Numerical simulation and analysis of solid-liquid two-phase threedimensional unsteady flow in centrifugal slurry pump

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.

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）.

Numerical Simulation of Erosion-Corrosion in the Liquid-Solid Two-Phase Flow

Erosion-corrosion of liquid-solid two-phase flow occurring in a pipe with sudden expansion in cross-section is numerically simulated in this paper. The global model for erosion-corrosion process includes three main components: the liquid-solid two-phase flow model, erosion model and corrosion model. The Eulerian-Lagrangian approach is used to simulate liquid-solid two-phase flow, while the stochastic trajectory model was adopted to obtain properties of particle phase. Two-way coupling effect between the fluid and the particle phase is considered in the model. The accuracy of the models is tested by the data in the reference. The comparison shows that the model is basically correct and feasible.

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.

COUPLING MODEL OF TWO PHASE FLOW IN A FRACTURE-ROCK MATRIX SYSTEM AND ITS STOCHASTIC FEATURE ANALYSIS

This study is concerned with developing a two-dimensional two-phase model that simulate the movement of non-aqueous phase liquid (NAPL) in a fracture-rock matrix system. The intrinsic permeability and the fracture aperture are represented in the model via its KarhunenLoeve expansion. Other parameters and the nodal unknowns, water saturations and water pressures, are represented by their stochastic spectral expansions. The errors resulting from truncation of Karhunen - Loeve and polynomial chaos expansions to a finite number of terms are analyzed. The eigenvalues of stochastic process is found out for any point in the special domain of the problem at any instant in time.

Study on gas–liquid flow characteristics in stirred tank with dual-impeller based on CFD-PBM coupled model

Study on gas–liquid flow in stirred tank with two combinations of dual-impeller(six-bent-bladed turbine(6BT)+six-inclined-blade down-pumping turbine(6 ITD),the six-bent-bladed turbine(6BT)+six-inclinedblade up-pumping turbine(6ITU))was conducted using computational fluid dynamics(CFD)and population balance model(PBM)(CFD-PBM)coupled model.The local bubble size was captured by particle image velocimetry(PIV)measurement.The gas holdup,bubble size distribution and gas–liquid interfacial area were explored at different conditions through numerical simulation.The results showed that the 4 mm bubbles accounted for the largest proportion of 33%at the gas flow rates Q=0.76 m^(3)·h^(-1) and 22%at Q=1.52 m^(3)·h^(-1) for combined impeller of 6BT+6ITU,while the bubbles of 4.7 mm and 5.5 mm were the largest proportion for 6BT+6ITD combination,i.e.25%at Q=0.76 m^(3)·h^(-1) and 22%at Q=1.52 m^(3)·h^(-1),respectively,which indicated that 6BT+6ITU could reduce bubble size effectively and promote gas dispersion.In addition,the gas holdup around impellers was increased obviously with the speed compared with gas flow rate.So it was concluded that 6ITU impeller could be more conductive to the bubble dispersion with more uniform bubble size,which embodied the advantages of 6BT+6ITU combination in gas–liquid mixing.

Study on the Effect of Solid Particles on Jet Flow and Base Thermal Environment for Solid-Liquid Bundled Rocket

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.

Electrochemical machining gap prediction with multi-physics coupling model based on two-phase turbulence flow

Considering the influence of hydrogen gas generated during electrochemical machining on the conductivity of electrolyte, a two-phase turbulent flow model is presented to describe the gas bubbles distribution.The k-e turbulent model is used to describe the electrolyte flow field.The Euler–Euler model based on viscous drag and pressure force is used to calculate the twodimensional distribution of gas volume fraction.A multi-physics coupling model of electric field,two-phase flow field and temperature field is established and solved by weak coupling iteration method.The numerical simulation results of gas volume fraction, temperature and conductivity in equilibrium state are discussed.The distributions of machining gap at different time are analyzed.The predicted results of the machining gap are consistent with the experimental results, and the maximum deviation between them is less than 50 lm.

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.

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.

Numerical Investigation of Particle Temperature Change in Supersonic Flows

Gas-particle two-phase flow is a very important consideration in designing various machines. Although a great deal of theoretical, experimental, and numerical research has been carried out, particle motion in a supersonic flow has not been sufficiently clarified. Hence, in order to clarify the interactions between flow and particles, the authors consider the characteristics of particle motion, especially at high temperatures. In the present study, the flow of a gas with a diluted particle load is to be simulated in a conventional converging-diverging supersonic nozzle. The turbulent gas flow in the nozzle is computed with the finite difference and RANS （raynolds averaged navier-stokes simulation） methods. The particle motion is simulated in a Lagrangian manner. In addition, taking into account the light particle loading, a weak coupling method is used. Through this investigation, it is shown that the particle velocity increases monotonically from the nozzle throat to the outlet. And it is shown that particles can be accelerated to higher velocities in helium than in nitrogen, and smaller particles tend to attain higher speed and lower static temperature.

A simple approach for the estimation of CO_2 penetration depth into a caprock layer

Caprock is a water-saturated formation with a sufficient entry capillary pressure to prevent the upward migration of a buoyant fluid. When the entry capillary pressure of caprock is smaller than the pressure exerted by the buoyant CO2plume, CO2gradually penetrates into the caprock. The CO2penetration depth into a caprock layer can be used to measure the caprock sealing efficiency and becomes the key issue to the assessment of caprock sealing efficiency. On the other hand, our numerical simulations on a caprock layer have revealed that a square root law for time and pore pressure exists for the CO2penetration into the caprock layer. Based on this finding, this study proposes a simple approach to estimate the CO2penetration depth into a caprock layer. This simple approach is initially developed to consider the speed of CO2invading front. It explicitly expresses the penetration depth with pressuring time, pressure difference and pressure magnitude. This simple approach is then used to fit three sets of experimental data and good fittings are observed regardless of pressures, strengths of porous media, and pore fluids(water,hydrochloric acid, and carbonic acid). Finally, theoretical analyses are conducted to explore those factors affecting CO2penetration depth. The effects of capillary pressure, gas sorption induced swelling, and fluid property are then included in this simple approach. These results show that this simple approach can predict the penetration depth into a caprock layer with sufficient accuracy, even if complicated interactions in penetration process are not explicitly expressed in this simple formula.

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.

Analysis of influencing factors on suction capacity in seabed natural gas hydrate by cutter-suction exploitation

The mathematical and simulation models of working head in the deep-sea working environment were built to analyze the effects of cutter-suction flow,cutter-head rotating speed,cutting depth and suction port position on the cutter-suction capacity.The efficiency of the cutter-suction is analyzed based on the analysis of the variation law of the solid-phase volume fraction of the flow field,the variation law of the velocity distribution in the flow field and the distribution law of the solid-phase concentration.The results show that the increase of cutter-suction flow can significantly improve the cutter-suction efficiency when it is less than1000m3/h.However,when it is more than1000m3/h,it is helpless.When the cutter-head rotate speed is within the range of10–25r/min,the cutter-suction efficiency stabilizes at about95%.While the speed is greater than25r/min,the cutter-suction efficiency decreases sharply with the increase of cutter-head rotate speed.With the increase of cutting depth,the cutter-suction efficiency first increases and then remains stable and finally decreases.The cutter-suction efficiency remains at about94%when the suction port position deviation ranges from0°to30°,but it has a sharply reduction when the deviation angle is more than30°.

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.

Analysis of the Agglomeration of Powder in a Coaxial Powder Feeding Nozzle Used for Laser Energy Deposition

To improve the agglomeration of powder in a coaxial powder feeding nozzle used in the frame of a laser energy deposition technique,the influence of several parameters must be carefully assessed.In the present study the problem is addressed by means of numerical simulations based on a DEM-CFD(Discrete Element Method and Discrete Element Method)coupled model.The influence of the powder flow concentration,powder flow focal length and the amount of powder at the nozzle outlet on the rate of convergence of the powder flow is considered.The role played by the nozzle outlet width,the angle between the inner and outer walls and the powder incident angle in determining the powder flow concentration is also considered.The results show that,with increasing of nozzle outlet width,the powder flow concentration per unit volume at the nozzle focal point undergoes a non-monotonic behaviour(it first increases and then decreases).When the nozzle outlet widthδis 1.00 mm,the powder flow concentration at the focal point is maximal and the powder flow convergence can be considered optimal.By increasing the angle between the inner and outer walls,the powder flow concentration related to the upper focus decreases,the focus diameter increases and the powder flow aggregation worsens.The powder flow concentration increases first and then decreases with increasing incident angle.When the incident angleθis 30°,the powder flow exhibits the best agglomeration properties.When the outlet width is smaller,the angle between the inner and outer walls is larger,and when the incident angle is set at 30°,the powder flow concentration of the coaxial nozzle can be effectively improved.

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.

Analysis of the motion of small-scale ellipsoidal particles in a horizontal laminar flow field

A particle movement model for a horizontal laminar flow field was established in this study,using a modified Basset-Boussinesq-Oseen equation for multiphase fluid dynamics,The motion of ellipsoidal and spherical particles in this flow field was compared to determine the differences in entrainment of ellipsoidal versus spherical particles.Our theoretical results indicate that ellipsoidal particles move more rapidly and smoothly within the fluid than spherical particles under the same conditions.Moreover,this feature is enhanced,as the ellipsoidal degree of the particle increases.Based on a dimensional analysis,flow experiments were carried out to verify the behavior of ellipsoidal versus spherical particles in practice.Both our theoretical and experimental results show that ellipsoidal particles approach the fluid velocity more quickly than spherical particles.Future work would need to address effects of velocity gradients and rotation on particle behavior.

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.