结冰机翼自适应非结构化网格生成及流场分析
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摘要
飞机结冰是指飞机在飞行过程中,机翼、发动机进气口等某些迎风部位聚集冰层的现象。飞机结冰将会引发升力下降、阻力增加、操纵面失效等现象。飞机结冰已成为影响飞机飞行的主要因素之一,严重影响到民用飞机的安全性,因此研究用飞机结冰的气动问题对民用飞机设计具有重要的应用价值。
本文首先在以机翼外形为主导的简化模型下模拟不同条件下的二维冰型的增长,在各种结冰条件中融入物体外形边界函数,获得二维结冰模型。然后利用NURBS样条曲线来逼近现有的实验数据以简化模型。最后在已获得的二维模型基础上根据医学影像技术进行了三维冰型建模的研究,提出一种具有反馈机制的速度函数,以此作为不同截面上冰型的变化情况,建立了一种具有展向变化的非周期性三维冰型模型,数值描述的精度较高。
网格生成是CFD研究中的重要组成部分,是数值分析和计算的一个重要研究领域。网格是适应计算机使用而发展起来的一种有效的数值分析方法。生成反映结构物理特征和几何特征的自适应网格是应用自适应网格单元法的必要环节。本文对三维非结构化网格的生成算法和网格自适应方法进行了研究,通过编程完成了结冰机翼的非结构化网格的生成。
在实际的物理流场,尤其在超声速流场中,往往存在复杂的波系结构和不同的时间、空间尺度,这些尺度的跨度往往很大,能否数值模拟出不同尺度的流动,直接影响到数值模拟结果的好坏。最直接的做法是流场中全部采用最细的网格,使得所有特征尺度的问题都能得到足够的分辨率。但这种做法使得网格数目很大,时间步长很小,计算机的计算时间很长,存储空间要求也非常大,在高维情况下,上述现象更为严重,甚至超出了目前最先进计算机的计算能力。自适应方法的出现在某种程度上解决或缓解了上述问题。本文并利用加入单元体积控制函数和准最佳三角形算法对结冰机翼的非结构化网格进行了基于实体模型几何形状的自适应加密调整,结果表明所生成的网格质量良好,能满足对结冰机翼的气动性能研究。
最后本文利用基于Euler方程的流场求解程序对结冰机翼与无冰机翼作了流场计算并分析了气动特性变化。模拟结果显示,结冰对气动性能影响较大。
The accumulation of ice on aircraft components, such as wings, engine intakes, occurs when the aircraft flies. The present of ice accretion on unprotected aircraft components can greatly reduce lift, increase drag, make control surfaces fail, and so on. Ice accretion of aircraft has been a major concern to flight safety, and the study of ice accretion is absolutely necessary.
Firstly in this paper, the two-dimension model of the icing airfoil was gained by simulating the growth of ice of the simplified model at different freezing conditions while the boundary function was added. Then use the NURBS curve to simplify the model with experiment data. At last build the three-dimension model with two-dimension models by using the Level set method. A speed function with feeding back theory was given to modify the change on different cut piece of the ice. So that a kind of three-dimension ice model with non-periodic change could be found.
Mesh generating is an important part of CFD research as well as an important field in numerical analysis and calculation. Numerical method is an effective numerical analyzing method developing depend on computer. Generating adaptive mesh which could show the structure and the sharp is necessary to the application of adaptive finite element method. The generation algorithm of unstructured mesh in three-dimension and the adaptive mesh algorithm was studied in this paper and generated the unstructured mesh of icing wing by programming.
In real flow field especially in the supersonic flow field, complicated wave structure and different space-time metric always appears. And the numerical simulation result could be affected greatly by these metrics. Most directly, smallest mesh element volume can be taken to match all the metrics. But it would be a great number of mesh elements and short time step which may take long time to calculate and lager room to store the date. This problem may be figured out by the adaptive method. In this paper, unstructured mesh adaption of icing wing base on model sharp was done by adding a space control function and the quasi-optimal tetrahedron algorithm. The mesh was satisfied to the numerical simulation research of the icing wing.
At last in this paper, the flow field calculation of icing wing was compared with the clean one based on Euler equation. The results indicated that ice had adverse impact on aerodynamic.
本文首先在以机翼外形为主导的简化模型下模拟不同条件下的二维冰型的增长,在各种结冰条件中融入物体外形边界函数,获得二维结冰模型。然后利用NURBS样条曲线来逼近现有的实验数据以简化模型。最后在已获得的二维模型基础上根据医学影像技术进行了三维冰型建模的研究,提出一种具有反馈机制的速度函数,以此作为不同截面上冰型的变化情况,建立了一种具有展向变化的非周期性三维冰型模型,数值描述的精度较高。
网格生成是CFD研究中的重要组成部分,是数值分析和计算的一个重要研究领域。网格是适应计算机使用而发展起来的一种有效的数值分析方法。生成反映结构物理特征和几何特征的自适应网格是应用自适应网格单元法的必要环节。本文对三维非结构化网格的生成算法和网格自适应方法进行了研究,通过编程完成了结冰机翼的非结构化网格的生成。
在实际的物理流场,尤其在超声速流场中,往往存在复杂的波系结构和不同的时间、空间尺度,这些尺度的跨度往往很大,能否数值模拟出不同尺度的流动,直接影响到数值模拟结果的好坏。最直接的做法是流场中全部采用最细的网格,使得所有特征尺度的问题都能得到足够的分辨率。但这种做法使得网格数目很大,时间步长很小,计算机的计算时间很长,存储空间要求也非常大,在高维情况下,上述现象更为严重,甚至超出了目前最先进计算机的计算能力。自适应方法的出现在某种程度上解决或缓解了上述问题。本文并利用加入单元体积控制函数和准最佳三角形算法对结冰机翼的非结构化网格进行了基于实体模型几何形状的自适应加密调整,结果表明所生成的网格质量良好,能满足对结冰机翼的气动性能研究。
最后本文利用基于Euler方程的流场求解程序对结冰机翼与无冰机翼作了流场计算并分析了气动特性变化。模拟结果显示,结冰对气动性能影响较大。
The accumulation of ice on aircraft components, such as wings, engine intakes, occurs when the aircraft flies. The present of ice accretion on unprotected aircraft components can greatly reduce lift, increase drag, make control surfaces fail, and so on. Ice accretion of aircraft has been a major concern to flight safety, and the study of ice accretion is absolutely necessary.
Firstly in this paper, the two-dimension model of the icing airfoil was gained by simulating the growth of ice of the simplified model at different freezing conditions while the boundary function was added. Then use the NURBS curve to simplify the model with experiment data. At last build the three-dimension model with two-dimension models by using the Level set method. A speed function with feeding back theory was given to modify the change on different cut piece of the ice. So that a kind of three-dimension ice model with non-periodic change could be found.
Mesh generating is an important part of CFD research as well as an important field in numerical analysis and calculation. Numerical method is an effective numerical analyzing method developing depend on computer. Generating adaptive mesh which could show the structure and the sharp is necessary to the application of adaptive finite element method. The generation algorithm of unstructured mesh in three-dimension and the adaptive mesh algorithm was studied in this paper and generated the unstructured mesh of icing wing by programming.
In real flow field especially in the supersonic flow field, complicated wave structure and different space-time metric always appears. And the numerical simulation result could be affected greatly by these metrics. Most directly, smallest mesh element volume can be taken to match all the metrics. But it would be a great number of mesh elements and short time step which may take long time to calculate and lager room to store the date. This problem may be figured out by the adaptive method. In this paper, unstructured mesh adaption of icing wing base on model sharp was done by adding a space control function and the quasi-optimal tetrahedron algorithm. The mesh was satisfied to the numerical simulation research of the icing wing.
At last in this paper, the flow field calculation of icing wing was compared with the clean one based on Euler equation. The results indicated that ice had adverse impact on aerodynamic.
引文
[1]Bragg, M.B., Broeren, A.P., Blumenthal, L.A., "Iced-airfoil aerodynamics" Progress in Aerospace Sciences 41(2005),323-362.
[2]Harold E. Addy, Jr. Mark G. Potapczuk, David W. Sheldon. Modern Airfoil Ice Accretions. AIAA-97-0174, January 1997.
[3]陈维建,张大林.飞机机翼结冰过程的数值模拟.航空动力学报[J],2005,20(6)：1010-1017.
[4]Paraschivoiu, I., Overview of J.-A. "Bombardier Aeronautical Chair Projects at Ecole Polytechnique de Montreal" 1st Bombardier International Workshop on Aircraft Icing/Boundary-Layer Stability and Transition, edited by I. Paraschivolu, Ecole Polythecnique, Bombardier Canadair, Montreal, Quebec, Canada, Sept.1994.
[5]Fortin, G, Ilinca, A., Laforte, J., and Brandi, V, "New Roughness Computation Method and Geometric Accretion Model for Airfoil Icing" JOURNAL OF AIRCRAFT Vol.41, No.1, January-February.2004.
[6]Sherif, S., Pasumarthi, N., Bartlett, C.,"A semi-empirical model for heat transfer and ice accretion on aircraft wings in supercooled clouds"Cold Regions Science and Technology,26(1997).165-179.
[7]Weimin Sang, Shengju Jiang and Fengwei Li,"Icing Research for Airfoil and Multi-element Airfoil" AIAA Paper,2006-3647,2003.
[8]张洪武,关振群,李云鹏等.有限元分析与CAE技术基础[M].清华大学出版社,2004
[9]Zienkiewicz O C and Zhu J Z. A Simple Error Estimator and AdaptivePractical Engineering Analysis [J]. International Journal for NumericalEngineering,1987,24:337-357
[10]Frey P J, George P L. Mesh Generation [C]. Application to finite elements. Hermes, Paris,2000
[11]Cook W A, Oakes W R. Mapping Methods for Generating Three-dimensional meshes [J].Computers in mechanical engineering, CIME research supplement. 1982,67-72
[12]Shimada K, Mori N, Kondo T, et al. Automated Mesh Generation for Sheet Metal FormingSimulation [J]. International Journal of Vehicle Design.1999, 21:278-291
[13]Tchon K F, Khachan M, Guibault F, Camarero R. Three-dimensional Anisotropic GeometricMetrics Based on Local Domain Curvature and Thickness [J). Computer-Aided Design,2005,37(2):173-187
[14]Konstantin Lipnikov. A.Agouzal. Y.Vassilevski, Adaptive generation of quasi-optimal tetrahedral meshes. East-West Journal, V.7,No.4, pp.223-244.
[15]Myers, T.G., Charpin, J.P.F., "A mathematical model for atmospheric ice accretion and water flow on a cold surface" International Journal of Heat and Mass Transfer 47(2004) 5483-5500.
[16]David N. Anderson, Jen-Ching Tsao. Additional Results of Ice-Accretion Scaling at SLD Conditions. AIAA-2003-0390.
[17]G. Fortin, J.-L. Laforte et. al. Prediction of 2D Airfoil Ice Accretion by Bisection Method And by Rivulets and Beads Modeling. AIAA 2003-1076.
[18]Harold E. Addy, Jr. Mark G. Potapczuk, David W. Sheldon. Modern Airfoil Ice Accretions. AIAA-97-0174, January 1997.
[19]裘燮纲,韩凤华.飞机防冰系统[M].北京：航空专业教材编审组出版,1985.
[20]Loren H. Dill. Representation of Ice Geometry by Parametric Functions: Construction of Approximating NURBS Curves and Quantification of Ice Roughness—Year 1:Approximating NURBS Curves. NASA/CR—2004-213071
[21]L. Piegl, W. Tiller. The NURBS Book,2nded., Monographs in Visual Communication, Springer-Verlag, New York,1997.
[22]David Thompson, Satish Chalasani et.al. Geometry Modeling and Mesh Generation Strategies for Complex Three-Dimensional Iced Wing Configurations:Year 1 Report (NAG3-2562). NASA GRC, February 2002.
[23]R. Malladi, J. A. Sethian, B. C. Vemuri. Shape Modeling with Front Propagation:A Level Set Approach. IEEE Trans. Pattern Analysis and Machine Intelligence,17(2):158-175, February 1995.
[24]S. Osher, J A. Sethian. Fronts Propagating with Curvature-dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations. Journal of Computational Physics,1988,79:12-49.
[25]王峥,杨新,李俊,施鹏飞.水平集方法中曲线跟踪算法的改进[J].上海交通大学学报,2002,36(12)：1833-1836.
[26]J. A. Sethian. Curvature and the Evolution of Fronts. Communications in Mathematical Physics,101:487-499,1985.
[27]魏红宁,周本宽.自适应有限元分析的网格自动生成方法的选择.西南交通大学学报[J],1997.32(5)：477482
[28]George P L, Hecht F, Saltel E. Automatic mesh generator with specified boundary. ComputerMethods in Applied Mechanics and Engineering 1991.92(3):269-288
[29]George P, L Borouchaki H. Delaunay Triangulation and Meshing. Application to FiniteElements, Paris:Editions HERMES,1998
[30]Weatherill N P, Hassan O. Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constrains.International Journal for NumericalMethods in Engineering,1994.37(12):2005-2039
[31]Joe B.GEOMPACK-A software package for algorithms. Advances in Engineering Softwaregeneration of meshes using geometric 1991.56(13): 325-332
[32]M S. Approaches to the Applied Mechanics Review, automatic generation and control of finite element meshes.1988.4(4):169-185
[33]Michale E. Agishtein, Alexzander A Mighal. Smooth surface reconstruction from soattered data ooints. Computer&Graphics} 1991.15(1):29-39
[34]Chew L P, Drysdale R L. Voronoi diagrams based on convex distance functions. Technical Report Tech Report PCSTR, Department of Computer Science, Darmouh College, November,1986:86-132
[35]Nielson GM, Foley T A. A survey of applications of an affineinvariannorm. Mathematics methods in CAGD, Boston, MA:Academic Press 1989: 445-467
[36]OkabeA, BootsB. Concepts and applications of Voronoi diagrams. Application to Finite Elements. New York:Wiley,1992
[37]D Azzevedo E F, SimPson R B. On optimal interpolation triangle incidences. SIAM Journal of Science and Statistical Computation,1989.10(6): 1063-1076
[38]George P L, Seveno E. The advancing-front mesh generation method revisited[J], International Journal for Numerical Methods in Engineering, 1994,37(21):3605-3619.
[39]Baker T J.Developments and trends in-three-dimensional mesh generation.Applied Numerical Mathematics,1989.5(4):275-304
[40]黄海峰.阵面推进法生成3D非结构网格及运动网格研究与应用.南京理工大硕士论文[D],2003,12
[41]Pascal Jean Frey, Paul-Louis George, Mesh Generation Application to finite elements, HERMES Science Europe Ltd,2000
[42]Pirzadeh S. Structured background grids for generation of unstructured grids by Advancing Front Method[J],AIAA Journal,1993,31(2):257-265.
[43]Thompson Joe F. A reflection on grid generation in the 90s:trends, needs, and influences [A]. In:5th International Conferences on Grid Generation in Computational Field Simulation[C],1996
[44]王彩玲.基于CAD三维表面网格生成与应用.南京理工大学硕士学位论文[D],2004,6.
[45]Joe F.Thompson, Bharat K.Soni, Nigel P.Weatherill, Handbook of Grid Generation, CRC Press, Boca Raton London New York Washington, D.C, 1999
[46]Lohner, R., Extensions and improvements of the Advancing Front Grid Generation Technique, Communications in Numerical Methods in Engineering, John Wiley & Sons, Ltd,1996, Vol 12:683-702.
[47]王俊杰.基于Euler方程的三维自适应笛卡尔网格在复杂外形上的应用研究.西北工业大学硕士学位论文[D],2005,3.
[48]G.C. Buscaglia and E.A. Dari, Anisotropic mesh optimization and its application in adaptivity.Int.J.Number.Meth.Engrg.(1997)40,4119-4136
[2]Harold E. Addy, Jr. Mark G. Potapczuk, David W. Sheldon. Modern Airfoil Ice Accretions. AIAA-97-0174, January 1997.
[3]陈维建,张大林.飞机机翼结冰过程的数值模拟.航空动力学报[J],2005,20(6)：1010-1017.
[4]Paraschivoiu, I., Overview of J.-A. "Bombardier Aeronautical Chair Projects at Ecole Polytechnique de Montreal" 1st Bombardier International Workshop on Aircraft Icing/Boundary-Layer Stability and Transition, edited by I. Paraschivolu, Ecole Polythecnique, Bombardier Canadair, Montreal, Quebec, Canada, Sept.1994.
[5]Fortin, G, Ilinca, A., Laforte, J., and Brandi, V, "New Roughness Computation Method and Geometric Accretion Model for Airfoil Icing" JOURNAL OF AIRCRAFT Vol.41, No.1, January-February.2004.
[6]Sherif, S., Pasumarthi, N., Bartlett, C.,"A semi-empirical model for heat transfer and ice accretion on aircraft wings in supercooled clouds"Cold Regions Science and Technology,26(1997).165-179.
[7]Weimin Sang, Shengju Jiang and Fengwei Li,"Icing Research for Airfoil and Multi-element Airfoil" AIAA Paper,2006-3647,2003.
[8]张洪武,关振群,李云鹏等.有限元分析与CAE技术基础[M].清华大学出版社,2004
[9]Zienkiewicz O C and Zhu J Z. A Simple Error Estimator and AdaptivePractical Engineering Analysis [J]. International Journal for NumericalEngineering,1987,24:337-357
[10]Frey P J, George P L. Mesh Generation [C]. Application to finite elements. Hermes, Paris,2000
[11]Cook W A, Oakes W R. Mapping Methods for Generating Three-dimensional meshes [J].Computers in mechanical engineering, CIME research supplement. 1982,67-72
[12]Shimada K, Mori N, Kondo T, et al. Automated Mesh Generation for Sheet Metal FormingSimulation [J]. International Journal of Vehicle Design.1999, 21:278-291
[13]Tchon K F, Khachan M, Guibault F, Camarero R. Three-dimensional Anisotropic GeometricMetrics Based on Local Domain Curvature and Thickness [J). Computer-Aided Design,2005,37(2):173-187
[14]Konstantin Lipnikov. A.Agouzal. Y.Vassilevski, Adaptive generation of quasi-optimal tetrahedral meshes. East-West Journal, V.7,No.4, pp.223-244.
[15]Myers, T.G., Charpin, J.P.F., "A mathematical model for atmospheric ice accretion and water flow on a cold surface" International Journal of Heat and Mass Transfer 47(2004) 5483-5500.
[16]David N. Anderson, Jen-Ching Tsao. Additional Results of Ice-Accretion Scaling at SLD Conditions. AIAA-2003-0390.
[17]G. Fortin, J.-L. Laforte et. al. Prediction of 2D Airfoil Ice Accretion by Bisection Method And by Rivulets and Beads Modeling. AIAA 2003-1076.
[18]Harold E. Addy, Jr. Mark G. Potapczuk, David W. Sheldon. Modern Airfoil Ice Accretions. AIAA-97-0174, January 1997.
[19]裘燮纲,韩凤华.飞机防冰系统[M].北京：航空专业教材编审组出版,1985.
[20]Loren H. Dill. Representation of Ice Geometry by Parametric Functions: Construction of Approximating NURBS Curves and Quantification of Ice Roughness—Year 1:Approximating NURBS Curves. NASA/CR—2004-213071
[21]L. Piegl, W. Tiller. The NURBS Book,2nded., Monographs in Visual Communication, Springer-Verlag, New York,1997.
[22]David Thompson, Satish Chalasani et.al. Geometry Modeling and Mesh Generation Strategies for Complex Three-Dimensional Iced Wing Configurations:Year 1 Report (NAG3-2562). NASA GRC, February 2002.
[23]R. Malladi, J. A. Sethian, B. C. Vemuri. Shape Modeling with Front Propagation:A Level Set Approach. IEEE Trans. Pattern Analysis and Machine Intelligence,17(2):158-175, February 1995.
[24]S. Osher, J A. Sethian. Fronts Propagating with Curvature-dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations. Journal of Computational Physics,1988,79:12-49.
[25]王峥,杨新,李俊,施鹏飞.水平集方法中曲线跟踪算法的改进[J].上海交通大学学报,2002,36(12)：1833-1836.
[26]J. A. Sethian. Curvature and the Evolution of Fronts. Communications in Mathematical Physics,101:487-499,1985.
[27]魏红宁,周本宽.自适应有限元分析的网格自动生成方法的选择.西南交通大学学报[J],1997.32(5)：477482
[28]George P L, Hecht F, Saltel E. Automatic mesh generator with specified boundary. ComputerMethods in Applied Mechanics and Engineering 1991.92(3):269-288
[29]George P, L Borouchaki H. Delaunay Triangulation and Meshing. Application to FiniteElements, Paris:Editions HERMES,1998
[30]Weatherill N P, Hassan O. Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constrains.International Journal for NumericalMethods in Engineering,1994.37(12):2005-2039
[31]Joe B.GEOMPACK-A software package for algorithms. Advances in Engineering Softwaregeneration of meshes using geometric 1991.56(13): 325-332
[32]M S. Approaches to the Applied Mechanics Review, automatic generation and control of finite element meshes.1988.4(4):169-185
[33]Michale E. Agishtein, Alexzander A Mighal. Smooth surface reconstruction from soattered data ooints. Computer&Graphics} 1991.15(1):29-39
[34]Chew L P, Drysdale R L. Voronoi diagrams based on convex distance functions. Technical Report Tech Report PCSTR, Department of Computer Science, Darmouh College, November,1986:86-132
[35]Nielson GM, Foley T A. A survey of applications of an affineinvariannorm. Mathematics methods in CAGD, Boston, MA:Academic Press 1989: 445-467
[36]OkabeA, BootsB. Concepts and applications of Voronoi diagrams. Application to Finite Elements. New York:Wiley,1992
[37]D Azzevedo E F, SimPson R B. On optimal interpolation triangle incidences. SIAM Journal of Science and Statistical Computation,1989.10(6): 1063-1076
[38]George P L, Seveno E. The advancing-front mesh generation method revisited[J], International Journal for Numerical Methods in Engineering, 1994,37(21):3605-3619.
[39]Baker T J.Developments and trends in-three-dimensional mesh generation.Applied Numerical Mathematics,1989.5(4):275-304
[40]黄海峰.阵面推进法生成3D非结构网格及运动网格研究与应用.南京理工大硕士论文[D],2003,12
[41]Pascal Jean Frey, Paul-Louis George, Mesh Generation Application to finite elements, HERMES Science Europe Ltd,2000
[42]Pirzadeh S. Structured background grids for generation of unstructured grids by Advancing Front Method[J],AIAA Journal,1993,31(2):257-265.
[43]Thompson Joe F. A reflection on grid generation in the 90s:trends, needs, and influences [A]. In:5th International Conferences on Grid Generation in Computational Field Simulation[C],1996
[44]王彩玲.基于CAD三维表面网格生成与应用.南京理工大学硕士学位论文[D],2004,6.
[45]Joe F.Thompson, Bharat K.Soni, Nigel P.Weatherill, Handbook of Grid Generation, CRC Press, Boca Raton London New York Washington, D.C, 1999
[46]Lohner, R., Extensions and improvements of the Advancing Front Grid Generation Technique, Communications in Numerical Methods in Engineering, John Wiley & Sons, Ltd,1996, Vol 12:683-702.
[47]王俊杰.基于Euler方程的三维自适应笛卡尔网格在复杂外形上的应用研究.西北工业大学硕士学位论文[D],2005,3.
[48]G.C. Buscaglia and E.A. Dari, Anisotropic mesh optimization and its application in adaptivity.Int.J.Number.Meth.Engrg.(1997)40,4119-4136