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基于边界元方法, 使空泡表面和细长体表面分别满足Dirichlet 边界条件和Neumann边界条件, 数值迭代获得小攻角下三维细长体的定常空化形态. 采用线性三角形单元, 将控制点布置在网格节点上, 应用局部正交坐标系并采用迭代方法获得空泡表面的速度势, 进而通过边界积分方程确定空泡厚度的分布. 采用拉格朗日插值方法得到空泡末端的厚度, 避免了迭代过程中网格的重新划分. 数值结果与实验值符合良好, 验证了该方法的合理性. 系统研究了空化数、攻角以及锥角对于三维细长体空化形态的影响规律. 数值结果表明: 攻角使得细长体的空化形态呈现不对称性, 出现空泡向背流面“堆积”的现象; 而空化数越小或锥角越大, 空泡形态的不对称性将越严重.In this paper, based on the boundary element method, the cavitation shape of the three-dimensional slender at a small attack angle in a steady flow is simulated through the iterative method, while Dirichlet boundary conditions and Neumann boundary conditions are satisfied in cavitation and slender respectively. The linear triangular elements are adopted and the control points are arranged in grid nodes. The velocity potential for cavity surface is determined through an iterative method in a local orthogonal coordinate system, and then the distribution of cavitation thickness can be determined by the boundary integral equation. To prevent the remeshing operation in the iterative process, the Lagrange interpolation method is used to determine the thickness at the end of cavity. The numerical results are in good agreement with the experimental data. The influence of those on cavitation shape of the three-dimensional slender are investigated, such as cavitation number, attack angle and cone angle. Numerical results show that the cavitation shape of the three-dimensional slender is asymmetric at an attack angle and is analogous to the cavitation stacking in the lee side. While with the decrease in the cavity number or the increase in cone angle, the asymmetry for the cavity shape will be more serious.
[1] Ingber M S, Hailey C E 1992 Int. J. Numerical Methods in Fluids 15 251
[2] Wolfe W P, Hailey C E, Oberkampf W 1989 J. Fluids Eng. 111 300
[3] Huang B, Wang G Y, Hu C L, Gao D M 2012 Engin. Mech. 29 320 (in Chinese) [黄彪, 王国玉, 胡常莉, 高德明 2012 工程力学 29 320]
[4] Wang Y W, Huang C G, Du T Z, Wu X Q, Fang X, Liang N G, Wei Y P 2012 Chin. Phys. Lett. 29 014601
[5] Liu X M, He J, Lu J, Ni X W 2008 Chin. Phys. B 17 2574
[6] Wang C H, Cheng J C 2013 Chin. Phys. B 22 014304
[7] Singhal A K, Athavale M M, Li H Y, Jiang Y 2002 J. Fluids Eng. 124 617
[8] Srinivasan V, Salazar A J, Saito K 2009 Appl. Math. Model. 33 1529
[9] Chen Y, Lu C J, Guo J H 2010 J. Hydrodyn. 22 893
[10] Zhang L X, Khoo B C 2013 Comput. Fluids 73 1
[11] Rastgou H, Saedodin S 2013 J. Fluids Struct. DOI: 10.1016/j. jfluidstructs. 2013.05.006
[12] Owis F M, Nayfeh A H 2004 Eur. J. Mech. B: Fluids 23 339
[13] Zhang X M, Zhou C Y, Shams I, Liu J Q 2009 Acta Phys. Sin. 58 8406 (in Chinese) [张新明, 周超英, Shams I, 刘家琦 2009 58 8406]
[14] Kinnas S A, Fine N E 1991 In Boundary Integral Methods Theory and Applications 10 289
[15] Kinnas S A, Fine N E 1993 J. Fluid Mech. 254 151
[16] Arakeri V H 1975 J. Fluid Mech. 68 779
[17] Wu T Y 1972 Annu. Rev. Fluid. Mech. 4 243
[18] Leng H J, Lu C J 2002 J. Shanghai Jiaotong Univ. 36 395 (in Chinese) [冷海军, 鲁传敬 2002 上海交通大学学报 36 395]
[19] Jia C J, Xu H, Zhang Y W 2004 Ship Sci. Technol. 26 16 ( in Chinese) [贾彩娟, 许晖, 张宇文 2004 舰船科学技术 26 16]
[20] Chen J H, Weng Y C 2005 J. Chin. Instit. Engin. 28 735
[21] Rashidi I, Pasandide M, Ghafoorianfar N, Mansour M 2008 Proceedings of the 12th Asian Congress of Fluid Mechanics Korea, August 18-21, 2008 p1
[22] Liu Y L, Zhang A M, Wang S P, Tian Z L 2013 Acta Phys. Sin. 62 144703 (in Chinese) [刘云龙, 张阿漫, 王诗平, 田昭丽 2013 62 144703]
[23] Zhang A M, Wang S P, Wu G X 2013 Eng. Anal. Bound. Elem. DOI: 10.1016/j.enganabound.2013.04.013
[24] Rouse H, McNown J S 1948 Cavitat. Pressure Distribut. Head Forms at Zero Angle of Yaw (Iowa City: The State University of Iowa)
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[1] Ingber M S, Hailey C E 1992 Int. J. Numerical Methods in Fluids 15 251
[2] Wolfe W P, Hailey C E, Oberkampf W 1989 J. Fluids Eng. 111 300
[3] Huang B, Wang G Y, Hu C L, Gao D M 2012 Engin. Mech. 29 320 (in Chinese) [黄彪, 王国玉, 胡常莉, 高德明 2012 工程力学 29 320]
[4] Wang Y W, Huang C G, Du T Z, Wu X Q, Fang X, Liang N G, Wei Y P 2012 Chin. Phys. Lett. 29 014601
[5] Liu X M, He J, Lu J, Ni X W 2008 Chin. Phys. B 17 2574
[6] Wang C H, Cheng J C 2013 Chin. Phys. B 22 014304
[7] Singhal A K, Athavale M M, Li H Y, Jiang Y 2002 J. Fluids Eng. 124 617
[8] Srinivasan V, Salazar A J, Saito K 2009 Appl. Math. Model. 33 1529
[9] Chen Y, Lu C J, Guo J H 2010 J. Hydrodyn. 22 893
[10] Zhang L X, Khoo B C 2013 Comput. Fluids 73 1
[11] Rastgou H, Saedodin S 2013 J. Fluids Struct. DOI: 10.1016/j. jfluidstructs. 2013.05.006
[12] Owis F M, Nayfeh A H 2004 Eur. J. Mech. B: Fluids 23 339
[13] Zhang X M, Zhou C Y, Shams I, Liu J Q 2009 Acta Phys. Sin. 58 8406 (in Chinese) [张新明, 周超英, Shams I, 刘家琦 2009 58 8406]
[14] Kinnas S A, Fine N E 1991 In Boundary Integral Methods Theory and Applications 10 289
[15] Kinnas S A, Fine N E 1993 J. Fluid Mech. 254 151
[16] Arakeri V H 1975 J. Fluid Mech. 68 779
[17] Wu T Y 1972 Annu. Rev. Fluid. Mech. 4 243
[18] Leng H J, Lu C J 2002 J. Shanghai Jiaotong Univ. 36 395 (in Chinese) [冷海军, 鲁传敬 2002 上海交通大学学报 36 395]
[19] Jia C J, Xu H, Zhang Y W 2004 Ship Sci. Technol. 26 16 ( in Chinese) [贾彩娟, 许晖, 张宇文 2004 舰船科学技术 26 16]
[20] Chen J H, Weng Y C 2005 J. Chin. Instit. Engin. 28 735
[21] Rashidi I, Pasandide M, Ghafoorianfar N, Mansour M 2008 Proceedings of the 12th Asian Congress of Fluid Mechanics Korea, August 18-21, 2008 p1
[22] Liu Y L, Zhang A M, Wang S P, Tian Z L 2013 Acta Phys. Sin. 62 144703 (in Chinese) [刘云龙, 张阿漫, 王诗平, 田昭丽 2013 62 144703]
[23] Zhang A M, Wang S P, Wu G X 2013 Eng. Anal. Bound. Elem. DOI: 10.1016/j.enganabound.2013.04.013
[24] Rouse H, McNown J S 1948 Cavitat. Pressure Distribut. Head Forms at Zero Angle of Yaw (Iowa City: The State University of Iowa)
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