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 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.

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）.

Pressure Drop of Liquid–Solid Two-Phase Flow in the Vertical Tube Bundle of a Cold-Model Circulating Fluidized Bed Evaporator

A cold-model vertical multi-tube circulating fluidized bed evaporator was designed and built to conduct a visualization study on the pressure drop of a liquid–solid two-phase flow and the corresponding particle distribution.Water and polyformaldehyde particle(POM)were used as the liquid and solid phases,respectively.The effects of operating parameters such as the amount of added particles,circulating flow rate,and particle size were systematically investigated.The results showed that the addition of the particles increased the pressure drop in the vertical tube bundle.The maximum pressure drop ratios were 18.65%,21.15%,18.00%,and 21.15%within the experimental range of the amount of added particles for POM1,POM2,POM3,and POM4,respectively.The pressure drop ratio basically decreased with the increase in the circulating flow rate but fluctuated with the increase in the amount of added particles and particle size.The difference in pressure drop ratio decreased with the increase in the circulating flow rate.As the amount of added particles increased,the difference in pressure drop ratio fluctuated at low circulating flow rate but basically decreased at high circulating flow rate.The pressure drop in the vertical tube bundle accounted for about 70%of the overall pressure drop in the up-flow heating chamber and was the main component of the overall pressure within the experimental range.Three-dimensional phase diagrams were established to display the variation ranges of the pressure drop and pressure drop ratio in the vertical tube bundle corresponding to the operating parameters.The research results can provide some reference for the application of the fluidized bed heat transfer technology in the industry.

Numerical Study of Solid-Liquid Two-Phase Flow in Stirred Tanks with Rushton Impeller (Ⅰ) Formulation and Simulation of Flow Field

The critical impeller speed, NJs, for complete suspension of solid particles in the agitated solid-liquid two-phase system in baffled stirred tanks with a standard Rushton impeller is predicted using the computational procedure proposed in Part I. Three different numerical criteria are tested for determining the critical solid suspension. The predicted NJS is compared with those obtained from several empirical correlations. It is suggested the most reasonable criterion for determining the complete suspension of solid particles is the positive sign of simulated axial velocity of solid phase at the location where the solid particles are most difficult to be suspended.

Numerical Study of Solid-Liquid Two-Phase Flow in StirredTanks with Rushton Impeller(Ⅱ) Prediction of Critical Impeller Speed

Three-dimensional solid-liquid flow is mathematically formulated by means of the 'two-fluid' approach and the two-phase k-ε-AP turbulence model. The turbulent fluctuation correlations appearing in the Reynolds time averaged governing equations are fully incorporated. The solid-liquid flow field and solid concentration distribution in baffled stirred tanks with a standard Rushton impeller are numerically simulated using an improved 'inner-outer'iterative procedure. The flow pattern is identified via the velocity vector plots and a recirculation loop with higher solid concentration is observed in the central vicinity beneath the impeller. Comparison of the simulation with experimental data on the mean velocities and the turbulence quantities of the solid phase is made and quite reasonable agreement is obtained except for the impeller swept volume. The counterpart of liquid phase is presented as well.The predicted solid concentration distribution for three experimental cases with the average solid concentration up to 20% is also found to agree reasonably with the experimental results published in the literature.

Mechanism from particle compaction to fluidization of liquid–solid two-phase flow

A new model of particle yield stress including cohesive strength is proposed,which considers the friction and cohesive strength between particles.A calculation method for the fluidization process of liquid–solid two-phase flow in compact packing state is given,and the simulation and experimental studies of fluidization process are carried out by taking the sand–water two-phase flow in the jet dredging system as an example,and the calculation method is verified.

K-ε-T MODEL OF DENSE LIQUID-SOLID TWO-PHASE TURBULENT FLOW AND ITS APPLICATION TO THE PIPE FLOW

To predict the characteristics of dense liquid-solid two-phase flow, K-Ε-T model is established, in which the turbulent flow of fluid phase was described with fluid turbulent kinetic energy Kf and its dissipation rate Εf, and the particles random motion was described with particle turbulent energy Kp and its dissipation rate Εp and pseudothermal temperature Tp. The governing equations were also derived. With K-Ε-T model, numerical study of dense liquid-solid two-phase turbulent up-flow in a pipe is performed. The calculated results are in good agreement with experimental data of Alajbegovic et al. (1994), and some flow features are captured.

SIMULATION OF GAS AND LIQUID TWO-PHASE FLOW THROUGH THE BLAST FURNACE DROPPING ZONE

A three-dimensional mathematical model,based on differential balances of mass and momentum,hasbeen developed to describe the two-phase flow of gas and liquid through the dropping zone of the blast fur-nace.Agreement between observed and calculated values verifies the validity of this model.On the basis of this model,various parameters for the surrounding of the dry zone of Blast FurnaceNo.I-BF of the Beijing Iron and Steel Company have been computed,from which a diagram for demar-cation of fluidization of coke and flooding of slag has been proposed.

Investigation of erosion behavior of 304 stainless steel under solid–liquid jet flow impinging at 30°

This work carried out liquid-solid two-phase jet experiments and simulations to study the erosion behavior of 304 stainless steel at 30° impingement.The single-phase impinging jet was simulated using dense grid by one-way coupling of solid phase due to its dilute distribution.The simulation results agreed well with experiments.It was found that after impinging particle attrition occurred and particles became round with decreasing length-ratio and particle breakage occurred along the "long" direction.Both experiment and simulations found that the erosion generated on the sample could be divided into three regions that were nominated as stagnant region,cutting transition region and wall jet region.Most particle-wall impacts were found to occur in the cutting transition region and the wall jet region.In the cutting transition region,holes and lip-shaped hogbacks were generated in the same direction as the flow imping.In the wall jet region,furrows and grooves were generated.The averaged grooves depth tended to become constant with the progress of impinging and reach the steady state of erosion in the end.In addition,it was found that impinging effect increased erosion and anti-wear rate.

RESEARCH ON METHOD TO CALCULATE VELOCITIES OF SOLID PHASE AND LIQUID PHASE IN DEBRIS FLOW

Velocities of solid phase and liquid phase in debris flow are one key problem to research on impact and abrasion mechanism of banks and control structures under action of debris flow. Debris flow was simplified as two-phase liquid composed of solid phase with the same diameter particles and liquid phase with the same mechanical features. Assume debris flow was one-dimension two-phase liquid moving to one direction, then general equations of velocities of solid phase and liquid phase were founded in two-phase theory. Methods to calculate average pressures, volume forces and surface forces of debris flow control volume were established. Specially, surface forces were ascertained using Bingham＇s rheology equation of liquid phase and Bagnold＇s testing results about interaction between particles of solid phase. Proportional coefficient of velocities between liquid phase and solid phase was put forward, meanwhile, divergent coefficient between theoretical velocity and real velocity of solid phase was provided too. To state succinctly before, method to calculate velocities of solid phase and liquid phase was obtained through solution to general equations. The method is suitable for both viscous debris flow and thin debris flow. Additionally, velocities every phase can be identified through analyzing deposits in-situ after occurring of debris flow. It is obvious from engineering case the result in the method is consistent to that in real-time field observation.

Effects of tube cross-sectional shapes on flow pattern, liquid film and heat transfer of n-pentane across tube bundles

The heat transfer of hydrocarbon refrigerant across tube bundles have been widely used in refrigeration.Three-dimensional simulation model using volume of fluid(VOF) was presented to study the effects of tube shapes on flow pattern, film thickness and heat transfer of n-pentane across tube bundles, including circle, ellipse-shaped, egg-shaped and cam-shaped tube bundles. Simulation results agree well with experimental data in the literature. The liquid film thickness of sheet flow and heat transfer for different tube shapes were obtained numerically. The flow pattern transition occurs lower vapor quality for ellipse-shaped tube than other tube shapes. For sheet flow, the liquid film on circle tube and ellipseshaped tube is symmetrically distributed along the circumferential direction. However, the liquid film on egg-shaped tube at circumferential angles(θ) = 15°–60° is thicker than θ = 135°–165°. The liquid film on cam tube at θ = 15°–60° is slightly thinner than θ = 135°–165°. The liquid film thickness varies from thinner to thicker for ellipse-shaped, cam-shaped, egg-shape and circle within θ = 15°–60°. The effect of tube shape is insignificant on thin liquid film thickness. Ellipse-shaped tube has largest heat transfer coefficient for sheet flow. In practical engineering, the tube shape could be designed as ellipse to promote heat transfer.

Two-flow model for piping erosion based on liquid-solid coupling

Previous studies have indicated that piping erosion greatly threatens the safe operation of various hydraulic structures. However, few mathematical models are available to perfectly describe the erosion process due to the complexity of piping. The focus of the present work is to propose a new fluid solid coupling model to eliminate the shortcomings of existing work. A 'pseudo-liquid' assumption is suggested to simulate the particle movement in the erosion process. Then, based on the mass and momentum conservations of the moving particles and flowing water, a new two-flow model is established by using the continuity equations and motion equations. In the model, the erosion rate of soil is determined with a particle erosion law derived from tests results of STERPI. And ERGUN's empirical equation is used to determine the interaction forces between the liquid and the solid. A numerical approach is proposed to solve the model with the finite volume method and SIMPLE algorithm. The new model is validated with the tests results of STERPI. And the soil erosion principles in piping are also explored.

Coupling of discrete-element method and smoothed particle hydrodynamics for liquid-solid flows

Particle based methods can be used for both the simulations of solid and fluid phases in multiphase medium, such as the discrete-element method for solid phase and the smoothed particle hydrodynamics for fluid phase. This paper presents a computational method combining these two methods for solid-liquid medium. The two phases are coupled by using an improved model from a reported Lagrangian-Eulerian method. The technique is verified by simulating liquid-solid flows in a two-dimensional lid-driven cavity.

Flux vector splitting solutions for coupling hydraulic transient of gas-liquid-solid three-phase flow in pipelines

The gas-liquid-solid three-phase mixed flow is the most general in multiphase mixed transportation. It is significant to exactly solve the coupling hydraulic transient problems of this type of multiphase mixed flow in pipelines. Presently, the method of characteristics is widely used to solve classical hydraulic transient problems. However, when it is used to solve coupling hydraulic transient problems, excessive interpolation errors may be introduced into the results due to unavoidable multiwave interpolated calculations. To deal with the problem, a finite difference scheme based on the Steger- Warming flux vector splitting is proposed. A flux vector splitting scheme is established for the coupling hydraulic transient model of gas-liquid-solid three-phase mixed flow in the pipelines. The flux subvectors are then discretized by the Lax-Wendroff central difference scheme and the Warming-Beam upwind difference scheme with second-order precision in both time and space. Under the Rankine-Hugoniot conditions and the corresponding boundary conditions, an effective solution to those points located at the boundaries is developed, which can avoid the problem beyond the calculation region directly induced by the second-order discrete technique. Numerical and experimental verifications indicate that the proposed scheme has several desirable advantages including high calculation precision, excellent shock wave capture capability without false numerical oscillation, low sensitivity to the Courant number, and good stability.

THE STUDY OF INTERACTION OF SOLID-LIQUID ADSORPTION SYSTEM BY USING THE FLOW INJECTION-SPECTROPHOTOMETRY SYSTEM

The flow injection analysis was firstly used for studying a solid-liquid adsorption system, and the dynamics process in the adsorption of dyestuff with regenerable chitin was traced by an online method of flow injection-spectrophotometry. Experimental results indicate that there is a linearization between the tested signals and the height of peaks with reciprocity coefficient 0.9999 by using the flow injection-spectrophotometry system to study the dynamics adsorption process in solidliquid system. The method shows a good stability and reproducibility. It provides a new method for the studies on adsorption dynamics in solid- liquid system.

Experimental Investigation of Vibration Response of A Free-Hanging Flexible Riser Induced by Internal Gas-Liquid Slug Flow

The vibration response of a free-hanging flexible riser induced by internal gas-liquid slug flow was studied experimentally in a small-diameter tube model based on Froude number criterion. The flow regime in a curved riser model and the response displacements of the riser were simultaneously recorded by high speed cameras. The gas superficial velocity ranges from 0.1 m/s to 0.6 m/s while the liquid superficial velocity from 0.06 m/s to 0.3 m/s.Severe slugging type 3, unstable oscillation flow and relatively stable slug flow were observed in the considered flow rates. Severe slugging type 3 characterized by premature gas penetration occurs at relatively low flow rates. Both the cycle time and slug length become shorter as the gas flow rate increases. The pressure at the riser base undergoes a longer period and larger amplitude of fluctuation as compared with the other two flow regimes. Additionally, severe slugging leads to the most vigorous in-plane vibration. However, the responses in the vertical and horizontal directions are not synchronized. The vertical vibration is dominated by the second mode while the horizontal vibration is dominated by the first mode. Similar to the vortex-induced vibration, three branches are identified as initial branch, build-up branch and descending branch for the response versus the mixture velocity of gas-liquid flow.

ON EQUATION OF DISCRETE SOLID PARTICLES' MOTION IN ARBITRARY FLOW FIELD AND ITS PROPERTIES

The forces on rigid particles moving in relation to fluid having been studied and the equation of modifications of their expressions under different flow conditions discussed, a general form of equation for discrete particles' motion in arbitrary flow field is obtained. The mathematical features of the linear form of the equation are clarified and analytical solution of the linearized equation is gotten by means of Laplace transform. According to above theoretical results, the effects of particles' properties on its motion in several typical flow field are studied, with some meaningful conclusions being reached.

Numerical Simulation of Gas-Solid Flow in Square Cyclone Separators with Downward Exit

Cyclone separators are widely used in industrial applications. The separation efficiency and pressure drop are the most important parameters to evaluate the performance of processing system. In the simulations,the flow behavior of gas and particles within a square cyclone separator is simulated by means of computational fluid dynamics. The RNG k- ε model and the Reynolds stress model( RSM) are used to model gas turbulence. The flow behavior is examined in the term of tangential velocity components,static pressure and pressure drop contour plots for flow field and solid volume fraction. The effects of the turbulence model and solid volume fraction on the square cyclone are discussed. The results indicate that the pressure drop increases with the increase of solid volume fraction,and increase with the increase of inlet velocities for two turbulence models, moreover,the simulations results are compared with pressure field. For all runs,the RSM model gives a higher pressure drop compared to the RNG k- ε model. The RSM model provides well the forced vortex and free vortex,and captures better the phenomena occurring during intense vortex flow in the presence of walls within cyclone separators.