Numerical Simulation and Analysis of Solid-liquid Two-phase Flow in Centrifugal Pump

The flow with solid-liquid two-phase media inside centrifugal pumps is very complicated and the relevant method for the hydraulic design is still immature so far. There exist two main problems in the operation of the two-phase flow pumps, i.e., low overall efficiency and severe abrasion. In this study, the three-dimensional, steady, incompressible, and turbulent solid-liquid two-phase flows in a low-specific-speed centrifugal pump are numerically simulated and analyzed by using a computational fluid dynamics （CFD） code based on the mixture model of the two-phase flow and the RNG k-~ two-equation turbulence model, in which the influences of rotation and curvature are fully taken into account. The coupling between impeller and volute is implemented by means of the frozen rotor method. The simulation results predicted indicate that the solid phase properties in two-phase flow, especially the concentration, the particle diameter and the density, have strong effects on the hydraulic performance of the pump. Both the pump head and the efficiency are reduced with increasing particle diameter or concentration. However, the effect of particle density on the performance is relatively minor. An obvious jet-wake flow structure is presented near the volute tongue and becomes more remarkable with increasing solid phase concentration. The suction side of the blade is subject to much more severe abrasion than the pressure side. The obtained results preliminarily reveal the characteristics of solid-liquid two-phase flow in the centrifugal pump, and are helpful for improvement and empirical correction in the hydraulic design of centrifugal pumps.

Computational Analysis of Centrifugal Pump Delivering Solid-liquid Two-phase Flow during Startup Period

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.

Numerical simulation of predicting and reducing solid particle erosion of solid-liquid two-phase flow in a choke

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）.

MICHAEL REACTION OF CHLOROESTERS IN A TWO-PHASE SOLID-LIQUID SYSTEM

The Michael addition of α-chloroesters to α,β-unsaturated systems was catalyzed bytraalkylammonium salt in a two-phase solid-liquid system, and some polysubstitnted evclopropanes were facilely synthesized.

Nanostructured lubricant additives for titanium alloy:Lubrication by the solid-liquid interface with Coulomb repulsion

In this work,the advantage of Coulomb repulsion in the intermolecular forces experienced by molecules on the solid–liquid nanosized contact interface is taken,and the superior friction-reducing property of Cu_(3)(PO_(4))2·3H_(2)O(CuP)oil-based additives has been confirmed for titanium alloy.Three-dimensional(3D)CuP nanoflowers(CuP-Fs)with a strong capillary absorption effect are prepared to achieve the homogeneous mixing of solid CuP and lubricating oil.Lubrication by CuP-Fs additives for titanium alloy,friction coefficient(COF)can be reduced by 73.68%,and wear rate(WR)reduced by 99.69%.It is demonstrated that the extraordinary friction-reducing property is due to the repulsive solid–liquid interface with low viscous shear force originating from Coulomb repulsion between polar water molecules in CuP and non-polar oil molecules.However,any steric hindrance or connection between this repulsive solid–liquid interface will trigger the adhesion and increase the viscous shear force,for example,dispersant,hydrogen bondings,and shaky adsorbed water molecules.Besides,the lamellar thickness of CuP and the molecular size of lubricant both have a great influence on tribological properties.Here the lubrication mechanism based on interface Coulomb repulsion is proposed that may help broaden the scope of the exploration in low-friction nanomaterial design and new lubricant systems.

Influence on the Solid−Liquid Two-Phase Flow from Cross-Section Area of Slurry Pumps for Deep-Sea Mining

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.

Experimental and modelling studies of the transient tribological behaviour of a two-phase lubricant under complex loading conditions

The transient tribological phenomenon and premature lubricant breakdown have been widely observed in metal forming,leading to excessive friction at the contact interfaces.In this research,the transient tribological behaviour of a two-phase lubricant were studied under complex loading conditions,featuring abrupt interfacial temperature,contact load,and sliding speed changes,thus representing the severe interfacial conditions observed in warm/hot metal forming applications.The strong experimental evidence indicates that the evolution of friction was attributed to the physical diminution and chemical decomposition effects.As such,a visco-mechanochemical interactive friction model was developed to accurately predict the transient tribological behaviour of the two-phase lubricant under complex loading conditions.The new friction model exhibited close agreements between the modelling and experimental results.

Numerical Investigation on Flow Pattern of Air-Oil with Different Viscosities Lubrication

In the present work, the performance of oil-air two-phase flow under different lubricant oils was investigated. The simulation method was applied to study the influence of the oil viscosity on the flow pattern, velocity distribution and Re number in oil-air lubrication by FLUENT software with VOF model to acquire the working performance of oil-air lubrication for high-speed ball bearing. This method was used to obtain the optimum lubrication conditions of high-speed ball bearing. The optimum operating conditions that produce the optimum flow pattern were provided. The optimum annular flow was obtained by PAO6 oil with the low viscosity. Reynolds number influences the fluid shape and distribution of oil and air in pipe. The annular flow can be formed when Reynolds number is an appropriate value. The velocity distribution of oil-air two-phase flow at outlet was also discussed by different oil viscosities. The simulating results show that due to the effect of the oil viscosity and flow pattern the velocity decreased and expanded gradually close to the pipe wall, and the velocity increased close to the central pipe. The simulation results provide the proposal for the design and operation of oil-air two-phase flow lubrication experiments in the present work. This work provides a useful method in designing oil-air lubrication with the optimum flow pattern and the optimum operating conditions.

Characteristics of lubrication at nanoscale in two-phase fluid system

Thin film lubrication (TFL) is a condition in which the lubricating features between two surfaces in relative motion are determined by the combination of the properties of the surfaces and the lubricant and viscosity of the lubricant. The effects imposed by couple stress on lubrication characteristics cannot be disregarded in this regime where the ordered molecules dominate the fluid field. There are different tensor measures and constitutive equations in this case other than Newtonian case. The lubrication of two-phase (solid phase and liquid phase) fluid is investigated in this paper. The existence of couple stress will enhance the lubricant viscosity and hence increase the film thickness and improve the load-carrying capability. Size-dependent effects can be seen in the lubrication with couple stress, and the thinner the lubricating film is, the more obvious the effect will be.

A three-dimensional solid-liquid two-phase turbulence model with the effect of vegetation in non-orthogonal curvilinear coordinates

A three-dimensional k-ε-Ap solid-liquid two-phase two-fluid model with the effect of vegetation is solved numerically with a finite-volume method on an adaptive grid to study water-sediment movements and bed evolution in vegetated channels. The additional drag force and additional turbulence generation due to vegetation are added to the relevant control equations for simulating the interaction between vegetation and flow. The flow structure and the bed-topography changes in a 60° partly vegetated channel bend are calculated by the model. The numerical results agree well with the measured ones. Calculated and measured results show that the primary flow velocity reduces much in the vegetation zone and increases in the non-vegetation zone, the secondary flow velocity weakens in the vegetation zone and strengthens in the non-vegetation zone, the sediment movement and bed-topography change also weaken in the vegetation zone and strengthen in the non-vegetation zone, a well-planed vegetation arrangement can improve bank stabilization program, and the k-ε-Ap model can deal with bed-load transport with a more reasonable method than the one-fluid model.

Estimation of solid concentration in solid-liquid two-phase flow in horizontal pipeline using inverse-problem approach

In this study,an inverse-problem method was applied to estimate the solid concentration in a solid-liquid two-phase flow.An algebraic slip mixture model was introduced to solve the forward problem of solid-liquid convective heat transfer.The time-average conservation equations of mass,momentum,energy,as well as the volume fraction equation were computed in a computational fluid dynamics(CFD)simulation.The solid concentration in the CFD model was controlled using an external program that included the inversion iteration,and an optimal estimation was performed via experimental measurements.Experiments using a fly-ash-water mixture and sand-water mixture with different solid concentrations in a horizontal pipeline were conducted to verify the accuracy of the inverse-problem method.The estimated results were rectified using a method based on the relationship between the estimated results and estimation error;consequently,the accuracy of the corrected inversion results improved significantly.After a verification through experiments,the inverse-problem method was concluded to be feasible for predicting the solid concentration,as the estimation error of the corrected results was within 7%for all experimental samples for a solid concentration of less than 50%.The inverse-problem method is expected to provide accurate predictions of the solid concentration in solid-liquid two-phase flow systems.

Theoretical analysis of effect of solid phase on cavitation performance of deep-sea mining pump

In view of the present situation of low cavitation performance of deep-sea mining slurry pump, the effect of solid phase on the cavitation performance of deep-sea mining pump is analyzed theoretically. The relationship between gas and liquid phases are established by cavitation nucleon theory and mass energy equation as well as solid phase and liquid phase, and then we explored the relationship between gas phase and solid phase. The results show that the critical bubble radius and solid-phase concentration flow rate during the cavitation can be related to the liquid pressure. Eq.(19) show that the larger the solid particle concentration and the solid phase flow, the earlier the cavitation will occur, and pump anti-cavitation performance will decline.

Numerical Simulation of Proppant Dynamics in a Rough Inclined Fracture

Although the dynamics of proppant(small ceramic balls used to prevent opened fractures from closing on the release of pressure)have been the subject of several numerical studies over recent years,large-scale inclined fractures exist in unconventional reservoirs for which relevant information is still missing.In the present study,this problem is investigated numerically considering the influence of several relevant factors such as the fracture roughness,inclination,the proppant particle size,the injection rate and the fluid viscosity.The results show that a rough wall enables the proppant to travel farther and cover larger areas.The inclination angle has little effect on the dune but a significant influence on the suspension zone.The area of this zone increases with a decrease in the inclination angle,and its value for an inclination of 15°is 20 times that at 90°.Small particle size,high injection rate,and high fracturing fluid viscosity have a beneficial influence on proppant transport;vice versa they hinder settling phenomena.

Effects of Particle Concentration on the Dynamics of a Single-Channel Sewage Pump under Low-Flow-Rate Conditions

Single-channel sewage pumps are generally used to transport solid-liquid two-phase media consisting of a fluid and solid particles due to the good non-clogging property of such devices.However,the non-axisymmetric structure of the impeller of this type of pumps generally induces flow asymmetry,oscillatory outflow during operations,and hydraulic imbalance.In severe cases,these effects can jeopardize the safety and stability of the overall pump.In the present study,such a problem is investigated in the framework of a Mixture multiphase flow method coupled with a RNG turbulence model used to determine the structure of the flow field and the related motion of transported particles.It is shown that under different inlet particle concentrations,the flow field in the pump exhibits periodic variations of the pressure.The volume fraction of solid particles at the trailing edge of the suction surface of the blade is the largest,and solid particles tend to be concentrated at the outer edge of the pump body.With a rise in import particle content,the pressure and volume fraction of particles in the sewage pump also increase;for a fixed inlet particle concentration,the pressure pulsation amplitude increases with an increase in the flow rate.In addition,under small flow conditions,as the inlet particle concentration increases,the flow field leaving the sewage pump diaphragm near the outlet of the volute becomes more turbulent,and even a secondary back-flow vortex appears.

Density Calculation for NaCl-H_2O Solutions in the Liquid-Solid TwoPhase Field in NaCI-H_2O Three-Phase Inclusions

Three-phase NaCl-H_2O fluid inclusions featuring halite dissolution temperature（Tm）higher than vapor bubble disappearance temperature（T_h） are commonly observed in porphyry copper/molybdenum deposits,skarn-type deposits and other magmatic- hydrothermal ore deposits.Based on ｜ΔV_1｜（the absolute value of volume variation of NaCl-H_2O solution in a heating or cooling process of inclusions）= ｜ΔV_s｜（the absolute value of volume variation of the halite crystal in a heating or cooling process of inclusions） and on the principle of conservation of the mass of NaCl and H_2O,we systematically calculated the densities of NaCl-H_2O solutions in the solid-liquid two-phase field for temperatures（T_h） from 0.1℃ to 800℃ and salinities from 26.3 wt%to 99.2wt%.Consequently for the first time we obtained the upper limit of the density of NaCI-H_2O solutions in the solid-liquid twophase field for T_b〈T_m inclusions with variant salinities.The results indicate that for inclusions of the T_h〈T_m type with the same T_h,the higher the T_m or salinity is,the higher the density of the NaClsaturated solution will be.If a group of fluid inclusions were homogeneously trapped,they must have the same T_h value and the same T_m or salinity value.This may be used to distinguish homogeneous,inhomogeneous,and multiple entrapments of fluid inclusions.

固体颗粒对喷流流场及底部热环境影响规律研究

Compared with using liquid rocket engines,there are a lot of high-temperature solid particles in the solid-liquid bundled rocket,which make the rocket base thermal environment worse.In order to study the influence of high-temperature solid particles on the base thermal environment,firstly,the effect of particle diameter on the jet distribution and the thermal environment in a single solid motor jet was analyzed using a numerical simulation method,and the results were compared with those of a ground test.Further,the effects of high-temperature solid particles on the jet and the thermal environment of the solid-liquid bundled rocket were analyzed and compared with flight data.The results show that high-temperature solid particles can increase the jet temperature and reduce the jet velocity.The larger the particle diameter,the greater the impact on the jet core temperature.The role of high-temperature solid particles cannot be ignored in the study of the base thermal environment.

Effect of particle motion on the hydraulic collection of coarse spherical particles

Deep-sea mining,through which shattered coarse solid mineral resources are hydraulically collected and transported,is a promising solution for problems associated with resource exhaustion.This study reports some interesting phenomena observed in a series of upward pumping experiments conducted on a coarse sphere with a 2-cm radius.The sphere was hydraulically lifted using a vertical pipe with a 5-cm radius suspended above the sphere.Remarkably,the tangential motion benefited the collection.The discrete element method-computational fluid dynamics was used to investigate the collection mechanism;this method was used to simulate the collecting processes of the sphere under different initial motion conditions.The simulated results agreed well with the experimental observations.The vortices over the sphere induced by its motion coupled with the main stream mainly provide sufficient lift force to raise the sphere.

Research into Configuration and Flow of Wall Oil Film in Bearing Chamber Based on Droplet Size Distribution

The lubrication design and heat transfer determination of bearing chambers in aeroengine require a sufficient understanding of the oil droplet-film interaction and physical characteristic in an oil/air two-phase flow state. The analyses of oil droplet movement, mass and momentum transfer during the impingement of droplet/wall, as well as wall oil film thickness and flow velocity are very important for the bearing chamber lubrication and heat transfer calculation. An integrated model in combination with droplet movement, droplet/wall impact and film flow analysis is put forward initially based on the consideration of droplet size distribution. The model makes a contribution to provide more practical and feasible technical approach, which is not only for the study of droplet-film interaction and physical behavior in bearing chambers with oil/air two-phase flow phenomena, but also useful for an insight into the essence of physical course through droplet movement and deposition, film formation and flow. The influences of chamber geometries and operating conditions on droplet deposition mass and momentum transfer, and wall film thickness and velocity distribution are discussed. The feasibility of the method by theoretical analysis is also verified by the ex- isting experimental data. The current work is conducive to expose the physical behavior of wall oil film configuration and flow in bearing chamber, and also significant for bearing chamber lubrication and heat transfer study under oil/air two-phase flow conditions.

EFFECT OF DRILLPIPE ROTATION ON BOREHOLE CLEANING FOR EXTENDED REACH WELL

Wellbore cleaning is a key technology for the Extended Reach Drilling （ERD）. The success of drilling extended reach wells depends directly upon the quality of wellbore cleaning. The rotation of the drillpipe, and hydraulic and rheological parameters, are the key factors for wellbore cleaning. In this study, Computational Fluid Dynamics （CFD） is applied to simulate solid-liquid two-phase flows in wellbore annulus. The annual flow field with the presence of drillpipe rotation is described through analyzing various rotation conditions. The results indicate that the quasi-spiral flow is the main flow pattern for liquid-solid transport in the horizontal annulus. The influence of rotation on the cuttings transport is also investigated, as the rotation of drillpipe increases the disturbance of liquid to solid in annulus. As a result, the solid flow becomes favorable and the solid volume is reduced. Comparisons with previously published results are also performed to prove the importance of drillpipe rotation in the wellbore clearing for the ERD.

STUDIES OF SOLID－LIQUID TWO－PHASE TURBULENT FLOWS AND WEAR IN HYDRAULIC TURBOMACHINERY

The Lagrangian equation of motion for solid particles in an arbitrary flow field is derived. The linear differential equation form and the general solution of this equation are obtained. Motion of solid particles in dilute solid-liquid turbulent flows is numerically solved and analysed. The K-εtwo-equation turbulence model, the volume fraction turbulence model, the mixed Eulerian-Lagrangian turbulence model, and the dense mixture turbulence model as well as the erosive wear model are developed. Using these models, the turbulent flows and the erosive wear in some hydraulic turbomachinery ducts are numerically predicted. The numerical results show good agreement with the experiments.