基于目标压力分布优化的翼型反设计方法研究
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摘要
先进跨音速翼型的设计研究成为当前设计空气动力学的重要研究方向，而翼型设计方法本身的发展也希望能够跟上CFD技术总的发展步调。飞行器气动设计方法可简略分成两类：直接优化方法和反设计方法。直接优化方法直接以飞机气动性能为目标进行外形设计，可以按工程上的要求对型面提出各种约束，但其缺点是计算工作量大，尤其是针对本身计算量就很大的气动分析问题。反设计方法求解经典的空气动力反问题，即由给定的目标压力分布求解满足这一压力分布的气动外形，通常比直接优化设计方法省时高效，但也存在难以给定合理的目标压力分布的问题。通过对这两类设计方法中比较典型的两种方法的对比研究，即基于余量修正原理的翼型反设计方法和遗传优化设计方法，了解到了两种方法的优缺点。
本文在分析两种气动设计方法优缺点的基础上，以Takanashi提出的基于正反迭代、余量修正原理的翼型反设计方法为基础，针对翼型反设计方法中目标压力分布难以给定的问题，进行了反设计方法与优化方法相结合的研究，建立了翼型反设计方法中定义目标压力分布的遗传优化模型。首先提出翼型表面压力分布参数化方法，选择遗传算法作为压力分布的优化算法并对其做有约束优化，将优化结果作为反设计的目标压力分布，减小设计中的经验性影响；然后应用华俊等开发发展的基于Takanashi余量修正原理的反设计方法，通过反设计得出翼型气动外形，发挥反设计高效省时的优点。翼型设计结果表明，这种方法是可行的。
The design techniques of modern transonic airfoils have been the important goals of design aerodynamics, and the airfoil design methods themselves are also hoped to match the overall progress of CFD. The aerodynamic design methods are categorized into two classes simply: direct optimization methods and inverse design methods. The direct optimization methods minimize (or maximize) a given aerodynamic object function directly with the constraints gotten from the project. Such procedures, however, become extremely expensive at computation quantity. The inverse design methods solve the classical inverse problem of determining the aerodynamic shape that will produce given pressure distribution. However, they leave the users with the problem of translating the design goals into properly defined pressure distribution exhibiting the required aerodynamic characteristics. Here we have studied two classical design methods with compare, the iterative residual correction inverse design method and the genetic algorithm optimization method.
Since the problem of hard to specify the target pressure distribution for the airfoils inverse design method, we try to carry out the research on combining the inverse methods and the optimization methods. A genetic algorithm has been applied to optimize target pressure distribution for inverse design methods. Pressure distributions around airfoils are parameterized and the airfoil drag is minimized under constraints on lift, airfoil thickness, and other design principles. Once target pressure distributions are obtained, corresponding airfoil geometries can be computed by an inverse design code coupled with a Navier-Stokes solver. The presented results of designed airfoil show that the method developed is feasible.
本文在分析两种气动设计方法优缺点的基础上，以Takanashi提出的基于正反迭代、余量修正原理的翼型反设计方法为基础，针对翼型反设计方法中目标压力分布难以给定的问题，进行了反设计方法与优化方法相结合的研究，建立了翼型反设计方法中定义目标压力分布的遗传优化模型。首先提出翼型表面压力分布参数化方法，选择遗传算法作为压力分布的优化算法并对其做有约束优化，将优化结果作为反设计的目标压力分布，减小设计中的经验性影响；然后应用华俊等开发发展的基于Takanashi余量修正原理的反设计方法，通过反设计得出翼型气动外形，发挥反设计高效省时的优点。翼型设计结果表明，这种方法是可行的。
The design techniques of modern transonic airfoils have been the important goals of design aerodynamics, and the airfoil design methods themselves are also hoped to match the overall progress of CFD. The aerodynamic design methods are categorized into two classes simply: direct optimization methods and inverse design methods. The direct optimization methods minimize (or maximize) a given aerodynamic object function directly with the constraints gotten from the project. Such procedures, however, become extremely expensive at computation quantity. The inverse design methods solve the classical inverse problem of determining the aerodynamic shape that will produce given pressure distribution. However, they leave the users with the problem of translating the design goals into properly defined pressure distribution exhibiting the required aerodynamic characteristics. Here we have studied two classical design methods with compare, the iterative residual correction inverse design method and the genetic algorithm optimization method.
Since the problem of hard to specify the target pressure distribution for the airfoils inverse design method, we try to carry out the research on combining the inverse methods and the optimization methods. A genetic algorithm has been applied to optimize target pressure distribution for inverse design methods. Pressure distributions around airfoils are parameterized and the airfoil drag is minimized under constraints on lift, airfoil thickness, and other design principles. Once target pressure distributions are obtained, corresponding airfoil geometries can be computed by an inverse design code coupled with a Navier-Stokes solver. The presented results of designed airfoil show that the method developed is feasible.
引文
[1] 屈西曼．D(英) 飞机空气动力设计 国防工业出版社
[2] Hyoung-jin Kim, Oh-hyun Rho: "Aerodynamic Design of Transonic Wing Using the Target Pressure Optimization Approach." AIAA-98-0599,1998
[3] Shigeru Obayashi, S Takanash :"Genetic Optimization of Target Pressure Distributions for Inverse Design Methods." AIAA-95-1649-CP, 1995
[4] Hyoung-jin Kim, Oh-hyun Rho :"Dual-point Design of Transonic Airfoils Using the Hybrid Inverse Optimization Method." AIAA-97-0512,1997
[5] Van Egmond J A. :"Numerical Optimization of Target Pressure Distributions for Subsonic and Transonic Airfoil Design ." AGARD CP No.463, Ref. 17, 1990.
[6] Van den Dam, R. F., van Egmond, J. A. and slooff, J. W., "Optimization of Target Pressure Distributions," Special Course on Inverse Methods for Airfoil Design for Aeronautical and Turbomachinery Applications, AGARD Report No. 780, Reference 3, Nov. 1990.
[7] Van den Dam, R. F., "Constrained Spanload Optimization for Minimum Drag of Multi-Lifting Surface Configurations," Computational Methods for Aerodynamic Design (Inverse) and Optimization, AGARD Conference Proceedings No. 463, Reference 16, March 1990.
[8] Richard L, Campbell: "An Approach to Constrained Aerodynamic Design With Application to Airfoils". NASA TP-3260, 1992
[9] Masashi, Shiokawa, Kisa Matsushima and Kazuhiro Nakahashi :"Design and Aerodynamics of Lift Enhancement Control for a single Element Airfoil". AIAA 2005-853 2005
[10] Takanashi, S.: "An Iterative Procedure for Three-Dimensional Transonic Wing Design by the Integral Equation Method". AIAA-84-2155,1984
[11] Whitcomb, Richard T. "Review of NASA Super-critical Airfoils". ICAS Paper No. 74-10. 1974
[12] Alfred Walz. Boundary Layers of Flow and Temperature. 1966
[13] Harris, Charles D. "Aerodynamic Characteristics of the 10-Percent-Thick NASA Supercritical Airfoil 33 Designed for a Normal-Force Coefficient of 0.7". NASA TM X-72711, 1975.
[14] Harris, Charles D. "NASA Supercritical Airfoils- A Matrix of Family-related Airfoils," NASA TP-2969, March 1990
[15] Inger, G. R, "Application of Oswatitsch's Theorem to Supercritical Airfoil Drag Calculation," Journal of Aircraft, Vol.30 No. 3, 1993
[16] Volpe G.M, Melnik R.E. "The Role of Constraintsin the Inverse Design Problem for Transonic Airfoils." AIAA Paper 81-1233, 1981.
[17] Volpe G. :"The Inverse Design of Closed Airfoils in Transonic Flow." AIAA Paper 83-0504, 1983.
[18] Volpe G.: "Geometric and Surface Pressure Restrictions in Airfoil Design" AGARD CPNo.463, Ref.4, 1990
[19] Carlson L.A. "Transonic Airfoil Analysis and Design Using Cartesian Coordinates." J. Aircraft, Vol. 13,No.5,1976.
[20] Sobieczky H, Fung K.Y, Seebass A.R. "A New Method For Designing Shock-free Transonic Configurations." AIAA Paper 78-1114, 1978.
[21] Trane T.L. "A Rapid Computer Aided Transonic Airfoil Design Method." AIAA Paper 74-501, 1974
[22] Mcfadden G.B. "An Artificial Viscosity Method for the Design of Supercritical Airfoils." PhD. Thesis, N.Y.University, 1979.
[23] Abbott, I.H. and von Doenhoff, A.E. : "Theory of Wing Sections", Dover Publications, ING, 1959
[24] R. Eppler: "Airfoil and Data."
[25] Hirose, N. ; Takanashi, S and Kawai, N : "Transonic Airfoil Design Based on NS Equation to Attain Arbitrarily Specified Pressure Distribution - an Iterative Procedure." AIAA-85-1592, 1985
[26] Tatsumi, S. and Takanashi, S. : "Experimental Verification of Three-Dimensional Transonic Inverse Method". AIAA-85-4077, 1985
[27] G..S. Dulikravich : "Shape Inverse Design and Optimization for Three Dimensional Aerodynamics", AIAA-95-0695, 1995
[28] Helmut Sobieczky : "Research on inverse design and optimization in Germany", Appl. Mech. Rev Vol. 41, No. 6, 1988
[29] Helmut Sobieczky: "Progress in Inverse Design and Optimization in Aerodynamics" AGARD CP No.463, Ref.1, 1990.
[30] A. J Bocci. : "Aerofoil Design Techniques", AGARD CP No.463, Ref.2, 1990
[31] Laburujere, T.E., and Slooff, J.W. : "Computational Methods for the Aerodynamic design of Aircraft Components," Annual Review of Fluid Mechanics, Vol.25, 1993
[32] George S. Dulikravich : "Aerodynamic Shape Design." AGARD Report No. 780, Reference 1, Nov. 1990.
[33] Hyoung-jin Kim, Chongam Kim, Oh-hyun Rho : "Multipoint Inverse Design Method for Transonic Wings." Journal of Aircraft, Vol.36, No.6, 1999
[34] Taisut Ahn, Hyoung-jin Kim, Chongam Kim, Oh-hyun Rho: "Inverse Design of Transonic Wings Using Wing Platform and Target Pressure Optimization." Journal of Aircraft, Vol.38, No.4, 2001
[35] Masashi Shiokawa , Kisa Matsushima and Kazuhiro Nakahashi : "Design and Aerodynamics of Lift Enhancement Control for a Single Element Airfoil." AIAA 2005-853,2005
[36] A. Jameson: "The Evolution of Computational Methods in Aerodynamics", J of Applied Mechanics, Vol. 50 1983
[37] 华俊．跨音速机翼和翼型的设计研究．西北工业大学博士论文 1989
[38] 白俊强 基于欧拉方程的跨声速翼型设计 空气动力学报 1997
[39] 白俊强 含粘性修正的二维欧拉方程及其在跨音速翼型设计中的应用 西北工业大学硕士论文 1994
[40] 詹浩 基于余量修正原理的多翼面气动力反设计方法 航空学报 2003
[41] 詹浩 基于遗传算法和分布式计算的气动优化设计 计算物理 2004
[42] 詹浩 西北工业大学博士后论文 2005
[43] 王晓鹏 遗传算法及其在气动优化设计中的应用研究 西工大博士论文，2000
[44] 王晓鹏 基于遗传算法的翼型气动优化设计 空气动力学学报 2000
[45] 夏智勋 跨音速翼型和机翼的反设计计算方法 北京航空航天大学博士论文，1991
[46] 符同军 跨音速翼型反设计 西北工业大学硕士论文 1995
[47] 杨绪东 基于欧拉方程数值解的跨音速机翼设计 西北工业大学硕士论文 1998
[48] 吴彦森 基于DISC方法的翼型反设计软件开发 西北工业大学硕士论文 2003
[49] 孙若姿 跨音速机翼设计方法的改进 北京航空航天大学学报 2003
[50] 黄守志 NS方程求解器 西北工业大学硕士论文
[51] 朱军 三维混合网格生成与N-S方程求解 西北工业大学硕士论文 2004
[52] 张勇：“跨音速二维和轴对称附面层计算”，西北工业大学硕士论文，1992
[53] 乔志德 方宝瑞等 飞机气动布局设计 航空工业出版社 1997
[54] 沈克扬 计算空气动力学的进展 民用飞机设计与研究
[55] 沈克扬 超临界机翼气动设计概论 民用飞机设计与研究 1988-4，1988
[56] G．S．Dulikravich高速运输机设计的新概念 第十二章 三维气动外形的组合优化与反设计 国防工业出版社
[2] Hyoung-jin Kim, Oh-hyun Rho: "Aerodynamic Design of Transonic Wing Using the Target Pressure Optimization Approach." AIAA-98-0599,1998
[3] Shigeru Obayashi, S Takanash :"Genetic Optimization of Target Pressure Distributions for Inverse Design Methods." AIAA-95-1649-CP, 1995
[4] Hyoung-jin Kim, Oh-hyun Rho :"Dual-point Design of Transonic Airfoils Using the Hybrid Inverse Optimization Method." AIAA-97-0512,1997
[5] Van Egmond J A. :"Numerical Optimization of Target Pressure Distributions for Subsonic and Transonic Airfoil Design ." AGARD CP No.463, Ref. 17, 1990.
[6] Van den Dam, R. F., van Egmond, J. A. and slooff, J. W., "Optimization of Target Pressure Distributions," Special Course on Inverse Methods for Airfoil Design for Aeronautical and Turbomachinery Applications, AGARD Report No. 780, Reference 3, Nov. 1990.
[7] Van den Dam, R. F., "Constrained Spanload Optimization for Minimum Drag of Multi-Lifting Surface Configurations," Computational Methods for Aerodynamic Design (Inverse) and Optimization, AGARD Conference Proceedings No. 463, Reference 16, March 1990.
[8] Richard L, Campbell: "An Approach to Constrained Aerodynamic Design With Application to Airfoils". NASA TP-3260, 1992
[9] Masashi, Shiokawa, Kisa Matsushima and Kazuhiro Nakahashi :"Design and Aerodynamics of Lift Enhancement Control for a single Element Airfoil". AIAA 2005-853 2005
[10] Takanashi, S.: "An Iterative Procedure for Three-Dimensional Transonic Wing Design by the Integral Equation Method". AIAA-84-2155,1984
[11] Whitcomb, Richard T. "Review of NASA Super-critical Airfoils". ICAS Paper No. 74-10. 1974
[12] Alfred Walz. Boundary Layers of Flow and Temperature. 1966
[13] Harris, Charles D. "Aerodynamic Characteristics of the 10-Percent-Thick NASA Supercritical Airfoil 33 Designed for a Normal-Force Coefficient of 0.7". NASA TM X-72711, 1975.
[14] Harris, Charles D. "NASA Supercritical Airfoils- A Matrix of Family-related Airfoils," NASA TP-2969, March 1990
[15] Inger, G. R, "Application of Oswatitsch's Theorem to Supercritical Airfoil Drag Calculation," Journal of Aircraft, Vol.30 No. 3, 1993
[16] Volpe G.M, Melnik R.E. "The Role of Constraintsin the Inverse Design Problem for Transonic Airfoils." AIAA Paper 81-1233, 1981.
[17] Volpe G. :"The Inverse Design of Closed Airfoils in Transonic Flow." AIAA Paper 83-0504, 1983.
[18] Volpe G.: "Geometric and Surface Pressure Restrictions in Airfoil Design" AGARD CPNo.463, Ref.4, 1990
[19] Carlson L.A. "Transonic Airfoil Analysis and Design Using Cartesian Coordinates." J. Aircraft, Vol. 13,No.5,1976.
[20] Sobieczky H, Fung K.Y, Seebass A.R. "A New Method For Designing Shock-free Transonic Configurations." AIAA Paper 78-1114, 1978.
[21] Trane T.L. "A Rapid Computer Aided Transonic Airfoil Design Method." AIAA Paper 74-501, 1974
[22] Mcfadden G.B. "An Artificial Viscosity Method for the Design of Supercritical Airfoils." PhD. Thesis, N.Y.University, 1979.
[23] Abbott, I.H. and von Doenhoff, A.E. : "Theory of Wing Sections", Dover Publications, ING, 1959
[24] R. Eppler: "Airfoil and Data."
[25] Hirose, N. ; Takanashi, S and Kawai, N : "Transonic Airfoil Design Based on NS Equation to Attain Arbitrarily Specified Pressure Distribution - an Iterative Procedure." AIAA-85-1592, 1985
[26] Tatsumi, S. and Takanashi, S. : "Experimental Verification of Three-Dimensional Transonic Inverse Method". AIAA-85-4077, 1985
[27] G..S. Dulikravich : "Shape Inverse Design and Optimization for Three Dimensional Aerodynamics", AIAA-95-0695, 1995
[28] Helmut Sobieczky : "Research on inverse design and optimization in Germany", Appl. Mech. Rev Vol. 41, No. 6, 1988
[29] Helmut Sobieczky: "Progress in Inverse Design and Optimization in Aerodynamics" AGARD CP No.463, Ref.1, 1990.
[30] A. J Bocci. : "Aerofoil Design Techniques", AGARD CP No.463, Ref.2, 1990
[31] Laburujere, T.E., and Slooff, J.W. : "Computational Methods for the Aerodynamic design of Aircraft Components," Annual Review of Fluid Mechanics, Vol.25, 1993
[32] George S. Dulikravich : "Aerodynamic Shape Design." AGARD Report No. 780, Reference 1, Nov. 1990.
[33] Hyoung-jin Kim, Chongam Kim, Oh-hyun Rho : "Multipoint Inverse Design Method for Transonic Wings." Journal of Aircraft, Vol.36, No.6, 1999
[34] Taisut Ahn, Hyoung-jin Kim, Chongam Kim, Oh-hyun Rho: "Inverse Design of Transonic Wings Using Wing Platform and Target Pressure Optimization." Journal of Aircraft, Vol.38, No.4, 2001
[35] Masashi Shiokawa , Kisa Matsushima and Kazuhiro Nakahashi : "Design and Aerodynamics of Lift Enhancement Control for a Single Element Airfoil." AIAA 2005-853,2005
[36] A. Jameson: "The Evolution of Computational Methods in Aerodynamics", J of Applied Mechanics, Vol. 50 1983
[37] 华俊．跨音速机翼和翼型的设计研究．西北工业大学博士论文 1989
[38] 白俊强 基于欧拉方程的跨声速翼型设计 空气动力学报 1997
[39] 白俊强 含粘性修正的二维欧拉方程及其在跨音速翼型设计中的应用 西北工业大学硕士论文 1994
[40] 詹浩 基于余量修正原理的多翼面气动力反设计方法 航空学报 2003
[41] 詹浩 基于遗传算法和分布式计算的气动优化设计 计算物理 2004
[42] 詹浩 西北工业大学博士后论文 2005
[43] 王晓鹏 遗传算法及其在气动优化设计中的应用研究 西工大博士论文，2000
[44] 王晓鹏 基于遗传算法的翼型气动优化设计 空气动力学学报 2000
[45] 夏智勋 跨音速翼型和机翼的反设计计算方法 北京航空航天大学博士论文，1991
[46] 符同军 跨音速翼型反设计 西北工业大学硕士论文 1995
[47] 杨绪东 基于欧拉方程数值解的跨音速机翼设计 西北工业大学硕士论文 1998
[48] 吴彦森 基于DISC方法的翼型反设计软件开发 西北工业大学硕士论文 2003
[49] 孙若姿 跨音速机翼设计方法的改进 北京航空航天大学学报 2003
[50] 黄守志 NS方程求解器 西北工业大学硕士论文
[51] 朱军 三维混合网格生成与N-S方程求解 西北工业大学硕士论文 2004
[52] 张勇：“跨音速二维和轴对称附面层计算”，西北工业大学硕士论文，1992
[53] 乔志德 方宝瑞等 飞机气动布局设计 航空工业出版社 1997
[54] 沈克扬 计算空气动力学的进展 民用飞机设计与研究
[55] 沈克扬 超临界机翼气动设计概论 民用飞机设计与研究 1988-4，1988
[56] G．S．Dulikravich高速运输机设计的新概念 第十二章 三维气动外形的组合优化与反设计 国防工业出版社
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