离心泵内部流场PIV实验研究
摘要
本文是国家自然科学基金委资助项目“水泵转轮内流场激光测量研究”
（No.59949010）的一部分。经过近十年的发展，PIV技术已获得了人们的
普遍认可，它的应用范围越来越广泛，并已成为一种研究流场的基本测试手
段。
本文首次建立了一套2.2kW的清水透明离心泵试验装置。转轮采用速
度系数法设计，转轮外径180mm，共有5张单圆弧圆柱形叶片，其出口安
放角、进口安放角分别为32.3°、39.5°。蜗壳采用等速度矩法设计，其内断
面为矩形。本试验装置设计新颖，结构独特。既能进行水泵性能试验，又满
足PIV的测试要求。
本文在转速为1200r/min工况下，进行了水泵的外特性试验，获得了水
泵的性能曲线。
本文首次采用PIV测试技术，对离心泵在1.5、1.0、0.4倍最优工况下
分别进行叶轮内部流场实验研究。测试窗口取在三个不同的叶槽中，每个叶
槽沿轴向测试三个断面。测得转轮内部的绝对速度矢量后，按速度三角形原
理进行分解，得到了绝对速度切向分量、相对速度及相对速度切向分量在转
轮内的分布，分析了转轮内部流场的分布规律，并与前人的测试和计算结果
进行了比较。
The dissertation is a part of the study on PTV measurements of the flow fields
inside the pump impeller sponsored by the State Nature Science Fund of China. In
recent decade years, with the development of the PlY, the applied domain of it is
becoming broader and broader. Now the PlY is accepted and regarded as the
fundamcntality measurements for the flow fields by the people.
The author set up a test rig for the transparent centrifugal pump driven by the
2.2kW electronic motor. The method of velocity coefficient was used to design a
180mm diameter impeller with five single-arc-cylinder blades. The exit angle and
outlet angle of the segment are 32.3 and 39.5 in degrees respectively. The volute抯
cross-section is the rectangle .Thc inlet of the pump and the axis is in the same
side. Although the structure of the pump is different from the normal one, the
performance of the pump can be measured and the internal flow fields in the
volute and impellers can be investigated by using PlY easily.
This paper acquired the performance curve when pump operating at the
speed of 1200 rpm.
Ply was firstly applied to the measurements of the flow fields of the
shrouldcd impeller in a centrifugal pump. During the measuring, three operation
points of the pump were taken. The ratios (Q/Q) of the flow rate are 1.5. 1.0~. 0.4
respectively. Three blade-to-blade passages and the three cross-section along the
axial direction at each of the passages were selected for measurements. The
absolute velocity was decomposed .Based on the law of velocity triangle , the
figure of the absolute velocity, the absolute tangential velocity, the relative
velocity and the relative tangential velocity were presented in this paper. The
measurements flow fields are compared with the existing one from the
experiments and numerical computation.
（No.59949010）的一部分。经过近十年的发展，PIV技术已获得了人们的
普遍认可，它的应用范围越来越广泛，并已成为一种研究流场的基本测试手
段。
本文首次建立了一套2.2kW的清水透明离心泵试验装置。转轮采用速
度系数法设计，转轮外径180mm，共有5张单圆弧圆柱形叶片，其出口安
放角、进口安放角分别为32.3°、39.5°。蜗壳采用等速度矩法设计，其内断
面为矩形。本试验装置设计新颖，结构独特。既能进行水泵性能试验，又满
足PIV的测试要求。
本文在转速为1200r/min工况下，进行了水泵的外特性试验，获得了水
泵的性能曲线。
本文首次采用PIV测试技术，对离心泵在1.5、1.0、0.4倍最优工况下
分别进行叶轮内部流场实验研究。测试窗口取在三个不同的叶槽中，每个叶
槽沿轴向测试三个断面。测得转轮内部的绝对速度矢量后，按速度三角形原
理进行分解，得到了绝对速度切向分量、相对速度及相对速度切向分量在转
轮内的分布，分析了转轮内部流场的分布规律，并与前人的测试和计算结果
进行了比较。
The dissertation is a part of the study on PTV measurements of the flow fields
inside the pump impeller sponsored by the State Nature Science Fund of China. In
recent decade years, with the development of the PlY, the applied domain of it is
becoming broader and broader. Now the PlY is accepted and regarded as the
fundamcntality measurements for the flow fields by the people.
The author set up a test rig for the transparent centrifugal pump driven by the
2.2kW electronic motor. The method of velocity coefficient was used to design a
180mm diameter impeller with five single-arc-cylinder blades. The exit angle and
outlet angle of the segment are 32.3 and 39.5 in degrees respectively. The volute抯
cross-section is the rectangle .Thc inlet of the pump and the axis is in the same
side. Although the structure of the pump is different from the normal one, the
performance of the pump can be measured and the internal flow fields in the
volute and impellers can be investigated by using PlY easily.
This paper acquired the performance curve when pump operating at the
speed of 1200 rpm.
Ply was firstly applied to the measurements of the flow fields of the
shrouldcd impeller in a centrifugal pump. During the measuring, three operation
points of the pump were taken. The ratios (Q/Q) of the flow rate are 1.5. 1.0~. 0.4
respectively. Three blade-to-blade passages and the three cross-section along the
axial direction at each of the passages were selected for measurements. The
absolute velocity was decomposed .Based on the law of velocity triangle , the
figure of the absolute velocity, the absolute tangential velocity, the relative
velocity and the relative tangential velocity were presented in this paper. The
measurements flow fields are compared with the existing one from the
experiments and numerical computation.
引文
1、冯汉民主编，水泵学．水利电力出版社．1991，5．
2、陈池等．低比速离心泵研究现状与展望．流体机械．1998(7)：29～34
3、Anderson H.H., Mine pumps. Journal of Mining Society. 1938
4、R.C. Worseter, The Flow In Volutes And Its Effect On Centrifugal Pump Performance. Proc Instn. Mech Engrs. 1963，117(31): 843～865
5、Moore J. A Wake and an eddy in a Rotation Radial-flow Passage Trans. ASME. J. Eng. for power,1973(July): 205～219
6、陈次昌等，离心泵叶轮内的二次流及泵性能的研究．水泵技术 25～33
7、袁卫星等，离心泵射流—尾迹模型的三元流动计算，水泵技术 12～18
8、彭国义，水力机械转轮反问题数值研究与进展．甘肃大学学报．1997(4)：31～36
9、常近时，叶片式水力机械水动力学计算基础．水利电力出版社．1989
10、罗兴等，流体机械叶轮设计的研究与发展，力学进展，1997(3)：372～388
11、李世煌，吴桐林等编译，水泵设计教程，机械工业出版社,1987
12、A.Demealeaaere Three-Dimensional Inverse Method for Turbomachinery Blading Design. Journal of Turbomachinery. 1998(120)：247～255
13、陈池等，离心泵叶轮内流计算方法综述，流体机械。1999(2)
14、彭国义，曹树良，林汝长，水力机械转轮正问题数值研究与进展．甘肃大学学报．1997(3)：30～32
15、曹立新，离心泵叶轮全三维势流的间接边界元法研究，农业机械学报，1999(4)：23～42
16、吴玉林等，离心泵叶轮中紊流的计算．水泵技术．1997．(1)：9～15
17、Harnkins S P. Flack RD., Laser Velocimetry Measurements In Shrouded and Unshrouded Radial Flow Impellers. J Turbomach(Trans ASME), 1987, 109: 70～79
18、Miner S M, Beaudoin R J, Flack R D., Laser velocimeter in a Centrifugal Pump. J Turbomach (Tans ASME), 1989,111(3)：205～212
19、Cader T Masbernat O, Roco M C.LDV Measurements in a centrifugal Slurry Pump: Water and Dilute Slurry Flow. ASME Journal of Fluid Engineering, 1992. 114:606～615
20、Abramian M. Howard J H G.Aroing, LDA System for Unsteady Relativate Flow in a Model Centrifugal Impellers ASME Journal of Turbomachineary, 1994,116:260～268
21、Fischer.K., and Thoma,D., Investitgation of the Flow Conditions in a Centrifugal Pump, Transactions of the ASME, 1932 HYD—54—8:141—155
22、Acosta A.J., and Bowerman,R.D., Anexperimental Study of Centrifugal Pump Imperllers. Transactions of the ASME.Vol.79: 1821～1839
23、Howard,H.J.G., and Kittmer,C.W., Measured Passage Velocities in a Radial Impeller With Shrouded and Unshrouded Configurations, Journal of Engineering for Power, Vol.97,No. 2:207～213
24、Michael K.M. Laser Velocimetry Study of the Flow Field in a Centrifugal Pump With a Shrouded Impeller. May, 1994
25、张武高等，影响离心蜗壳内速度场分布的流量因素，流体机械，1999(12)：14～17
26、刘超等，离心泵叶轮内旋转流场激光测量研究，江苏农学院学报．1994,15(4)：64～71
27、李文广，离心油泵蜗壳与叶轮内部流动 LDV 测量与数值计算．[博士学位论文]．北京：石油大学．1996
28、李文广等，大出口角离心泵叶轮内部清水流动测量．农业机械学报．1999(2)：54～59
29、Mark P. Wemet. PIV for Turbomachinery Applications. NASA Technical Technical Memorandum 107525 1997
30、Paone,N.,Riethmuller,M.l., Van den Braembussche,R.A.,Applicatiin of Particle Image Displacemetn Velocimetry to a Centrifugal pump ,Fourth International Symposium on Applications of Laser techniques to Fluid Mechanics. Lisbon, Portugal, July 1988:11-14,
31、Post,M.E., goss,L.P.,Brainard, L.f., Two-Color particle Imaging Velocimetry in a Turbine Cascade, proceedings of the AIAA, Aerospace Sciences Mtg, AIAA 91—0274,Reno Nv,Jan ,1991:7-10
32、Shepherd, I.C.,et al, Velocity Measurement in Fan Rotors Using Particle Imaging Velocimetry, ASME Conference on Laser emometry. 1994:Advances and Applications,Vol. 191:179-183
33、Tisserant,D. and Breugelmans,F.A.E., rotor blade—to—blade Measurements Using Particle Image Velocimetry, ASME j. of Turbomachinery,April, 1997 Vol. 119:176—181
34、Rothlubbers et al, Particle Tracking Velocimetry Measurements in a Radial Pump with Particle Pair Detection using the Hough transform, Eighth international Symposium on Applications of Laser Techniques to Fluid Mechanics,Lisbon, Portugal,July 8-11,1996:8.6.1～8.6.6.
35、Oldenburg,M. And Pap,E, Velocity Measurement in the Impeller and in the volute of a Centrifugal pump by Particle Image Displacement Velocimetry, Eighth International Symposium on Applications of Laser techniques to Fluid Mechanics. Lisbon, Portugal, July8-11,1996:8.2.1-8.2.5.
36、Oh J S and Ro S H. Application of Time Marching Method to Incompressible Centrifugal Pump Flow. The 2nd International Symposium on Fluid Machinery and Fluid Engineering.22～25 October,2000,Beijing:219～225
37、Adler D, Levy Y. A Laser-Doppler Investigation of the Flow inside a Backswept, Closed, Centrifugal Impeller. J Mech Eng. Sci, 1979,21 (1): 1～6
38、 Kannemans H. Radial Pump Impeller Measurements Using a Laser Doppler Velocimetr. USA: ASME Paper No 80-GT-94,ASME, 1980,1～8
39、 Kikuyama K,Minemura K.Hasegawa Y, et al. Unsteady pressure Distributions on the Impeller Blades of Centrifugal Pump-Impeller Operating Off-Design. USA:ASME paper, No 87-GT-144,ASME, 1987,1～8
40、 Hayami H, Ueki H, Semno Y. Flow Measurements Using A Laser-2-Focus Velocimeter in a High-Pressure Ratio Centrifugal Imepller, Engingeering Applications of Laser Velocimetry, Winter Annual Meeting of the ASME Phoenix, Arizona, USA:Published by ASME, 1982.111～116
41、 J.A.Lorett ,S. Gopalakrishnan. Interaction Between Impeller And Volute Of Pumps At Off-Design Conditions. Transactions of The ASME. 1986(108): 12～18
42、黄建德．开式和闭式离心泵进口回流的研究．工程热物理学报．1997(1)：43～46
43、王正宾等．离心式水泵叶栅流动研究．北方交通大学学报
44、刘正先等，离心泵内三维湍流流场的实验研究,工程执物理学报，1999(5)：558～562
45、 B.Neumann, The Interaction Between Geometry And Performance of A Centrifugal Pump .Mechanical Engineering Publication Limited, London, 1991
46、 Ci-Chang Chen, Xiao-Feng Zhang. Study of Inner Flow And Performance of Two-Dimensional Pump Centrifugal Impeller. Fluid Machinery Forum ASME. 1991(119):21～25
47、康琦等．全场院测速技术进展．力学进展．1997(1)：106～120
48、 Richard D. Keane ,Ronald J. Adrian. Theory Of Cross-Correlation Analysis Of PIV Images. Applied Scientific Research. 1992(49): 191～215
49、 A.Cenedese and A.Paglialunga Digital Direct Anaalysis Of A Multiexposed Photograp In PIV. Experiments In Fluids. 1990(8): 273～280
50、 Adrian R.J Multi-point optical measurement of simultaneous vectors in unsteady flow—a review. Int. j. heat and fluid flow, 7(1996): 127
51、 Adrian R J. Particle image technique for experimental fluid mechanics. Ann. Rev. Fluid mech. 23(1991):261
52、杜斯特 F，梅林 A，怀特洛J H．激光多普勒测速技术的原理和实践，科学出版社，北京，1992
53、 Huntley J M. Speckle photography fringe analysis assessment of current algorithms. Appl. Opt. ,28(1989):4216
54、 Huntley J M.Fast Transfor for speckle photography fringe analysis .Optics and Laser in Eng.,7(1987): 149
55、Navone H D Haufman G H. Automatic digital processing in speckle photography: Comparison of two algorithms. Appl. Opt., 28(1989): 350
56、Tang F P et al PIV for Propeller Pumps. The 2~(na) International Symposium on Fluid Machinery and Fluid Engineering. 22～25 October, 2000,Beijing: 128～134
57、姬忠礼，席葆树等．PIV 技术测量振荡射流流场．流体力学实验与测量．1998(12)：87-91
58、Y. Senoo. M. Yamaguchi, M. Nishi, A Photograpic Study Of The Three dimensional Flow In A Radial Compressor. Journal Of Engineerign For Power July, 1968: 237～244
59、刘宝杰等．PIV在低速风洞中的应用．流体力学实验与测量．1998.6
60、赵亚宾等．用 PIV 测量法研究燃气轮机与导叶轮间流体的速度场．热能动力工程 1994(4)
61、盛森芝等．日新月异的现代流动测量技术．北京大学特赛流动测量研究中心．1999.9
62、Particle Image Velocimetry Software Manual
63、R. Dong et al Effect of Modification to Tongue and Impeller Geometry on Unsteady Flow ,Pressure Fluctuations,and Noise in a Centrifugal Pump. Transactions of the ASME July 1997,Vol(119): 506～515
64、张楚华等．旋转离心叶轮内湍流的非结构化网格数值计算．航空学报．1998(9)：556～559
65、Ubaldi.M.et al An Experimental Investigation of stator Induced unsteadiness on Centrifugal Impeller Outflow. Journal of Turbomachinery Jan.1996 Vol(118):41～54
2、陈池等．低比速离心泵研究现状与展望．流体机械．1998(7)：29～34
3、Anderson H.H., Mine pumps. Journal of Mining Society. 1938
4、R.C. Worseter, The Flow In Volutes And Its Effect On Centrifugal Pump Performance. Proc Instn. Mech Engrs. 1963，117(31): 843～865
5、Moore J. A Wake and an eddy in a Rotation Radial-flow Passage Trans. ASME. J. Eng. for power,1973(July): 205～219
6、陈次昌等，离心泵叶轮内的二次流及泵性能的研究．水泵技术 25～33
7、袁卫星等，离心泵射流—尾迹模型的三元流动计算，水泵技术 12～18
8、彭国义，水力机械转轮反问题数值研究与进展．甘肃大学学报．1997(4)：31～36
9、常近时，叶片式水力机械水动力学计算基础．水利电力出版社．1989
10、罗兴等，流体机械叶轮设计的研究与发展，力学进展，1997(3)：372～388
11、李世煌，吴桐林等编译，水泵设计教程，机械工业出版社,1987
12、A.Demealeaaere Three-Dimensional Inverse Method for Turbomachinery Blading Design. Journal of Turbomachinery. 1998(120)：247～255
13、陈池等，离心泵叶轮内流计算方法综述，流体机械。1999(2)
14、彭国义，曹树良，林汝长，水力机械转轮正问题数值研究与进展．甘肃大学学报．1997(3)：30～32
15、曹立新，离心泵叶轮全三维势流的间接边界元法研究，农业机械学报，1999(4)：23～42
16、吴玉林等，离心泵叶轮中紊流的计算．水泵技术．1997．(1)：9～15
17、Harnkins S P. Flack RD., Laser Velocimetry Measurements In Shrouded and Unshrouded Radial Flow Impellers. J Turbomach(Trans ASME), 1987, 109: 70～79
18、Miner S M, Beaudoin R J, Flack R D., Laser velocimeter in a Centrifugal Pump. J Turbomach (Tans ASME), 1989,111(3)：205～212
19、Cader T Masbernat O, Roco M C.LDV Measurements in a centrifugal Slurry Pump: Water and Dilute Slurry Flow. ASME Journal of Fluid Engineering, 1992. 114:606～615
20、Abramian M. Howard J H G.Aroing, LDA System for Unsteady Relativate Flow in a Model Centrifugal Impellers ASME Journal of Turbomachineary, 1994,116:260～268
21、Fischer.K., and Thoma,D., Investitgation of the Flow Conditions in a Centrifugal Pump, Transactions of the ASME, 1932 HYD—54—8:141—155
22、Acosta A.J., and Bowerman,R.D., Anexperimental Study of Centrifugal Pump Imperllers. Transactions of the ASME.Vol.79: 1821～1839
23、Howard,H.J.G., and Kittmer,C.W., Measured Passage Velocities in a Radial Impeller With Shrouded and Unshrouded Configurations, Journal of Engineering for Power, Vol.97,No. 2:207～213
24、Michael K.M. Laser Velocimetry Study of the Flow Field in a Centrifugal Pump With a Shrouded Impeller. May, 1994
25、张武高等，影响离心蜗壳内速度场分布的流量因素，流体机械，1999(12)：14～17
26、刘超等，离心泵叶轮内旋转流场激光测量研究，江苏农学院学报．1994,15(4)：64～71
27、李文广，离心油泵蜗壳与叶轮内部流动 LDV 测量与数值计算．[博士学位论文]．北京：石油大学．1996
28、李文广等，大出口角离心泵叶轮内部清水流动测量．农业机械学报．1999(2)：54～59
29、Mark P. Wemet. PIV for Turbomachinery Applications. NASA Technical Technical Memorandum 107525 1997
30、Paone,N.,Riethmuller,M.l., Van den Braembussche,R.A.,Applicatiin of Particle Image Displacemetn Velocimetry to a Centrifugal pump ,Fourth International Symposium on Applications of Laser techniques to Fluid Mechanics. Lisbon, Portugal, July 1988:11-14,
31、Post,M.E., goss,L.P.,Brainard, L.f., Two-Color particle Imaging Velocimetry in a Turbine Cascade, proceedings of the AIAA, Aerospace Sciences Mtg, AIAA 91—0274,Reno Nv,Jan ,1991:7-10
32、Shepherd, I.C.,et al, Velocity Measurement in Fan Rotors Using Particle Imaging Velocimetry, ASME Conference on Laser emometry. 1994:Advances and Applications,Vol. 191:179-183
33、Tisserant,D. and Breugelmans,F.A.E., rotor blade—to—blade Measurements Using Particle Image Velocimetry, ASME j. of Turbomachinery,April, 1997 Vol. 119:176—181
34、Rothlubbers et al, Particle Tracking Velocimetry Measurements in a Radial Pump with Particle Pair Detection using the Hough transform, Eighth international Symposium on Applications of Laser Techniques to Fluid Mechanics,Lisbon, Portugal,July 8-11,1996:8.6.1～8.6.6.
35、Oldenburg,M. And Pap,E, Velocity Measurement in the Impeller and in the volute of a Centrifugal pump by Particle Image Displacement Velocimetry, Eighth International Symposium on Applications of Laser techniques to Fluid Mechanics. Lisbon, Portugal, July8-11,1996:8.2.1-8.2.5.
36、Oh J S and Ro S H. Application of Time Marching Method to Incompressible Centrifugal Pump Flow. The 2nd International Symposium on Fluid Machinery and Fluid Engineering.22～25 October,2000,Beijing:219～225
37、Adler D, Levy Y. A Laser-Doppler Investigation of the Flow inside a Backswept, Closed, Centrifugal Impeller. J Mech Eng. Sci, 1979,21 (1): 1～6
38、 Kannemans H. Radial Pump Impeller Measurements Using a Laser Doppler Velocimetr. USA: ASME Paper No 80-GT-94,ASME, 1980,1～8
39、 Kikuyama K,Minemura K.Hasegawa Y, et al. Unsteady pressure Distributions on the Impeller Blades of Centrifugal Pump-Impeller Operating Off-Design. USA:ASME paper, No 87-GT-144,ASME, 1987,1～8
40、 Hayami H, Ueki H, Semno Y. Flow Measurements Using A Laser-2-Focus Velocimeter in a High-Pressure Ratio Centrifugal Imepller, Engingeering Applications of Laser Velocimetry, Winter Annual Meeting of the ASME Phoenix, Arizona, USA:Published by ASME, 1982.111～116
41、 J.A.Lorett ,S. Gopalakrishnan. Interaction Between Impeller And Volute Of Pumps At Off-Design Conditions. Transactions of The ASME. 1986(108): 12～18
42、黄建德．开式和闭式离心泵进口回流的研究．工程热物理学报．1997(1)：43～46
43、王正宾等．离心式水泵叶栅流动研究．北方交通大学学报
44、刘正先等，离心泵内三维湍流流场的实验研究,工程执物理学报，1999(5)：558～562
45、 B.Neumann, The Interaction Between Geometry And Performance of A Centrifugal Pump .Mechanical Engineering Publication Limited, London, 1991
46、 Ci-Chang Chen, Xiao-Feng Zhang. Study of Inner Flow And Performance of Two-Dimensional Pump Centrifugal Impeller. Fluid Machinery Forum ASME. 1991(119):21～25
47、康琦等．全场院测速技术进展．力学进展．1997(1)：106～120
48、 Richard D. Keane ,Ronald J. Adrian. Theory Of Cross-Correlation Analysis Of PIV Images. Applied Scientific Research. 1992(49): 191～215
49、 A.Cenedese and A.Paglialunga Digital Direct Anaalysis Of A Multiexposed Photograp In PIV. Experiments In Fluids. 1990(8): 273～280
50、 Adrian R.J Multi-point optical measurement of simultaneous vectors in unsteady flow—a review. Int. j. heat and fluid flow, 7(1996): 127
51、 Adrian R J. Particle image technique for experimental fluid mechanics. Ann. Rev. Fluid mech. 23(1991):261
52、杜斯特 F，梅林 A，怀特洛J H．激光多普勒测速技术的原理和实践，科学出版社，北京，1992
53、 Huntley J M. Speckle photography fringe analysis assessment of current algorithms. Appl. Opt. ,28(1989):4216
54、 Huntley J M.Fast Transfor for speckle photography fringe analysis .Optics and Laser in Eng.,7(1987): 149
55、Navone H D Haufman G H. Automatic digital processing in speckle photography: Comparison of two algorithms. Appl. Opt., 28(1989): 350
56、Tang F P et al PIV for Propeller Pumps. The 2~(na) International Symposium on Fluid Machinery and Fluid Engineering. 22～25 October, 2000,Beijing: 128～134
57、姬忠礼，席葆树等．PIV 技术测量振荡射流流场．流体力学实验与测量．1998(12)：87-91
58、Y. Senoo. M. Yamaguchi, M. Nishi, A Photograpic Study Of The Three dimensional Flow In A Radial Compressor. Journal Of Engineerign For Power July, 1968: 237～244
59、刘宝杰等．PIV在低速风洞中的应用．流体力学实验与测量．1998.6
60、赵亚宾等．用 PIV 测量法研究燃气轮机与导叶轮间流体的速度场．热能动力工程 1994(4)
61、盛森芝等．日新月异的现代流动测量技术．北京大学特赛流动测量研究中心．1999.9
62、Particle Image Velocimetry Software Manual
63、R. Dong et al Effect of Modification to Tongue and Impeller Geometry on Unsteady Flow ,Pressure Fluctuations,and Noise in a Centrifugal Pump. Transactions of the ASME July 1997,Vol(119): 506～515
64、张楚华等．旋转离心叶轮内湍流的非结构化网格数值计算．航空学报．1998(9)：556～559
65、Ubaldi.M.et al An Experimental Investigation of stator Induced unsteadiness on Centrifugal Impeller Outflow. Journal of Turbomachinery Jan.1996 Vol(118):41～54