heat transfer area, enhanced coolant mixing and self-supporting, which contribute to increasing power density and safety margins. Compared with the square lattice configuration, the hexagonal arrangement of HCF assembly is more compact, which can help achieve a higher power density. In this paper, the flow characteristics and heat transfer behaviors of HCF in hexagonal lattice were predicted at high and low vapor quality during boiling crisis based on Eulerian two-fluid model. The influence of twist pitches and cross-sections of the fuel rod on heat transfer efficiency and fuel temperature was also studied. The cross-flow intensity changed periodically with a 30° cycle at low vapor quality, and did not fluctuate periodically at high vapor quality, which decreased with the increase of flow resistance. The highest heat flux of HCF rod was the at the blade root and the lowest was at the blade tip, and the maximum to average heat flux ratio was about 1.8. The peak vapor fraction and temperature occurred at leeside side of the fuel rods. The increase of the twist pitch reduced the critical heat flux (CHF), and the increase of blade length enhanced the non-uniformity of heat flux distribution. During boiling crisis, the maximum temperature of the fuel was lower than the phase transition temperature of U-50 wt%Zr alloy, which means the cladding meltdown caused by boiling crisis will occur before phase transition of the fuel.

Numerical Simulation and Parameter Optimization of a New Slant Insertion-Opening Combination Sand Fence

This paper presents a new slant insertion-opening combination sand fence designed to reduce the hazards of traditional railway sand damage along the line. This new fence aims to decrease the disturbance caused by lateral wind on the high-speed railway and minimize the deposition of track sand particles. Numerical modeling and wind tunnel testing were employed to examine the structure’s defensive capabilities. Using the computational fluid dynamics (CFD) method and the Eulerian–Eulerian two-fluid model, the wind protection effect and airflow characteristics of the new sand fence with different slant insertion angles and spacings were simulated, and the optimal configuration parameters were selected. The study found that the new mechanical sand fence exhibits similar performance to the traditional sand fence. Since there is a “narrow tube effect”, the leeward side of the inclined plate generates a local high-speed airflow zone. In the top acceleration zone, the new mechanical sand fence efficiently lowers air velocity, thereby enhancing its protective capabilities. Moreover, the optimal protective performance of the new mechanical sand fence is achieved with an inclination angle of 15°, with improved protection observed as the angle increases. Additionally, the protective performance of double rows of these fences is influenced by the spacing between them. Increasing the distance between the two rows enhances protective performance, with the optimal protection achieved at a spacing of 25H. Beyond this distance, protective performance decreases.

Numerical analysis of performance and internal flow characteristics of a gas-liquid multiphase rotodynamic pump

Abstract Inlet Gas Void Fraction (IGVF) and rotating speed are key parameters influencing the flow characteristics of gas-liquid multiphase pumps. To explore the influence of these two factors on the flow characteristics of gas-liquid multiphase rotodynamic pumps, CFD simulations were carried out based on the Euler two-fluid model to analyze the flow characteristics in an axial-flow pump at three different rotating speeds (1450 r/min, 2200 r/min, 2950 r/min) with different IGVFs. The numerical results indicate that the pump efficiency and head are first increased and then decreased with the increase of IGVF. When the IGVF is 5%, the head and efficiency reach their maximum values. This is attributed to the minimum vorticity and turbulence kinetic energy in the impeller passage at IGVF= 5%, and the small vortex range at the hub of the guide vane, thus resulting in the stable two-phase flow state in the impeller and guide vane. At the same IGVF, with the increase of the rotating speed, the head and efficiency of the multiphase pump increase accordingly. This is closely related to the smallest vortex range formed by gas-liquid flow separation at n=2950 r/min, indicating a better flow state.

Numerical study of heat transfer and pressure drop characteristics in helical tubes based on OpenFOAM

Due to the structural characteristics of the helical tube, centrifugal force complicates the flow boiling phenomenon inside the tube. How to accurately describe and predict the parameter distributions involved in helical tube flow and heat transfer is a concern for scientists. Based on the OpenFOAM, this paper combines the wall boiling model, the interphase model, other closed models with the Eulerian two-fluid model, analysed changes of void fraction, surface heat transfer coefficient, pressure drop with working conditions in the single-phase to nuclear boiling section in the tube. The results show that this solver and the corresponding empirical relational model have the ability to accurately simulate the boiling of the flow in helical tube; In nuclear boiling section at the working conditions of P=4–8 MPa, q = 200–350 kW/m2, Re = 66827–89103, The degree of gas-phase buildup near the inner wall surface of the spiral tube decreases with the increase of Re number, increases with the increase of heat flux and pressure, and the ratio of friction pressure drop to total pressure drop decreases with the increase of Re number, heat flux, and pressure by a maximum of 1.4 %, 4.26 %, and 17.35 %. This paper can provide a reference for adding new models and developing new solvers in the OpenFOAM to simulate boiling in helical tube flows.

Thermal transfer characteristics and thermoelasticity analysis of direct-steam-generation parabolic trough collector

Parabolic trough solar direct-steam-generation technology integrates clean energy with green carriers and is one of the favorable low-carbon technologies. However, the non-uniform heat flow distribution and flow stratification of collectors are susceptible to variations in climatic conditions, causing dry spots and raising the failure risk, and there are fewer studies on their influence laws based on three-dimensional two-fluid modeling. Therefore, the three-dimensional optical-thermal-stress-hydrodynamic model of the collector is built in this work based on Monte Carlo Ray Tracing method, finite volume method, finite element method and Eulerian two-fluid modeling method, and the model validation results agree with the experimental results. The impacts of direct solar radiation (I) and inlet pressures (Pin) on heat transfer performance and thermoelasticity characteristics of the three flow stages are analyzed. The results revealed that heat transfer performance in two-phase flow is better than single-phase flow at the same working conditions. The elevation of I effectively improves the Nusselt number and collector efficiency, but also dramatically raises the circumferential temperature difference (CTD) and thermal stresses. Especially, the CTD, maximum deformation, and maximum equivalent stresses in the superheated stage are as high as 54.37 K, 32.82 mm, and 38.23 MPa at Pin = 3 MPa and I = 1000 W m−2, similarly the maximum equivalent stress is also as high as 32.96 MPa in the stratified flow. The results serve as a reminder to pay particular attention to the superheated stage and the laminar flow, particularly at low Pin and high I. Furthermore, the lower the Pin, the higher the deformation and equivalent stresses in the stratified flow phase and the higher the risk of induced failure. Therefore, this implies that higher operating pressures are more appropriate for stratified flow, but this may be limited by high heat loss and low collector efficiency.

Treatment for the Singularity Problem in the Phase Segregation

In the Eulerian–Eulerian two-fluid model, comprising air and droplets, singularities often arise as the phase fraction of dispersed droplets approaches zero. The nonconservative momentum equations can address this issue, but it will lead to inaccurate solutions when encountering discontinuities. To tackle the singularity problem and ensure accurate solutions for the droplet field, a novel adaptive form of momentum equations is proposed. The adaptive form defaults to the conservative form and smoothly transitions to the phase-intensive form when the phase fraction falls below a critical value, specifically 1/1000 of the inlet. The LU-SGS algorithm, enhanced with the inner iteration step method, is employed for numerical solutions of the droplet field. Comparative analysis reveals that the discrepancy between the results obtained from the adaptive form and the conservative form is negligible, under 0.5‰. Notably, with larger Courant numbers, the conservative form diverges from waterless regions despite imposing the minimum phase fraction constraint. Conversely, the adaptive form consistently maintains a Courant number of five times or more, potentially exceeding a hundredfold in complex flows. Although the adaptive form moderately increases complexity and computational time for a single time step, the improvement of the maximum Courant number will bring significant computational efficiency advantages. Moreover, the adaptive form holds promise for application in various other multiphase flow scenarios.

Numerical simulation and analysis of initial plume discharge of deep-sea mining

Deep-sea mining involved environmental issues that urgently need to be addressed. The fine particle plume released from the surface vessel during deep-sea mining can impact the sea ecosystem, so investigating the characteristics of initial plume discharge is of significant importance for deep-sea mining systems. By numerical simulating the plume discharge process based on the two-fluid Eulerian model, this study explores the influence of initial discharge velocity, initial particle concentration, pipe diameter, and particle size on the surface plume discharge. The evolution mechanism of the plume is investigated through classic plume models involving the interaction of volume flux, momentum flux, buoyancy flux and the numerical simulation results exhibit a consistent trend with theoretical expectations. The results indicate that fine particle discharge velocity, discharge concentration, and pipe diameter are key influencing factors in plume evolution. The discharge velocity and pipe diameter primarily affect the evolution morphology of the plume through momentum flux and buoyancy flux. The discharge concentration mainly affects the plume's evolution through buoyancy flux.

Design and Optimization of Geometry of Liquid Feed Conveyor Pipes

The promotion and use of liquid feeding face the challenge of insufficiently stable delivery. This issue can be resolved, in part, by using the spiral flow produced by a spiral pipe (SPP). The aim of this study is to investigate how the structural characteristics of the spiral pipe affect the flow state of the liquid feed, and for this purpose, the computational fluid dynamics (CFD) technique has been employed and the liquid feed delivery process has been simulated by means of an Eulerian two-fluid model The results reveal a significant improvement in the slurry’s homogeneity as it traveled through a spiral pipe compared with a straight pipe (STP). The swirl number normally increased with the number, length, height, and angle of the spiral pipe’s guide vanes. The solid-phase distribution was more homogeneous when values of N = 1, L = 1D, H = 3/8R, and θ = 20° were used, respectively, and the COV within 10D downstream of the outlet of the spiral pipe was 3.902% smaller than that of the straight pipe. The results of this study can be used as a reference for the design of liquid feed-conveying pipes.

A Numerical Case Study of Particle Flow and Solar Radiation Transfer in a Compound Parabolic Concentrator (CPC) Photocatalytic Reactor for Hydrogen Production

Compound parabolic concentrator (CPC) photocatalytic reactors are commonly used for photocatalytic water splitting in hydrogen production. This study aimed to gain a better understanding of the physical processes in CPC photocatalytic reactors and provide theoretical support for their design, optimization, and operation. The analysis involved the ray tracing approach, Euler–Euler two-fluid model, and discrete ordinates method (DOM) to study solar radiation transfer and particle flow in the reactor. The distribution of solar radiation on the receiving tube’s surface after CPC concentration was obtained by conducting the ray tracing approach. This solar radiation distribution was then coupled into the Euler–Euler two-fluid model to solve for the natural convection flow field, the temperature field, and particle phase volume fraction distribution inside the receiving tube over a period of 120 s. Lastly, the discrete ordinates method (DOM) was used to analyze the transfer of radiation inside the receiving tube at different times, obtaining the distribution of local volume radiative power absorption (LVRPA) and the total radiative power absorption (TRPA) inside the tube. The results showed that the TRPA reached its maximum at 120 s, accounting for 66.61% of the incident solar UV radiation. According to the above results, it could be suggested that adopting an intermittent operation mode in CPC photocatalytic reactors is reasonable and efficient.

Study on characteristics of gas–liquid two-phase flow in pump as turbine using multiple-size group model

The multi-size group (MUSIG) model is employed in this paper to simulate the gas–liquid two-phase flow in pump as turbine (PAT) since the traditional Eulerian–Eulerian two-fluid model is unable to take into account the phenomena of breakup and coalescence of bubbles. First, the simulation of gas–liquid two-phase flow in a square column is compared with the experiment to verify the accuracy of the MUSIG model. Then, the results of gas–liquid two-phase flow in PAT simulated by the MUSIG model are compared with those by the conventional uniform bubble (UB) model and find that the MUSIG model is more favorable to capture the flow pattern at high gas content compared to the UB model. Based on the MUSIG model, the internal flow characteristics, pressure fluctuation, and bubble size distribution of the PAT are analyzed. The rotation of the blades breaks a part of big bubbles into small bubbles in the volute, resulting in a smaller diameter of the bubbles entering the impeller. As the gas content increases, the number and size of vortices in the impeller flow channel increase. The vortex is formed at locations where the gas phase distribution in the impeller flow channel is concentrated. The outlet of the impeller is more prone to bubble consolidation under high gas content conditions. In conclusion, the MUSIG model can well predict the complex flow characteristics of gas–liquid two-phase inside the PAT and identify the key influencing factors of energy acquisition, which can provide support for improving the performance of the PAT design.

Anisotropic turbulence of dense and dilute phases of particles in fluidized risers characterized using four-way coupled second-order moment method

The gas-particle flow in a fluidized bed is characterized as a “core-annulus” pattern with transient clusters moving along the circulating fluidized bed riser. These clusters exist as regions with a higher concentration of particles and are surrounded by dispersed particles at lower concentrations. In this study, fluid dynamics of both the clusters and dispersed particles suspended in the risers were investigated using the four-way coupled second-order moment method of the fluid–particle Eulerian–Eulerian two-fluid model. In the simulation, the anisotropic turbulence of either phase in the clusters and dispersed particles was studied in the risers. According to the turbulence intensities of both phases, the gas-particle flow in the fluidized riser was classified into six zones, the wall effect, cluster edge, cluster rising, cluster falling, and transient zone between the cluster rising and falling zones. As the volume fraction of the particles increased, the anisotropic ratios of the turbulence intensities in both phases increased in the dispersed zone and decreased in the cluster zone, respectively.

Thermo-hydraulic analysis of direct steam generation in a 500 m long row of parabolic trough solar collector using Eulerian two-fluid modeling approach

Direct steam generation (DSG) in the parabolic trough solar collectors is a potential alternative for economic and performance improvement of the solar thermal system. This process comprises the preheating, evaporation, and superheating of water/steam in the solar collectors. The modeling and simulation of the evaporation section are challenging because of the complex physics associated with the boiling phase change process. This work describes the Eulerian two-fluid modeling of the once-through mode of the DSG process in solar collectors. The interfacial interactions between phases have been modeled using the appropriate empirical correlations. The experimental data from the Spanish DISS test facility is used to validate the numerical model. Further, the 3-D thermal–hydraulic investigation of DSG in a 500 m long solar collectors' row has been performed for operating pressures of 60 bar and 100 bar; inlet mass flow rates of 0.4 kg/s and 0.6 kg/s; DNI of 750 W/m2 for the solar time at 12:00 h and 13:00 h. It has been observed that the maximum absorber temperature is reduced by 27 % at 60 bar and 20 % at 100 bar operating pressure when the inlet mass flow rate increases from 0.4 kg/s to 0.6 kg/s. Similarly, the maximum circumferential temperature difference reduces by 12 % and 14 %, respectively. Moreover, the fluid temperature, steam quality, absorber temperature distributions, fluid velocity, and pressure loss under the subjected boundary conditions have been summarized.

Study on transient flow behaviors in a three-stage helico-axial multiphase pump under slug flow condition from wellhead

Oilfield recovery often has extreme flow patterns of slug flow, and its gas volume fraction (GVF) still fluctuates strongly after being buffered by a homogenizer. After entering the multiphase pump, it causes transient fluctuations in pump performance, which challenges the stable operation of the multiphase pump. This paper simulates the flow field in a three-stage multiphase pump using the Euler–Euler two-fluid model and the shear stress transport k-omega (SST k−ω) turbulence model with the buffered slug flow as the boundary conditions. The results show that the differential pressure and torque of each impeller vary with the fluctuation of the inlet gas volume fraction (IGVF) and the maximum fluctuation rate reaches 36.48% and 32.97%, respectively; the maximum fluctuation rate of axial force and radial force is 1.02% and 51.18%, respectively, and the buffered slug flow has limited effect on the axial force. The main factor of pressure pulsation is the fluctuation of GVF flow and the interaction of static and dynamic. The main frequency in the impeller is the fluctuation frequency of the GVF or the diffuser blade frequency. The main frequency in the diffuser is the impeller blade frequency and its double frequency. The fluctuation frequency of the GVF is the secondary frequency, and the amplitude is relatively stable.

Numerical Simulation of Fluidization Behavior and Chemical Performance for Hydrochlorination of Silicon Tetrachloride in a Fluidized Bed Reactor

Exploring the fluidization behaviors and chemical performance in silicon tetrachloride (SiCl4) hydrochlorination processes within a fluidized bed reactor (FBR) poses significant challenges. In this study, we developed an Eulerian-granular model (EGM) by integrating the Eulerian–Eulerian two-fluid model with the kinetic theory of granular flow (KTGF). The effect of fluidization velocities on the flow regime, heat transfer, and chemical reaction performance were investigated. The applicability of the simulation method and the validity of the model were confirmed through comprehensive comparisons, including the simulated values of the maximum bed expansion height (Hmax) with theoretical values derived from empirical formulas and the simulated gas temperature profile with Hsu’s experimental data. The results indicate that the present EGM can be feasible to describe the variation of the flow regime within the FBR. An increase in bed voidage over time, coinciding with transitions in the flow regime, can be observed. Particularly noteworthy was the attainment of a more uniform distribution of SiCl4 under the bubbling fluidization state. Furthermore, the FBR possess high heat transfer characteristics, and the reaction gas can reach the set temperature of the bed after entering a small distance (about 10 mm). The presence of circulating bubbles within the FBR enhances the mixing uniformity of the SiCl4 reaction gas and silicon particles, particularly in the central and upper regions of the bed under the bubbling fluidization state. As a result, the predicted highest concentration of SiHCl3 was 13.08% and the conversion rate of SiCl4 was 28.97% under the bubbling fluidization state. Our results can provide a theoretical basis for further understanding of the hydrochlorination process of SiCl4 within the FBR.

Three-Dimensional Flow Simulation by a Hybrid Two-Phase Solver for the Assessment of Liquid/Gas Transport in a Volute-Type Centrifugal Pump with Twisted Blades

A hybrid two-phase flow solver is proposed, based on an Euler–Euler two-fluid model with continuous blending of a Volume-of-Fluid method when phase interfaces of coherent gas pockets are to be resolved. In a preceding study on a two-dimensional bladed research pump with reduced rotational speed, the transition from bubbly flow to coherent steady gas pockets observed in optical experiments with liquid/gas flow could be well captured by the hybrid solver. In the present study, the experiments and solver validation are extended to an industrial-scale centrifugal pump with twisted three-dimensional blades and elevated design rotational speed. The solver is combined with a population balance model, and a scale-adaptive turbulence model is employed. Compared to the two-dimensional bladed pump, the transition from agglomerated bubbles flow to attached gas pockets is shifted to larger gas loading, which is well captured by the simulation. The pump head drop with increasing gas load is also reproduced, showing the hybrid solver’s validity for realistic pump operation conditions.

Validation of the Eulerian–Eulerian Two-Fluid Method and the RPI Wall Partitioning Model Predictions in OpenFOAM with Respect to the Flow Boiling Characteristics within Conventional Tubes and Micro-Channels

Flow boiling within conventional, mini and micro-scale channels is encountered in a wide range of engineering applications such as nuclear reactors, steam engines and cooling of electronic devices. Due to the high complexity and importance of the boiling process, several numerical and experimental investigations have been conducted for the better understanding of the underpinned physics and heat transfer characteristics. One of the most widely used numerical approaches that can analyse such phenomena is the Eulerian–Eulerian two-fluid method in conjunction with the RPI model. However, according to the current state-of-the-art methods this modelling approach heavily relies on empirical closure relationships derived for conventional channels, limiting its applicability to mini- and micro-scale channels. The present paper aims to give further insights into the applicability of this modelling approach for non-conventional channels. For this purpose, a numerical investigation utilising the Eulerian–Eulerian two-fluid model and the RPI wall heat flux partitioning model in OpenFOAM 8.0 is conducted. Initially the parameters comprising the empirical closure relationships used in the RPI sub-models are tuned against the DEBORA experiments on conventional channels, through an extensive sensitivity analysis. In the second part of the investigation, numerical simulations against flow boiling experiments within micro-channels are performed, utilising the previously optimised and validated model setup. Furthermore the importance of including a bubble coalescence and break-up sub-model to capture parameters such as the radial velocity profiles, is also illustrated. However, when the optimal model setup, in conventional tubes, is used against micro-channel experiments, the need to develop new correlations from data obtained from mini and micro-scale channel studies, not from experimental data on conventional channels, is revealed.

State of the Art on Two-Phase Non-Miscible Liquid/Gas Flow Transport Analysis in Radial Centrifugal Pumps Part C: CFD Approaches with Emphasis on Improved Models

Predicting pump performance and ensuring operational reliability under two-phase conditions is a major goal of three-dimensional (3D) computational fluid dynamics (CFD) analysis of liquid/gas radial centrifugal pump flows. Hence, 3D CFD methods are increasingly applied to such flows in academia and industry. The CFD analysis of liquid/gas pump flows demands careful selection of sub-models from several fields in CFD, such as two-phase and turbulence modeling, as well as high-quality meshing of complex geometries. This paper presents an overview of current CFD simulation strategies, and recent progress in two-phase modeling is outlined. Particular focus is given to different approaches for dispersed bubbly flow and coherent gas accumulations. For dispersed bubbly flow regions, Euler–Euler Two-Fluid models are discussed, including population balance and bubble interaction models. For coherent gas pocket flow, essentially interface-capturing Volume-of-Fluid methods are applied. A hybrid model is suggested, i.e., a combination of an Euler–Euler Two-Fluid model with interface-capturing properties, predicting bubbly flow regimes as well as regimes with coherent gas pockets. The importance of considering scale-resolving turbulence models for highly-unsteady two-phase flow regions is emphasized.

Research on energy recovery and gas–liquid separation characteristics in diffuser of Helico-Axial Multiphase Pump

An Euler two-fluid model and a Shear Strain Transports (SST) turbulence model were used to study the gas–liquid flow law in a diffuser of a Helico-Axial Multiphase Pump by building a bedstand in this paper and studied energy recovery and gas–liquid separation characteristics of the diffuser in the Helico-Axial Multiphase Pump at different stages. The results show that the pressurization capacity of an impeller decreases gradually when the increase in IGVF (inlet gas volume fraction), and static pressure drops slightly in a dynamtic–static interface. Energy recovery characteristics are more complex at medium and high IGVF in the diffuser. The pressure gradient change perpendicular to the flow direction is the main factor causing two-phase separation on the back surface of the diffuser. The gas–liquid separation is mainly caused by the pressure gradient difference perpendicular to the flow direction on the working surface of the diffuser under the low IGVF, while the pressure gradient difference in the two directions is jointly influenced by the pressure gradient difference at medium and high IGVF.

Numerical simulation and multi-objective parameter optimization of gas−liquid flow in horizontal stirred tank

AbstractThe gas−liquid two-phase flow behavior in a stirred tank was numerically simulated using Euler−Euler two-fluid model, SST k−ω turbulence model and the multiple reference frame method. The results showed that among all the influencing factors, the rotation speed had the most significant effect on the stirred tank performance, followed by the damping board width. The parameter combination that can produce the most effective stirring was found through orthogonal test and matrix analysis, to be a paddle height of 950 mm, a paddle spacing of 1300 mm, a damping board width of 525 mm and a rotation speed of 123 r/min. Under this condition, the mixing time decreased from 31.620 to 25.845 s when the gas holdup and relative power consumption was basically unchanged.

Study on Performance and Operation Mechanism of a Separation Equipment for a PWR Steam Generator

Computational fluid dynamics (CFD) is adopted to calculate and analyze the performance and separation mechanism of a steam-water separation equipment for a pressurized water reactor (PWR) steam generator. The steam-water two-phase flow is simulated by the Euler two-fluid model, and several representative water droplet diameters are selected among 50 to 400 μm. The influence mechanism of water droplet diameter on the performance is investigated by analyzing the flow parameters such as phase volume fraction, velocity, and turbulent kinetic energy. The results show that the integrated calculation and analysis of the separation equipment can more truly reflect the flow state between the separators, improving the reliability of the performance prediction and mechanism analysis. With the increase in water droplet diameter, the separation efficiency of the separation equipment and each separator gradually increases, the outlet wetness gradually decreases, and the pressure loss first decreases and then stabilizes. When 400 μm is taken as the characteristic value of the actual droplet diameter distribution at the inlet of the separation equipment, the performance prediction is more accurate, the pressure loss of each separator is relatively close, and the pressure loss of the primary separator is less affected by the droplet diameter and smaller than that of the swirl-vane primary separator, which is conducive to achieving a higher circulation ratio (CR). Re-entrainment occurs at the perforations of the primary separator and the outlet of the secondary separator, and the corresponding structure is suggested to be optimized to further improve separation efficiency of the separation equipment.