Eulerian Multiphase Model Research Articles

Boiling critical characteristics in narrow rectangular channel under local heat flux concentration conditions

For the establishment of predicting method of local concentrated critical heat flux (CHF) in narrow rectangular channels, and also technical support for the preparation of long-life and high-performance dispersive plate fuel, this work simulates Dry-out type CHF under local concentration of heat flux condition by using Eulerian multiphase model and Enhanced near-wall treatment. The distribution of near-wall temperature and void fraction under different heat flux was calculated by Computational Fluid Dynamics (CFD) method. Dry-out CHF was predicted based on highly and quickly wall temperature rise. The influence of system pressure, mass flow rate and inlet subcooling degree were discussed on Dry-out CHF. Compared with uniform heating, the predicted average heat flux on CHF is lower under local heat flux concentration, and location of CHF is related to the position of heat flux concentration area. This work’s research method in Ansys Fluent could be applied to forecast Dry-out CHF in narrow rectangular channel under local concentration of heat flux condition.

Separation Time of Aluminothermic Reduction Products for Sustainable Silicon Production

Background This work was carried out within the framework of the SisAl Pilot project, which is devoted to the environmentally friendly production of silicon. This new method relies on the aluminothermic reduction of quartz in slag, offering a more sustainable alternative to the traditional reduction of silica with carbon in submerged arc furnaces. Methods The process takes place in a rotary kiln producing silicon (Si) and alumina slag (actually, a CaO – Al2O3 slag), which must be separated at the end to extract the silicon. This separation process is analyzed through mathematical modelling and numerical simulation, as it is of industrial interest to know how much time it takes for Si and CaO – Al2O3 slag to separate once the process has ended. Generally, a multiphase flow model is used to estimate the separation time of the two components once aluminothermic reduction has ended. Results Several scenarios are considered for the numerical simulation of the separation time, namely different initial configurations and material properties of both fluids are covered. Moreover, the separation times obtained with two distinct multiphase flow models -VOF (volume of fluid) and Eulerian- are compared. Conclusions The separation times resulting from simulations using the multiphase Eulerian model are more realistic compared to those from the VOF model, which clearly tends to underestimate separation times. Furthermore, apart from the selected multiphase flow model, the density difference between silicon and alumina slag plays a critical role in determining the separation time.

Investigation of the steady state subcooled boiling regime in the hot subchannel of a VVER-1200 reactor core: A CFD analysis

A Computational Fluid Dynamics (CFD) analysis is carried out on a three-dimensional subchannel representing the most intensive fuel assembly to simulate the thermal-hydraulic performance of the VVER-1200 hot channel under steady-state operation. It is found that, subcooled boiling is predicted for both the rated and the conservative operational parameters with the intensity of bubble generation found to be higher for the conservative scenario compared with the rated one. The predicted boiling phenomenon at the cladding surface may result in the formation of deposits, and pits, and may impair the strength of the fuel elements, and increase the inhomogeneity in fuel burnup. Therefore; a thorough investigation of the predicted boiling regime is required to shed light on the development of this phenomenon in a typical reactor subchannel using CFD tools. The CFD work conducted in this work is based on the Eulerian multiphase model in ANSYS in conjunction with the RPI wall boiling model. The developed model has been validated against other one-dimensional models found in the literature. The variation of mass-averaged quantities (across the channel) along the subchannel generally agrees with the 1D models, which builds confidence in the modeling approach. Contours showing the spatial variations of temperatures, vapor void ratio, as well as heat fluxes are presented. Profiles of the different components of heat flux during boiling are presented. It has been found that the heat flux variations during boiling pass through three distinct regimes. In the first, a steady increase in quenching and evaporation heat flux is observed, while convective heat flux declines. In the second regime, the quenching and evaporation heat fluxes plateau with a slight decrease, while the convective heat flux becomes zero. This signifies that the outer clad surface is largely covered with vapor bubbles and the only heat transfer mechanisms are due to quenching and evaporation. During the last regime, quenching and evaporation heat fluxes decline due to the decline of the imposed heat flux at the clad surface, and hence convective heat transfer starts to increase. In addition, profiles of the mass-averaged coolant temperature, void fraction, and outer clad surface temperatures along the hot element underrated and conservative operating conditions are also generated.

COMPARATIVE STUDY USING CFD OF COUNTER-CURRENT AND CO-CURRENT HYDROTREATING REACTORS USING JATROPHA CURCAS L VEGETABLE OIL

In this work, mathematical modeling and CFD simulation of two countercurrent and cocurrent hydrotreatment reactors were carried out, validating the results with a drained bed reactor (TBR), a commercial CoMo/γ-Al2O3 catalyst was used, the material the raw material was Jatropha Curcas L vegetable oil. The operating conditions were temperature 380 ° C, pressure 8 MPag. The kinetic model that was used considered 13 reactions that involve processes of decarboxylation, decarbonization, hydrodeoxygenation and hydrocracking reactions for triolein and tristearin triglycerides. The CFD simulation was carried out in Fluent 18.2 in a transient state and in 3D, considering the standard κ - ε turbulence models, Eulerian multiphase model and porous medium model, it was shown that the countercurrent reactor has less pressure drop than the countercurrent, the conversion the countercurrent reactor has a greater conversion of reactants of 99%, the generation of products from the countercurrent reactor has higher concentrations than the cocurrent reactor, this is because it has more contact areas between phases in the reactor.

Simulation and modelling approach for bubblers effect into molten glass tank

The usage of air bubblers plays an important role in the glass-making industrial process because it enhances the global heat transfer efficiency and especially the uniformity and quality of the finished products. However, glass manufacturers rely on field practice to run their plants, due to the extreme difficulty of conducting experimental investigations in melting tanks. CFD analysis represents a powerful tool to optimize operating parameters and positioning of bubblers and other components, not only in existing plants, but also in the design of new furnaces.In the present paper, the behaviour of bubble columns in highly viscous liquids at high temperature was analysed using the Eulerian multiphase model. The macroscopic effect of the column on the surrounding fluid was translated in a locally momentum source term that was introduced in the single-phase CFD model developed in this study. This solution approximates the multiphase nature of the problem in a reliable way and it is of fast integration in comprehensive models of furnaces.A clear methodology to determine the diameter of the bubbles and the velocity of the bubble chain in the buoyancy source term calculus are presented and analysed in detail. In addition, a validation process based on the comparison with other theoretical and empirical studies on the subject was carried out in detail: it includes the evaluation of the bubble chains properties and effects by varying the liquid viscosity and the inlet gas flow, that is the real operational parameter in industry. Moreover, the effects of the variable height of the bubblers were investigated using the results of a single-phase model of a real industrial glass tank.The analysis of the obtained results shows that the model and the calculation methodologies followed in this work can be effectively applied in the dimensioning process of industrial glass tanks or to optimize existing plants.

Numerical Investigation of Film Formation Characteristics and Mechanisms through Airless Spraying on Spherical Surfaces

This paper focuses on key engineering issues, particularly the overall turbulent transport of paint spray and coating film distribution characteristics, in the process of airless spraying film formation. By deeply considering the geometric features of spherical surfaces and their impact on the near-wall region of the flow field, an airless spraying film formation model consisting of the Eulerian multiphase model, the realizable k–ε turbulence model, and the Eulerian Wall Film model was established. Through numerical simulations of static spraying on the inner and outer walls of spherical surfaces with different radii, the influence of geometric features on the spray flow field and film formation characteristics on spherical surfaces was investigated. Subsequently, based on numerical simulations of dynamic spraying on different nozzle trajectories, the film formation characteristics were analyzed, and the optimal spray trajectory planning method was determined. Additionally, this study examined the coating distribution characteristics during dynamic spraying on spherical surfaces with varying geometric dimensions. Finally, a kind of chlorinated rubber anti-corrosion primer was chosen to carry out spraying experiments, which validated that the airless spray coating model and the corresponding numerical simulation methods established in this paper were reasonable and feasible for investigating the film formation characteristics on spherical surfaces. This work is expected to further promote the application of airless spray techniques in machinery, automotive, shipbuilding, and aviation industries.

A four-way coupled numerical investigation of draft tube baffled crystallizer

In the present paper, the liquid–solid two-phase turbulent flow in a Draft Tube Baffled crystallizer has been simulated using Computational Fluid Dynamics. In this respect, multiphase Eulerian model along with population balance equations were applied. To implement four-way coupling, aggregation and breakage were considered. The RNG k-ε and RSM turbulence models were employed to conduct numerical simulation of two phase turbulent flow. Results demonstrated that applying RNG k-ε and RSM turbulence models, a significant difference in axial velocity profiles along the x-axis is observed, while those along the z-axis exhibit less difference. Moreover, a significant difference in volume fraction between the two models was observed which mostly concerns the region within the draft tube and the distance between the baffle and crystallizer wall. Furthermore, changing the propeller speed from 165 to 495 rpm, the speed of 330 rpm showed to be optimal in terms of particles residence time. The results also showed that a rise in impeller speed is one of the major contributors to mass exchange enhancement between the liquid and the solid phases. Accordingly, as the impeller speed rises, the rate of mass exchange increases from 9.92 kg/h for 165 rpm to 29.07 kg/h for 495 rpm.

A numerical analysis of pressure characteristics in the deflector jet pilot stage valve with an innovative deflector deflection

Electric-hydraulic servo-valves are extensively used in the aerospace, mechanical, and aerodynamics industries to control missile wings or airplanes precisely. Aiming to reduce undesired flow phenomena inside the deflector jet pilot valve, innovative deflections of deflector are proposed in this paper. A numerical analysis is performed using STAR CCM + to investigate the pressure and flow characteristics inside the pilot stage of deflector jet servo-valve. For observing the pressure, cavitation and flow characteristics, the Eulerian multi-phase model, VOF phase interaction, and realizable k−ε model for the turbulent flow are used during numerical simulations. The supply and outlet pressure are kept at 24 MPa and 1 MPa, respectively. To verify the calculated numerical results for turbulent flows, the velocity distribution to the V-groove exit of the deflector jet pilot stage is calculated and discussed with the theoretical results. The numerically calculated results show good agreement with published analytical results. The result shows that by the innovative rotation of the deflector both in clockwise and anti-clockwise directions, significant pressure in the receivers is obtained than traditionally moving deflector to the left and right for the same supply pressure. Moreover, when the deflector is positioned clockwise or anti-clockwise by 5°, less cavitation is observed than in the traditional model. The key finding of this paper shows that innovative structural optimization of the amplifier disk and deflector is of utmost importance.

A study on the scale dependence of mixing indices for Eulerian multiphase models

AbstractMixing can vary based on the scale at which the system is observed, and a mixing index that can capture the features at different length scales is desirable. In this article, we analyze the scale dependence of the mixing indices developed for Eulerian multiphase models. Relevant length scales are distinguished by filtering solid fraction fields. The scale‐dependence study is first done on manufactured fields of solid fraction to assess the performance of the mixing indices. The study is extended to a two‐dimensional CFD simulation of the segregation of a bidisperse gas–solid mixture. The local mixing index performs well in capturing the spatial variation of mixing at different scales. The scale dependence of two global mixing indices is considered in the study, where the state of mixing is defined based on statistical measures. We demonstrate that the choice of measures influences the sensitivity of mixing indices to mixing at different scales.

Analysis of numerical simulations and semi-empirical models on distribution characteristics of wind-driven rain on low-rise building facades

Wind-driven rain (WDR) is a significant contributor to indoor moisture in buildings, directly impacting the thermal and moisture performance of facades. Previous research on WDR in China focused on a limited number of low-rise pilot buildings, whose materials, shapes, and environmental settings are not entirely representative of typical applications. Aim to improve the accuracy of WDR predictions on low-rise building facades, there is a need for assessing different WDR calculation methods under various rain events. The paper presented high-resolution WDR measurements from a low-rise concrete building in Chongqing to investigate the distribution of WDR on building facades under local meteorological conditions. The study compared the performance of numerical simulations and two semi-empirical models with different meteorological data averaging techniques. The results indicated that Computational Fluid Dynamics (CFD) simulations using the Eulerian multiphase (EM) model more closely matched the actual catch ratio across various locations and the WDR amount across the facade, with errors ranging between 10%-25 % and 2%–23 %, respectively. Furthermore, the ISO model with weighted averaging (WA) technique outperformed others in estimating catch ratios at various locations and the WDR amount across the facade, particularly when estimating the midline catch ratio. When considering both cumuliform and stratiform rainfall, the arithmetic averaging (AA) technique was a viable method for the ASHRAE model to forecast WDR. The ISO model's predictions corresponded to 54%–81 % of the field measurements, while the ASHRAE model's estimates varied more widely, ranging from 33 % to 229 % of the measured values.

Nanofluid heat transfer enhancement in microchannels: Investigating phases interactions using multiphase Eulerian model

This study employs a robust multiphase Eulerian model to mimic heat transfer enhancement using nanofluids in a circular microchannel. Unlike the Eulerian models reported in the literature, the current model incorporates phase interactions, and its accuracy is significantly improved by integrating collision viscosity, kinetic viscosity, and frictional viscosity. Comparative analysis against other models like mixture and discrete phase models demonstrates superior performance of the current model, particularly for solid particle volume fractions exceeding 1 %. The model evaluates water-based nanofluids (Ag NPs, MgO, ZnO, Al2O3, ZrO2, SiO2) in circular microchannels. Ag NPs/water excels at low volume fractions and high Reynolds numbers, while MgO/water performs better at higher volume fractions. Moreover, the analysis of the Euler number indicates a decreasing trend with increasing Reynolds number across all nanofluids. However, no notable variation in the Euler number is observed when maintaining constant volume fraction and Reynolds number. Ultimately, the model is applied to obtain bulk fluid properties, such as viscosity and thermal conductivity, after suspending the nanoparticles. Subsequently, these properties were incorporated into the single-phase model. Utilizing these derived bulk properties was found to substantially enhance the accuracy of the single-phase model, demonstrating its reliability by yielding results within 13.52 % of experimental data.

Numerical modeling and analysis of nanofluids subcooled boiling in a horizontal circular tube

Subcooled flow boiling, characterized by large heat transfer coefficient (HTC), is widely encountered and of great significance in energy industry. To enhance its thermal efficiency for compact applications, nanofluids are employed by improving the thermophysical properties. This article numerically investigates nanofluids subcooled boiling in a horizontal tube under wide-range, multi-factor impacts, including Reynolds number of 40,000–50,000, nanoparticle type, that is, Al2O3, TiO2, Cu, and volume fraction of 1%–5%. The thermal equilibrium assumption and Eulerian multiphase model are utilized after numerical validations. Results indicate that the vapor volume fraction augments along the tube while nanoparticles reduce the vapor production during boiling. As for thermal and flow performance, nanofluids can enhance the HTC at the expense of a rising pressure drop. In the case of Al2O3/Water nanofluid, the maximum of HTC increases by 10.56%. In contrast, the pressure drop increases by 2.1 times when the Al2O3 concentration changes from 1% to 5%. The performance evaluation criterion (PEC) in this article always exceeds 1 for nanofluids, demonstrating that the heat transfer enhancement outweighs the pressure drop penalty, and the Al2O3/Water nanofluid show superior performance with PEC achieving 1.1. This work can provide support for a profound understanding and utilization of nanofluids subcooled boiling.

CFD MODELING AND SIMULATION OF A COUNTERCURRENT REACTOR OF HIDROTREATMENT PROCESS WITH JATROPHA CURCAS L. VEGETABLE OIL

In this work, a microscale countercurrent reactor was analyzed and simulated in CFD, and the results were compared with a drained bed reactor (TBR) which is held in the CMP+L research center. The importance of this study is to find the mathematical model of the countercurrent reactor to produce clean fuels from Jatropha Curcas L. vegetable oil and in the future scale it to an industrial level. For the hydrotreatment process, a commercial CoMo/γ-Al2O3 catalyst was used, and Jatropha Curcas L vegetable oil was used as raw material. The operating conditions that were considered for the CFD simulation were temperature 380 °C, pressure 8 MPag, LHSV 8.0 h−1. The reactor model considers a reaction mechanism 13 hydrocracking reactions of triglycerides towards renewable fuels. The CFD simulation was carried out in Fluent 18.2 in a transient state and in 3 dimensions, considering the standard k-ϵ turbulence model, the Eulerian multiphase model and the porous medium model, obtaining results very similar to the experimental ones, with a conversion of triglycerides of 0.996% and the retention time of the liquid temperature was 169 seconds and in the simulation is 200 seconds, the molar concentration profiles of the products were obtained whereby this model can be applied to the industrial scale.

Hole cleaning evaluation and installation spacing optimization of cuttings bed remover in extended-reach drilling

In extended-reach or long-horizontal drilling, cuttings usually deposit at the bottom of the annulus. Once cuttings accumulate to a certain thickness, complex problems such as excessive torque and drag, tubing buckling, and pipe stuck probably occur, which results in a lot of non-productive time and remedial operations. Cuttings bed remover can efficiently destroy deposited cuttings in time through hydraulic and mechanical stirring effects. This paper aims to build a method for hole cleaning evaluation and installation spacing optimization of cuttings bed remover to improve the wellbore cleaning effect. Firstly, a Computational Fluid Dynamics approach with Eulerian–Eulerian multiphase model was utilized to investigate the mechanism of cuttings transportation, and a new type of cuttings bed remover was designed. Next, an evaluation method of hole cleaning effect of remover was established. After that, the effects of several drilling parameters on hole cleaning including flow rate of drilling fluid, rotational speed of drillpipe, rate of penetration, wellbore size, rheological property of drilling fluid, and remover eccentricity on the performance of cuttings bed remover were investigated. The results demonstrate that the new type of remover with streamline blade performs better than conventional removers. The efficiency of hole cleaning is greatly improved by increasing the rotational speed of drillpipe, flow rate of drilling fluid, remover eccentricity, and 6 rpm Fann dial reading for drilling fluid. While higher rate of penetration and large wellbore size result in worse hole cleaning. These findings can serve as an important guide for the structure optimization design of cuttings bed remover and installation spacing of removers.

The Impact of Marangoni and Buoyancy Convections on Flow and Segregation Patterns during the Solidification of Fe-0.82wt%C Steel.

Due to the high computational costs of the Eulerian multiphase model, which solves the conservation equations for each considered phase, a two-phase mixture model is proposed to reduce these costs in the current study. Only one single equation for each the momentum and enthalpy equations has to be solved for the mixture phase. The Navier-Stokes and energy equations were solved using the 3D finite volume method. The model was used to simulate the liquid-solid phase transformation of a Fe-0.82wt%C steel alloy under the effect of both thermocapillary and buoyancy convections. The alloy was cooled in a rectangular ingot (100 × 100 × 10 mm3) from the bottom cold surface to the top hot free surface by applying a heat transfer coefficient of h = 600 W/m2/K, which allows for heat exchange with the outer medium. The purpose of this work is to study the effect of the surface tension on the flow and segregation patterns. The results before solidification show that Marangoni flow was formed at the free surface of the molten alloy, extending into the liquid depth and creating polygonized hexagonal patterns. The size and the number of these hexagons were found to be dependent on the Marangoni number, where the number of convective cells increases with the increase in the Marangoni number. During solidification, the solid front grew in a concave morphology, as the centers of the cells were hotter; a macro-segregation pattern with hexagonal cells was formed, which was analogous to the hexagonal flow cells generated by the Marangoni effect. After full solidification, the segregation was found to be in perfect hexagonal shapes with a strong compositional variation at the free surface. This study illuminates the crucial role of surface-tension-driven Marangoni flow in producing hexagonal patterns before and during the solidification process and provides valuable insights into the complex interplay between the Marangoni flow, buoyancy convection, and solidification phenomena.

Mixed Convection in a Lid-Driven Cavity Filled with Nanofluids Using Single- and Two-Phase Eulerian Modeling Methods

The numerical simulation of the classical lid-driven cavity problem has been carried out to investigate the suitability of two-phase flow modeling techniques for nanofluids in computational fluid dynamics. The nanofluid investigated comprises water as base fluid and Al2O3 nanoparticles. Three types of the Eulerian-multiphase models, including the Eulerian, mixture, and volume of fluid (VOF) were compared with the single-phase model. The model equations were solved using ANSYS Fluent software for the nanoparticle volume fraction, the Richardson and Reynolds numbers in the range 0 ≤ ø ≤ 0.10, 10−4 ≤ Ri ≤ 102, and 1 ≤ Re ≤ 1000, respectively at a fixed Grashof number, Gr = 100. The results were compared with that of single-phase nanofluid modeling. There were similarities in the flow structure and temperature distribution for the single-phase and multi-phase methods when the convection is natural and mixed. However, the Nusselt number computed by the mixture and Eulerian models is higher than that of the single-phase and VOF models under the forced convection regime, with the percentage deviation from that of the single-phase as high as 10%. So, the three multiphase models are suitable for nanofluid convection problems and give results comparable to the single-phase model, especially under the natural and mixed convection regimes.

Enhancing Efficiency in Alkaline Electrolysis Cells: Optimizing Flow Channels through Multiphase Computational Fluid Dynamics Modeling

The efficient operation of alkaline water electrolysis cells hinges upon understanding and optimizing gas–liquid flow dynamics. Achieving uniform flow patterns is crucial to minimize stagnant regions, prevent gas bubble accumulation, and establish optimal conditions for electrochemical reactions. This study employed a comprehensive, three-dimensional computational fluid dynamics Euler–Euler multiphase model, based on a geometric representation of an alkaline electrolytic cell. The electrochemical model, responsible for producing hydrogen and oxygen at the cathode and anode during water electrolysis, is integrated into the flow model by introducing mass source terms within the user-defined function. The membrane positioned between the flow channels employs a porous medium model to selectively permit specific components to pass through while restricting others. To validate the accuracy of the model, comparisons were made with measured data available in the literature. We obtained an optimization design method for the channel structure; the three-inlet model demonstrated improved speed and temperature uniformity, with a 22% reduction in the hydrogen concentration at the outlet compared to the single-inlet model. This resulted in the optimization of gas emission efficiency. As the radius of the spherical convex structure increased, the influence of the spherical convex structure on the electrolyte intensified, resulting in enhanced flow uniformity within the flow field. This study may help provide recommendations for designing and optimizing flow channels to enhance the efficiency of alkaline water electrolysis cells.

Experimental and CFD modeling of a progressive cavity pump (PCP) using overset unstructured mesh part 2: Two-phase flow.

In oil well operations, accurate modeling of two-phase liquid-gas flow in Progressive Cavity Pumps (PCPs) is vital. This study aimed to comprehensively analyze such flow in a metal-metal PCP using computational fluid dynamics (CFD) simulations validated by experimental data. The methodology applied to the High-Resolution Interface Capturing (HRIC) scheme is to compute the convective transport of phase fractions, yielding insights into the intricate dynamics of these flows. Validation was achieved using laboratory-acquired data and comparisons with extant publications. The findings confirmed the CFD simulations' alignment with field data for two-phase liquid-gas flows. Gas compression and effective viscosity gradient were crucial for accurate pump performance prediction. An investigation into the “gas seal” phenomenon using the Eulerian Multiphase Model elucidated the distinct separation of gas and liquid phases. The influence of the gas volume fraction on pump metrics like torque, power, and efficiency was explored, with CFD predictions exhibiting less than 8% error. The study underscores the pivotal role of CFD tools in predicting pump behavior under diverse conditions. It advances our understanding of two-phase flows in oil wells, especially regarding the gas's impact on pump components. This research offers the oil industry a refined modeling tool, enhancing the comprehension of oil well pump dynamics.

Multi-phase simulation for understanding morphodynamics of gravel beaches

This paper presents the use of an Eulerian–Eulerian multi-phase model to examine sediment transport over a gravel beach under regular waves. A previously published full-scale experiment is reproduced numerically; the simulated wave deformation, flow velocity, pore pressure, and morphological evolution are consistent with measurements. The multi-phase model can produce berm formation for smaller waves and beach erosion for larger waves as observation in previous field studies. The sensitivity analysis suggests that the nonlinear component of drag has significant effect on the berm formation through infiltration and exfiltration. The two simulated forces applied on the sediment (drag and buoyancy) are examined. The drag is the main force directly for sediment transport; therefore the sediment transport rate has high correlation with depth-averaged flow velocity. The buoyancy that is caused by plunging flow impacting beach face can push the sediment landward in the bore front, where the flow acceleration has its peak. The flow acceleration is considered in some previous sediment transport models empirically for simulating morphological evolution of gravel beach under waves. The buoyancy links the flow acceleration and sediment transport rate in the bore front.

Distribution characteristics of non-Newtonian fluid swirling flow field in a vane-type separator

Most of the fluids encountered in the oil and gas exploitation process exhibit non-Newtonian fluid characteristics, which presents new challenges for the treatment of produced liquid. In this paper, the Eulerian multiphase model and the power law model were coupled to simulate the distribution characteristics of non-Newtonian fluid swirling flow fields in a vane-type separator. Larger oil droplets are able to migrate to the pipe center at relatively weak vortex intensities, which helps to accelerate the formation of the oil core. Due to the rapid decay of the vortex strength, the tangential velocity of the oil droplets drops more rapidly than that of the axial component, thereby reducing the axial energy loss. As the volume fractions of inlet oil increase, the oil core becomes more pronounced, but the convergence of the oil phase gets worse. During the migration, the interaction between dense oil droplets increases the viscosity of the non-Newtonian fluid and decreases the tangential velocity, leading to a maximum apparent viscosity at the center of the pipe. A higher vortex intensity tends to stabilize the vortex core, whilst higher flow velocities, which increases rotational velocities at the exit of the deflection section, deforms the vortex more severely. Moreover, higher inlet flow velocities contribute to better convergence of the oil cores. All these factors are important to better understand the smooth characteristics of non-Newtonian fluids and to provide a theoretical basis for future design and optimization of efficient separators.