A mathematical model is set to evaluate the 3-D dense solid-liquid two-phaseturbulent flow in a non-clogging mud pump, the flow feature in the impeller channel is simulatedwith the tool of IPSA. Meanwhile, resort to T...A mathematical model is set to evaluate the 3-D dense solid-liquid two-phaseturbulent flow in a non-clogging mud pump, the flow feature in the impeller channel is simulatedwith the tool of IPSA. Meanwhile, resort to TECPLOT as the post-processor, the simulation results isvisualized. The results show the main flow characteristics: There exists backflow and aberrantvelocities at inlet area and a relative velocity slip between two phases; A jet-wake flow pattern isdiscerned around the shroud-suction side area; The relative velocity vector of solid phase iscloser to the pressure surface than that of liquid phase and the trend is more obvious with theincrease of diameter; The kinetic energy of turbulence k and the dissipation rate e reach theirpeaks at the corner of pressure and suction surface. The simulation results show a good agreementwith the experimental flow features in the impeller channel, which prove the turbulent model used isvalid and provide a theoretical design basis to non-clogging pumps.展开更多
The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision ter...The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow,the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations.Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale(SGS)model,in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor,is proposed to model the two-phase governing equations by applying dimension analyses.Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls,the velocity and pressure fields,and the volumetric concentration are calculated.The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.展开更多
Particle-fluid two-phase flows in rock fractures and fracture networks play a pivotal role in determining the efficiency and effectiveness of hydraulic fracturing operations,a vital component in unconventional oil and...Particle-fluid two-phase flows in rock fractures and fracture networks play a pivotal role in determining the efficiency and effectiveness of hydraulic fracturing operations,a vital component in unconventional oil and gas extraction.Central to this phenomenon is the transport of proppants,tiny solid particles injected into the fractures to prevent them from closing once the injection is stopped.However,effective transport and deposition of proppant is critical in keeping fracture pathways open,especially in lowpermeability reservoirs.This review explores,then quantifies,the important role of fluid inertia and turbulent flows in governing proppant transport.While traditional models predominantly assume and then characterise flow as laminar,this may not accurately capture the complexities inherent in realworld hydraulic fracturing and proppant emplacement.Recent investigations highlight the paramount importance of fluid inertia,especially at the high Reynolds numbers typically associated with fracturing operations.Fluid inertia,often overlooked,introduces crucial forces that influence particle settling velocities,particle-particle interactions,and the eventual deposition of proppants within fractures.With their inherent eddies and transient and chaotic nature,turbulent flows introduce additional complexities to proppant transport,crucially altering proppant settling velocities and dispersion patterns.The following comprehensive survey of experimental,numerical,and analytical studies elucidates controls on the intricate dynamics of proppant transport under fluid inertia and turbulence-towards providing a holistic understanding of the current state-of-the-art,guiding future research directions,and optimising hydraulic fracturing practices.展开更多
A statistical formalism overcoming some conceptual and practical difficulties arising in existing two-phase flow (2PHF) mathematical modelling has been applied to propose a model for dilute 2PHF turbulent Hows. Phase ...A statistical formalism overcoming some conceptual and practical difficulties arising in existing two-phase flow (2PHF) mathematical modelling has been applied to propose a model for dilute 2PHF turbulent Hows. Phase interaction terms with a clear physical meaning enter the equations and the formalism provides some guidelines for the avoidance of closure assumptions or the rational approximation of these terms. Continuous phase averaged continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations have been rigorously and systematically obtained in a single step. These equations display a structure similar to that for single-phase flows. It is also assumed that dispersed phase dynamics is well described by a probability density function (pdf) equation and Eulerian continuity, momentum and fluctuating kinetic energy equations for the dispersed phase are deduced. An extension of the standard k-e turbulence model for the continuous phase is used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of momentum and kinetic energy at the non-colliding, large inertia limit. This model is then used to predict the behaviour of three axisymmetric turbulent jets of air laden with solid particles varying in size and concentration. Qualitative and quantitative numerical predictions compare reasonably well with the three different sets of experimental results, studying the influence of particle size, loading ratio and flow confinement velocity.展开更多
Based on RNG k-ε turbulence model and sliding grid technique, solid-liquid two-phase three-dimensional(3-D) unsteady turbulence of full passage in slurry pump was simulated by means of Fluent software. The effects of...Based on RNG k-ε turbulence model and sliding grid technique, solid-liquid two-phase three-dimensional(3-D) unsteady turbulence of full passage in slurry pump was simulated by means of Fluent software. The effects of unsteady flow characteristics on solid-liquid two-phase flow and pump performance were researched under design condition. The results show that clocking effect has a significant influence on the flow in pump, and the fluctuation of flow velocity and pressure is obvious, particularly near the volute tongue, at the position of small sections of volute and within diffuser. Clocking effect has a more influence on liquid-phase than on solid-phase, and the wake-jet structure of relative velocity of solid-phase is less obvious than liquid-phase near the volute tongue and the impeller passage outlet. The fluctuation of relative velocity of solid-phase flow is 7.6% smaller than liquid-phase flow at the impeller outlet on circular path. Head and radial forces of the impeller are 8.1% and 85.7% of fluctuation, respectively. The results provide a theoretical basis for further research for turbulence, improving efficient, reducing the hydraulic losses and wear. Finally, field tests were carried out to verify the operation and wear of slurry pump.展开更多
The transient behavior of centrifugal pumps during transient operating periods, such as startup and stopping, has drawn more and more attention recently because of urgent needs in engineering. Up to now, almost all th...The transient behavior of centrifugal pumps during transient operating periods, such as startup and stopping, has drawn more and more attention recently because of urgent needs in engineering. Up to now, almost all the existing studies on this behavior are limited to using water as working fluid. The study on the transient behavior related to solid-liquid two-phase flow has not been seen yet. In order to explore the transient characteristics of a high specific-speed centrifugal pump during startup period delivering the pure water and solid-liquid two-phase flow, the transient flows inside the pump are numerically simulated using the dynamic mesh method. The variable rotational speed and flow rate with time obtained from experiment are best fitted as the function of time, and are written into computational fluid dynamics （CFD） code-FLUENT by using a user defined function. The predicted heads are compared with experimental results when pumping pure water. The results show that the difference in the transient performance during startup period is very obvious between water and solid-liquid two-phase flow during the later stage of startup process. Moreover, the time for the solid-liquid two-phase flow to achieve a stable condition is longer than that for water. The solid-liquid two-phase flow results in a higher impeller shaft power, a larger dynamic reaction force, a more violent fluctuation in pressure and a reduced stable pressure rise comparing with water. The research may be useful to tmderstanding on the transient behavior of a centrifugal pump under a solid-liquid two-phase flow during startup period.展开更多
A second-order moment two-phase turbulence model for simulating dense gas-particle flows （USM-Θ model）, combining the unified second-order moment twophase turbulence model for dilute gas-particle flows with the kin...A second-order moment two-phase turbulence model for simulating dense gas-particle flows （USM-Θ model）, combining the unified second-order moment twophase turbulence model for dilute gas-particle flows with the kinetic theory of particle collision, is proposed. The interaction between gas and particle turbulence is simulated using the transport equation of two-phase velocity correlation with a two-time-scale dissipation closure. The proposed model is applied to simulate dense gas-particle flows in a horizontal channel and a downer. Simulation results and their comparison with experimental results show that the model accounting for both anisotropic particle turbulence and particle-particle collision is obviously better than models accounting for only particle turbulence or only particle-particle collision. The USM-Θ model is also better than the k-ε-kp-Θ model and the k-ε-kp-εp-Θ model in that the first model can simulate the redistribution of anisotropic particle Reynolds stress components due to inter-particle collision, whereas the second and third models cannot.展开更多
Chokes are one of the most important components of downhole flow-control equipment. The particle erosion mathematical model, which considers particle-particle interaction, was established and used to simulate solid pa...Chokes are one of the most important components of downhole flow-control equipment. The particle erosion mathematical model, which considers particle-particle interaction, was established and used to simulate solid particle movement as well as particle erosion characteristics of the solid-liquid two-phase flow in a choke. The corresponding erosion reduction approach by setting ribs on the inner wall of the choke was advanced. This mathematical model includes three parts： the flow field simulation of the continuous carrier fluid by an Eulerian approach, the particle interaction simulation using the discrete particle hard sphere model by a Lagrangian approach and calculation of erosion rate using semiempirical correlations. The results show that particles accumulated in a narrow region from inlet to outlet of the choke and the dominating factor affecting particle motion is the fluid drag force. As a result, the optimization of rib geometrical parameters indicates that good anti-erosion performance can be achieved by four ribs, each of them with a height （H） of 3 mm and a width （B） of 5 mm equaling the interval between ribs （L）.展开更多
A full second-order moment (FSM) model and an algebraic stress (ASM) two-phase turbulence modelare proposed and applied to predict turbulent bubble-liquid flows in a 2D rectangular bubble column. Predictiongives the b...A full second-order moment (FSM) model and an algebraic stress (ASM) two-phase turbulence modelare proposed and applied to predict turbulent bubble-liquid flows in a 2D rectangular bubble column. Predictiongives the bubble and liquid velocities, bubble volume fraction, bubble and liquid Reynolds stresses and bubble-liquidvelocity correlation. For predicted two-phase velocities and bubble volume fraction there is only slight differencebetween these two models, and the simulation results using both two models are in good agreement with the particleimage velocimetry (PIV) measurements. Although the predicted two-phase Reynolds stresses using the FSM are insomewhat better agreement with the PIV measurements than those predicted using the ASM, the Reynolds stressespredicted using both two models are in general agreement with the experiments. Therefore, it is suggested to usethe ASM two-phase turbulence model in engineering application for saving the computation time.展开更多
There are contradicted opinions on whether bubbles enhance or reduce the liquid turbulence. In this paper, the effect of void fraction and inlet velocity on the bubble-liquid two-phase turbulence of the multiple bubbl...There are contradicted opinions on whether bubbles enhance or reduce the liquid turbulence. In this paper, the effect of void fraction and inlet velocity on the bubble-liquid two-phase turbulence of the multiple bubble-liquid jets in a two-dimensional channel is studied by using the two-phase second-order moment turbulence model. The results confirm the phenomena observed in experiments and reported in references that at a low void fraction and low inlet velocities the bubbles enhance the liquid turbulence, whereas at a high void fraction and high inlet velocities the bubbles reduce the liquid turbulence.展开更多
This study reported and discussed turbulence characteristics,such as turbulence intensity,correlation time scales,and advective length scales.The characteristic air–water time scale,including the particle chord time ...This study reported and discussed turbulence characteristics,such as turbulence intensity,correlation time scales,and advective length scales.The characteristic air–water time scale,including the particle chord time and length and their probability density functions(PDFs),was investigated.The results demonstrated that turbulence intensity was relatively greater on a rough bed in the roller length,whereas further downstream,the decay rate was higher.In addition,the relationship between turbulence intensity and dimensionless bubble count rate reflected an increase in turbulence intensity associated with the number of entrained particles.Triple decomposition analysis(TDA)was performed to determine the contributions of slow and fast turbulent components.The TDA results indicated that,regardless of bed type and inflow conditions,the sum of the band-pass(T'_(u))and high-pass(T″_(u))filtered turbulence intensities was equal to the turbulence intensity of the raw signal data(T_(u)).T″_(u) highlighted a higher turbulence intensity and larger vorticities on the rough bed for an identical inflow Froude number.Additional TDA results were presented in terms of the interfacial velocity,auto-and cross-correlation time scales,and longitudinal advection length scale,with the effects of low-and high-frequency signal components on each highlighted parameter.The analysis of the air chord time indicated an increase in the proportion of small bubbles moving downstream.The second part of this research focused on the basic properties of particle grouping and clustering.展开更多
An improved large eddy simulation using a dynamic second-order sub-grid-scale （SGS） stress model has been developed to model the governing equations of dense turbulent particle-liquid two-phase flows in a rotating c...An improved large eddy simulation using a dynamic second-order sub-grid-scale （SGS） stress model has been developed to model the governing equations of dense turbulent particle-liquid two-phase flows in a rotating coordinate system, and continuity is conserved by a mass-weighted method to solve the filtered governing equations. In the cur- rent second-order SGS model, the SGS stress is a function of both the resolved strain-rate and rotation-rate tensors, and the model parameters are obtained from the dimensional consistency and the invariants of the strain-rate and the rotation-rate tensors. In the numerical calculation, the finite volume method is used to discretize the governing equations with a staggered grid system. The SIMPLEC algorithm is applied for the solution of the discretized governing equations. Body- fitted coordinates are used to simulate the two-phase flows in complex geometries. Finally the second-order dynamic SGS model is successfully applied to simulate the dense turbu-lent particle-liquid two-phase flows in a centrifugal impeller. The predicted pressure and velocity distributions are in good agreement with experimental results.展开更多
The basic equations of turbulent gas-solid flows are derived by using the pseudo-fluid model of particle phase with a refined two-phase turbulence model.These equations are then applied to swirling gas-particle flows ...The basic equations of turbulent gas-solid flows are derived by using the pseudo-fluid model of particle phase with a refined two-phase turbulence model.These equations are then applied to swirling gas-particle flows for analyzing the collection efficiency in cyclone separators.展开更多
A mathematical modei of two-dimensional turbulent gas-particle twophase flow based on the modified diffusion flux modei (DFM) and a numerical simulation method to analyze the gas-particle flow structures are developed...A mathematical modei of two-dimensional turbulent gas-particle twophase flow based on the modified diffusion flux modei (DFM) and a numerical simulation method to analyze the gas-particle flow structures are developed. The modified diffusion flux modei, in which the acceleration due to various forces is taken into account for the calculation of the diffusion velocity of particles, is applicable to the analysis of multi-dimensional gas-particle two-phase turbulent flow. In order to verify its accuracy and efficiency, the numerical simulation by DFM is compared with experimental studies and the prediction by k-ε-kp two-fluid modei, which shows a reasonable agreement. It is confirmed that the modified diffusion flux modei is suitable for simulating the multi-dimensional gas-particle two-phase flow.展开更多
This study investigates the effect of injecting nanofluids containing nano-SiO_2 as drag reducing agents(DRA) at different concentrations on the pressure drop of air-water flow through horizontal pipe.The test fluid u...This study investigates the effect of injecting nanofluids containing nano-SiO_2 as drag reducing agents(DRA) at different concentrations on the pressure drop of air-water flow through horizontal pipe.The test fluid used in this study was air-water with nano-SiO_2 particles at 0.1%-1%mass concentration.The test sections of the experimental set-up were five pipes of the same length of 9 m with ID from 0.0127m-0.03175m(0.5 to 1.25 in).Airwater flow was run in slug flow regime under different volumetric flow rates.The results of drag reduction(η%)indicated that the addition of DRA could be efficient up to some dosage.Drag reduction performed much better for smaller pipe diameters than it did for larger ones.For various nanosilica concentrations,the maximum drag reduction was about 66.8%for 0.75%mass concentration of nanosilica.展开更多
To explore the mechanism of solid-liquid two-phase flow in deep-sea mining pumps,this paper investigates the influences of the impeller cross-section area on the multi-phase flow in the slurry pump.Experimental and nu...To explore the mechanism of solid-liquid two-phase flow in deep-sea mining pumps,this paper investigates the influences of the impeller cross-section area on the multi-phase flow in the slurry pump.Experimental and numerical results are presented for two-phase flow in four impellers with different cross-section areas.They show that the degree of vortex strength and the passing capacity of particles increase as the cross-section area of the impeller.In addition,the correlations between the two-phase flow and cross-section area have been revealed by a mathematical model taking the force of the flow field into account.The simulation results confirm the theoretical analysis,while the experimental pump performances validate the numerical calculation.The influence of the cross-section area on two-phase flow and pump performance could provide theoretical support for the design of high-performance deep-sea mining slurry pumps.展开更多
The fluid fluctuating velocity equations which include the term of cylinder particles were established. The turbulent intensity and Reynolds stress of fluid were obtained by averaging fluctuating velocity based on the...The fluid fluctuating velocity equations which include the term of cylinder particles were established. The turbulent intensity and Reynolds stress of fluid were obtained by averaging fluctuating velocity based on the solution of the fluctuating velocity equations. Above approach was used to solve the channel turbulent flows, and computational results were compared with the experimental ones for the case of single phase flow. The effects of volume fraction of particles, the ratio of particle length to diameter and the particle relaxation time on turbulent properties were illustrated by changing cylinder particle parameters. It is shown that particles play a restraining role to turbulent properties in the flows. The degree of restraint is directly proportional to the volume fraction of particle, the ratio of particle length to diameter and inversely proportional to particle relaxation time.展开更多
The phenomenon of water aeration is serious after the overflow weir in the siphon well at the cooling water circulation system of coastal power plants.At present,designing special hydraulic structures is an effective ...The phenomenon of water aeration is serious after the overflow weir in the siphon well at the cooling water circulation system of coastal power plants.At present,designing special hydraulic structures is an effective way to reduce the intensity of aeration.In this paper,three engineering structure schemes were designed,and the three-dimensional Realizable k-ε turbulence model was used.The volume of fluid method was introduced to capture the free water surface,and the unstructured grid was used to construct the two-phase turbulent flow field.The aeration concentration and pressure distribution,obtained by numerical simulation,were basically consistent with the physical model test results.The results showed that the flow field at the orifice plates of cases 1 and 2 changed drastically,and the turbulent kinetic energy downstream of the orifice plate decreased with the increase of the number of holes.As for case 3,it showed that the high-speed water flow fell into the water cushion pool,tumbling and sucking up a lot of air,and the turbulent kinetic energy and Reynolds stress were significantly greater than the other two cases.The hydraulic structure changed the cavitation characteristics of the downflow water,and the sequence of aeration concentration of the horizontal section was case 3>case 1>case 2.The aeration concentration was only 9.18%-17.86% in case 2.The aeration concentration at stable time is expressed as a function of the relative water depth y/y_(90) and the turbulent diffusion coefficient D.The distribution formula of aeration concentration was established,and its validity was verified by literatures.The results of this study will provide a certain reference for in-depth analysis of water-air mixing motion characteristics,and simultaneously,it will have a guiding significance for the design of siphon well defoaming engineering.展开更多
Free surface flows aeration potential causing the in macro- and intermediate flow characteristics to vary roughness conditions have a high with slopes and discharges. The underlying mechanism of two-phase flow charact...Free surface flows aeration potential causing the in macro- and intermediate flow characteristics to vary roughness conditions have a high with slopes and discharges. The underlying mechanism of two-phase flow characteristics in macro- and intermediate roughness conditions were analyzed in an experimental setup assembled at the Laboratory of Hydraulic Protection of the Territory （PITLAB） of the University of Pisa, Italy. Crushed angular rocks and hemispherical boulders were used to intensify the roughness of the bed. Flow rates per unit width ranging between 0.03 m^2/s and 0.09 m^2/s and slopes between 0.26 and 0.46 were tested over different arrangements of a rough bed. Analyses were mainly carried out in the inner flow region, which consists of both bubbly and intermediate flow regions. The findings revealed that the two-phase flow properties over the rough bed were much affected by rough bed arrangements. Turbulence features of two-phase flows over the rough bed were compared with those of the stepped chute data under similar flow conditions. Overall, the results highlight the flow features in the inner layers of the two-phase flow, showing that the maximum turbulence intensity decreases with the relative submergence, while the bubble frequency distribution is affected by the rough bed elements.展开更多
The turbulence behavior of gas-liquid two-phase flow plays an important role in heat transfer and mass transfer in many chemical processes. In this work, a 2D particle image velocimetry (PIV) was used to investigate t...The turbulence behavior of gas-liquid two-phase flow plays an important role in heat transfer and mass transfer in many chemical processes. In this work, a 2D particle image velocimetry (PIV) was used to investigate the turbulent characteristic of fluid induced by a chain of bubbles rising in Newtonian and non-Newtonian fluids. The instantaneous flow field, turbulent kinetic energy (TKE) and TKE dissipation rate were measured. The results demonstrated that the TKE profiles were almost symmetrical along the column center and showed higher values in the central region of the column. The TKE was enhanced with the increase of gas flow and decrease of liquid viscosity. The maximum TKE dissipation rate appeared on both sides of the bubble chain, and increased with the increase of gas flow rate or liquid viscosity. These results provide an understanding for gas-liquid mass transfer in non-Newtonian fluids.展开更多
文摘A mathematical model is set to evaluate the 3-D dense solid-liquid two-phaseturbulent flow in a non-clogging mud pump, the flow feature in the impeller channel is simulatedwith the tool of IPSA. Meanwhile, resort to TECPLOT as the post-processor, the simulation results isvisualized. The results show the main flow characteristics: There exists backflow and aberrantvelocities at inlet area and a relative velocity slip between two phases; A jet-wake flow pattern isdiscerned around the shroud-suction side area; The relative velocity vector of solid phase iscloser to the pressure surface than that of liquid phase and the trend is more obvious with theincrease of diameter; The kinetic energy of turbulence k and the dissipation rate e reach theirpeaks at the corner of pressure and suction surface. The simulation results show a good agreementwith the experimental flow features in the impeller channel, which prove the turbulent model used isvalid and provide a theoretical design basis to non-clogging pumps.
基金The project supported by the National Natural Science Foundation of China (50176022)
文摘The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow,the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations.Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale(SGS)model,in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor,is proposed to model the two-phase governing equations by applying dimension analyses.Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls,the velocity and pressure fields,and the volumetric concentration are calculated.The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.
基金the Australian Research Council Discovery Project(ARC DP 220100851)scheme and would acknowledge that.
文摘Particle-fluid two-phase flows in rock fractures and fracture networks play a pivotal role in determining the efficiency and effectiveness of hydraulic fracturing operations,a vital component in unconventional oil and gas extraction.Central to this phenomenon is the transport of proppants,tiny solid particles injected into the fractures to prevent them from closing once the injection is stopped.However,effective transport and deposition of proppant is critical in keeping fracture pathways open,especially in lowpermeability reservoirs.This review explores,then quantifies,the important role of fluid inertia and turbulent flows in governing proppant transport.While traditional models predominantly assume and then characterise flow as laminar,this may not accurately capture the complexities inherent in realworld hydraulic fracturing and proppant emplacement.Recent investigations highlight the paramount importance of fluid inertia,especially at the high Reynolds numbers typically associated with fracturing operations.Fluid inertia,often overlooked,introduces crucial forces that influence particle settling velocities,particle-particle interactions,and the eventual deposition of proppants within fractures.With their inherent eddies and transient and chaotic nature,turbulent flows introduce additional complexities to proppant transport,crucially altering proppant settling velocities and dispersion patterns.The following comprehensive survey of experimental,numerical,and analytical studies elucidates controls on the intricate dynamics of proppant transport under fluid inertia and turbulence-towards providing a holistic understanding of the current state-of-the-art,guiding future research directions,and optimising hydraulic fracturing practices.
基金Supported by the Spanish CICYTR &D National Programs,under contract PB91-0699.
文摘A statistical formalism overcoming some conceptual and practical difficulties arising in existing two-phase flow (2PHF) mathematical modelling has been applied to propose a model for dilute 2PHF turbulent Hows. Phase interaction terms with a clear physical meaning enter the equations and the formalism provides some guidelines for the avoidance of closure assumptions or the rational approximation of these terms. Continuous phase averaged continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations have been rigorously and systematically obtained in a single step. These equations display a structure similar to that for single-phase flows. It is also assumed that dispersed phase dynamics is well described by a probability density function (pdf) equation and Eulerian continuity, momentum and fluctuating kinetic energy equations for the dispersed phase are deduced. An extension of the standard k-e turbulence model for the continuous phase is used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of momentum and kinetic energy at the non-colliding, large inertia limit. This model is then used to predict the behaviour of three axisymmetric turbulent jets of air laden with solid particles varying in size and concentration. Qualitative and quantitative numerical predictions compare reasonably well with the three different sets of experimental results, studying the influence of particle size, loading ratio and flow confinement velocity.
基金Project(51375498)supported by the National Natural Science Foundation of China
文摘Based on RNG k-ε turbulence model and sliding grid technique, solid-liquid two-phase three-dimensional(3-D) unsteady turbulence of full passage in slurry pump was simulated by means of Fluent software. The effects of unsteady flow characteristics on solid-liquid two-phase flow and pump performance were researched under design condition. The results show that clocking effect has a significant influence on the flow in pump, and the fluctuation of flow velocity and pressure is obvious, particularly near the volute tongue, at the position of small sections of volute and within diffuser. Clocking effect has a more influence on liquid-phase than on solid-phase, and the wake-jet structure of relative velocity of solid-phase is less obvious than liquid-phase near the volute tongue and the impeller passage outlet. The fluctuation of relative velocity of solid-phase flow is 7.6% smaller than liquid-phase flow at the impeller outlet on circular path. Head and radial forces of the impeller are 8.1% and 85.7% of fluctuation, respectively. The results provide a theoretical basis for further research for turbulence, improving efficient, reducing the hydraulic losses and wear. Finally, field tests were carried out to verify the operation and wear of slurry pump.
基金supported by National Natural Science Foundation of China(Grant Nos.51076144,51276172)Zhejiang Provincial Natural Science Foundation of China(Grant Nos.R1100530,LY12E06002)National Basic Research Program of China(973 Program,Grant No.2009CB724303)
文摘The transient behavior of centrifugal pumps during transient operating periods, such as startup and stopping, has drawn more and more attention recently because of urgent needs in engineering. Up to now, almost all the existing studies on this behavior are limited to using water as working fluid. The study on the transient behavior related to solid-liquid two-phase flow has not been seen yet. In order to explore the transient characteristics of a high specific-speed centrifugal pump during startup period delivering the pure water and solid-liquid two-phase flow, the transient flows inside the pump are numerically simulated using the dynamic mesh method. The variable rotational speed and flow rate with time obtained from experiment are best fitted as the function of time, and are written into computational fluid dynamics （CFD） code-FLUENT by using a user defined function. The predicted heads are compared with experimental results when pumping pure water. The results show that the difference in the transient performance during startup period is very obvious between water and solid-liquid two-phase flow during the later stage of startup process. Moreover, the time for the solid-liquid two-phase flow to achieve a stable condition is longer than that for water. The solid-liquid two-phase flow results in a higher impeller shaft power, a larger dynamic reaction force, a more violent fluctuation in pressure and a reduced stable pressure rise comparing with water. The research may be useful to tmderstanding on the transient behavior of a centrifugal pump under a solid-liquid two-phase flow during startup period.
基金the Special Funds for Major State Basic Research of China(G-1999-0222-08)the National Natural Science Foundation of China(50376004)Ph.D.Program Foundation,Ministry of Education of China(20030007028)
文摘A second-order moment two-phase turbulence model for simulating dense gas-particle flows （USM-Θ model）, combining the unified second-order moment twophase turbulence model for dilute gas-particle flows with the kinetic theory of particle collision, is proposed. The interaction between gas and particle turbulence is simulated using the transport equation of two-phase velocity correlation with a two-time-scale dissipation closure. The proposed model is applied to simulate dense gas-particle flows in a horizontal channel and a downer. Simulation results and their comparison with experimental results show that the model accounting for both anisotropic particle turbulence and particle-particle collision is obviously better than models accounting for only particle turbulence or only particle-particle collision. The USM-Θ model is also better than the k-ε-kp-Θ model and the k-ε-kp-εp-Θ model in that the first model can simulate the redistribution of anisotropic particle Reynolds stress components due to inter-particle collision, whereas the second and third models cannot.
基金supported by the Fund of Innovation Research Group of National Natural Science Foundation of China (Grant NO.5052160450323001)Major Program of National Natural Science Foundation of China (Grant No.50536020)
文摘Chokes are one of the most important components of downhole flow-control equipment. The particle erosion mathematical model, which considers particle-particle interaction, was established and used to simulate solid particle movement as well as particle erosion characteristics of the solid-liquid two-phase flow in a choke. The corresponding erosion reduction approach by setting ribs on the inner wall of the choke was advanced. This mathematical model includes three parts： the flow field simulation of the continuous carrier fluid by an Eulerian approach, the particle interaction simulation using the discrete particle hard sphere model by a Lagrangian approach and calculation of erosion rate using semiempirical correlations. The results show that particles accumulated in a narrow region from inlet to outlet of the choke and the dominating factor affecting particle motion is the fluid drag force. As a result, the optimization of rib geometrical parameters indicates that good anti-erosion performance can be achieved by four ribs, each of them with a height （H） of 3 mm and a width （B） of 5 mm equaling the interval between ribs （L）.
基金Supported by the Special Funds for Major State Basic Research Projects, PRC(G1999-0222-08) and the National Natural Science Foundation of China(No. 19872039).
文摘A full second-order moment (FSM) model and an algebraic stress (ASM) two-phase turbulence modelare proposed and applied to predict turbulent bubble-liquid flows in a 2D rectangular bubble column. Predictiongives the bubble and liquid velocities, bubble volume fraction, bubble and liquid Reynolds stresses and bubble-liquidvelocity correlation. For predicted two-phase velocities and bubble volume fraction there is only slight differencebetween these two models, and the simulation results using both two models are in good agreement with the particleimage velocimetry (PIV) measurements. Although the predicted two-phase Reynolds stresses using the FSM are insomewhat better agreement with the PIV measurements than those predicted using the ASM, the Reynolds stressespredicted using both two models are in general agreement with the experiments. Therefore, it is suggested to usethe ASM two-phase turbulence model in engineering application for saving the computation time.
基金The project supported by the China Special Funds for Major State Basic Research (G-1999-0222-08)the Innovation and Technology Commission of Hong Kong and Aoyagi (H.K.) Ltd, Hong Kong, under the Grant No. UIM/122.
文摘There are contradicted opinions on whether bubbles enhance or reduce the liquid turbulence. In this paper, the effect of void fraction and inlet velocity on the bubble-liquid two-phase turbulence of the multiple bubble-liquid jets in a two-dimensional channel is studied by using the two-phase second-order moment turbulence model. The results confirm the phenomena observed in experiments and reported in references that at a low void fraction and low inlet velocities the bubbles enhance the liquid turbulence, whereas at a high void fraction and high inlet velocities the bubbles reduce the liquid turbulence.
文摘This study reported and discussed turbulence characteristics,such as turbulence intensity,correlation time scales,and advective length scales.The characteristic air–water time scale,including the particle chord time and length and their probability density functions(PDFs),was investigated.The results demonstrated that turbulence intensity was relatively greater on a rough bed in the roller length,whereas further downstream,the decay rate was higher.In addition,the relationship between turbulence intensity and dimensionless bubble count rate reflected an increase in turbulence intensity associated with the number of entrained particles.Triple decomposition analysis(TDA)was performed to determine the contributions of slow and fast turbulent components.The TDA results indicated that,regardless of bed type and inflow conditions,the sum of the band-pass(T'_(u))and high-pass(T″_(u))filtered turbulence intensities was equal to the turbulence intensity of the raw signal data(T_(u)).T″_(u) highlighted a higher turbulence intensity and larger vorticities on the rough bed for an identical inflow Froude number.Additional TDA results were presented in terms of the interfacial velocity,auto-and cross-correlation time scales,and longitudinal advection length scale,with the effects of low-and high-frequency signal components on each highlighted parameter.The analysis of the air chord time indicated an increase in the proportion of small bubbles moving downstream.The second part of this research focused on the basic properties of particle grouping and clustering.
基金the National Natural Science Foundation of China(50779069 and 90510007)the Start-up Scientific Research Foundation of China Agricultural University(2006021)the Beijing Natural Science Foundation(3071002).
文摘An improved large eddy simulation using a dynamic second-order sub-grid-scale （SGS） stress model has been developed to model the governing equations of dense turbulent particle-liquid two-phase flows in a rotating coordinate system, and continuity is conserved by a mass-weighted method to solve the filtered governing equations. In the cur- rent second-order SGS model, the SGS stress is a function of both the resolved strain-rate and rotation-rate tensors, and the model parameters are obtained from the dimensional consistency and the invariants of the strain-rate and the rotation-rate tensors. In the numerical calculation, the finite volume method is used to discretize the governing equations with a staggered grid system. The SIMPLEC algorithm is applied for the solution of the discretized governing equations. Body- fitted coordinates are used to simulate the two-phase flows in complex geometries. Finally the second-order dynamic SGS model is successfully applied to simulate the dense turbu-lent particle-liquid two-phase flows in a centrifugal impeller. The predicted pressure and velocity distributions are in good agreement with experimental results.
文摘The basic equations of turbulent gas-solid flows are derived by using the pseudo-fluid model of particle phase with a refined two-phase turbulence model.These equations are then applied to swirling gas-particle flows for analyzing the collection efficiency in cyclone separators.
基金Special Funds for Major State Basic Research Projects of China(G1999022200)
文摘A mathematical modei of two-dimensional turbulent gas-particle twophase flow based on the modified diffusion flux modei (DFM) and a numerical simulation method to analyze the gas-particle flow structures are developed. The modified diffusion flux modei, in which the acceleration due to various forces is taken into account for the calculation of the diffusion velocity of particles, is applicable to the analysis of multi-dimensional gas-particle two-phase turbulent flow. In order to verify its accuracy and efficiency, the numerical simulation by DFM is compared with experimental studies and the prediction by k-ε-kp two-fluid modei, which shows a reasonable agreement. It is confirmed that the modified diffusion flux modei is suitable for simulating the multi-dimensional gas-particle two-phase flow.
文摘This study investigates the effect of injecting nanofluids containing nano-SiO_2 as drag reducing agents(DRA) at different concentrations on the pressure drop of air-water flow through horizontal pipe.The test fluid used in this study was air-water with nano-SiO_2 particles at 0.1%-1%mass concentration.The test sections of the experimental set-up were five pipes of the same length of 9 m with ID from 0.0127m-0.03175m(0.5 to 1.25 in).Airwater flow was run in slug flow regime under different volumetric flow rates.The results of drag reduction(η%)indicated that the addition of DRA could be efficient up to some dosage.Drag reduction performed much better for smaller pipe diameters than it did for larger ones.For various nanosilica concentrations,the maximum drag reduction was about 66.8%for 0.75%mass concentration of nanosilica.
基金This work was financially supported by the National Natural Science Foundation of China(Grant No.52071296)the Key Research and Development Program of Zhejiang Province(Grant No.2020C01027)+1 种基金the Top-notch Talent Support Program of Zhejiang Province(Grant No.2019R51002)the National Key Research and Development Program of China(Grant Nos.2021YFC2800803 and 2021YFC2801504).
文摘To explore the mechanism of solid-liquid two-phase flow in deep-sea mining pumps,this paper investigates the influences of the impeller cross-section area on the multi-phase flow in the slurry pump.Experimental and numerical results are presented for two-phase flow in four impellers with different cross-section areas.They show that the degree of vortex strength and the passing capacity of particles increase as the cross-section area of the impeller.In addition,the correlations between the two-phase flow and cross-section area have been revealed by a mathematical model taking the force of the flow field into account.The simulation results confirm the theoretical analysis,while the experimental pump performances validate the numerical calculation.The influence of the cross-section area on two-phase flow and pump performance could provide theoretical support for the design of high-performance deep-sea mining slurry pumps.
文摘The fluid fluctuating velocity equations which include the term of cylinder particles were established. The turbulent intensity and Reynolds stress of fluid were obtained by averaging fluctuating velocity based on the solution of the fluctuating velocity equations. Above approach was used to solve the channel turbulent flows, and computational results were compared with the experimental ones for the case of single phase flow. The effects of volume fraction of particles, the ratio of particle length to diameter and the particle relaxation time on turbulent properties were illustrated by changing cylinder particle parameters. It is shown that particles play a restraining role to turbulent properties in the flows. The degree of restraint is directly proportional to the volume fraction of particle, the ratio of particle length to diameter and inversely proportional to particle relaxation time.
文摘The phenomenon of water aeration is serious after the overflow weir in the siphon well at the cooling water circulation system of coastal power plants.At present,designing special hydraulic structures is an effective way to reduce the intensity of aeration.In this paper,three engineering structure schemes were designed,and the three-dimensional Realizable k-ε turbulence model was used.The volume of fluid method was introduced to capture the free water surface,and the unstructured grid was used to construct the two-phase turbulent flow field.The aeration concentration and pressure distribution,obtained by numerical simulation,were basically consistent with the physical model test results.The results showed that the flow field at the orifice plates of cases 1 and 2 changed drastically,and the turbulent kinetic energy downstream of the orifice plate decreased with the increase of the number of holes.As for case 3,it showed that the high-speed water flow fell into the water cushion pool,tumbling and sucking up a lot of air,and the turbulent kinetic energy and Reynolds stress were significantly greater than the other two cases.The hydraulic structure changed the cavitation characteristics of the downflow water,and the sequence of aeration concentration of the horizontal section was case 3>case 1>case 2.The aeration concentration was only 9.18%-17.86% in case 2.The aeration concentration at stable time is expressed as a function of the relative water depth y/y_(90) and the turbulent diffusion coefficient D.The distribution formula of aeration concentration was established,and its validity was verified by literatures.The results of this study will provide a certain reference for in-depth analysis of water-air mixing motion characteristics,and simultaneously,it will have a guiding significance for the design of siphon well defoaming engineering.
文摘Free surface flows aeration potential causing the in macro- and intermediate flow characteristics to vary roughness conditions have a high with slopes and discharges. The underlying mechanism of two-phase flow characteristics in macro- and intermediate roughness conditions were analyzed in an experimental setup assembled at the Laboratory of Hydraulic Protection of the Territory （PITLAB） of the University of Pisa, Italy. Crushed angular rocks and hemispherical boulders were used to intensify the roughness of the bed. Flow rates per unit width ranging between 0.03 m^2/s and 0.09 m^2/s and slopes between 0.26 and 0.46 were tested over different arrangements of a rough bed. Analyses were mainly carried out in the inner flow region, which consists of both bubbly and intermediate flow regions. The findings revealed that the two-phase flow properties over the rough bed were much affected by rough bed arrangements. Turbulence features of two-phase flows over the rough bed were compared with those of the stepped chute data under similar flow conditions. Overall, the results highlight the flow features in the inner layers of the two-phase flow, showing that the maximum turbulence intensity decreases with the relative submergence, while the bubble frequency distribution is affected by the rough bed elements.
基金Supported by the National Natural Science Foundation of China (21076139)the Opening Project of State Key Laboratory of Chemical Engineering (SKL-ChE-08B03)the Program of Introducing Talents of Discipline to Universities (B06006)
文摘The turbulence behavior of gas-liquid two-phase flow plays an important role in heat transfer and mass transfer in many chemical processes. In this work, a 2D particle image velocimetry (PIV) was used to investigate the turbulent characteristic of fluid induced by a chain of bubbles rising in Newtonian and non-Newtonian fluids. The instantaneous flow field, turbulent kinetic energy (TKE) and TKE dissipation rate were measured. The results demonstrated that the TKE profiles were almost symmetrical along the column center and showed higher values in the central region of the column. The TKE was enhanced with the increase of gas flow and decrease of liquid viscosity. The maximum TKE dissipation rate appeared on both sides of the bubble chain, and increased with the increase of gas flow rate or liquid viscosity. These results provide an understanding for gas-liquid mass transfer in non-Newtonian fluids.
