涡轮冷却叶片CFD网格生成
|
摘要
非结构化网格对复杂模型具有较强的适应性,因此被广泛地应用到CFD计算当中。本文采用Delaunay算法,利用面向对象的编程技术开发了一套非结构网格生成软件。该网格生成软件可以进行二维平面、三维曲面、三维实体非结构化网格生成以及半结构化网格生成。并且成功地生成了涡轮冷却叶片非结构化网格。
论文详细研究了Delaunay三角剖分的关键问题以及相应的解决方案,包括插点算法、浮点运算误差处理、网格优化技术、边界恢复问题。其中边界恢复问题采用了将一致边界恢复和约束边界恢复相结合的方式,实验证明此种方法能够较好地完成三维网格边界恢复工作,对复杂模型具有一定的适应性。在Delaunay三角剖分算法的基础上,通过引入黎曼度量矩阵完成了曲面非结构网格生成,并给出了黎曼空间下的近似外接圆准则。该方法能够对复杂曲面生成高质量的非结构网格。通过物面映射法生成半结构化网格,并与外层非结构化网格对接形成了混合网格。
根据Delaunay方法的自身特点设计了合理的数据存储结构以及几何拓扑体系;运用C++语言开发了实现非结构化网格生成的各功能模块。并且将该网格生成体系与已有的几何造型体系进行了有机的融合,使得对于特定模型能够快速地生成几何模型和计算网格。
For complex model unstructured grid has preferable adaptability, and which is widely applied to the CFD. In this paper, we use Delaunay triangulation as base algorithm, and object-oriented programming as technology to develop a set of unstructured grid generation software. The grid generation software can be applied to two-dimension plane, surface, three-dimension entity’s unstructured grid generation, as well as semi-structured grid generation. And the adoption of the software is successfully generated unstructured grid cooling turbine blade.
This paper study the Delaunay triangulation of the key issues and corresponding solutions, including the insertion point algorithm, floating-point error handling, mesh optimization techniques, the boundary recovery. And the combination of conforming boundary recovery and constrained boundary recovery is used to deal with boundary recovery. Experiment proves that the method can complete three-dimensional grid boundary recovery preferable, and has a certain degree of adaptability to complex model. Based on the algorithm of Delaunay triangulation, introduce a metric tensor to complete the surface triangulation. And the definition of the cavity in a Riemannian space is given. The examples demonstrate the advantages of the surface triangulation software which indicating that dealing with complex model and high quality. Surface mapping method is adapted for generating semi-structured grid. Joining the grids near the wall and in the other fields into hybrid grids is the final step for generating hybrid grids. And has carried on this mesh generation system and the existing geometric modeling system the organic fusion, enables to be able to produce the geometric model and the computation grid fast regarding the specific model.
According to the Delaunay method’s inherent characteristics designed the rational data storage structures and geometric topology system. The use of C + + language development unstructured grid generation for achieving the various functional modules. And has carried on this mesh generation system and the existing geometric modeling system the organic fusion, enables to be able to produce the geometric model and the computation grid fast regarding the specific model.
论文详细研究了Delaunay三角剖分的关键问题以及相应的解决方案,包括插点算法、浮点运算误差处理、网格优化技术、边界恢复问题。其中边界恢复问题采用了将一致边界恢复和约束边界恢复相结合的方式,实验证明此种方法能够较好地完成三维网格边界恢复工作,对复杂模型具有一定的适应性。在Delaunay三角剖分算法的基础上,通过引入黎曼度量矩阵完成了曲面非结构网格生成,并给出了黎曼空间下的近似外接圆准则。该方法能够对复杂曲面生成高质量的非结构网格。通过物面映射法生成半结构化网格,并与外层非结构化网格对接形成了混合网格。
根据Delaunay方法的自身特点设计了合理的数据存储结构以及几何拓扑体系;运用C++语言开发了实现非结构化网格生成的各功能模块。并且将该网格生成体系与已有的几何造型体系进行了有机的融合,使得对于特定模型能够快速地生成几何模型和计算网格。
For complex model unstructured grid has preferable adaptability, and which is widely applied to the CFD. In this paper, we use Delaunay triangulation as base algorithm, and object-oriented programming as technology to develop a set of unstructured grid generation software. The grid generation software can be applied to two-dimension plane, surface, three-dimension entity’s unstructured grid generation, as well as semi-structured grid generation. And the adoption of the software is successfully generated unstructured grid cooling turbine blade.
This paper study the Delaunay triangulation of the key issues and corresponding solutions, including the insertion point algorithm, floating-point error handling, mesh optimization techniques, the boundary recovery. And the combination of conforming boundary recovery and constrained boundary recovery is used to deal with boundary recovery. Experiment proves that the method can complete three-dimensional grid boundary recovery preferable, and has a certain degree of adaptability to complex model. Based on the algorithm of Delaunay triangulation, introduce a metric tensor to complete the surface triangulation. And the definition of the cavity in a Riemannian space is given. The examples demonstrate the advantages of the surface triangulation software which indicating that dealing with complex model and high quality. Surface mapping method is adapted for generating semi-structured grid. Joining the grids near the wall and in the other fields into hybrid grids is the final step for generating hybrid grids. And has carried on this mesh generation system and the existing geometric modeling system the organic fusion, enables to be able to produce the geometric model and the computation grid fast regarding the specific model.
According to the Delaunay method’s inherent characteristics designed the rational data storage structures and geometric topology system. The use of C + + language development unstructured grid generation for achieving the various functional modules. And has carried on this mesh generation system and the existing geometric modeling system the organic fusion, enables to be able to produce the geometric model and the computation grid fast regarding the specific model.
引文
[1]何立明,飞机推进系统原理,北京:国防工业出版社,2006。
[2]林宏镇,汪火光,蒋章焰等,高性能抗空发动机传热技术,北京:国防工业出版社2005。
[3]彭泽琰,刘刚等,航空燃气轮机原理,北京:国防工业出版社,2000。
[4]徐伟祖,叶轮机CFD网格预处理研究,[硕士学位论文]。南京:南京航空航天大学,2008。
[5]刘学强,基于混合网格和多重网格上的N-S方程求解及应用研究,[博士学位论文]。南京:南京航空航天大学,2001。
[6]陈建军,非结构化网格生成及其并行化的若干问题研究,[博士学位论文]。杭州:浙江大学,2006。
[7] Stephen Prata,C++Primer Plus(孙建春,韦强)。北京:人民邮电出版社,2002。
[8] J. F. Thomposon, B. K. Soni, N. P. Weatherill, Handbook of Grid Generation. Boca Raton and London: CRC Press, 1999.
[9] A. Bowyer, Computing dirichlet tessellations. The Computer Journal, 1981, 24:162~166.
[10] D. F. Watson, Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes. The Computer Journal, 1981, 24:167~172.
[11] N. P. Weatherill, O. Hassan, Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraint. International Journal for Numerical Methods in Engineering, 1994, 37:2005~2039.
[12] P. L. George, F. Hecht, E. Saltel, Automatic mesh generator with specified boundary. Computer Methods in Applied Mechanics and Engineering, 1991, 92:269~288.
[13] N. P. Weatherill, Delaunay Triangulation in computational fluid dynamics, Computers Math. Applic., 1992, 24:129~150.
[14] P. L. George, Improvements on Delaunay-based three-dimensional automatic mesh generator. Finite Elements in Analysis and Design, 1997, 25:297~317.
[15] P. L. George, Delaunay’s mesh of a convex polyhedron in dimension d. application to arbitrary polyhedra. International Journal for Numerical Methods in Engineering, 1992, 33:975~995.
[16] T. J. Baker, Three dimensional mesh generation by triangulation of arbitrary point sets. Proc.AIAA 8th CFD Conf, Hawaii, 1987.
[17] W. J. Schroeder, M.S. Shephard, Geometry-based fully automatic mesh generation and the Delaunay triangulation. International Journal for Numerical Methods in Engineering, 1988, 26:2503~2515.
[18] N. P. Weatherill, The integrity of geometrical boundaries in the two-dimensional Delaunay triangulation. Communications in Applied Numerical Methods, 1990, 6:101~109.
[19] H. Borouchaki, S.H. Lo, Fast Delaunay triangulation in three dimensions. Computer Methods in Applied Mechanics and Engineering, 1995,128:153~167.
[20] Yao Zheng, R. W. Lewis, D. T. Gethin, Three-dimensional unstructured mesh generation: Part 1. Fundamental aspects of triangulation and point creation. Computer Methods in Applied Mechanics and Engineering, 1996,134:249~268.
[21] Yao Zheng, R. W. Lewis, D. T. Gethin, Three-dimensional unstructured mesh generation: Part 2. Surface meshes. Computer Methods in Applied Mechanics and Engineering, 1996, 134:269~284.
[22] R. W. Lewis, Yao Zheng, D. T. Gethin, Three-dimensional unstructured mesh generation: Part 3. Volume meshes. Computer Methods in Applied Mechanics and Engineering, 1996,134:285~310.
[23] H. Borouchaki, P. L. George, Optimal Delaunay point insertion. International Journal for Numerical Methods in Engineering, 1996, 39:3407~3437.
[24] H. Borouchaki, P. L. George, Aspects of 2-D Delaunay mesh generation. International Journal for Numerical Methods in Engineering. 1997, 40:1957~1975.
[25] P. L. George, H. Borouchaki, E. Saltel,‘Ultimate’robustness in meshing an arbitrary polyhedron. International Journal for Numerical Methods in Engineering, 2003,58:1061~1089.
[26] Qiang Du, Desheng Wang, Boundary recovery for three dimensional conforming Delaunay triangulation. Computer Methods in Applied Mechanics and Engineering, 2004, 193:2547~2563.
[27] Qiang Du, Desheng Wang, Constrained boundary recovery for three dimensional Delaunay triangulations. International Journal for Numerical Methods in Engineering, 2004, 61:1471~1500.
[28] H. Borouchaki , P. L. George , F.Hecht , et al., Delaunay mesh generation governed by metric specifications. Part I. Algorithms. Finite Element Analysis and Design, 1997, 25:61~83.
[29] H. Borouchaki, P. L. George, B. Mohammadi, Delaunay mesh generation governed by metric specifications. PartⅡ. Applications. Finite Element Analysis and Design, 1997, 25:85~109.
[30] H. Borouchaki , P. Laug , P. L George, Parametric surface meshing using a combined advancing-front generalized Delaunay approach. International Journal for Numerical Methods in Engineering, 2000, 49:233~259.
[31] S. Gopalsamy , Y. TzuYi . A Geometry engine for CAD/Grid Integration. 41st Aerospace Sciences Meeting and Exhibit, 2003.
[32] S. Gopalsamy, Grid Generation in the framework of the unstructured grid consortium API using the geometry and grid toolkit GGTK, AIAA, 2006,2006-528.
[33] J. C. Cavendish, D. A. Field, and W. H. Frey, An approach to automatic three-dimension finite element mesh generation. International Journal for Numerical Methods in Engineering, 1997, 40:3979~4002.
[34] T. S. Lau, S. H. Lo, Finite element mesh generation over analytical surfaces. Computers and Structures, 1996, 59:301~309.
[35] T. S. Lau, S. H. Lo, C. K. Lee, Generation of quadrilateral mesh over analytical curved surfaces. Finite Element in Analysis and Design, 1997, 27:251~272.
[2]林宏镇,汪火光,蒋章焰等,高性能抗空发动机传热技术,北京:国防工业出版社2005。
[3]彭泽琰,刘刚等,航空燃气轮机原理,北京:国防工业出版社,2000。
[4]徐伟祖,叶轮机CFD网格预处理研究,[硕士学位论文]。南京:南京航空航天大学,2008。
[5]刘学强,基于混合网格和多重网格上的N-S方程求解及应用研究,[博士学位论文]。南京:南京航空航天大学,2001。
[6]陈建军,非结构化网格生成及其并行化的若干问题研究,[博士学位论文]。杭州:浙江大学,2006。
[7] Stephen Prata,C++Primer Plus(孙建春,韦强)。北京:人民邮电出版社,2002。
[8] J. F. Thomposon, B. K. Soni, N. P. Weatherill, Handbook of Grid Generation. Boca Raton and London: CRC Press, 1999.
[9] A. Bowyer, Computing dirichlet tessellations. The Computer Journal, 1981, 24:162~166.
[10] D. F. Watson, Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes. The Computer Journal, 1981, 24:167~172.
[11] N. P. Weatherill, O. Hassan, Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraint. International Journal for Numerical Methods in Engineering, 1994, 37:2005~2039.
[12] P. L. George, F. Hecht, E. Saltel, Automatic mesh generator with specified boundary. Computer Methods in Applied Mechanics and Engineering, 1991, 92:269~288.
[13] N. P. Weatherill, Delaunay Triangulation in computational fluid dynamics, Computers Math. Applic., 1992, 24:129~150.
[14] P. L. George, Improvements on Delaunay-based three-dimensional automatic mesh generator. Finite Elements in Analysis and Design, 1997, 25:297~317.
[15] P. L. George, Delaunay’s mesh of a convex polyhedron in dimension d. application to arbitrary polyhedra. International Journal for Numerical Methods in Engineering, 1992, 33:975~995.
[16] T. J. Baker, Three dimensional mesh generation by triangulation of arbitrary point sets. Proc.AIAA 8th CFD Conf, Hawaii, 1987.
[17] W. J. Schroeder, M.S. Shephard, Geometry-based fully automatic mesh generation and the Delaunay triangulation. International Journal for Numerical Methods in Engineering, 1988, 26:2503~2515.
[18] N. P. Weatherill, The integrity of geometrical boundaries in the two-dimensional Delaunay triangulation. Communications in Applied Numerical Methods, 1990, 6:101~109.
[19] H. Borouchaki, S.H. Lo, Fast Delaunay triangulation in three dimensions. Computer Methods in Applied Mechanics and Engineering, 1995,128:153~167.
[20] Yao Zheng, R. W. Lewis, D. T. Gethin, Three-dimensional unstructured mesh generation: Part 1. Fundamental aspects of triangulation and point creation. Computer Methods in Applied Mechanics and Engineering, 1996,134:249~268.
[21] Yao Zheng, R. W. Lewis, D. T. Gethin, Three-dimensional unstructured mesh generation: Part 2. Surface meshes. Computer Methods in Applied Mechanics and Engineering, 1996, 134:269~284.
[22] R. W. Lewis, Yao Zheng, D. T. Gethin, Three-dimensional unstructured mesh generation: Part 3. Volume meshes. Computer Methods in Applied Mechanics and Engineering, 1996,134:285~310.
[23] H. Borouchaki, P. L. George, Optimal Delaunay point insertion. International Journal for Numerical Methods in Engineering, 1996, 39:3407~3437.
[24] H. Borouchaki, P. L. George, Aspects of 2-D Delaunay mesh generation. International Journal for Numerical Methods in Engineering. 1997, 40:1957~1975.
[25] P. L. George, H. Borouchaki, E. Saltel,‘Ultimate’robustness in meshing an arbitrary polyhedron. International Journal for Numerical Methods in Engineering, 2003,58:1061~1089.
[26] Qiang Du, Desheng Wang, Boundary recovery for three dimensional conforming Delaunay triangulation. Computer Methods in Applied Mechanics and Engineering, 2004, 193:2547~2563.
[27] Qiang Du, Desheng Wang, Constrained boundary recovery for three dimensional Delaunay triangulations. International Journal for Numerical Methods in Engineering, 2004, 61:1471~1500.
[28] H. Borouchaki , P. L. George , F.Hecht , et al., Delaunay mesh generation governed by metric specifications. Part I. Algorithms. Finite Element Analysis and Design, 1997, 25:61~83.
[29] H. Borouchaki, P. L. George, B. Mohammadi, Delaunay mesh generation governed by metric specifications. PartⅡ. Applications. Finite Element Analysis and Design, 1997, 25:85~109.
[30] H. Borouchaki , P. Laug , P. L George, Parametric surface meshing using a combined advancing-front generalized Delaunay approach. International Journal for Numerical Methods in Engineering, 2000, 49:233~259.
[31] S. Gopalsamy , Y. TzuYi . A Geometry engine for CAD/Grid Integration. 41st Aerospace Sciences Meeting and Exhibit, 2003.
[32] S. Gopalsamy, Grid Generation in the framework of the unstructured grid consortium API using the geometry and grid toolkit GGTK, AIAA, 2006,2006-528.
[33] J. C. Cavendish, D. A. Field, and W. H. Frey, An approach to automatic three-dimension finite element mesh generation. International Journal for Numerical Methods in Engineering, 1997, 40:3979~4002.
[34] T. S. Lau, S. H. Lo, Finite element mesh generation over analytical surfaces. Computers and Structures, 1996, 59:301~309.
[35] T. S. Lau, S. H. Lo, C. K. Lee, Generation of quadrilateral mesh over analytical curved surfaces. Finite Element in Analysis and Design, 1997, 27:251~272.