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 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.

Design and Experimental Analyses of Small-flow High-head Centrifugal-vortex Pump for Gas-Liquid Two-phase Mixture

The design method of small-flow high-head centrifugal-vortex pump was presented. This pump, configured with inducer, complex-centrifugal impeller and open-vortex impeller, was put forward to deliver gas-liquid two-phase mixture. An HTB-5/60 type sample pump was developed and tested on a closed-loop test rig. Experimental studies on performance and cavitation tests for gas-liquid two-phase mixture were carried out compared with pure-water experimental results. Also the effect of gas phase on pump was analyzed and discussed. The experimental results show that performance and cavitation characteristics of the sample purnp deteriorates progressively with increasing volume fraction of gas. When the total capacity Qm is between 4.5 m^3·h^-1 and 6 m^3·h^-1 and the gas flow rate qg below 0.66 m^3·h^-1, or qg/Qm is lower than 15%, the characteristic curves are approximately parallel to those in pure water test, but the performance deteriorates sharply until an abrupt flow-cutting at a critical volume fraction of gas. This pump is found suitable for transporting gas-liquid two-phase mixture when working around rated capacity of 5 m^3·h^-1 with qglQm below 15%.

A Numerical Study on the Effect of the Backflow Hole Position on the Performances of a Self-Priming Pump

A self-priming pump is a centrifugal pump that has the ability to prime itself. Typically, its performance dependson the configuration of its reflux hole. In this study, the ANSYS FLUENT software is used to investigate the effectsof three different radial positions of the reflux hole on gas-liquid two-phase distribution, pressure pulsation, andimp during self-priming. The research results indicate that: (1) The effective channel size for the reflux liquid toenter the volute varies depending on the location of the reflux hole. The effect of the impeller rotation on thereflux liquid becomes more obvious as the setting distance of the reflux aperture decreases. (2) The position ofthe reflux hole significantly affects the gas phase mass fraction inside the impeller, resulting in a significant reductionin the time it takes for the mass fraction to exceed 80%. (3) The position of the reflux hole significantly affectsthe average pressure on each monitoring surface. (4) Placing the reflux hole at a excessively distant radial distancecan result in an excessive vertical component. (5) The self-priming performance of the pump can be improved tosome extent by placing the return hole at a small radial distance.

Performance Prediction of an Optimized Centrifugal Pump with High Efficiency

The main structural parameters of the IR100-80-100A type chemical centrifugal pump have been optimized by means of an orthogonal test approach.The centrifugal pump has been modeled using the CFturbo software,and 16 sets of orthogonal-test schemes have been defined on the basis of 4 parameters,namely,the blade number,blade outlet angle,impeller outlet diameter,and impeller outlet width.Such analysis has been used to determine the influence of each index parameter on the pump working efficiency and identify a set of optimal combinations of such parameters.The internalflowfield in the centrifugal pump has been simulated by using the PumLinx software.These numerical results have shown that,compared with the prototype pump,the outlet pressure and shaft power of the optimized pump can be significantly reduced,and the pump working efficiency can be improved by 5.59%.In the present study,some arguments are also provided to demonstrate that,with respect to other optimization methods,the orthogonal test approach is more convenient,and requires less test times.

Unsteady Flow and Structural Behaviors of Centrifugal Pump under Cavitation Conditions

Cavitation has a significant e ect on the flow fields and structural behaviors of a centrifugal pump. In this study, the unsteady flow and structural behaviors of a centrifugal pump are investigated numerically under di erent cavitation conditions. A strong two-way coupling fluid-structure interaction simulation is applied to obtain interior views of the e ects of cavitating bubbles on the flow and structural dynamics of a pump. The renormalization-group k-ε turbulence model and the Zwart–Gerbe–Belamri cavitation model are solved for the fluid side, while a transient structural dynamic analysis is employed for the structure side. The di erent cavitation states are mapped in the head-net positive suction head(H-NPSH) curves and flow field features inside the impeller are fully revealed. Results indicate that cavitating bubbles grow and expand rapidly with decreasing NPSH. In addition, the pressure fluctuations, both in the impeller and volute, are quantitatively analyzed and associated with the cavitation states. It is shown that influence of the cavitation on the flow field is critical, specifically in the super-cavitation state. The e ect of cavitation on the unsteady radial force and blade loads is also discussed. The results indicate that the averaged radial force increased from 8.5 N to 54.4 N in the transition progress from an onset cavitation state to a super-cavitation state. Furthermore, the structural behaviors, including blade deformation, stress, and natural frequencies, corresponding to the cavitation states are discussed. A large volume of cavitating bubbles weakens the fluid forces on the blade and decreases the natural frequencies of the rotor system. This study could enhance the understanding of the e ects of cavitation on pump flow and structural behaviors.

NUMERICAL SIMULATION OF 3-D DENSE SOLID-LIQUID TWO-PHASE TURBULENT FLOW IN A NON-CLOGGING MUD PUMP

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.

Influence of Blade Outlet Angle on Inner Flow Field of Centrifugal Pump Transporting Salt Aqueous Solution

During transportation of salt aqueous solutions with centrifugal pump, crystallization phenomenon is frequently encountered. For this kind of two-phase flow, it is difficult to be accurately modeled since there are various medium properties and phase change characteristics. In view of experiment, several problems are hampering the implementation of precise measurement. Influences of blade outlet angle and medium temperature on crystallization rate were studied. Sodium sulfate solution was applied to simulate practical fluid in chemical industry. Particle image velocimetry（PIV） was employed to measure velocity distributions in rotating impeller. Crystallization processes in three impellers with different blade outlet angles were investigated. Relations among crystallization and flow parameters such as temperature and velocity were obtained. With the same blade wrap angle, when blade outlet angle is larger, diffusion of single flow passage gets stronger, relative velocity at blade outlet decreases and large scale vortex tends to appear near the blade working surface. For the impact of volume effect of particle phase on fluid viscosity, both liquid and solid phase velocities decrease with continual forming and growing of crystal particles. Velocity of solid phase is greater than that of liquid phase and its direction leans more closely to blade working surface. Solid particles tend to move towards blade working surface, as is more obvious in the impeller with large blade outlet angle. Therefore, collision between solid particles with stem part of blade working surface is more intensive in impeller with large blade outlet angle. Concerning transportation of salt aqueous solution, accurate PIV measurement is conducted in centrifugal impellers with different blade outlet angles. The results are useful and instructive in relevant engineering design and operation.

An improved large eddy simulation of two-phase flows in a pump impeller

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.

Influence of Blade Thickness on Transient Flow Characteristics of Centrifugal Slurry Pump with Semi-open Impeller

As the critical component, the impellers of the slurry pumps usually have blades of a large thickness. The increasing excretion coefficient of the blades affects the flow in the impeller resulting in a relatively higher hydraulic loss, which is rarely reported. In order to investigate the influence of blade thickness on the transient flow characteristics of a centrifugal slurry pump with a semi-open impeller, transient numerical simulations were carried out on six impellers, of which the meridional blade thickness from the leading edge to trailing edge varied from 5-10 mm, 5-15 mm, 5-20 mm, 10-10 mm, 10-15 mm, and 10-20 mm, respectively. Then, two of the six impellers, namely cases 4 and 6, were manufactured and experimentally tested for hydraulic performance to verify the simulation results. Results of these tests agreed reasonably well with those of the numerical simulation. The results demonstrate that when blade thickness increases, pressure fluctuations at the outlet of the impeller become severe. Moreover, the standard deviation of the relative velocity in the middle portion of the suction sides of the blades decreases and that at the outlet of the impeller increases. Thus, the amplitude of the impeller head pulsation for each case increases. Meanwhile, the distribution of the time-averaged relative flow angle becomes less uniform and decreases at the outlet of the impeller. Hence, as the impeUer blade thickness increases, the pump head drops rapidly and the maximum efficiency point is offset to a lower flow rate condition. As the thickness of blade trailing edge increases by 10 mm, the head of the pump drops by approximately 5 m, which is approximately 10 % of the original pump head. Futhermore, it is for the first time that the time-averaged relative flow angle is being considered for the analysis of transient flow in centrifugal pump. The presented work could be a useful guideline in engineering practice when designing a centrifugal slurry pump with thick impeller blades.

THREE-DIMENSIONAL COUPLED IMPELLER-VOLUTE SIMULATION OF FLOW IN CENTRIFUGAL PUMP AND PERFORMANCE PREDICTION

A three-dimensional turbulent flow through an entire centrifugal pump is simulated using k-ε turbulence model modified by rotation and curvature, SIMPLEC method and body-fitted coordinate. The velocity and pressure fields are obtained for the pump under various working conditions, which is used to predict the head and hydraulic efficiency of the pump, and the results correspond well with the measured values. The calculation results indicate that the pressure is higher on the pressure side than that on the suction side of the blade; The relative velocity on the suction side gradually decreases from the impeller inlet to the outlet, while increases on the pressure side, it finally results in the lower relative velocity on the suction side and the higher one on the pressure side at the impeller outlet; The impeller flow field is asymmetric, i.e. the velocity and pressure fields arc totally different among all channels in the impeller; In the volute, the static pressure gradually increases with the flow route, and a large pressure gratitude occurs in the tongue; Secondary flow exists in the rear part of the spiral.

Differential amplification method for flow structures analysis of centrifugal pump between design and off-design points

The three-dimensional internal flow field of centrifugal pump is complex and variable with design parameters and operation conditions. The post-processing technique named differential amplification method was proposed for the comparison study of different flow structures. The full steady flow fields of an industrial centrifugal pump working on-design and off-design points were numerically investigated by solving Reynolds average Navier-Stokes equations together with a shear-stress transport(SST) k-? turbulence model. And the numerically predicted performance curves of the studied pump agree well with test measurement results. Compared with the flow flied on design point under the help of differential amplification method, the disturbance caused by interaction between blade and volute tongue is very obvious and it extends to the diffuser pipe on the working point with 0.8 times rated flux. While on the point with 1.2 times rated flux, the flow distribution in impeller region is roughly even and it flows more to the bottom section of the diffuser pipe. The above method was proved to be good at displaying the subtle secondary flow structure changes with a higher resolution effect relative to single isolated case observation, which helps the optimization decision-making from multiple design cases.

Experimental Investigation on the Flow-induced Noise under Variable Conditions for Centrifugal Pumps

With extensively using of centrifugal pumps,noise generation in these pumps is increasingly receiving research attention in recent years.The noise sources in centrifugal pumps are mainly composed of mechanical noise and flow-induced noise.And the study of flow-induced noise has become a hotspot and important domain in the field.The flow-induced noise closely related to the inner pressure pulses and vibration of volute in pumps,therefore,it is necessary to research the interaction and mechanism among them.To investigate the relationships,a test system is designed which includes a test loop and a measurement system.The hydrophones and pressure sensors are installed on the outlet of the pump and vibration acceleration sensors are disposed on the pump body.Via these instruments,the signals of noise,pressure pulses and vibration are collected and analyzed.The results show that the level of flow-induced noise becomes smaller as the flow increment during low flow rate operations,and it is steadily close to the design point,then it increases with the growing of flow rate in high flow rate conditions.Furthermore,there are some similar peak points in the power spectrum charts of noise,pressure pulses and vibration.The broadband noise at low flow rate is mostly focused on the region of 0-40 times shaft frequency,which is mostly made by rotating stall and vortex;while the noise at high flow rate conditions is focused on the region of 60-100 times shaft frequency,which may be mostly made by cavitations.The proposed research is of practical and academic significance to the study of noise reduction for centrifugal pumps.

Numerical and Experimental Study on Flow-induced Noise at Blade-passing Frequency in Centrifugal Pumps

With the increasing noise pollution, low noise optimization of centrifugal pimps has become a hot topic. However, experimental study on this problem is unacceptable for industrial applications due to unsustainable cost. A hybrid method that couples computational fluid dynamics （CFD） with computational aeroacoustic software is used to predict the flow-induced noise of pumps in order to minimize the noise of centrifugal pumps in actual projects. Under Langthjem＇s assumption that the blade surface pressure is the main flow-induced acoustic source in centrifugal pumps, the blade surface pressure pulsation is considered in terms of the acoustical sources and simulated using CFX software. The pressure pulsation and noise distribution in the near-cutoff region are examined for the blade-passing frequency （BPF） noise, and the sound pressure level （SPL） reached peaks near the cutoff that corresponded with the pressure pulsation in this region. An experiment is performed to validate this prediction. Four hydrophones are fixed to the inlet and outlet ports of the test pump to measure the flow-induced noise from the four-port model. The simulation results for the noise are analyzed and compared with the experimental results. The variation in the calculated noise with changes in the flow agreed well with the experimental results. When the flow rate was increased, the SPL first decreased and reached the minimum near the best efficient point （BEP）; it then increased when the flow rate was further increased. The numerical and experimental results confirmed that the BPF noise generated by a blade-rotating dipole roughly reflects the acoustic features of centrifugal pumps. The noise simulation method in current study has a good feasibility and suitability, which could be adopted in engineering design to predict and optimize the hydroacoustic behavior of centrifugal pumps.

Left Ventricle Failure and Blood Flow Estimation for Centrifugal Blood Pumps

This paper shows the blood flow control （FwC） performance to adjust rotational speed of an ICBP （implantable centrifugal blood pump） in order to provide an adequate flow to left ventricle in different patient conditions. ICBP is a totally implantable LVAD （left ventricular assist device） with ceramic bearings developed for long term circulatory assistance. FwC uses PI （proportional-integral） control to adjust rotational speed in order to provide blood flow. FwC does not use sensor for feedback, as there is an estimation system to provide blood flow measurement. Control strategy has being studied in a HCS （hybrid cardiovascular simulator） as a tool that allows the physical connection of ICBP during evaluation. In addition, HCS allows changes of some cardiovascular parameters in order to simulate specific heart disease： ejection fraction （10-25%） and heart rate （50-110 bpm）. FwC was able to adjust blood flow with steady error less than 2%. Results demonstrated that FwC is adequate to LVAD control irL different left ventricle failure conditions.

Numerical simulation on centrifugal pump compressible flow field with different gas volume fractions

In order to study the influence of gas-liquid two-phase flow on the performance and internal flow field of a centrifugal pump,the steady three-dimensional flow with different gas volume fractions was simulated by applying the Reynolds-average N-S equation and mixture gas-liquid two-phase flow model,and the compressibility of gas was taken into consideration in the simulation. Then the centrifugal pump characteristic and the gas distribution law in different gas volume fractions were analyzed. The computational results show that gas volume fraction has a certain influence on the performance of the centrifugal pump,and the efficiency and head of the pump are on the decline with the increase of it.Static pressure in the impeller increases in the radial direction,but the pressure gradient in the flow direction is different under the different gas volume fractions. The gas volume is distributed mainly in the ipsilateral direction of impeller back shroud in the flow channel of the volute. On the suction side of the blade inlet there is an obvious low-pressure area,which causes bubbles agglutination and higher gas volume fraction. With the gas entering passage flow,gas volume fraction in the suction decreases and the pressure surface rises gradually. Higher gas volume fraction causes air blocking phenomenon in the flow passage and the discharge capacity reduces. The increase of gas volume makes the turbulent motion within the impeller more and more intense,which leads to more and more energy loss.

Effects of silt particle on cavitation flow in centrifugal pump

Based on numerical method, effects of silt particle with certain silt mean diameter and silt concentration on the evolution of cavitation in a centrifugal pump were studied. Silt mean diameter 0.005 mm and silt concentration 1.0% were adopted in numerical simulations. Cavitation flow in a flat- nosed cylinder was simulated to validate the designed algorithm. Cavitaton flows of water and silt-laden water were simulated and compared. The results indicate that the silt particles promote the evolution of cavitation. At the outlet pressure of 6.0×10^5 Pa, cavitation bubbles do not exist in the water flow, but a few cavitation bubbles appeare in the silt-laden water flow, demonstrating the silt particles induce the formation of cavitation bubbles. At the outlet pressure of 5.29×10^5 Pa, the vapor volume fraction in the silt-laden water flow is much larger than that in the water flow, indicating that the silt particles enhance the evolution of cavitation. The properties of silt particle, static pressure, flow field structure, turbulent kinetic energy and density difference have a close relationship with the evolution of cavitation.

Numerical simulation of transient flow performance during different periods in centrifugal pumpNumerical simulation of transient flow performance during different periods in centrifugal pump

The instantaneous variations of the hydraulic characteristics take place in centrifugal pumps during their start-up,shutdown and other variable speed operations.In this paper,the variable speed method was proposed to simulate the transient internal flow field and the external performance of the pump during starting and stopping periods.The terms of accelerations due to variable speeds in the flow governing equations were analyzed in a multiple reference of frame(MRF).A transient CFD simulation was performed for a typical centrifugal pump by using ANSYS-CFX with the standard k-εturbulence model.The entire simulation process was composed of four stages:start-up,normal run,shutdown and post-shutdown.The function of rotating speed with regard to time was set by CEL language directly into the impeller domain in the pre-processor of the software to conduct variable speed simulation.The variations of the flow field in the centrifugal pump were obtained from the transient simulation.The changing laws of flow rate,head and other performance parameters over time were also analyzed and summarized.

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.