四桨两舵大型船舶螺旋桨的面元法设计研究
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摘要
螺旋桨的理论设计方法的成熟为精确设计出满足设计要求的螺旋桨提供了可能,但是从升力线到流行的升力面设计理论设计螺旋桨都无法回避这样一个问题。即理论研究对于物体实际表面的假设与提高设计精确度之间的矛盾。想要用升力线或升力面对螺旋桨表面形状进行设计必须对物面条件进行简化,同时对于设计精确性的要求又需要设计的桨与实际形状更加接近。采用面元法设计螺旋桨可以更精确地设计螺旋桨的几何形形状,从而更好的满足高性能船舶对于螺旋桨具体性能的要求。
本文采用升力线理论求解满足设计要求的初始螺旋桨理论设计参数,与传统的升力线理论相比,增加了桨毂、黏性的影响。与采用复杂的数值计算的Cony方法比较表明两者几乎具有相等的精度,并且在高进速下环量更加均匀。
将面元法应用到三维翼型剖面设计的数值方法进行了详细的研究并举例计算,并对具体过程作了数值上的改进和创新。并提出了一种根据良好的压力分布形式母翼型精确设计满足给定升力系数和最大厚度限制的面元法设计方法。
引入智能优化领域中的粒子群算法(PSO)结合面元法对设计的翼型剖面进行了优化。并对优化的结果作了CFD验证,结果表明采用面元法设计的翼型具有相当高的准确性,同时采用PSO方法对于翼型的优化也是合理和有效的。
提出了一种能够使最终的设计桨环量满足设计环量分布的方法。成功的完成了既定的设计目标并在理论计算中得到了效率更高、空泡性能更优的设计螺旋桨。并针对四桨两舵螺旋桨推进系统的特殊性,把前桨的影响计入到后桨的伴流当中重新设计了后桨。理论计算表明设计的桨比原型桨具有更好的水动力性能。
本文用经典的升力线理论作为螺旋桨初步设计获取基本的设计参数,将面元法精确设计三维翼型剖面应用到螺旋桨翼型剖面的设计中,使得翼型剖面具有更均匀的压力分布,对结构强度的提高和空泡性能的改善起到积极的作用,设计翼型剖面的同时还引入了粒子群优化算法(PSO)来优化三维翼型翼型剖面,使得设计的螺旋桨剖面不仅具有良好的压力分布还具有更高的升阻比。从每个剖面的性能优化的角度出发,提高螺旋桨整体运行效率。对面元法在螺旋桨理论设计中的应用做了许多有益的尝试和探索。
The mature of precise propeller design theory provides a possible to design requirements of the propeller. but from the lift line to the popular design of the propeller lifting surface design theory can not avoid such a problem. Theoretical research that is practical for the objects, the surface of the assumptions and improve the design accuracy of the contradiction between. Want to use the lift line or lift the surface shape of the face of the propeller design must be simplified to the body boundary condition, while the accuracy requirements for the design of the paddle also need to design the actual shape of closer. Using boundary element method for design of the propeller can be more precisely designed geometric shape of the propeller so as to better meet the specific performance of high-performance marine propeller for the requirements.
In this paper, lift line theory to meet the design requirements for solving the initial propeller theory, design parameters, and compared with the traditional lift-line theory, an increase of propeller hub, viscous effects. Comparison with the use of complex numerical calculation of the cony’s research, This method have less calculation but almost get the same precision, and at high speed the optimum circulation was more uniformly.
The boundary element method applied to the three-dimensional numerical method for airfoil section design carried out a detailed study and an example calculation, and made a value on a specific process improvement and innovation. And presents a good pressure distribution under the form of precisely designed to meet the original of a given airfoil lift coefficient and maximum thickness of the boundary element method for limit design method.
The introduction of particle swarm optimization (PSO) with boundary element method for the design of the airfoil section optimizing. CFD and optimization results are validated results show that the boundary element method for the design of the airfoil has a very high accuracy while using PSO method for airfoil optimization is reasonable and effective.
Proposed a way to make the final design of paddle circulation to meet the design circulation distribution methods. Successful completion of the established design goals, and in theoretical calculations, the new design propellers have more efficient, better performance, and improve the performance of cavity. In the design of the 4 propellers with 2 rudders propulsion system, the impact of the former propeller to the rear propeller included in the accompanying flow were re-designed after the propeller. Theoretical calculations show that the design of the propeller blade is better than the prototype hydrodynamic performance.
In this paper, the classical lifting-line theory as a preliminary design of the propeller to obtain the basic design parameters, the precise design of three-dimensional panel method applied to the propeller airfoil cross-section profile design, makes the airfoil cross-section of a more uniform pressure distribution on the structural strength of the to enhance and improve the performance of cavity play an active role, while the introduction of particle swarm optimization (PSO) to optimize the three-dimensional airfoil cross-section, making the design of the propeller section not only has good pressure distribution also has a higher lift-drag ratio. From each profile point of view of performance optimization and improve overall operating efficiency of the propeller. The opposite element method in the design of propeller theory, has done a lot of useful attempts and exploration.
本文采用升力线理论求解满足设计要求的初始螺旋桨理论设计参数,与传统的升力线理论相比,增加了桨毂、黏性的影响。与采用复杂的数值计算的Cony方法比较表明两者几乎具有相等的精度,并且在高进速下环量更加均匀。
将面元法应用到三维翼型剖面设计的数值方法进行了详细的研究并举例计算,并对具体过程作了数值上的改进和创新。并提出了一种根据良好的压力分布形式母翼型精确设计满足给定升力系数和最大厚度限制的面元法设计方法。
引入智能优化领域中的粒子群算法(PSO)结合面元法对设计的翼型剖面进行了优化。并对优化的结果作了CFD验证,结果表明采用面元法设计的翼型具有相当高的准确性,同时采用PSO方法对于翼型的优化也是合理和有效的。
提出了一种能够使最终的设计桨环量满足设计环量分布的方法。成功的完成了既定的设计目标并在理论计算中得到了效率更高、空泡性能更优的设计螺旋桨。并针对四桨两舵螺旋桨推进系统的特殊性,把前桨的影响计入到后桨的伴流当中重新设计了后桨。理论计算表明设计的桨比原型桨具有更好的水动力性能。
本文用经典的升力线理论作为螺旋桨初步设计获取基本的设计参数,将面元法精确设计三维翼型剖面应用到螺旋桨翼型剖面的设计中,使得翼型剖面具有更均匀的压力分布,对结构强度的提高和空泡性能的改善起到积极的作用,设计翼型剖面的同时还引入了粒子群优化算法(PSO)来优化三维翼型翼型剖面,使得设计的螺旋桨剖面不仅具有良好的压力分布还具有更高的升阻比。从每个剖面的性能优化的角度出发,提高螺旋桨整体运行效率。对面元法在螺旋桨理论设计中的应用做了许多有益的尝试和探索。
The mature of precise propeller design theory provides a possible to design requirements of the propeller. but from the lift line to the popular design of the propeller lifting surface design theory can not avoid such a problem. Theoretical research that is practical for the objects, the surface of the assumptions and improve the design accuracy of the contradiction between. Want to use the lift line or lift the surface shape of the face of the propeller design must be simplified to the body boundary condition, while the accuracy requirements for the design of the paddle also need to design the actual shape of closer. Using boundary element method for design of the propeller can be more precisely designed geometric shape of the propeller so as to better meet the specific performance of high-performance marine propeller for the requirements.
In this paper, lift line theory to meet the design requirements for solving the initial propeller theory, design parameters, and compared with the traditional lift-line theory, an increase of propeller hub, viscous effects. Comparison with the use of complex numerical calculation of the cony’s research, This method have less calculation but almost get the same precision, and at high speed the optimum circulation was more uniformly.
The boundary element method applied to the three-dimensional numerical method for airfoil section design carried out a detailed study and an example calculation, and made a value on a specific process improvement and innovation. And presents a good pressure distribution under the form of precisely designed to meet the original of a given airfoil lift coefficient and maximum thickness of the boundary element method for limit design method.
The introduction of particle swarm optimization (PSO) with boundary element method for the design of the airfoil section optimizing. CFD and optimization results are validated results show that the boundary element method for the design of the airfoil has a very high accuracy while using PSO method for airfoil optimization is reasonable and effective.
Proposed a way to make the final design of paddle circulation to meet the design circulation distribution methods. Successful completion of the established design goals, and in theoretical calculations, the new design propellers have more efficient, better performance, and improve the performance of cavity. In the design of the 4 propellers with 2 rudders propulsion system, the impact of the former propeller to the rear propeller included in the accompanying flow were re-designed after the propeller. Theoretical calculations show that the design of the propeller blade is better than the prototype hydrodynamic performance.
In this paper, the classical lifting-line theory as a preliminary design of the propeller to obtain the basic design parameters, the precise design of three-dimensional panel method applied to the propeller airfoil cross-section profile design, makes the airfoil cross-section of a more uniform pressure distribution on the structural strength of the to enhance and improve the performance of cavity play an active role, while the introduction of particle swarm optimization (PSO) to optimize the three-dimensional airfoil cross-section, making the design of the propeller section not only has good pressure distribution also has a higher lift-drag ratio. From each profile point of view of performance optimization and improve overall operating efficiency of the propeller. The opposite element method in the design of propeller theory, has done a lot of useful attempts and exploration.
引文
[1]谭廷寿.非均匀流场中螺旋桨性能预报和理论设计研究.武汉理工大学博士学位论文.2003.1
[2] Rankine J M.On the mechanical principles of the action of propellers.TINA,1865,6:13
[3] Betz. A. Schraubenpropeller mit geringstem energieverlust. Gottingen Nachrichten, Math, phys KI. 1919:193
[4] Lerbs. H.W.. Moderately Loaded Propellers with a Finite Number of Blades and an Arbitrary Distribution of Circulation,Trans. SNAME, 1952,vol.60
[5] Morgan, W.B.,Silovic,V and Deny, S.B“Propeller Lifting Surface Corrections”SNAME, 1968,Vo1.76
[6]谭廷寿.非均匀流场中螺旋桨性能预报和理论设计研究.武汉理工大学博士学位论文.2003.2
[7] Ginzel G I,ludweing H.On the theory of the broad blade propeller.U.M.3079,A.R.C.,1944
[8] Cox.G;G.Corrections to the camber of constant pitch propellers .RINA,1961,103
[9] Pien, P.C.: The calculation of marine propellers based on lifting-surface theory. JSR, 1961,Vol.5, No.2
[10] English. J.W.: The application of a simplified lifting surface technique to the designof marine propellers. NPL Ship Division SH Report 1962,30/62
[11] Kerwin,J.E., Lee, C.S.: Prediction of steady and unsteady marine propeller performance by numerical lifting surface theory. Trans. SNAME, 1978,Vol.86
[12] Cummings, D.E.: Numerical prediction of propeller characteristics. JSR, 1973.Vol.17, No.1
[13]董世汤.船舶螺旋桨理论[M].上海:上海交通大学出版社,1985
[14]王国强.盛振邦.船舶推进[M].北京:国防工业出版社,1985
[15]螺旋桨升力面理论边值问题的精细化处理[R] CSSRC技术报告.2003
[16] Hess, J.T., Smith, A.M.: Calculation of Nonlifting Potential Flow about Arbitrary Three Dimentional Bodies. Journal of Ship Research, 1964.Vol.8.N0.2
[17] Morino,L.: Subsonic Potential Aerodynamics for Complex Configurations: A General Theory. AIAA Journal, 1974. Vol.12, Feb
[18]苏玉民,陈玉霞:具有任意给定压力分布形式的三维机翼数值设计。海洋工程,第21卷,第1期,2003
[19] Lee,C.S. and Kim,Y.G. and Suh,J.C.: A Surface Panel Method for Design of Hydrofoil, JSR, Vol.38, Sept.1994
[20] Morgan, W.B.,Silovic, V and Deny, S.B“Propeller Lifting SurfaceCorrections”SNAME, Vo1.76, 1968
[21]叶永兴.“螺旋桨升力线理论设计计算程序”,舰船性能研究,1978年第3期
[22]王国强.董世汤.船舶螺旋桨理论与应用.2.哈尔滨工程大学2007:38-39
[23] Prandtl,l L, Application of Modern Hydrodynamics to Aeronautics , NACA Report 116
[24] Sparenberg, J.A.: Application of lifting surface theory to ship screw. ISP, 1960
[25] Koyama, K.: Application of a Panel Method to the Unsteady Hydrodynamic Analysis of Marine Propellers. Proceedings of the 19th symposium on Naval Hydrodynamics, Seoul, Aug. 1992
[26]王国强.董世汤.船舶螺旋桨理论与应用.2.哈尔滨工程大学2007:45
[27]苏玉民.黄胜.船舶螺旋桨理论.1.哈尔滨工程大学.2003:59
[28]苏玉民.黄胜.船舶螺旋桨理论.1.哈尔滨工程大学.2003:62-67页
[29] Kerwin, J.E.: Computer techniques for propeller blades section design. Second Lips Propeller Symposium, 1973
[30] Van Manen, J.D., Troost, L.: The design of ship screws of optimum diameter for an unequal velocity field. Trans. SNAME, 1952
[31] Glauert,H.,The Elements of Aerofoil and Airscrew Theory, Cambridge University Press, 1959
[32] CONEY W,A method for the design of a class of marine propulsors[D] . Boston : MIT , 1989
[33] Justin.E,Kerwin.Lecture Notes Hydrofoils And Propeller.January 2001
[34] Hess J L. Calculation of potential flow about arbitary three dimensional lifting bodies[R].technical report MDC J5679-01,mcdonnel douglas,oct,1973
[35]苏玉民.黄胜.船舶螺旋桨理论.1.哈尔滨工程大学.2003:152
[36]吴望一.流体力学(下).1983年3月第一版.北京大学出版社2006.4:179
[37]戴遗山.舰船在波浪中运动的频域与时域势流理论.国防工业出版社,1998年
[38]王献孚.周树信.陈泽梁.杨驰.刘应中.计算船舶流体力学.上海交通大学出版社.1992年
[39]杨德全.赵忠生.边界元理论及应用.1.北京理工大学出版社.2006:37
[40]苏玉民.黄胜.船舶螺旋桨理论.1.哈尔滨工程大学.2003:158
[41]苏玉民.黄胜.船舶螺旋桨理论.1.哈尔滨工程大学.2003:163-168页
[42] Su, Y.: A study on design of marine propellers by lifting-bodytheory. Yokohama National University, Ph.D Thesis, 1999
[43]Parkin,B.R., Peebles,B.H.: Calculation of Hydrofoil Sections for Prescribed Pressure Distributions, SNAME Technical and Research Bulletin No.1-17, 1956
[44] Eppler,R., Shen,Y.T.: Wing Sections for Hydrofoils--Part 1: Symmetrical Profiles, JSR, Vol.23, Sept.1979
[45] Eppler,R., Shen,Y.T.: Wing Sections for Hydrofoils--Part 2: Nonsymmetrical Profiles, JSR, Vol.25, Sept.1981
[46] Ormsbee, A.I., Chen,A.W.: Multiple Element Airfoils Optimized for Maximum Lift Coefficient, AIAA Journal,Vol.10, Dec.1972
[47] Kennedy,J.L. and Marsden,D.J.: A Potential Flow Design Method for Multicomponent Airfoil Sections, Journal of Aircraft, Vol.15, Jan.1978
[48] Soinne,E. and Laine,S.: An Inverse Boundary Element Method for Single Component Airfoil Design, Journal of Aircraft, Vol.22, un.1985;
[49] Dutt,H.N.V. and Sreekanth,A.K.: Design of Aerofoils for Prescribed Pressure Distribution in Viscous Incompressible flows, Aeronautical Quarterly, Feb.1980
[50] Lee,C.S. and Kim,Y.G. and Suh,J.C.: A Surface Panel Method for Design of Hydrofoil, JSR, Vol.38, Sept.1994
[51]郑慧娆.陈绍林.莫忠息.黄象鼎.数值计算方法。2002.1武汉大学出版社,149-152页
[52]王国强.董世汤.船舶螺旋桨理论与应用.2.哈尔滨工程大学.2007:35
[53]王晓鹏.高正红.基于遗传算法的翼型气动优化设计[J].空气动力学学报,2000,21(3):70-75页
[54] Kennedy.JEbehtartR.etal. SwarmIntelligence.San rnaeiseo,MorganKuafann publishers[M].2001
[55]金欣磊.基于PSO多目标优化算法研究及应用[D]浙江大学2006
[56]张丽平.粒子群优化算法的理论及实践[D].浙江大学.2005:13-15页
[57]莫愿斌.粒子群优化算法的扩展与应用[D].浙江大学.2006:40-42页
[58]许平.姜长生.基于粒子群算法的翼型优化设计[J].飞机设计.Vol128.N o15.2008.10
[59]张亚锋,宋笔锋,李占科.高升力翼型的气动优化设计和实验研究[J].飞行力学,2006,24(4):70:2+
[60]于勇.Fluent入门与进阶教程.北京理工大学.2008.9:57-64页
[61] Kerwin, J.E.: Computer techniques for propeller blades section design. Second Lips Propeller Symposium, 1973
[62]盛振邦.刘应中.船舶原理(下).第一版.上海交通大学出版社,2004:141-149页
[63]苏玉民.黄胜.船舶螺旋桨理论.1.哈尔滨工程大学.2003:178
[64]覃新川.黄胜.常欣.四桨两舵推进系统的水动力干扰研究. 2008年3月. 49卷第1期
[2] Rankine J M.On the mechanical principles of the action of propellers.TINA,1865,6:13
[3] Betz. A. Schraubenpropeller mit geringstem energieverlust. Gottingen Nachrichten, Math, phys KI. 1919:193
[4] Lerbs. H.W.. Moderately Loaded Propellers with a Finite Number of Blades and an Arbitrary Distribution of Circulation,Trans. SNAME, 1952,vol.60
[5] Morgan, W.B.,Silovic,V and Deny, S.B“Propeller Lifting Surface Corrections”SNAME, 1968,Vo1.76
[6]谭廷寿.非均匀流场中螺旋桨性能预报和理论设计研究.武汉理工大学博士学位论文.2003.2
[7] Ginzel G I,ludweing H.On the theory of the broad blade propeller.U.M.3079,A.R.C.,1944
[8] Cox.G;G.Corrections to the camber of constant pitch propellers .RINA,1961,103
[9] Pien, P.C.: The calculation of marine propellers based on lifting-surface theory. JSR, 1961,Vol.5, No.2
[10] English. J.W.: The application of a simplified lifting surface technique to the designof marine propellers. NPL Ship Division SH Report 1962,30/62
[11] Kerwin,J.E., Lee, C.S.: Prediction of steady and unsteady marine propeller performance by numerical lifting surface theory. Trans. SNAME, 1978,Vol.86
[12] Cummings, D.E.: Numerical prediction of propeller characteristics. JSR, 1973.Vol.17, No.1
[13]董世汤.船舶螺旋桨理论[M].上海:上海交通大学出版社,1985
[14]王国强.盛振邦.船舶推进[M].北京:国防工业出版社,1985
[15]螺旋桨升力面理论边值问题的精细化处理[R] CSSRC技术报告.2003
[16] Hess, J.T., Smith, A.M.: Calculation of Nonlifting Potential Flow about Arbitrary Three Dimentional Bodies. Journal of Ship Research, 1964.Vol.8.N0.2
[17] Morino,L.: Subsonic Potential Aerodynamics for Complex Configurations: A General Theory. AIAA Journal, 1974. Vol.12, Feb
[18]苏玉民,陈玉霞:具有任意给定压力分布形式的三维机翼数值设计。海洋工程,第21卷,第1期,2003
[19] Lee,C.S. and Kim,Y.G. and Suh,J.C.: A Surface Panel Method for Design of Hydrofoil, JSR, Vol.38, Sept.1994
[20] Morgan, W.B.,Silovic, V and Deny, S.B“Propeller Lifting SurfaceCorrections”SNAME, Vo1.76, 1968
[21]叶永兴.“螺旋桨升力线理论设计计算程序”,舰船性能研究,1978年第3期
[22]王国强.董世汤.船舶螺旋桨理论与应用.2.哈尔滨工程大学2007:38-39
[23] Prandtl,l L, Application of Modern Hydrodynamics to Aeronautics , NACA Report 116
[24] Sparenberg, J.A.: Application of lifting surface theory to ship screw. ISP, 1960
[25] Koyama, K.: Application of a Panel Method to the Unsteady Hydrodynamic Analysis of Marine Propellers. Proceedings of the 19th symposium on Naval Hydrodynamics, Seoul, Aug. 1992
[26]王国强.董世汤.船舶螺旋桨理论与应用.2.哈尔滨工程大学2007:45
[27]苏玉民.黄胜.船舶螺旋桨理论.1.哈尔滨工程大学.2003:59
[28]苏玉民.黄胜.船舶螺旋桨理论.1.哈尔滨工程大学.2003:62-67页
[29] Kerwin, J.E.: Computer techniques for propeller blades section design. Second Lips Propeller Symposium, 1973
[30] Van Manen, J.D., Troost, L.: The design of ship screws of optimum diameter for an unequal velocity field. Trans. SNAME, 1952
[31] Glauert,H.,The Elements of Aerofoil and Airscrew Theory, Cambridge University Press, 1959
[32] CONEY W,A method for the design of a class of marine propulsors[D] . Boston : MIT , 1989
[33] Justin.E,Kerwin.Lecture Notes Hydrofoils And Propeller.January 2001
[34] Hess J L. Calculation of potential flow about arbitary three dimensional lifting bodies[R].technical report MDC J5679-01,mcdonnel douglas,oct,1973
[35]苏玉民.黄胜.船舶螺旋桨理论.1.哈尔滨工程大学.2003:152
[36]吴望一.流体力学(下).1983年3月第一版.北京大学出版社2006.4:179
[37]戴遗山.舰船在波浪中运动的频域与时域势流理论.国防工业出版社,1998年
[38]王献孚.周树信.陈泽梁.杨驰.刘应中.计算船舶流体力学.上海交通大学出版社.1992年
[39]杨德全.赵忠生.边界元理论及应用.1.北京理工大学出版社.2006:37
[40]苏玉民.黄胜.船舶螺旋桨理论.1.哈尔滨工程大学.2003:158
[41]苏玉民.黄胜.船舶螺旋桨理论.1.哈尔滨工程大学.2003:163-168页
[42] Su, Y.: A study on design of marine propellers by lifting-bodytheory. Yokohama National University, Ph.D Thesis, 1999
[43]Parkin,B.R., Peebles,B.H.: Calculation of Hydrofoil Sections for Prescribed Pressure Distributions, SNAME Technical and Research Bulletin No.1-17, 1956
[44] Eppler,R., Shen,Y.T.: Wing Sections for Hydrofoils--Part 1: Symmetrical Profiles, JSR, Vol.23, Sept.1979
[45] Eppler,R., Shen,Y.T.: Wing Sections for Hydrofoils--Part 2: Nonsymmetrical Profiles, JSR, Vol.25, Sept.1981
[46] Ormsbee, A.I., Chen,A.W.: Multiple Element Airfoils Optimized for Maximum Lift Coefficient, AIAA Journal,Vol.10, Dec.1972
[47] Kennedy,J.L. and Marsden,D.J.: A Potential Flow Design Method for Multicomponent Airfoil Sections, Journal of Aircraft, Vol.15, Jan.1978
[48] Soinne,E. and Laine,S.: An Inverse Boundary Element Method for Single Component Airfoil Design, Journal of Aircraft, Vol.22, un.1985;
[49] Dutt,H.N.V. and Sreekanth,A.K.: Design of Aerofoils for Prescribed Pressure Distribution in Viscous Incompressible flows, Aeronautical Quarterly, Feb.1980
[50] Lee,C.S. and Kim,Y.G. and Suh,J.C.: A Surface Panel Method for Design of Hydrofoil, JSR, Vol.38, Sept.1994
[51]郑慧娆.陈绍林.莫忠息.黄象鼎.数值计算方法。2002.1武汉大学出版社,149-152页
[52]王国强.董世汤.船舶螺旋桨理论与应用.2.哈尔滨工程大学.2007:35
[53]王晓鹏.高正红.基于遗传算法的翼型气动优化设计[J].空气动力学学报,2000,21(3):70-75页
[54] Kennedy.JEbehtartR.etal. SwarmIntelligence.San rnaeiseo,MorganKuafann publishers[M].2001
[55]金欣磊.基于PSO多目标优化算法研究及应用[D]浙江大学2006
[56]张丽平.粒子群优化算法的理论及实践[D].浙江大学.2005:13-15页
[57]莫愿斌.粒子群优化算法的扩展与应用[D].浙江大学.2006:40-42页
[58]许平.姜长生.基于粒子群算法的翼型优化设计[J].飞机设计.Vol128.N o15.2008.10
[59]张亚锋,宋笔锋,李占科.高升力翼型的气动优化设计和实验研究[J].飞行力学,2006,24(4):70:2+
[60]于勇.Fluent入门与进阶教程.北京理工大学.2008.9:57-64页
[61] Kerwin, J.E.: Computer techniques for propeller blades section design. Second Lips Propeller Symposium, 1973
[62]盛振邦.刘应中.船舶原理(下).第一版.上海交通大学出版社,2004:141-149页
[63]苏玉民.黄胜.船舶螺旋桨理论.1.哈尔滨工程大学.2003:178
[64]覃新川.黄胜.常欣.四桨两舵推进系统的水动力干扰研究. 2008年3月. 49卷第1期