离心泵直锥形吸水室的内流特性分析及其结构研究
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摘要
本文以离心泵直锥形吸水室为研究对象,采用CFD数值模拟方法,对吸水室内部流动状态进行了模拟分析,同时对吸水室形状、结构与离心泵整体性能之间存在的关系进行了理论分析和试验研究。
本文的主要研究工作包括：
1.简述了计算流体力学CFD及Pro/ENGINEER软件的发展历程,确立了"Pro/e建模,Gambit划分网格,Fluent模拟仿真”的离心泵内部流场的数值计算方法。通过Pro/E软件构建了HCZ系列50-160、65-160、150-250三种规格的耐腐蚀化工流程泵的三维水力模型；应用Gambit软件的分块网格技术,采用非结构网格为主、结构网格为辅的单元体,对水力模型进行网格划分；介绍了Fluent数值计算的基本方程,确定了适合离心泵内部流场数值计算的解算策略。
2.对三种不同形状直锥形吸水室内部流动特点进行了研究一平直型吸水室(HCZ50-160)、渐扩型吸水室(HCZ65-160)、渐缩型吸水室(HCZ150-250)。通过分析吸水室流体速度的三维分量与流量、径向位置、轴向位置的关系,得出吸水室内部流态为伴有少量径向漩涡的三维螺旋流,小流量工况下出现回流现象(即轴向漩涡)。
3.研究了吸水室形状对离心泵水力性能的影响。以HCZ65-160和HCZ150-250水力模型为基础,分别将其吸水室改为平直型吸水室,CFD性能预测结果表明：应用于同一台离心泵时,采用平直型吸水室的离心泵水力性能优于渐扩型吸水室和渐缩型吸水室。在此基础上,本文创新性地提出直管与锥形管相结合的新型吸水室模型,应用于工程实际时表明：设计工况点扬程提高0.4m左右,效率提高1%左右。
4.对吸水室内置隔板对离心泵性能的影响进行了研究。隔板能够有效减弱预旋,本文对隔板的轴向长度、径向长度、数量以及安放位置做了一系列研究,结果表明：径向长度a以吸水室进口直径的1/4为宜,轴向长度b取吸水室轴向长度的3/4,在靠近叶轮入口处安放隔板2块时,离心泵性能最佳。
5.完成了离心泵外特性的试验研究。应用稳定可靠的试验装置和数据采集系统,结合与之相适应的试验数据处理方法,对6套对比方案进行了对比试验,试验结果与预测结果基本一致。
The conoid suction side of the centrifugal pump is investigated in this paper based on the CFD numerical simulation and experimental test, and the flow characteristic closed by the inlet of the impeller is studied. The research on the relationship between the structure and shape of the suction chamber and the performance of centrifugal pump is carried out, also.
The main works are as follows:
1. Based on the development course of CFD (Computational Fluid Dynamic) and Pro/ENGINEERING, the numerical simulation method for interior flow state in centrifugal pump is built up, described as:the software of Pro/E for modeling, Gambit for meshing, and Fluent for simulations. The 3D models of there types of anti-corrosion chemical process pump as HCZ 50-160,65-160,150-250 are built by Pro/E, and blocking meshing method is applied to mesh the entity fluid field, and the simulation numerical method suit for centrifugal pump is determined.
2. The interior flow state is studied in the cylindric (50-160), the tapered (65-160) and the diverging (150-250) suction side, relatively. With different flow mess, racial and axial position, the variation trend of 3D velocity components is studied. The flow state could be described as 3D spiral flow with racial and axial recirculations.
3. The relationship between the shape of suction side and the performance of centrifugal pump was studied. Compared to tapered or diverging suction side, the same centrifugal pump with the cylindric model has higher performance. According to the conclusion above, new-type suction side is presented, described as cylindric section and coniod section. With the new-type suction side applied, the hydraulic performance is improved.
4. The effective solution to weaken the prerotation and back flow in suction side is the built-in baffles. With different number, location, axial and radial length of the baffles in suction chamber, CFD numerical simulation is applied to predict the variation trend of performance parameters of centrifugal pump. According to the performance curve and the flow state in the chamber, the optimum baffle came out:the radial length is 1/4D0 (inlet diameter), and the 3/4 of the length of chamber is the value range of axial length for the baffle. And, two baffles should be put closed by inlet of the impeller.
5. The experimental test of the centrifugal pump with different shape of suction chamber is reported. The test methods are explained by introducing structure of testing facility and data acquire system. With effective data processing methods, the results of 6 compassion programmes are concordant with the prediction data.
本文的主要研究工作包括：
1.简述了计算流体力学CFD及Pro/ENGINEER软件的发展历程,确立了"Pro/e建模,Gambit划分网格,Fluent模拟仿真”的离心泵内部流场的数值计算方法。通过Pro/E软件构建了HCZ系列50-160、65-160、150-250三种规格的耐腐蚀化工流程泵的三维水力模型；应用Gambit软件的分块网格技术,采用非结构网格为主、结构网格为辅的单元体,对水力模型进行网格划分；介绍了Fluent数值计算的基本方程,确定了适合离心泵内部流场数值计算的解算策略。
2.对三种不同形状直锥形吸水室内部流动特点进行了研究一平直型吸水室(HCZ50-160)、渐扩型吸水室(HCZ65-160)、渐缩型吸水室(HCZ150-250)。通过分析吸水室流体速度的三维分量与流量、径向位置、轴向位置的关系,得出吸水室内部流态为伴有少量径向漩涡的三维螺旋流,小流量工况下出现回流现象(即轴向漩涡)。
3.研究了吸水室形状对离心泵水力性能的影响。以HCZ65-160和HCZ150-250水力模型为基础,分别将其吸水室改为平直型吸水室,CFD性能预测结果表明：应用于同一台离心泵时,采用平直型吸水室的离心泵水力性能优于渐扩型吸水室和渐缩型吸水室。在此基础上,本文创新性地提出直管与锥形管相结合的新型吸水室模型,应用于工程实际时表明：设计工况点扬程提高0.4m左右,效率提高1%左右。
4.对吸水室内置隔板对离心泵性能的影响进行了研究。隔板能够有效减弱预旋,本文对隔板的轴向长度、径向长度、数量以及安放位置做了一系列研究,结果表明：径向长度a以吸水室进口直径的1/4为宜,轴向长度b取吸水室轴向长度的3/4,在靠近叶轮入口处安放隔板2块时,离心泵性能最佳。
5.完成了离心泵外特性的试验研究。应用稳定可靠的试验装置和数据采集系统,结合与之相适应的试验数据处理方法,对6套对比方案进行了对比试验,试验结果与预测结果基本一致。
The conoid suction side of the centrifugal pump is investigated in this paper based on the CFD numerical simulation and experimental test, and the flow characteristic closed by the inlet of the impeller is studied. The research on the relationship between the structure and shape of the suction chamber and the performance of centrifugal pump is carried out, also.
The main works are as follows:
1. Based on the development course of CFD (Computational Fluid Dynamic) and Pro/ENGINEERING, the numerical simulation method for interior flow state in centrifugal pump is built up, described as:the software of Pro/E for modeling, Gambit for meshing, and Fluent for simulations. The 3D models of there types of anti-corrosion chemical process pump as HCZ 50-160,65-160,150-250 are built by Pro/E, and blocking meshing method is applied to mesh the entity fluid field, and the simulation numerical method suit for centrifugal pump is determined.
2. The interior flow state is studied in the cylindric (50-160), the tapered (65-160) and the diverging (150-250) suction side, relatively. With different flow mess, racial and axial position, the variation trend of 3D velocity components is studied. The flow state could be described as 3D spiral flow with racial and axial recirculations.
3. The relationship between the shape of suction side and the performance of centrifugal pump was studied. Compared to tapered or diverging suction side, the same centrifugal pump with the cylindric model has higher performance. According to the conclusion above, new-type suction side is presented, described as cylindric section and coniod section. With the new-type suction side applied, the hydraulic performance is improved.
4. The effective solution to weaken the prerotation and back flow in suction side is the built-in baffles. With different number, location, axial and radial length of the baffles in suction chamber, CFD numerical simulation is applied to predict the variation trend of performance parameters of centrifugal pump. According to the performance curve and the flow state in the chamber, the optimum baffle came out:the radial length is 1/4D0 (inlet diameter), and the 3/4 of the length of chamber is the value range of axial length for the baffle. And, two baffles should be put closed by inlet of the impeller.
5. The experimental test of the centrifugal pump with different shape of suction chamber is reported. The test methods are explained by introducing structure of testing facility and data acquire system. With effective data processing methods, the results of 6 compassion programmes are concordant with the prediction data.
引文
[1]《离心泵设计基础》编写组.离心泵设计基础[M].北京：机械工业出版社,1974.
[2]关醒凡.泵的理论与设计[M].北京：机械工业出版社,1987.
[3]朱玉峰,王春林,李平.单级单吸卧式离心泵泵体的吸入室及吐出管设计[J].河北工业科技,2002,19(4)：8-11.
[4]黄思,王国玉.离心泵内流场非对称性及受力的三维数值分析[J].农业机械学报,2006,37(10)：66-69.
[5]王秀勇,王灿星.基于数值模拟的离心泵性能预测[J].流体机械,2007,35(10)：9-13.
[6]张峥.基于FLUENT的离心泵内部流动的数值模拟[J].科技信息,2008,26：93.
[7]张振山,张艳伟,杨玉敏.离心泵蜗壳对叶轮内部流动的影响研究[J].水泵技术,2007,2：15-18.
[8]范恒灵,王幼民,唐铃凤等.离心泵内流场的三维数值模拟及流动分析[J].机械工程师,2007,1：49-51.
[9]阎庆绂,陈仰吾,张淑英等.锥形吸水室离心泵的入口旋流[J].太原工业大学学报,1990,21(2)：90-94.
[10]阎庆绂,陈仰吾,李治勤.离心泵的入口预旋与吸入室中的旋流[J].太原工业大学学报,1991,3：13-17.
[11]阎庆绂,陈仰吾,高恩恩等.离心泵入口旋流的试验研究[J].农业机械学报,1992,23(1)：45-51.
[12]阎庆绂,马素霞,李治勤.泵系统的流体力学特性[J].农业机械学报,1996,27(2)：60-65.
[13]马素霞.泵系统入口旋流的试验研究[D].硕士学位论文,太原工业大学,1997.
[14]苗文斌.泵入口侧涡量场的实验研究与数值计算[D].硕士学位论文,太原理工大学,2002.
[15]朱红耕,陆林广,奚斌等.水泵进口预旋及涡流强度测试新技术[J].灌溉排水学报,2003,22(3)：57-60.
[16]翟学广,赵卫东,李强.新技术在离心泵技术工作中的应用与发展[J].通用机械,2006,10：49-51.
[17]周正富,陈松山,耿卫明等.3 叶片离心泵内流场的PIV测量[J].扬州大学学报(自然科学 版),2006,9(3)：72-75.
[18]Nicholas Pedersen, Poul S. Larsen. Flow in a Centrifugal Pump Impeller at Design and Off-Design Conditions-Part Ⅰ:Particle Image Velocimetry (PIV) and Laser Doppler Velocimetry (LDV) Measurements [J]. ASME, Journal of Fluids Engineering,2003,25:61-72.
[19]S. Boipaire, J. P. Barrand. Experimental Study of the Flow in the Suction Pipe of a Centrifugal Pump at Partial Flow Rates in Unsteady Conditions[J]. Journal of Pressure Vessel Technology, 1999,121:291-295.
[20]阎庆绂,高恩恩,李仲平.吸入室结构对泵效率的影响[J].流体机械,1991,11：10-12.
[21]张德胜,施卫东,陆伟刚等.高效区宽离心泵的研制与试验研究[J].中国农村水利水电,2008,7：95-97.
[22]李益民.水泵回流理论与研究[J].流体机械,1995,23(9)：29-31.
[23]史宏超,李益民.离心泵进口回流及其控制的研究水泵技术[J].水泵技术,2000,3：27-29.
[24]Schiavelo B, Sen M. Performance prediction of centrifugal pump and compressors. ASME, Proc 22nd Ann Fluids Eng Conf, New Orleans, Luoisiana,1983:9-13.
[25]Schiavello B. A diffusion factor correlation for the prediction of the reverse flow onset at the centrifugal pump inlet[J]. Proc 7th Conf Fluid Mach, HUN,1983,2:751-760.
[26]Sen H M. Prediction of the reverse flow and prerotation in centrifugal pumps[J]. Proc 7th Conf Fluid Mach, HUN,1983,2:805-814.
[27]黄建德.离心泵进口回流的发生机理及预估[J].上海交通大学学报,1998,32(7)：5-8.
[28]A·T·特罗斯刻兰斯基.叶片泵的计算与结构[M].北京：机械工业出版社,1981.
[29]杨琳.消除离心泵特性曲线的驼峰[J].新疆大学学报(自然科学版),2002,6：32-34.
[30]朱国华.降低离心泵特性曲线驼峰的途径[J].水泵技术,1991,3：28-30.
[31]刘甲凡.离心泵叶轮前的预旋与回流[J].水泵技术,1997,5：17-19.
[32]赵家新.关于消除泵的驼峰现象的试验[J].流体工程,1992,20(9)：11-14.
[33]王福军.计算流体动力学分析—CFD软件原理与应用[M].北京：清华大学出版社,2004.
[34]Xiewei Song. Computational Fluid Dynamics (CFD) Study of the 4th Generation Prototype of a Continuous Flow Ventricular Assist Device (VAD)[J]. Journal of Bimechanical Engineering, 2004,126(2):180-187.
[35]Kitano Majidi. Numerical Study of Unsteady Flow in a Centrifugal Pump[J]. Jouranl of Turbomachinery,2005,127(2):363-371.
[36]耿少娟,聂超群,黄伟光等.不同叶轮形式下离心泵整机非定常流场的数值研究[J].机械工程学报,2006,42(5)：27-31.
[37]J.JMoore, A. B. Palazzolo. Rotordynamic Force Prediction of Whirling Centrifugal Impeller Shroud Passages Using Computational Fluid Dynamics Techniques[J]. Journal of engineering for Gas Turbines and Power,2001,123(4):910-918.
[38]Yasushi Tatebayashi, Kazuhiro Tanaka. Pump Performance Improvement by Rastraining Back Flow in Screw-Type Centrifugal Pump[J]. Journal of Turbomachinery,2005,127(4):755-762.
[39]李贤华.双吸式离心泵内部流场数值模拟研究[D].杭州,浙江工业大学,2007.
[40]李新宏,黄淑娟.切线泵整机多相位定常流动数值模拟[J].工程热物理学报,2003,24(3)：423-425.
[41]邵国辉,赖喜德,唐立新.扭曲叶片双吸离心泵内部流场的三维数值模拟[J].水力发电,2007,33(6)：49-52.
[42]曹国强,梁冰,包明宇.基于Fluent的叶轮机械三维紊流流场数值模拟[J].机械设计与制造,2005,8：22-24.
[43]曹树良,王万鹏,祝宝山.离心泵压水室内部流动数值模拟[J].江苏大学学报(自然科学版),2004,25(3)：185-188.
[44]Marc Gugau离心泵叶轮和蜗壳的非定常数值模拟[J].德国达姆施塔特工业大学叶轮机械及流体动.
[45]刘宜,惠伟安,赵希枫等.高比转数离心泵叶轮内空蚀两相流动的数值模拟[J].兰州理工大学学报,2008,34(5)：60-63.
[46]刘宜,赵希枫,齐学义等.离心泵空蚀湍流的非定常数值模拟[J].兰州理工大学报,2008,34(3)：44-47.
[47]刘宜,张文军,杜杰.离心泵内部空化流动的数值预测[J].甘肃科学学报,2008,20(3)：19-21.
[48]张文军.离心泵全流道内空化流场的数值模拟及预测[D].兰州理工大学,硕士学位论文,2008.
[49]李军,刘立军,李国君等.离心泵叶轮内空化流动的数值预测[J].工程热物理学报,2007,28(6)：948-950.
[50]朱荣生,付强,李维斌.低比转数离心泵叶轮内汽蚀两相流三维数值模拟[J].农业机械学报,2006,37(5)：75-79.
[51]付强.基于CFD技术改善低比速疏水泵其实性能的研究[D].江苏大学,硕士学位论文,2006.
[52]朱荣生,付强,李维斌等.基于混合模型的离心泵叶轮内汽蚀两相流的CFD分析[J].中国农村水利水电,2006,8：51-53.
[53]黄道见.离心泵叶轮内汽蚀发生的理论探讨[J].农机化研究,2006,6：88-89.
[54]卢金铃,席光,祁大同.离心泵叶轮内气液两相三维流动数值研究[J].工程热物理学报,2003,24(2)：237-240.
[55]杨军虎,张学静.离心泵的性能预测进展[J].通用机械,2003,(12)：48-51.
[56]袁建平,袁寿其,何志霞.流场测试技术及其在离心泵中的应用进展[J].水泵技术,2003,2：3-7.
[57]李龙,陈黎明.泵优化设计国内现状及发展趋势[J].水泵技术,2003,2：8-11.
[58]何有世,袁寿其,陈池.CFD进展及其在离心泵叶轮内流计算中的应用[J].水泵技术,2002,3：23-26.
[59]王晓燕.低比转速离心泵双吸叶轮及蜗壳内部流场的数值计算与分析[D].兰州理工大学,2006.
[60]郭圣路,杨岐朋.巧学巧用Peo/ENGINEER Wildfire 3.0典型设计实例[M].北京：电子工业出版社,2007.
[61]陶文铨.计算传热学的近代进展[M].北京：北京大学出版社,2008.
[62]朱自强,张正科,李津.网格生成的数值模拟的讨论[J].空气动力学报,1988,16(1)：64-67.
[63]周天孝,白文.CFD多块网格生成新进展[J].力学进展,1999,(29)3：344-368.
[64]李栋,孙刚,乔志德.网格嵌套法在复杂流场计算中的应用[J].空气动力学报,1998：16(2)：216-219.
[65]Rubbert P E, Lee K D. Patched coordinate systems[J]. Applied Mathematics and computation, 1982:235-252.
[66]张华娟,李春.离心式水泵冲击损失的计算与分析[J].流体机械.2006,34(8)：41-44.
[67]刘厚林,谈明高,袁寿其.离心泵圆盘摩擦损失计算[J].农业工程学报,2006,22(12)：107-109.
[68]R.Palgrave离心泵的小流量运转(中译文)[J].水泵技术,1987(2).
[2]关醒凡.泵的理论与设计[M].北京：机械工业出版社,1987.
[3]朱玉峰,王春林,李平.单级单吸卧式离心泵泵体的吸入室及吐出管设计[J].河北工业科技,2002,19(4)：8-11.
[4]黄思,王国玉.离心泵内流场非对称性及受力的三维数值分析[J].农业机械学报,2006,37(10)：66-69.
[5]王秀勇,王灿星.基于数值模拟的离心泵性能预测[J].流体机械,2007,35(10)：9-13.
[6]张峥.基于FLUENT的离心泵内部流动的数值模拟[J].科技信息,2008,26：93.
[7]张振山,张艳伟,杨玉敏.离心泵蜗壳对叶轮内部流动的影响研究[J].水泵技术,2007,2：15-18.
[8]范恒灵,王幼民,唐铃凤等.离心泵内流场的三维数值模拟及流动分析[J].机械工程师,2007,1：49-51.
[9]阎庆绂,陈仰吾,张淑英等.锥形吸水室离心泵的入口旋流[J].太原工业大学学报,1990,21(2)：90-94.
[10]阎庆绂,陈仰吾,李治勤.离心泵的入口预旋与吸入室中的旋流[J].太原工业大学学报,1991,3：13-17.
[11]阎庆绂,陈仰吾,高恩恩等.离心泵入口旋流的试验研究[J].农业机械学报,1992,23(1)：45-51.
[12]阎庆绂,马素霞,李治勤.泵系统的流体力学特性[J].农业机械学报,1996,27(2)：60-65.
[13]马素霞.泵系统入口旋流的试验研究[D].硕士学位论文,太原工业大学,1997.
[14]苗文斌.泵入口侧涡量场的实验研究与数值计算[D].硕士学位论文,太原理工大学,2002.
[15]朱红耕,陆林广,奚斌等.水泵进口预旋及涡流强度测试新技术[J].灌溉排水学报,2003,22(3)：57-60.
[16]翟学广,赵卫东,李强.新技术在离心泵技术工作中的应用与发展[J].通用机械,2006,10：49-51.
[17]周正富,陈松山,耿卫明等.3 叶片离心泵内流场的PIV测量[J].扬州大学学报(自然科学 版),2006,9(3)：72-75.
[18]Nicholas Pedersen, Poul S. Larsen. Flow in a Centrifugal Pump Impeller at Design and Off-Design Conditions-Part Ⅰ:Particle Image Velocimetry (PIV) and Laser Doppler Velocimetry (LDV) Measurements [J]. ASME, Journal of Fluids Engineering,2003,25:61-72.
[19]S. Boipaire, J. P. Barrand. Experimental Study of the Flow in the Suction Pipe of a Centrifugal Pump at Partial Flow Rates in Unsteady Conditions[J]. Journal of Pressure Vessel Technology, 1999,121:291-295.
[20]阎庆绂,高恩恩,李仲平.吸入室结构对泵效率的影响[J].流体机械,1991,11：10-12.
[21]张德胜,施卫东,陆伟刚等.高效区宽离心泵的研制与试验研究[J].中国农村水利水电,2008,7：95-97.
[22]李益民.水泵回流理论与研究[J].流体机械,1995,23(9)：29-31.
[23]史宏超,李益民.离心泵进口回流及其控制的研究水泵技术[J].水泵技术,2000,3：27-29.
[24]Schiavelo B, Sen M. Performance prediction of centrifugal pump and compressors. ASME, Proc 22nd Ann Fluids Eng Conf, New Orleans, Luoisiana,1983:9-13.
[25]Schiavello B. A diffusion factor correlation for the prediction of the reverse flow onset at the centrifugal pump inlet[J]. Proc 7th Conf Fluid Mach, HUN,1983,2:751-760.
[26]Sen H M. Prediction of the reverse flow and prerotation in centrifugal pumps[J]. Proc 7th Conf Fluid Mach, HUN,1983,2:805-814.
[27]黄建德.离心泵进口回流的发生机理及预估[J].上海交通大学学报,1998,32(7)：5-8.
[28]A·T·特罗斯刻兰斯基.叶片泵的计算与结构[M].北京：机械工业出版社,1981.
[29]杨琳.消除离心泵特性曲线的驼峰[J].新疆大学学报(自然科学版),2002,6：32-34.
[30]朱国华.降低离心泵特性曲线驼峰的途径[J].水泵技术,1991,3：28-30.
[31]刘甲凡.离心泵叶轮前的预旋与回流[J].水泵技术,1997,5：17-19.
[32]赵家新.关于消除泵的驼峰现象的试验[J].流体工程,1992,20(9)：11-14.
[33]王福军.计算流体动力学分析—CFD软件原理与应用[M].北京：清华大学出版社,2004.
[34]Xiewei Song. Computational Fluid Dynamics (CFD) Study of the 4th Generation Prototype of a Continuous Flow Ventricular Assist Device (VAD)[J]. Journal of Bimechanical Engineering, 2004,126(2):180-187.
[35]Kitano Majidi. Numerical Study of Unsteady Flow in a Centrifugal Pump[J]. Jouranl of Turbomachinery,2005,127(2):363-371.
[36]耿少娟,聂超群,黄伟光等.不同叶轮形式下离心泵整机非定常流场的数值研究[J].机械工程学报,2006,42(5)：27-31.
[37]J.JMoore, A. B. Palazzolo. Rotordynamic Force Prediction of Whirling Centrifugal Impeller Shroud Passages Using Computational Fluid Dynamics Techniques[J]. Journal of engineering for Gas Turbines and Power,2001,123(4):910-918.
[38]Yasushi Tatebayashi, Kazuhiro Tanaka. Pump Performance Improvement by Rastraining Back Flow in Screw-Type Centrifugal Pump[J]. Journal of Turbomachinery,2005,127(4):755-762.
[39]李贤华.双吸式离心泵内部流场数值模拟研究[D].杭州,浙江工业大学,2007.
[40]李新宏,黄淑娟.切线泵整机多相位定常流动数值模拟[J].工程热物理学报,2003,24(3)：423-425.
[41]邵国辉,赖喜德,唐立新.扭曲叶片双吸离心泵内部流场的三维数值模拟[J].水力发电,2007,33(6)：49-52.
[42]曹国强,梁冰,包明宇.基于Fluent的叶轮机械三维紊流流场数值模拟[J].机械设计与制造,2005,8：22-24.
[43]曹树良,王万鹏,祝宝山.离心泵压水室内部流动数值模拟[J].江苏大学学报(自然科学版),2004,25(3)：185-188.
[44]Marc Gugau离心泵叶轮和蜗壳的非定常数值模拟[J].德国达姆施塔特工业大学叶轮机械及流体动.
[45]刘宜,惠伟安,赵希枫等.高比转数离心泵叶轮内空蚀两相流动的数值模拟[J].兰州理工大学学报,2008,34(5)：60-63.
[46]刘宜,赵希枫,齐学义等.离心泵空蚀湍流的非定常数值模拟[J].兰州理工大学报,2008,34(3)：44-47.
[47]刘宜,张文军,杜杰.离心泵内部空化流动的数值预测[J].甘肃科学学报,2008,20(3)：19-21.
[48]张文军.离心泵全流道内空化流场的数值模拟及预测[D].兰州理工大学,硕士学位论文,2008.
[49]李军,刘立军,李国君等.离心泵叶轮内空化流动的数值预测[J].工程热物理学报,2007,28(6)：948-950.
[50]朱荣生,付强,李维斌.低比转数离心泵叶轮内汽蚀两相流三维数值模拟[J].农业机械学报,2006,37(5)：75-79.
[51]付强.基于CFD技术改善低比速疏水泵其实性能的研究[D].江苏大学,硕士学位论文,2006.
[52]朱荣生,付强,李维斌等.基于混合模型的离心泵叶轮内汽蚀两相流的CFD分析[J].中国农村水利水电,2006,8：51-53.
[53]黄道见.离心泵叶轮内汽蚀发生的理论探讨[J].农机化研究,2006,6：88-89.
[54]卢金铃,席光,祁大同.离心泵叶轮内气液两相三维流动数值研究[J].工程热物理学报,2003,24(2)：237-240.
[55]杨军虎,张学静.离心泵的性能预测进展[J].通用机械,2003,(12)：48-51.
[56]袁建平,袁寿其,何志霞.流场测试技术及其在离心泵中的应用进展[J].水泵技术,2003,2：3-7.
[57]李龙,陈黎明.泵优化设计国内现状及发展趋势[J].水泵技术,2003,2：8-11.
[58]何有世,袁寿其,陈池.CFD进展及其在离心泵叶轮内流计算中的应用[J].水泵技术,2002,3：23-26.
[59]王晓燕.低比转速离心泵双吸叶轮及蜗壳内部流场的数值计算与分析[D].兰州理工大学,2006.
[60]郭圣路,杨岐朋.巧学巧用Peo/ENGINEER Wildfire 3.0典型设计实例[M].北京：电子工业出版社,2007.
[61]陶文铨.计算传热学的近代进展[M].北京：北京大学出版社,2008.
[62]朱自强,张正科,李津.网格生成的数值模拟的讨论[J].空气动力学报,1988,16(1)：64-67.
[63]周天孝,白文.CFD多块网格生成新进展[J].力学进展,1999,(29)3：344-368.
[64]李栋,孙刚,乔志德.网格嵌套法在复杂流场计算中的应用[J].空气动力学报,1998：16(2)：216-219.
[65]Rubbert P E, Lee K D. Patched coordinate systems[J]. Applied Mathematics and computation, 1982:235-252.
[66]张华娟,李春.离心式水泵冲击损失的计算与分析[J].流体机械.2006,34(8)：41-44.
[67]刘厚林,谈明高,袁寿其.离心泵圆盘摩擦损失计算[J].农业工程学报,2006,22(12)：107-109.
[68]R.Palgrave离心泵的小流量运转(中译文)[J].水泵技术,1987(2).