Optimization on the impeller of a low-specific-speed centrifugal pump for hydraulic performance improvement

In order to widen the high-efficiency operating range of a low-specific-speed centrifugal pump, an optimization process for considering efficiencies under 1.0Q_d and 1.4Q_d is proposed. Three parameters, namely, the blade outlet width b_2, blade outlet angle β_2, and blade wrap angle φ, are selected as design variables. Impellers are generated using the optimal Latin hypercube sampling method. The pump efficiencies are calculated using the software CFX 14.5 at two operating points selected as objectives. Surrogate models are also constructed to analyze the relationship between the objectives and the design variables. Finally, the particle swarm optimization algorithm is applied to calculate the surrogate model to determine the best combination of the impeller parameters. The results show that the performance curve predicted by numerical simulation has a good agreement with the experimental results. Compared with the efficiencies of the original impeller, the hydraulic efficiencies of the optimized impeller are increased by 4.18% and 0.62% under 1.0Q_d and 1.4Q_d, respectively. The comparison of inner flow between the original pump and optimized one illustrates the improvement of performance. The optimization process can provide a useful reference on performance improvement of other pumps, even on reduction of pressure fluctuations.     

Effect of the blade loading distribution on hydrodynamic performance of a centrifugal pump with cylindrical blades

The effect of the blade loading distribution on head, radial force and pressure pulsation of a low specific-speed centrifugal pump with cylindrical impeller blades were investigated in the present study. Blade shapes were obtained by adopting the 1D inverse design method, impellers with different blade loading curves were obtained while the distribution of the blade loading was carefully tailored. Threedimensional URANS simulation method based on the Shear stress transport (SST) k-ω turbulence model was employed for the analyzation of flow patterns. Numerical results including the pressure distribution and velocity profile were validated by comparing with the available experimental data, and an acceptable agreement was obtained. Three typical parameters of the blade loading curve, including the location of the fore-loading point (m_pre), location of the aft-loading point (m_post) and slope of the rectilinear segment (K), were analyzed. Results showed that the well-designed blade loading curve, such as the fore-loading impeller, can effectively reduce the pressure pulsation amplitude and the radial force. The significant effect of the variation of the aft-loading point on pump hydrodynamic performance was also investigated. Meanwhile, pressure and velocity distributions at different slopes of the blade loading curves show that the fore-loading impeller produces more uniform flow issuing from the impeller than that of the pump with aft-loading impeller, thus reduces the radial force and pressure pulsation of the pump.     

Application of different surrogate models on the optimization of centrifugal pump

An optimization process for impellers was carried out based on numerical simulation, Latin hypercube sampling (LHS), surrogate model and Genetic algorithm (GA) to improve the efficiency of residual heat removal pump. The commercial software ANSYS CFX 14.5 was utilized to solve the Reynolds-averaged Navier-Stokes equations by using the Shear stress transport turbulence model. The impeller blade parameters, which contain the blade inlet incidence angle Δβ, blade wrap angle φ, and blade outlet angle β ₂, were designed by random sample points according to the LHS method. The efficiency predicted under the design flow rate was selected as the objective function. The best combination of parameters was obtained by calculating the surrogate model with the GA. Meanwhile, the prediction accuracies of three surrogate models, namely, Response surface model (RSM), Kriging model, and Radial basis neural network (RBNN), were compared. Results showed that the calculated findings agree with the experimental performance results of the original pump. The RSF model predicted the highest efficiency, while the RBNN had the highest prediction accuracy. Compared with the simulated efficiency of the original pump, the optimization increased efficiency by 8.34% under the design point. Finally, the internal flow fields were analyzed to understand the mechanism of efficiency improvement. The optimization process, including the comparison of the surrogate models, can provide reference for the optimization design of other pumps.     

Numerical and experimental investigation on the diffuser optimization of a reactor coolant pump with orthogonal test approach

The diffuser of a reactor coolant pump was optimized using an orthogonal approach with numerical simulation to improve the pump hydraulic performance. Steady simulation was conducted by solving Reynolds-averaged Naiver-Stokes equations with the SST k-ω turbulence model using CFX code. The influence of the diffuser geometric parameters, namely, S, φ, α ₄, b ₄, δ ₂, R _t and R ₄, on the pump performance were determined. L₁₈ (3⁷) orthogonal table was chosen for the optimization process. Best indicators were determined, and range analysis of energy losses, head, and efficiency at the rated condition was performed. Optimal parameters of the diffuser were S = 490 mm, φ = 36°, α ₄ = 30°, b ₄ = 200 mm, δ ₂ = 20 mm, R _t = 5 mm and R ₄ = 565 mm. The final design was experimentally tested. Simulation results showed more remarkable performance than the experimental result. However, the numerical predictions and experimental results were consistent, validating the design procedure. Loading of the impeller and diffuser blades was analyzed to investigate the direct impact on the hydrodynamic flow field. The head was 14.74 m, efficiency was 79.6 %, and efficiency of the prototype pump was 83.3 % when the model pump functioned at the rated conditions. Optimization results showed that efficiency and head were improved at the design condition.     

Study of flow instability in a centrifugal fan based on energy gradient theory

Flow instability in a centrifugal fan was studied using energy gradient theory. Numerical simulation was performed for the threedimensional turbulent flow field in a centrifugal fan. The flow is governed by the three-dimensional incompressible Navier-Stokes equations coupled with the RNG k-ε turbulent model. The finite volume method was used to discretize the governing equations and the Semi-implicit method for pressure linked equation (SIMPLE) algorithm is employed to iterate the system of the equations. The interior flow field in the centrifugal fan and the distribution of the energy gradient function K are obtained at different flow rates. According to the energy gradient method, the area with larger value of K is the place where the flow loses stability easier. The results show that instability is easier to generate in the regions of impeller outlet and volute tongue. The air flow near the hub is more stable than that near the shroud. That is due to the influences of variations of the velocity and the inlet angle along the axial direction. With the decrease of the flow rate, instability zone in a blade channel moves to the impeller inlet from the outlet and the unstable regions in different channels develop in opposite direction to the rotation of impeller.     

Multi-point optimization on meridional shape of a centrifugal pump impeller for performance improvement

A wide operating band is important for a pump to safely perform at maximum efficiency while saving energy. To widen the operating range, a multi-point optimization process based on numerical simulations in order to improve impeller performance of a centrifugal pump used in nuclear plant applications is proposed by this research. The Reynolds average Navier Stokes equations are utilized to perform the calculations. The meridional shape of the impeller was optimized based on the following four parameters; shroud arc radius, hub arc radius, shroud angle, and hub angle as the design variables. Efficiencies calculated under 0.6Q _d, 1.0Q _d and 1.62Q _d were selected as the three optimized objectives. The Design of experiment method was applied to generate various impellers while 35 impellers were generated by the Latin hypercube sampling method. A Response surface function based on a second order function was applied to construct a mathematical relationship between the objectives and design variables. A multi-objective genetic algorithm was utilized to solve the response surface function to obtain the best optimized objectives as well as the best combination of design parameters. The results indicated that the pump performance predicted by numerical simulation was in agreement with the experimental performance. The optimized efficiencies based on the three operating conditions were increased by 3.9 %, 6.1 % and 2.6 %, respectively. In addition, the velocity distribution, pressure distribution, streamline and turbulence kinetic energy distribution of the optimized and reference impeller were compared and analyzed to illustrate the performance improvement.     

Impeller inlet geometry effect on performance improvement for centrifugal pumps

This research treats the effect of impeller inlet geometry on performance improvement for a boiler feed pump, who is a centrifugal pump having specific speed of 183 m·m³min⁻¹·min⁻¹ and close type impeller with exit diameter of 450 mm. The hydraulic performance and cavitation performance of the pump have been tested experimentally. In order to improve the pump, five impellers have been considered by extending the blade leading edge or applying much larger blade angle at impeller inlet compared with the original impeller. The 3-D turbulent flow inside those pumps has been analyzed basing on RNG k-ɛ turbulence model and VOF cavitation model. It is noted that the numerical results are fairly good compared with the experiments. Based on the experimental test and numerical simulation, the following conclusions can be drawn: (1) Impeller inlet geometry has important influence on performance improvement in the case of centrifugal pump. Favorite effects on performance improvement have been achieved by both extending the blade leading edge and applying much larger blade angle at impeller inlet; (2) It is suspected that the extended leading edge have favorite effect for improving hydraulic performance, and the much larger blade angle at impeller inlet have favorite effect for improving cavitation performance for the test pump; (3) Uniform flow upstream of impeller inlet is helpful for improving cavitation performance of the pump. This paper was presented at the 9^th Asian International Conference on Fluid Machinery (AICFM9), Jeju, Korea, October 16–19, 2007.     

Numerical simulation and analysis of flow characteristics in the front chamber of a centrifugal pump

We performed numerical simulations to study the flow characteristic in a centrifugal pump based on the RANS equations and the RNG k-ε turbulent model. The flow field, including the front and back pump chambers, the impeller wear-ring, the impeller passage, the volute casing, the inlet section and outlet section was calculated to obtain accurate numerical results of fluid flow in a centrifugal pump. The flow characteristic was studied from the internal flow structure in pump chambers, the radial velocity at impeller outlet as well as the pressure inside of the pump, the circumferential velocity and the radial velocity in front pump chamber. The variation of flow parameters in internal flow versus flow rate in the centrifugal pump was analyzed. The results show that the overall performance of the pump is in good agreement with the experimental data. The simulation results show that the distribution of flow field in the front pump chamber is axial asymmetry. The energy dissipation at the impeller outlet is larger than other areas. The distribution of the circumferential velocity and that of radial velocity are similar along the axial direction in the front pump chamber, but the distribution of flow is different along the circumferential and the radial directions. It was also found that the vorticity is large at the impeller inlet compared with other areas.     

叶片进口修缘对离心泵汽蚀性能影响的数值计算与试验研究

为了改善离心泵的汽蚀性能,根据经验,确定了两种叶片进口修缘形式。首先通过原型泵的外特性试验,确定了能量性能和汽蚀性能曲线。基于完整空化模型和混合流体两相流模型,对原型泵运行工况下叶轮内空化流动进行全流道数值计算。预测得到原型泵能量性能和汽蚀性能曲线,与试验曲线吻合良好;同时得到汽蚀发生过程中叶轮流道内空化发展的静态特征,与理论相符。故采用相同的数值分析方法对两种叶片进口修缘后的叶轮进行分析,分析表明：进口修缘后泵的汽蚀性能得到了提高,叶片进口工作面修缘形状越接近流线型,泵的汽蚀性能越好。对较好修缘形式的泵进行试验,得到其能量性能曲线和汽蚀性能曲线,数值分析与试验研究的曲线吻合,修缘后泵的临界汽蚀余量得到改善。研究结果对离心泵汽蚀改善的方法具有一定的指导意义。     

Experimental investigation of the preferred Strouhal number used in self-resonating pulsed waterjet

Self-resonating pulsed waterjet (SRPW) is superior to plain waterjet in many ways and is being employed in numerous applications. To further improve the performance of SRPW, the optimal value of the preferred Strouhal number (S_d), which is used to determine the chamber length of a self-resonating nozzle, was experimentally studied at inlet pressures of 10 MPa and 20 MPa. The axial pressure oscillation peak and amplitude were used to evaluate the performance of SRPW, in order to find the optimum S_d value. Results show that S_d value determines the self-resonance behavior of an organ-pipe nozzle and greatly affects the intensity of the axial pressure oscillation. Under the experimental conditions, the optimum S_d values are 0.315 and 0.278 respectively, corresponding to inlet pressures of 10 MPa and 20 MPa. Compared with the default value of 0.3 obtained from air jet experiment, the optimum S_d value at inlet pressure of 10 MPa is a little larger and oppositely a bit smaller at inlet pressure of 20 MPa. Thus, if the inlet pressure is not considered, S_d value of 0.3 is reasonable for determining the chamber length of a self-resonating nozzle for generating effective SRPW.     

Numerical investigations on cavitating flows with thermodynamic effects in a diffuser-type centrifugal pump

A cavitation model with thermodynamic effects for cavitating flows in a diffuser-type centrifugal pump is developed based on the bubble two-phase flow model. The proposed cavitation model includes mass, momentum, and energy transportations according to the thermodynamic mechanism of cavitation. Numerical simulations are conducted inside the entire passage of the centrifugal pump by using the proposed cavitation model and the renormalization group-based k-? turbulent model coupled with the energy transportation equation. By using the commercial computational fluid dynamics software FLUENT 6.3, we have shown that the predicted performance characteristics of the pump, as well as the pressure, vapor, and density distributions in the impeller, agree well with that calculated by the full cavitation model. Simulation results show that cavitation initially occurs slightly behind the inlet of the blade suction surface, i.e., the area with maximum vapor concentration and minimum pressure. The predicted temperature field shows that the reduction in temperature restrains the growth of cavitating bubbles. Therefore, the thermodynamic effect should be treated as a necessary factor in cavitation models. Comparison results validate the efficiency and accuracy of the numerical technique in simulating cavitation flows in centrifugal pumps.     

The characteristics investigation under the unsteady cavitation condition in a centrifugal pump

Numerical simulation and experimental method are combined to investigate the pump inlet and outlet pressure fluctuations, the vibration characteristics and the internal flow instabilities under the unsteady cavitation condition in a centrifugal pump. It is found that the unsteady cavitation starts to generate as the NPSHa is lower than 5.93 m. Apparent asymmetric and uneven cavity volume distribution on each blade and in the impeller can be observed as the NPSHa decreases from 4.39 m to 1.44 m, which includes the cavitation develops from cavitation surge, rotating cavitation to asymmetric cavitation. The flow vortexes in each blade channel are produced in the cavity trailing edges by the shedding and collapse of cavitation, which interfere with each other and aggravate the flow instabilities. The dominant frequencies of the pump inlet and outlet pressure fluctuations are the shaft frequency and blade passing frequency under the unsteady cavitation conditions, respectively. Broadband pulses are obtained from both the pump inlet and outlet pressure pulsations, which results from the random shedding and collapse of unsteady cavitation bubbles. Obvious corresponding relationship between the root mean squares of the vibration measured in different positions and the suction performance curve is found under both the non-cavitation and unsteady cavitation conditions.

     

Effect of innovative circular shroud fences on a centrifugal fan for augmented performance - A numerical analysis

This paper presents the influence of circular front and back shroud fences on the performance of a backward swept centrifugal fan impeller handling air. The analysis is carried out to determine the main characteristics of the fan i.e. the variation of head and theoretical efficiency for various flow coefficients. The circular fence size is optimized parametrically by varying its diameter and the location on the shroud surface. The effect of the shroud fences on the flow field was analyzed for the fences placed on both front and back shroud surfaces of the impeller separately. The numerical simulation is carried out using an appropriate k - ε turbulence model. The relative flow inside the impeller passages is modeled using the standard sliding mesh technique. The numerical results for the base model (i.e. without the fence) are validated against experimental results obtained from the test rig built specially for validation study and are found to have good agreement. It is found from the analysis that the average percentage increase in head coefficient is significant and is about 2 % higher as compared to the base model for the optimized geometrical configuration of diameter ratio and radial fence location as determined in the study. The optimized geometrical configuration also yields a higher theoretical efficiency of about 2.3 % corroborating the improvement in head coefficient with respect to the base model. Hence the efficacy of optimally placed circular fence on the performance of centrifugal fan is established in this numerical study.     

双向轴流泵装置性能预测与内部流动分析

对一采用S形叶片的双向轴流泵装置进行数值研究,在不同流量工况条件下分析泵的正、反向运转性能,对该泵的瞬时启动过程进行了监测并对泵内的非定常空化现象进行了分析。研究表明,正、反向运转时,泵的性能存在明显的差异,反向的扬程和效率均高于正向;在泵正向启动过程中,叶轮背面进口边产生空化区,反向运转时未发生明显的空化现象;两种运转模式下,叶轮进出口断面上压力脉动特征频率分布相似,但叶轮进口的压力脉动幅值较高。     

Effects of Blade Number on Characteristics of Centrifugal Pumps

The blade number of impeller is an important design parameter of pumps,which affects the characteristics of pump heavily.At present,the investigation focuses mostly on the performance characteristics of axis flow pumps,the influence of blade number on inner flow filed and characteristics of centrifugal pump has not been understood completely.Therefore,the methods of numerical simulation and experimental verification are used to investigate the effects of blade number on flow field and characteristics of a centrifugal pump.The model pump has a design specific speed of 92.7 and an impeller with 5 blades.The blade number is varied to 4,6,7 with the casing and other geometric parameters keep constant.The inner flow fields and characteristics of the centrifugal pumps with different blade number are simulated and predicted in non-cavitation and cavitation conditions by using commercial code FLUENT.The impellers with different blade number are made by using rapid prototyping,and their characteristics are tested in an open loop.The comparison between prediction values and experimental results indicates that the prediction results are satisfied.The maximum discrepancy of prediction results for head,efficiency and required net positive suction head are 4.83%,3.9% and 0.36 m,respectively.The flow analysis displays that blade number change has an important effect on the area of low pressure region behind the blade inlet and jet-wake structure in impellers.With the increase of blade number,the head of the model pumps increases too,the variable regulation of efficiency and cavitation characteristics are complicated,but there are optimum values of blade number for each one.The research results are helpful for hydraulic design of centrifugal pump.     

Effects of flexible plate attached to the rear of the cylinder on flow structure

In this experimental study, the flow structure in the wake flow region was investigated with the Particle image velocimetry technique (PIV) by attaching elastic plates at different lengths behind the cylinder. The flow structure occurred at the wake flow region altered depending on the length of the flexible matter. In this experiment, the strips with the lengths of 75, 90, 120, 135 and 180 mm were used to control instabilities. Diameter of the cylinder (D) is 60 mm and the water height (h _w ) is 600 mm. Reynolds number was kept constant as 5000 based on cylinder diameter. The images were captured at mid-height of the cylinder (h _m ) which is 250 mm. As a result of experimental studies, attached flexible strip suppressed vortex shedding occurred in the behind of the cylinder and it is observed that effect of the length flexible of the strip is pretty much. Maximum level of flow characteristics such as Reynolds stress, fluctuation velocities and turbulent kinetic energy were decreased with flexible splitter plate and shifted through the downstream region.     

长短叶片离心泵汽蚀性能数值模拟分析及实验研究

为提高离心泵的汽蚀性能,利用CFD数值模拟分析与实验研究相结合的方法对长短叶片离心泵在不同汽蚀余量时叶轮内部气液两相的分布规律进行分析研究,分析了3种不同短叶片进口直径在不同汽蚀工况时气泡分布情况对叶轮内部流动和性能的影响。分析结果表明:选择合理短叶片的进口直径可以有效提高离心泵的抗汽蚀性能,避免叶轮进口堵塞和流道内发生漩涡汽蚀。当汽蚀余量减小到一定程度,离心泵短叶片进口直径为0.65D2(D2为叶轮外径)时,在长叶片和短叶片的背面都会出现漩涡汽蚀区;当离心泵短叶片进口直径为0.75D2时,在长叶片背面与短叶片工作面间的流道内会出现两个漩涡汽蚀区;当离心泵短叶片进口直径为0.85D2时,离心泵的抗汽蚀性能最佳。     

Numerical studies on two turbulence models and a laminar model for aerodynamics of a vertical-axis wind turbine

The purpose of this study is the analysis of flow around a one-bladed Darrieus-type wind turbine using computational fluid dynamics (CFD). The rotor geometry consists of a NACA 0015 airfoil with chord length of 0.15 m. Numerical simulations are performed using ANSYS Fluent, employing laminar model and two turbulence models: SST k-ω and RNG k-ε. The obtained numerical results of unsteady aerodynamic blade loads are compared with available experimental results from literature. Computed aerodynamic characteristics of normal and tangential forces comply with the experiment results. The RNG k-ε turbulence model has a good accuracy in determining aerodynamic blade loads for the upwind and downwind parts of the rotor. The laminar model and the SST k-ω turbulence model slightly overestimate the tangential aerodynamic blade loads at the downwind part of the rotor. An averaged wind turbine velocity profile computed at one rotor radius downstream of the rotor has a Gaussian shape. The steady-state airfoil characteristics are computed for the Reynolds number comparable to the Reynolds number of a moving blade employing the SST k-ω and RNG k-ε turbulence models and using the same computational grid as for unsteady simulations of the rotor.     

航空燃油离心泵抗汽蚀优化设计及仿真

针对航空燃油离心泵工作时出现的汽蚀问题,采用正交试验法对离心泵叶轮进行优化设计.选取叶轮出口直径D2、叶轮出口宽度b2、叶片数Z、叶片厚度H为正交试验的4个因素,完成了正交试验并对试验结果进行极差分析,得到了以泵汽蚀余量为优化指标的影响排序,并最终获得最优参数组合.通过流场仿真对现用离心泵和优化后离心泵的泵汽蚀余量和蒸...     

Vibration response analysis caused by rubbing between rotating blade and casing

Two types of blade-tip rubbing due to the static misalignment of the bladed-disk center and casing center and casing deformation are simulated. By applying aerodynamic load in the blade lateral/flexural direction, vibration responses due to blade-casing rubbing are analyzed under the run-up process with constant angular acceleration and the steady-state process at 10000 rev/min. The effects of some parameters, such as the static misalignment e _c, casing stiffness k _c and casing deformation n _p, on the system vibration responses are also illustrated by spectrum cascades, time-domain waveforms of displacement, normal rubbing forces, amplitude spectra and the impulse P in a single blade-casing rubbing period. The results show that blade-tip rubbing will cause amplitude amplification and harmonic resonance phenomena when the multiple frequencies (nf _r) of rotational frequency (f _r) coincide with the first three flexural dynamic frequencies of the blade (f _n1, f _n2 and f _n3). For example, the displacement amplitudes at 3f _r, 14f _r and 38f _r are large and the vibration is dominant near f _n1. In addition, the casing deformation mainly excites the dominant Blade passing frequency (BPF), which is related to the casing deformation coefficient n _p. By comparing these impulse values, for the selected parameters in this paper, the casing stiffness has a greater effect on impulse than the static misalignment and casing deformation coefficient. The impulse shows a linear increase trend with the increasing static misalignment, and it decreases under the large n _p because the contact time decreases with the increase of n _p.