Article 正式发布 Versions 5 Vol 28 (4) : 608-620 2019
Study on Unstable Characteristics of Centrifugal Pump under Different Cavitation Stages; 不同空化阶段离心泵不稳定特性研究
: 2019 - 07 - 05
218 0 0
Abstract & Keywords
Abstract: In order to reveal the regularity of unsteady flow of centrifugal pump under different cavitation stages, a visual closed test-bed is built to collect signals such as the distribution of cavitation bubbles at the impeller inlet and external characteristics, etc. in the process of cavitation of centrifugal pumps. Combined with the shape and distribution of bubbles captured by high-speed photography, the cavitation stage of the centrifugal pump is divided. In addition, the variation of vorticity distribution, pressure pulsation and radial force of centrifugal pump under different cavitation stages are studied using the standard k-ε turbulence model and the Kunz cavitation model. Main contributions are as follows: The cavitation bubbles can absorb the energy of vortex core to a certain extent and increase the volume of vortex core. Cavitation bubbles can also block the flow-path and induce the distortion of the internal flow field, resulting in unstable pressure waves that cause a significant increase in pressure pulsation rate. Besides, with the development of cavitation, the radial force on the impeller tends to remain invariable first and then decrease, and trajectory of the radial force changes from closed to open. 为了揭示离心泵在不同空化阶段的非定常流动规律,建立了可视化闭式试验台,对离心泵空化过程中叶轮进口空泡分布、外部特性等信号进行采集。结合高速摄影捕捉到的空泡形状和分布,对离心泵的空化阶段进行了划分。采用标准的k-ε湍流模型和kunz空化模型,研究了离心泵在不同空化阶段的涡度分布、压力脉动和径向力的变化。主要贡献如下:空化气泡能在一定程度上吸收涡核的能量,增加涡核的体积。空化气泡也会阻塞流道,导致内部流场变形,压力波不稳定以及压力脉动率显著增加。此外,随着空化的发展,叶轮径向力趋于先不变后减小,径向力的轨迹由封闭变为开放。
Keywords: centrifugal pump, cavitation development stage, cavitation bubble distribution, pressure pulsation, radial force
1. Introduction
Efficiency, reliability and cavitation are three important indicators to evaluate the performance of the centrifugal pump. Thereinto, cavitation is considered as the "cancer" in the pump field which has not been well solved for a long time [1-3]. The essence of cavitation flow is gas-liquid two-phase turbulent flow, including quite complex mass transfer, momentum transfer and energy exchange between bubbles and water. Cavitation of pump not only has great influence on pump efficiency, but also causes serious damage to materials. The most important research work for cavitation of centrifugal pumps is how to evaluate the state. The conventional energy method to judge the cavitation inception of a centrifugal pump is based on the drop of 3% of the head. It is regrettable that there is a great lag in this method. However, other methods of determining cavitation cannot guide the engineering application as well for the low sensitivity and poor universality. With the development of computer technology and computational fluid mechanics, the method of establishing the relationship between cavitation and the distribution of cavitation flow field, the regulation of the generation and the development of bubbles, etc. by CFD has been widely concerned [4-8].
Tan [9] has studied the internal transient flow of centrifugal pump under cavitation, and found that the motion of cavitation bubbles in impeller presents periodicity, and the dominant frequency of induced pressure pulsation changes from blade frequency to low frequency in comparison with the non-cavitating conditions. MM Athavale [10] carried out numerical simulation of cavitation-flow in hydraulic jet propulsion pump, centrifugal pump and turbopump, etc. by using the Singhal cavitation model. The results show that the occurrence of cavitation is always on the suction surface at the leading edge of blade. Li et al. [11] established a closed loop to analyze the relationship between the cavitation performance and the suction pressure signals. The static parameters used can only capture the critical cavitation condition and cavitation damage condition, whereas they are difficult for the detection of incipient cavitation in the pump. In addition, cavitation produces complex vortex structures inside the flow field, which enhance the interaction between turbulent flow and cavitation [12]. Friedrichs and Kosyna [13] discussed the effects of the cavitation number and the incidence angle of the blade on rotating cavitation through an experimental investigation of two similar centrifugal pump impellers of low specific speed.
The external characteristics of centrifugal pump and the change in the shape of cavitation bubbles attached to the impeller at varied cavitation numbers were conducted by Li et al. [14]. It is pointed out that the size of cavitation bubbles increases with the decrease of cavitation number and so does the decline in performance of a centrifugal pump. The application of the cavitation model has been implemented to investigate the internal relationship between the force of the impeller and cavitation [15]. The obtained results show that the axial force increases with the development of cavitation, however, the radial force changes little with cavitation under rated conditions, instead of reducing in low flow rate. Pouffary et al. [16] analyzed the variations of head and energy conversion process of the centrifugal pump under cavitation conditions, and found that the head decreases with reduction of power and blade load.
It should be noted that cavitating flow is complex multiphase turbulence [17], and the vortex structure can enhance the turbulent intensity of flow field [18]. Thus, the complex vortex structure generated by the cavitating flow contributes to the better interaction between turbulent flow and cavitation bubble [19]. Gopalan and Katz [20] studied enclosed area of the nozzle exit by using Particle Image Velocimetry and high-speed photography system. It is found that the collapse of the vapor cavity in the enclosed area is the main mechanism of vorticity, besides, the hairpin structure vortex generated by collapse of the cavity will dominate the flow in the downstream of the cavitation region. The simulation results of the unsteady flow of cavitation in centrifugal pump show that the cavitation has a pulsating characteristic under off-design conditions. Such phenomenon involves the vortex- induced response and the non-uniform pressure distribution on the volute [21]. Centrifugal pumps easily generate cavitation when running off-design conditions. The development of cavitation has an effect on the load distribution on blade. The head, pressure pulsation and radial force are influenced by the load distribution [22]. In addition, the load distribution on blade also changes the blade angle at the leading edge and affects the cavitation performance of pump [23]. Experimental investigations on pressure pulsation induced by cavitation in double suction centrifugal pumps were carried out by Yao et al. [24]. The results show that the amplitude of pressure pulsation at the shaft frequency and the special low frequency of the impeller increases first and then decreases with the development of cavitation.
Based on the available literatures about cavitation, the researchers were concerned with the following important questions: how to analyze cavitation stages of centrifugal pump, which signal treatment to use (in the frequency or time domain), and which parameter to calculate in order to quantify the degree of erosive cavitation. Few scholars have summarized the characteristics of the unsteady flow of cavitation in centrifugal pump based on a reasonable criterion for cavitation stages. Therefore, the primary work of the paper is to build a visual closed test-bed in order to judge the cavitation stages of centrifugal pump combined with high-speed photography. Then, the most applicable model is selected for the computation of cavitating-flow in centrifugal pump by comparing different turbulence models and cavitation models. Finally, the regularity of distribution for vortex structure, pressure pulsation and radial force distribution on the impeller under different cavitation stages are concentrated on to support the decision of different cavitation stages.
2. Test and Numerical Simulation Strategy
2.1   Test device and object

Fig. 1 Physical diagram of the test system
Table 1 The main geometric parameters of the pump
ImpellerInlet diameter, D1/mm90
Outlet diameter, D2/mm170
Number of blade, Z6
Scroll of blade, θ120
Outlet width, b2/mm13.1
VoluteBase diameter, D3/mm180
Inlet width, b3/mm32
Outlet diameter, D4/mm80
2.2   Numerical simulation method
Table 2 The test of grid correlation
ProgramInlet sectionOutlet sectionVoluteImpellerTotal gridsHead/m
2.3   Calculation model
2.3.1   Turbulence model

Fig. 2 Comparison between calculated results and experimental values
2.3.2   Cavitation model

Fig. 3 Comparison between performance curves of different cavitation models and experimental values
2.4 Definition of cavitation stage based on high-speed photography

Fig. 4 Test results of high speed photography under different cavitation number in the rated operating state of φ=0.065

Fig. 5 Schematic diagram of cavitation stage division
3. Effect of Cavitation on Internal Flow
3.1   Effect of cavitation on cavitating flow

Fig. 6 Cavitation region corresponding to cavitation number in rated flow
3.2   Effect of cavitation on vortex structure

Fig. 7 Regional distribution of vortex core with different Q-values under different cavitation stages in rated flow

Fig. 8 Variation of vortex core volume with different Q-values under different cavitation stages in rated conditions
4. Effect of Cavitation on Unsteady Force
4.1   Effect of cavitation on pressure pulsation

Fig. 9 Schematic diagram of monitoring points for pressure pulsation

Fig. 10 Influence of cavitation on time domain distribution of pressure pulsation

Fig. 11 Influence of cavitation on shaft frequency and frequency doubling distribution of pressure pulsation
4.2   Effect of cavitation on radial force

Fig. 12 Polar diagram of radial force on impeller under different cavitation stages
5. Conclusions
Combined with high-speed photography and performance test, the cavitation in centrifugal pump is divided into four stages. The standard k-ε turbulence model and Kunz cavitation model have higher accuracy in cavitation simulation of centrifugal pump.
(1) Under different cavitation stages, the high- intensity vortex in the internal flow mainly concentrates in the rotating region. The velocity gradient of vortex core in impeller at onset cavitation stage is smaller than non-cavitating stage. With the development of cavitation, the high-speed region of vortex core gradually spreads from the region attached of the blade to the whole flow-path. When the cavitation phenomenon is further aggravated, low velocity zone obviously appears on the suction surface and further shifts to the pressure surface.
(2) At onset cavitation stage, the production of cavitation bubbles is too small to affect the internal flow of the pump. At the same time, the rapid attenuation of high-frequency energy makes the amplitude of pressure pulsation coefficient smaller than the non-cavitating stage. With the development of cavitation, bubbles will block the flow-path and form unstable pressure waves, resulting in a significant raise in the change rate of pressure pulsation. Besides, the shaft frequency remains the main frequency, and its value increases obviously, although the regulation of shaft frequency and doubling frequency is quite complicated.
(3) At non-cavitating stage and onset cavitation stage, the distribution of the radial force corresponds to the number of impeller blades. Moreover, the radial force is smaller at onset cavitation stage than at non-cavitating stage. The trajectory of radial force is no longer closed with the further development of cavitation. In general, radial force has no definite regularity except for a decreasing tendency.
(4) The limitation of numerical calculation models and test signal acquisition equipment results in some certain error in cavitation flow field calculation. In the future, we can study and explore the accurate method of cavitation flow simulation and acquisition and processing of cavitation signal.
Li Y.Q., Yuan S.W., Lai H.X., Numerical study of unsteady flows with cavitation in a high-speed micro centrifugal pump. Journal of Thermal Science, 2017, 26(01): 18‒24.
Zhang N., Yang M.G., Gao B., Li Z., Vibration characteristics induced by cavitation in a centrifugal pump with slope volute. Shock and Vibration, 2015, 2015: 1‒10.
Huang B., Wu Q., Wang G.Y., Research status and progress of unstable cavitating flow. Journal of Irrigation and Drainage Machinery Engineering, 2018, 36(01): 1‒14. (in Chinese).
Lei T., Shan Z.B., Liang C.S., et al, Numerical simulation of unsteady cavitation flow in a centrifugal pump at off-design conditions. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2014, 228(11): 1994‒2006.
Li X.J., Jiang Z.W., Zhu Z.C., et al, Entropy generation analysis for the cavitating head-drop characteristic of a centrifugal pump. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2018: 095440621775345.
Dong L., Zhao Y.Q., Dai C., Wang Y., Research on cavitation acoustic characteristics of centrifugal pump based on fluid-acoustic field coupling method. Advances in Mechanical Engineering, 2018, 10(5): 1-13.
Li Q.F., Liu C., Wang Y.K., Cavitation characteristics of pump-turbine under partial load. Journal of Drainage and Irrigation Machinery Engineering, 2017, 35(08): 680‒684. (in Chinese).
Kang J.Y., Zhu R.S., et al, The influence of impeller geometric parameters on fracture cavitation performance in centrifugal pumps. Journal of Drainage and Irrigation Machinery Engineering, 2018, 36(02): 111‒117. (in Chinese).
Tan L., Zhu B.S., Wang Y.C., et al, Numerical study on characteristics of unsteady flow in a centrifugal pump volute at partial load condition. Engineering Computations, 2015, 32(6): 1549‒1566.
Athavale M.M., Li H.Y., Yu J., et al, Application of the full cavitation model to pumps and inducers. International Journal of Rotating Machinery, 2014, 8(1): 45‒56.
Li X.J., Yu B.X., Ji Y.C., Lu J.X., Yuan S.Q., et al, Statistical characteristics of suction pressure signals for a centrifugal pump under cavitating conditions. Journal of Thermal Science, 2017(26): 47‒53.
Belahadji B., Franc P., Michel M., Cavitation in the rotational structures of a turbulent wake. Journal of Fluid Mechanics, 1995, 287: 383‒403.
Friedrichs J., Kosyna G., Rotating cavitation in a centrifugal pump impeller of low specific speed. Journal of Fluids Engineering, 2002, 124(2): 356‒362.
Li J., Liu L.J., Li G.J., et al, Numerical study on the effect of cavitation number on the hydraulic performance of centrifugal pumps. Journal of Engineering Thermophysics, 2010, V31(5): 773‒776. (in Chinese).
He M., Wang C.C., Li X.Q., Study on impeller force characteristics of cavitation flow field in centrifugal pump. General Machinery, 2017(08): 79‒83. (in Chinese).
Pouffary B., Fortes-Patella R., Roboud J., et al, Numerical simulation of 3D cavitating flows: analysis of cavitation head drop in turbomachinery. ASME Journal of Fluids Engineering, 2008, 130, p.061301.
Li C.Y., Ceccio S.L., Interaction of single travelling bubbles with the boundary layer and attached cavitation. Journal of Fluid Mechanics, 1996, 322: 329‒353.
Arakeri V.H., Acosta A.J., Viscous effects in the inception of cavitation on axisymmetric bodies. Journal of Fluids Engineering, 1973, 95(4): 519‒527.
Belahadji B., Franc P., Michel M., Cavitation in the rotational structures of a turbulent wake. Journal of Fluid Mechanics, 1995, 287: 383‒403.
Gopalan S., Katz J., Flow structure and modeling issues in the closure region of attached cavitation. Physics of Fluids, 2000, 12(4): 3414‒3431.
Meng L., He M., Zhou L., et al., Influence of impeller- tongue interaction on the unsteady cavitation behavior in a centrifugal pump. Engineering Computations, 2016, 33(1): 171‒183.
Li X., Gao P., Zhu Z., et al, Effect of the blade loading distribution on hydrodynamic performance of a centrifugal pump with cylindrical blades. Journal of Mechanical Science & Technology, 2018, 32(3): 1161‒ 1170.
Huang R.F., Luo X.W., Ji B., et al., Multi-objective optimization of a mixed-flow pump impeller using modified NSGA-II algorithm. Science China Technolo- gical Sciences, 2015, 58(12): 2122‒2130.
Yao Z.F., Wang F.J., Xiao R.F., et al., Experimental investigation of pressure instabilities affected by cavitation for a double-suction centrifugal pump. IOP Conference Series: Earth and Environmental Science, 2012, 15(6): 062040.
Dong L., Zhao Y.Q., Liu H.L., Dai C.,Vladimirovich Gradov D, Wang Y., The effect of front streamline wrapping angle variation in a super-low specific speed centrifugal pump. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2018: 095440621877260.
Hunt J.C.R., Wray A.A., Moin P., Eddies, stream, and convergence zones in turbulent flows. Studying Turbulence Using Numerical Simulation Databases. Studying Turbulence Using Numerical Simulation Databases, 2, 1988.
Article and author information
DONG Liang
SHANG Huanhuan
LIU Houlin
DAI Cui*
This work was supported by the National Key Research and Development Program of China (2017YFC0804107), National Natural Science Foundation of China (No. 51879122, 51779106, 51509111), the association innovation fund of production, learning, and research (BY2016072-01), Zhenjiang key research and development plan (GY2017001, GY2018025), the Open Research Subject of Key Laboratory of Fluid and Power Machinery, Ministry of Education, Xihua University (szjj2015-017, szjj2017-094, szjj2016-068), Sichuan Provincial Key Lab of Process Equipment and Control (GK201614, GK201816), the Advanced Talent Foundation of Jiangsu University (15JDG052) and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), Jiangsu top six talent summit project (GDZB-017).
Publication records
Published: July 5, 2019 (Versions5
Journal of Thermal Science