Eulerian Two-fluid Model Research Articles

Unified Gas-Kinetic Wave-Particle Methods VI: Disperse Dilute Gas-Particle Multiphase Flow

In this paper, a unified gas-kinetic wave-particle scheme (UGKWP) for the disperse dilute gas-particle multiphase flow is proposed. The gas phase is always in the hydrodynamic regime. However, the particle phase covers different flow regimes from particle trajectory crossing to the hydrodynamic wave interaction with the variation of local particle phase Knudsen number. The UGKWP is an appropriate method for the capturing of the multiscale transport mechanism in the particle phase through its coupled wave-particle formulation. In the regime with intensive particle collision, the evolution of solid particle will be followed by the analytic wave with quasi-equilibrium distribution; while in the rarefied regime the non-equilibrium particle phase will be captured through particle tracking and collision, which plays a decisive role in recovering particle trajectory crossing behavior. The gas-kinetic scheme (GKS) is employed for the simulation of gas flow. In the highly collision regime for the particles, no particles will be sampled in UGKWP and the wave formulation for solid particle with the hydrodynamic gas phase will reduce the system to the two-fluid Eulerian model. On the other hand, in the collisionless regime for the solid particle, the free transport of solid particle will be followed in UGKWP, and coupled system will return to the Eulerian-Lagrangian formulation for the gas and particle. The scheme will be tested for in all flow regimes, which include the non-equilibrium particle trajectory crossing, the particle concentration under different Knudsen number, and the dispersion of particle flow with the variation of Stokes number. A experiment of shock-induced particle bed fluidization is simulated and the results are compared with experimental measurements. These numerical solutions validate suitability of the proposed scheme for the simulation of gas-particle multiphase flow.

Effect of transient concentrated solar flux profile on the absorber surface for direct steam generation in the parabolic trough solar collector

The parabolic trough solar collector with Direct Steam Generation (DSG) has the potential to bring down the electricity cost. The viability of DSG technology is proved using various experimental demonstrations (e.g., DISS test facility) and running commercial-scale power plants (Thai Solar One). However, the DSG technology is in the nascent stage and needs improvement in the solar collector's components and control mechanism. The thermo-hydrodynamic instability induced in the absorber tube due to the non-uniform concentrated solar flux and flow boiling. This study investigates the effects of transient solar flux profiles on the thermal-hydraulics of flow boiling in the DSG process using CFD software ANSYS Fluent. The Eulerian two-fluid model is developed using conservation equations, turbulence model, and phase change model. The concentrated solar flux profiles are considered corresponding to various times of the day from 12:00 h (solar noon) to 17:00 h at an interval of 1 h. The three dimensional (3-D) numerical investigations are performed for DNI of 750 W/m2 and 1000 W/m2; operating pressures 60 bar and 100 bar; mass flow rates 0.4 kg/s and 0.6 kg/s. The flow regimes under the considered boundary conditions are observed as stratified flow. The vapor volume fractions at the absorber outlet exist between 0.30 and 0.45 for DNI of 750 W/m2 and 0.35 to 0.50 for DNI of 1000 W/m2. The absorber surface temperature has been calculated for operation at various times of the day, and it stands between 550 K and 656 K. Further, the circumferential temperature distributions and temperature contours have been plotted for various operating conditions. The adopted multiphase model shows very good performance and is useful for designing and optimizing solar collectors for DSG.

Influence of proppant physical properties on sand accumulation in hydraulic fractures

The proppant accumulation form in fractures is related to the formation conductivity after fracture closure, also closely related to the production rate of oil/gas wells. In order to investigate the influence of proppant physical properties on sand accumulation in fractures, a particle–fluid coupling flow model is established based on the Euler two-fluid model. Geometric parameters of a fracture in tight oil wells are approximately scaled in equal proportion as the physical model, which is solved by the finite volume method. And the model accuracy is verified by comparing with the physical experimental simulation in the literature. Results show that the higher proppant concentration corresponds to the faster particle sedimentation rate, and the greater sand embankment accumulation as well. However, the fluid viscosity will increase, inhibiting proppant migration to the deep part of the fracture. Reducing proppant density and particle size will enhance the fluidization ability of particles, which is conducive to the migration to the deep fracture at the initial stage of pumping. But, it is not beneficial to have a desirable accumulation state in the middle and later pumping stage, so it is difficult to obtain a higher comprehensive equilibrium height.

Numerical investigation of the critical heat flux in a 5 × 5 rod bundle with multi-grid

To improve the heat transfer efficiency of the reactor fuel assembly, it is necessary to accurately calculate the two-phase flow boiling characteristics and the critical heat flux (CHF) in the fuel assembly. In this paper, a Eulerian two-fluid model combined with the extended wall boiling model was used to numerically simulate the 5 × 5 fuel rod bundle with spacer grids (four sets of mixing vane grids and four sets of simple support grids without mixing vanes). We calculated and analyzed 11 experimental conditions under different pressure, inlet temperature, and mass flux. After comparing the CHF and the location of departure from the nucleate boiling obtained by the numerical simulation with the experimental results, we confirmed the reliability of computational fluid dynamic analysis for the prediction of the CHF of the rod bundle and the boiling characteristics of the two-phase flow. Subsequently, we analyzed the influence of the spacer grid and mixing vanes on the void fraction, liquid temperature, and secondary flow distribution. The research in this article provides theoretical support for the design of fuel assemblies.

Computational fluid dynamics modeling of slurry flow in horizontal pipes: Effect of specularity coefficient on hydraulic gradient

The specularity coefficient is an important input parameter in the Johnson and Jackson boundary conditions. Thus far, research on this parameter has been lacking in the field of slurry flow simulations. In this study, the integration of the Eulerian–Eulerian two-fluid model with kinetic theory of granular flow and Johnson and Jackson boundary conditions is used to simulate the transportation of sand–water slurry in horizontal pipelines. A range of flow conditions, including high and low velocities, high and low concentrations, coarse and fine particles, and large and small pipes, is considered to study the effect of the specularity coefficient on the predicted hydraulic gradient. Then, the simulation results are compared with previous experimental measurements to determine the appropriate values of the specularity coefficient. The hydraulic gradient is found to be positively correlated with the specularity coefficient; in addition, it is more sensitive to the specularity coefficient when the specularity coefficient is less than 0.1. The appropriate value of the specularity coefficient decreases with the flow velocity and increases with the solid volume fraction. In the range of flow conditions considered, the findings may be used as a reference for future simulations in the research field of slurry transport.

Numerical simulation of micro-crack leakage on steam generator heat transfer tube

The pressure relief rate and loss rate of coolant, which affect largely safety of fission reactor systems, are determined by the flashing process inside cracked passages. Information about flashing phenomenon is of great significance for the leakage online monitoring system of SG (Steam Generator), which ensures the normal operation of SG and safety of the reactor system during early stage of tube rupture accidents. In this research, flashing flow inside a thin micro-crack in heat transfer tube of SG has been studied using ANSYS-FLUENT. The classic cavitation model and evaporation–condensation model, in combination with both the mixture two-phase flow model and Eulerian two-fluid model, are adopted to simulate flashing phenomenon. The real geometry and operation conditions of AP1000 nuclear system are adopted to reflect the reality leakage process in SG. Two types of micro-cracks including axial crack and circumferential crack, which both could happen in the reality operations, are considered. The CFD (Computational Fluid Dynamic) results gained from this research have been compared with test data, and good agreement is demonstrated. The results show that the evaporation–condensation model under Eulerian two-fluid model framework behaves superior to the classic cavitation models in simulating the flashing phenomenon after evaluating accuracy of leakage rate and rationality of thermal hydraulic parameters distribution. In addition, two-phase choking flow phenomenon is obtained by decreasing backpressure of cracked tubes. The simulation in this research reveals the flashing process in short and micro-crack and the results could be good reference for leakage prediction of SG under LBB (Leak Before Break) operations to improve operation performance of SG and safety of the whole nuclear power system.

Numerical simulation of bubble columns: LES turbulence model and interphase forces blending approach

In this study the large eddy simulation (LES) turbulence approach was adopted to simulate bubble columns in a wide range of gas velocity and operating conditions, in order to obtain a general model capable of simulating with satisfactory accuracy and moderate computational resources most industrial cases.The model used to carry out the numerical simulations stems on the Eulerian–Eulerian two-fluid model. A particular feature of the model is the implementation of a blending approach, which is adopted to describe the phase inversion at the surface of the gas–liquid mixture.An extended investigation of the main LES turbulence models was conducted at high gas velocity to find the most suitable one for the investigated test cases: the Smagorinsky model accounting also for the bubble induced turbulence provided the most notable results in a wide range of operating conditions. The validity of the model was also confirmed at lower gas velocity. A comparison with the standard k–ε RANS model showed that the LES methods produced significantly more accurate results, in particular for systems with non-symmetrical gas feed, even though the computational time required is marginally higher.

Parametric study of gas−liquid two-phase flow field in horizontal stirred tank

Based on Fluent software, the gas−liquid two-phase flow in the horizontal stirred tank was simulated with SST k−ω turbulence model, Eulerian−Eulerian two-fluid model, and multi-reference flame method. The mixing process in the tank was calculated by tracer method. The results show that increasing the rotating speed or gas flow is conducive to a more uniform distribution of the gas phase and accelerates the mixing of the liquid phase. When the rotating speed exceeds 93 r/min, the relative power demand remains basically constant. The change in the inclination angle of the upper impeller has minimal effect on the gas phase distribution. When the inclination angle is 50°, the relative power demand reaches the maximum. An appropriate increase in the impeller distance from the bottom improves the gas holdup and gas phase distribution but increases the liquid phase mixing time.

CFD study on onset of liquid entrainment through ADS-4 branch line in AP1000

The consequences of liquid entrainment through the fourth stage Automatic Depressurization System (ADS-4) of Advanced Passive nuclear power reactor (AP1000) are decreased reactor core coolant inventory and increased resistance to quick depressurization of the reactor primary coolant system. Therefore, the accurate knowledge of the Onset of Liquid Entrainment (OLE) is critical to nuclear reactor safety (NRS) assessment. In this study, three-dimensional computational fluid dynamics (CFD) simulations of OLE were carried out using a two-fluid Eulerian model of ANSYS Fluent CFD code along with the renormalization group (RNG) κ-ε turbulence model for each phase. In OLE phenomena, the interfacial drag has a significant effect but available choices of interfacial drag coefficient in Fluent were not suitable due to the presence of droplet clusters in entrainment. Therefore, a modified interfacial drag coefficient accounting for droplet clusters was used. The transient simulations were performed with this modified CFD model and validated against ADS-4 Depressurization and Entrainment TEst Loop (ADETEL) data. The comparison between CFD calculations and experimental data shows a good agreement. Furthermore, the effects of the liquid mass flow rates and single inlet on OLE were also investigated with the validated CFD model. To improve the understanding of OLE phenomena, the liquid volume fraction and gas velocity field distributions were also studied.

A Computational Study on Inter-Phase Heat Transfer in a Conical Fluidized Bed Reactor Using Hot Air

This paper presents a computational study on the inter-phase heat transfer inside a conical fluidized bed reactor when hot air is introduced through the bottom inlet. Two different diameters, 2.0[Formula: see text]mm and 4.0[Formula: see text]mm glass particles are used as the first and second solid phase and hot air is used as the third phase. A gas–particle heat transfer and particle–particle heat transfer are investigated by using computational fluid dynamics. Euler–Euler two-fluid model is used to describe dynamics of particles and fluid flow in the reactor. We observe that gas–particle heat transfer coefficient is large when solid particle is small. This is the same tendency as the gas–particle heat transfer coefficient when cold air is introduced among hot particles. Particle-to-particle heat transfer depends much on the superficial velocity at the inlet.

Studies on the critical heat flux in fuel assembly using a modified two-phase multi-scale interface model—validation and sensitivity analysis

The flow regime transition with the multi-scale interface is an important mechanism in the CFD simulation of boiling flow, especially in the saturated boiling and even departure nuclear boiling (DNB), while the current model is still immature. In this paper, a modified two-phase multi-scale interface model, which considering the concentration and morphology of interfacial area and the interfacial transfer of momentum, heat and mass, was compiled into the Eulerian two-fluid model in Fluent code to investigate the characteristics of two-phase flow. The improved model was validated systematically by the adiabatic two-phase flow data for different interface morphologies and the boiling flow data with different void fraction. And then the overall ability of the models in predicting the CHF values in a simplified fuel assembly was evaluated. The results showed that most predicting deviations were less than ±20%. Finally, the sensitivity of the empirical values in the modified two-phase multi-scale interface model was analyzed. In summary, the results proved that the modified two-phase multi-scale interface model based on two-fluid model could be used to simulate boiling flow with flow regime transition and was able to predict CHF in the fuel assembly reasonably.

Numerical investigation of the CHF in a vertical round tube and a single rod channel based on the eulerian two-fluid model

The critical heat flux (CHF) is essential to the operational safety of nuclear power plants (NPP), and it plays a vital role in the thermal-hydraulic and structural design of a fuel assembly. In this study, the commercial computational fluid dynamics package STAR-CCM+ was used to predict the departure from the nucleate boiling (DNB) phenomenon. Based on the Eulerian two-fluid model and the extended Rensselaer Polytechnic Institute (RPI) wall boiling model combined with the Weisman-Pei bubble crowding model, the DNB phenomenon was investigated for two coolants (water and R134a) with different geometric structures and working conditions. The results demonstrated that one set of Eulerian two-fluid models could accurately predict the CHF within a certain range of working conditions. The CHF value calculated in this study show good agreement with the experimental measured CHF data, which indicated that the Eulerian two-fluid model had a good application prospect for CHF prediction. The observed mean error was less than 10%. The results of this study may contribute to an advanced boiling model development for CHF prediction in complex geometric structures such as fuel assembly. In addition, these results demonstrated that it was feasible to use the refrigerant R134a, which had a low critical pressure and low latent heat of vaporization, as the modeling fluid to replace water, which had a high latent heat of vaporization and a high critical pressure in the experimental study.

Thermo-hydrodynamic modeling of flow boiling through the horizontal tube using Eulerian two-fluid modeling approach

The flow boiling process is common in many industrial applications as well as direct steam generation (DSG) in the receiver of parabolic trough solar collector (PTSC) and linear Fresnel reflector (LFR) systems. The objective of the present work is to investigate the flow boiling heat transfer through the horizontal tube numerically for the various potential applications in the DSG process in the solar collectors. The thermo-hydrodynamic study of flow boiling through the horizontal tube is presented through the two-fluid model (TFM) approach using computational fluid dynamics (CFD) software, ANSYS Fluent 19.0. Three dimensional (3-D), steady-state numerical simulations are performed by applying the Eulerian multiphase critical heat flux (CHF) boiling model. The flow conditions considered are similar as in the DSG in the solar collectors. The simulations are performed for 12 m length of the horizontal stainless-steel tube having inner and outer diameter 70 mm and 50 mm respectively with the mass flow rates ranging from 0.3 kg/s to 0.6 kg/s, operating pressures 30 to 100 bar, and wall heat flux 17.74 kW/m2. The variations in the pressure drop, vapor volume fraction, circumferential wall temperature, contours of vapor volume fraction, velocities have been predicted under the considered operating conditions. The pressure drop in the tube for the various operating conditions considered is in the range of 115 Pa to 426 Pa and the pressure drop is observed higher at the lower operating pressure. The pressure drops are observed as 222.4 Pa, 145 Pa, and 115.2 Pa respectively for the operating pressure of 30 bar, 60 bar, and 100 bar at the mass flow rate (MFR) of 0.3 kg/s. The large thermal gradient in the tube wall is observed in the circumferential direction at the liquid-vapor interface. The minimum and maximum value of ∆T (∆T = Tmax – Tmin) around the circumference are observed as 28.3 K and 77.1 K respectively for the given operating conditions. The circumferential temperature difference decreases with an increase in the operating pressure. The value of ∆T around the circumference is observed for the MFR of 0.3 kg/s as 77.1 K, 58.1 K, and 45.7 K respectively for operating pressure of 30 bar, 60 bar, and 100 bar. The contours of tube wall temperature at various axial positions have been plotted. The vapor volume fractions for the MFR of 0.3 kg/s are 0.6, 0.51, and 0.45 respectively for operating pressures of 30 bar, 60 bar, and 100 bar. The vapor volume fraction (VVF) decreases at the outlet of the tube as the MFR or operating pressure increases. The mixture velocity and the relative velocity between the phases have been predicted. The present study concluded that higher operating pressure is more suitable in terms of pressure loss and the thermal gradient. The presented numerical model is useful for the thermal performance analysis of DSG in the PTSC as well as the LFR system and other industrial applications having flow boiling through the horizontal tubes.

Comparative CFD modeling of a bubbling bed using a Eulerian–Eulerian two-fluid model (TFM) and a Eulerian-Lagrangian dense discrete phase model (DDPM)

Eulerian–Eulerian and Eulerian-Lagrangian numerical approaches are both widely used to investigate hydrodynamic behavior in dense gas-solid fluidized bed reactors, yet there has been a lack of comparative investigations involving the two. Therefore, the present work compares the numerical performance of a two-fluid model (TFM) and a dense discrete phase model (DDPM) in describing the hydrodynamic behavior of a pilot-scale bubbling bed reactor. The effects of several different parameters – drag force, grid size, fluid time-step, time-averaging interval, particle-wall specularity coefficient, particle-particle restitution coefficient, particle-wall reflection coefficient, and numbers of parcels (the latter two parameters only for the DDPM) – are investigated and compared for the two approaches using two-dimensional (2D) simulations. The numerical results for both models indicate that sub-grid drag correction based on the energy minimization and multiscale (EMMS) theory is the most essential modeling parameter to account for the multiscale structures (i.e., bubbles and void spaces) and to resolve the axial and radial solid distributions. Both the TFM and DDPM, coupled with the EMMS/bubbling drag, predict similar hydrodynamics behavior; however, the better accuracy in terms of axial and radial solids concentration profiles is achieved from the TFM approach. Further, our grid size analysis results indicate that the DDPM generates a better grid-independent solution than the TFM. This important advantage of the DDPM over TFM makes it a suitable candidate for large-scale industrial applications by employing it on much coarser grids. Meanwhile, the results from the time-step, time-averaging interval, specularity coefficient, restitution coefficient, reflection coefficient, and numbers of parcels represent a minor effect on the overall hydrodynamics behavior of the pilot-scale bubbling bed reactor.

Analysis of phase interaction and gas holdup in a multistage multiphase rotodynamic pump based on a modified Euler two-fluid model

Due to the effect of unit stages, the gas-liquid flow and the interphase forces in the multistage multiphase pump are more disordered, which will affect the energy conversion efficiency. However, the characteristics of phase interaction and gas holdup in such a pump are not clear. In this study, based on a modified Euler two-fluid model, simulations of a multiphase rotodynamic pump with two stages were carried out with medium combinations of air-water and air-crude. The characteristics of phase interaction and gas holdup were analyzed at different inlet gas void fractions (IGVFs), and inlet bubble diameters. The results show that the overall changing trend of interphase forces is the same between the first and second stages at different IGVFs, but the magnitudes of interphase forces in the second stage are slightly smaller, especially for the medium combination of air-water. Moreover, the drag is more sensitive to the IGVF, while the lift and added mass force are more sensitive to the medium viscosity. As the increase of the inlet bubble diameter, the difference of the gas holdup effect in the pump increases gradually at IGVF = 9.0%, and the maximum almost occurs in the first stage guide vane (S1). When the bubble diameter increases to 0.7 mm, the degree of gas accumulation and gas-liquid velocity difference increase significantly, resulting in a significant increase of the disordered degree of lift and added mass force.

CFD Modeling of the Catalyst Oil Slurry Hydrodynamics in a High Pressure and Temperature as Potential for Biomass Liquefaction

The paper presents the simulation of a catalyst-paraffin oil slurry hydrodynamics under high pressure and temperature in a convex bottom reactor with a Rushton turbine which was conducted with an application of computational fluid dynamics (CFD) modeling. An analysis to obtain a uniform distribution of solid catalyst particles suspended in paraffin oil was carried out as a potential for biomass liquefaction. The effects of the particle diameter, bed density, liquid viscosity, and the initial solid loading on slurry hydrodynamics in high pressure and temperature behavior were investigated using the Eulerian–Eulerian two-fluid model and the standard k-ε turbulence model. The main objective was to assess the performance in agitating highly concentrated slurries to obtain slurry velocity, concentration, the degree of homogeneity, and to examine their effect on the mixing quality. The results of the analysis are applied to predicting the impact of the most efficient conditions on slurry suspension qualities as potential for biomass liquefaction.

Experimental and numerical study of liquid–liquid interphase mass transfer in a pilot-scale extraction column

Liquid–liquid interphase mass transfer was experimentally and numerically studied in a pilot-scale pulsed disc-and-doughnut column (PDDC). The mass transfer coefficients, which were determined by analyzing experimental data through a transient axial dispersion model, increased from 2.27 × 10–6 to 3.06 × 10–6 m/s with an increase in the pulsation intensity from 0.0065 to 0.0105 m/s. The Euler–Euler two-fluid model was applied to simulate the interphase mass transfer in the PDDC. Three key issues, including the formulation of governing equations, selection of the mesh size, and determination of the mass transfer coefficient, which significantly influence the numerical accuracy, were discussed in detail. The simulated concentration profiles accorded well with that predicted by the experimentally verified mass transfer model. Local mass transfer performance was uncovered based on simulation results to elucidate the spatial and temporal variation of the solute concentrations, hold-up, and mass transfer coefficients in the PDDC.

Investigations on Effect of Lift and Wall Lubrication Forces on the Subcooled Flow Boiling

Abstract Subcooled flow boiling is widely used as a mode of heat transfer in many industries, especially in nuclear reactors. Despite its advantages, the heat transfer is hampered beyond a certain flux due to a phenomenon known as departure from nucleate boiling (DNB). It is important to determine the void fraction profiles, especially the near-wall void fractions, to evaluate the limiting heat flux conditions. The two-fluid Eulerian model, coupled with the heat flux partitioning model, is widely used to predict subcooled flow boiling characteristics. Over the years, many researchers have not considered lift and wall lubrication forces in their modeling of subcooled flow boiling. Few researchers have considered the Tomiyama model for lift force; however, their results were not encouraging. Moreover, there is no systematic study in evaluating the impact of lift and wall lubrication forces on subcooled flow boiling. In this paper, various lift and wall lubrication models are compared to understand the implications of these forces on void distribution. The advantages and limitations of the models are discussed in detail.

Two-phase modeling of water-air flow of dispersed and segregated flows

The accuracy of the Eulerian two-fluid model to solve dispersed and segregated multiphase flows was evaluated. Five air-water tests representing flow regimes commonly found in nuclear installations were considered: (a) bubbles ascending in a stagnation water column, (b) air-water upward flow crossing an obstacle in a vertical column, (c) liquid-liquid co-current horizontal flow, (d) air-water counter-current horizontal flow, and (e) air injection and swelling in the vertical water colu mn. The first four tests corresponded to steady-state benchmarks reported in the literature, and the last one was an experimental test proposed to assess the computational model under transient high void fraction flow. The five cases were simulated using the same set of interfacial force models in order to find one computational model suitable to solve all the regimes thanks to the use of a linear blending method to automatically switch the interfacial models accounting for the local rheology of the flow (drops in air, bubbles in water, segregated flow). The dispersed flow cases (cases a, b and e) were suitably modeled using the models proposed by Grace (drag), Tomiyama (lift), Frank (wall lubrication), and Burn (turbulent dispersion). On the other hand, the segregated systems (cases c and d) were solved using the drag model proposed by Marschall. Regarding turbulence, the κ-ω SST model was appropriated for both cases.

Scale-up of aerated bioreactors: CFD validation and application to the enzyme production by Trichoderma reesei

The application of Computational Fluid Dynamics to aerobic fermentations faces several issues, such as validation of multiphase models at high gas holdup and with complex liquids under turbulent condition. In this work, the Eulerian two-fluid model framework was adapted to simulate the enzyme production by the filamentous fungi T. reesei. Due to scarcity of data on turbulent mixing in complex fluids, every aspect of the numerical model (turbulence model, drag force law, rheology model, etc.) needed to be validated. First, the adequacy of the model was evaluated by the mean of comparison with new and previous experimental data in non-Newtonian aerated systems. Once coupled with an apparent oxygen and substrate uptake kinetics, the model was used to investigate the effect of scale-up on the enzyme productivity from biomass. Fully predictive results highlighted complex behaviors, such as: possible substrate heterogeneities, yield loss, and non-obvious interactions between mixing and oxygen transfer limitations.