The blade angle has a great effect on hydraulic performance and internal flow field for axial-flow pumps. This research investigated the effect of the blade angle on hydraulic performance and tip leakage vortex (TLV) of a slanted axial-flow pump. The hydraulic performance and the TLV are compared with different setting angles. The dimensionless turbulence kinetic energy (TKE) is used to investigate the TLV. A novel variable fv is utilized to analyze the relation among the TLV, strain tensor and vorticity tensor. The proper orthogonal decomposition (POD) method is used to analyze TLV structure. The results show that with the increase of the blade angle, the pump head is getting larger, the flow rate of the best efficiency moves to be larger, and both the primary TLV (P-TLV) and the secondary TLV (S-TLV) are getting stronger. The P-TLV often exists in the outer edge of TKE distribution and S-TLVs often exist in the largest value area of TKE. This phenomenon is more evident with blade angle increasing. Through POD method, it shows that the first six modes contain more than 90% of TKE. The reason why the TKE value near the region of S-TLV is high is that the tip leakage flow is a kind of jet-like flow with high kinetic energy. The main structure of the P-TLV is shown in modes 4−6, resulting in a reflux zone but not with the highest TKE.
ChenJShiHSivakumarB, et al. Population, water, food, energy and dams. Renew Sust Energ Rev2016; 56: 18–28.
2.
CoelhoBAndrade-CamposA.Efficiency achievement in water supply systems – a review. Renew Sust Energ Rev2014; 30: 59–84.
3.
WangSYuanPLiD, et al. An overview of ocean renewable energy in China. Renew Sust Energ Rev2011; 15: 91–111.
4.
KanKChenHZhengY, et al. Transient characteristics during power-off process in a shaft extension tubular pump by using a suitable numerical model. Renew Energy2021; 164: 109–121.
5.
WangCWangFTangY, et al. Investigation into the phenomenon of flow deviation in the S-shaped discharge passage of a slanted axial flow pumping system. J Fluids Eng – Trans ASME2020; 142: 041205.
6.
ZhangFAppiahDHongF, et al. Energy loss evaluation in a side channel pump under different wrapping angles using entropy production method. Int Commun Heat Mass Transf2020; 113: 104526.
7.
YouDWangMMoinP, et al. Vortex dynamics and low-pressure fluctuations in the tip-clearance flow. J Fluids Eng – Trans ASME2007; 129: 1002–1014.
8.
KanKZhengYChenH, et al. Numerical simulation of transient flow in a shaft extension tubular pump unit during runaway process caused by power failure. Renew Energy2020; 154: 1153–1164.
9.
BoothTCDodgePRHepworthHK.Rotor-Tip leakage: part I – basic methodology. J Eng Power – Trans ASME1982; 104: 154–161.
10.
FengJLuoXGuoP, et al. Influence of tip clearance on pressure fluctuations in an axial flow pump. J Mech Sci Technol2016; 30: 1603–1610.
11.
ArndtREA.Cavitation in vortical flows. Annu Rev Fluid Mech2002; 34: 143–175.
12.
LuoXJiBTsujimotoY.A review of cavitation in hydraulic machinery. J Hydrodyn2016; 28: 335–358.
13.
ZhangYKangCJiY, et al. Experimental and numerical investigation of flow patterns and performance of a modified Savonius hydrokinetic rotor. Renew Energy2019; 141: 1067–1079.
14.
DreyerMDecaixJMünch-AllignéC, et al. Mind the gap: a new insight into the tip leakage vortex using stereo-PIV. Exp Fluids2014; 55: 1849.
15.
GuoQZhouLWangZ.Numerical evaluation of the clearance geometries effect on the flow field and performance of a hydrofoil. Renew Energy2016; 99: 390–397.
16.
ShenSQianZJiB, et al. Numerical investigation of tip flow dynamics and main flow characteristics with varying tip clearance widths for an axial-flow pump. Proc IMechE, Part A: J Power Energy2019; 233: 476–488.
17.
WangLLuJLiaoW, et al. Numerical simulation of the tip leakage vortex characteristics in a semi-open centrifugal pump. Appl Sci Basel2019; 9: 5244.
18.
LiCXiangJSongL, et al. An aerothermal analysis of the effects of tip gap height and cavity depth of a gas turbine blade. Int J Therm Sci2020; 158: 106521.
19.
WuHMioriniRLKatzJ.Measurements of the tip leakage vortex structures and turbulence in the meridional plane of an axial water-jet pump. Exp Fluids2011; 50: 989–1003.
20.
TanDLiYWilkesI, et al. Experimental investigation of the role of large scale cavitating vortical structures in performance breakdown of an axial waterjet pump. J Fluids Eng – Trans ASME2015; 137: 111301.
21.
ShenXZhangDXuB, et al. Experimental and numerical investigation on the effect of tip leakage vortex induced cavitating flow on pressure fluctuation in an axial flow pump. Renew Energy2021; 163: 1195–1209.
22.
ShenXZhangDXuB, et al. Numerical and experimental investigation of the pressure fluctuation in a mixed-flow pump under low flow conditions. Proc IMechE, Part A: J Power Energy2020; 234: 46–57.
23.
ShiGLiuZXiaoY, et al. Tip leakage vortex trajectory and dynamics in a multiphase pump at off-design condition. Renew Energy2020; 150: 703–711.
24.
LiuYTanL.Theoretical prediction model of tip leakage vortex in a mixed flow pump with tip clearance. J Fluids Eng – Trans ASME2020; 142: 021203.
25.
ChengHBaiXLongX, et al. Large eddy simulation of the tip-leakage cavitating flow with an insight on how cavitation influences vorticity and turbulence. Appl Math Model2020; 77: 788–809.
26.
ZhangDShiWvan EschBPM, et al. Numerical and experimental investigation of tip leakage vortex trajectory and dynamics in an axial flow pump. Comput Fluids2015; 112: 61–71.
27.
ZhangDShiWPanD, et al. Numerical and experimental investigation of tip leakage vortex cavitation patterns and mechanisms in an axial flow pump. J Fluids Eng – Trans ASME2015; 137.
28.
LiuYTanL.Spatial-temporal evolution of tip leakage vortex in a mixed-flow pump with tip clearance. J Fluids Eng – Trans ASME2019; 141: 081302.
29.
LumleyJL. Coherent structures in turbulence. In: Meyer RE (ed.) Transition and turbulence. Cambridge, MA: Academic Press: 1981, pp.215–242.
30.
SirovichL.Turbulence and the dynamics of coherent structures. I. Coherent structures. Quart Appl Math1987; 45: 561–571.
31.
BerkoozGHolmesPLumleyJL.The proper orthogonal decomposition in the analysis of turbulent flows. Annu Rev Fluid Mech1993; 25: 539–575.
32.
MeyerKEPedersenJMÖzcanO.A turbulent jet in crossflow analysed with proper orthogonal decomposition. J Fluid Mech2007; 583: 199–227.
33.
XueYKumarCLeeS, et al. Identification and analysis of the meandering of a fin-tip vortex using proper orthogonal decomposition (POD). Int J Heat Fluid Flow2020; 82: 108556.
34.
HanYTanL.Dynamic mode decomposition and reconstruction of tip leakage vortex in a mixed flow pump as turbine at pump mode. Renew Energy2020; 155: 725–734.
35.
LiuYHanYTanL, et al. Blade rotation angle on energy performance and tip leakage vortex in a mixed flow pump as turbine at pump mode. Energy2020; 206: 118084.
36.
CelikIBGhiaURoachePJ, et al. Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J Fluids Eng – Trans ASME2008; 130: 078001.
37.
ZhangR.Research on the stall and cavitation flow characteristics and the performance improvement of axial-flow pump. PhD Thesis, Shanghai University, China, 2014.
38.
SpalartPRShurM.On the sensitization of turbulence models to rotation and curvature. Aerosp Sci Technol1997; 1: 297–302.
SmirnovPEMenterFR.Sensitization of the SST turbulence model to rotation and curvature by applying the Spalart–Shur correction term. J Turbomach – Trans ASME2009; 131: 041010.
41.
GuoQZhouLWangZ, et al. Numerical simulation for the tip leakage vortex cavitation. Ocean Eng2018; 151: 71–81.
