回转体流场三维结构特征及其电磁力控制效应的研究
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摘要
导电流体中电磁场产生的电磁力可以改变流体边界层的结构,是用于流体流动控制的一种有效手段。根据研究工作所采用的控制方法的不同,电磁流动控制(Electromagnetic Flow Control, EMFC)研究分为磁流体力学(Magnetic Hydrodynamics, MHD)和电磁流体力学(Electromagnetic Hydrodynamics, EMHD)问题。采用电磁力来控制具有一定电导率的流体的流动,尤其是弱导电流体(如海水、弱电解质溶液等)的流场结构,是通过对流体边界层结构的重构与调整以实现控制,其控制作用体现为非线性控制的综合效果,属于典型的EMHD方面的研究问题。这种流动控制技术可减小航行器的阻力、增强或抑制旋涡,对于增加航行器的推进效率、增加可操纵性和机动性等方面具有广阔的应用前景。随着人们对非线性科学(如非线性优化控制)的研究取得了重要的进展、对湍流机理研究的进一步深入(如流体混合层、近壁剪切湍流的拟序结构,湍流标度率的认识等),电磁场对弱导电流体流动控制研究的课题已经成为近年来流体力学和电磁流体力学研究领域的热点研究方向,形成了电磁湍流控制(Electromagnetic Turbulence Control, EMTC)的研究热点。
本文采用层次结构网格下的有限体积法求解带电磁力源项的Navier-Stokes方程,对圆柱绕流、圆球绕流和潜艇及其附体流场的三维结构特征及其电磁力控制效应的问题进行了数值模拟研究。
主要的研究结果如下：
(1)圆柱绕流在卡门涡街脱落过程中,随着雷诺数增大,展向的卡门涡逐渐失去稳定性,两种典型的三维不稳定性模式为模式A和模式B。研究结果表明,模式A流场不稳定性的展向波长约为3.3至5倍圆柱直径,模式B流场不稳定性的展向波长约为0.83倍圆柱直径。在圆柱绕流边界层区域内施加电磁力后,卡门涡的脱落得到有效抑制,圆柱后滞点附近的压力得到提升,阻力减小且升力的波动被抑制。
(2)与圆柱绕流的分离泡失去对称性变为非定常流动不同,圆球绕流在三维转捩过程中,尾迹从涡环变为双线涡,双线涡失稳后变为发夹涡脱落。在圆球绕流为非定常面对称流动过程中,随着发夹涡的脱落升阻力具有相同的变化频率和相位角。随着雷诺数继续增大至400左右,涡结构和受力曲线均呈现准周期性变化。通过在圆球边界层施加电磁力后,抑制了发夹涡的形成和脱落,缩小了圆球后滞点周围的最小压力区域,圆球在流向和垂直于流向方向的受力波动被抑制。
(3)针对具有复杂附体结构的潜艇模型,分析了由于附体的扰动对潜艇主体流场的影响,分析了不同雷诺数和航行姿态下潜艇主体及其附体流场的结构变化规律；通过利用电磁力对潜艇附体的局部流场进行控制,改善了潜艇的整体流场和动力学特性。结果表明,在潜艇及其附体流场中,随着雷诺数量级的增大,围壳后尾涡的脱落对流场的扰动作用越来越大。在其他参数相同且航行姿态不同时,偏航时的流场较直航时稳定,下俯时的流场较上仰时的流场稳定。通过在围壳边界层施加电磁力控制后,围壳后的尾涡被抑制为稳定的线状涡。对于带尾舵和鳍翼的潜艇流场,电磁力也可以有效抑制翼型后尾涡的脱落,具有较好的减阻控制效果。
通过对圆柱、圆球和潜艇等典型回转体的流场三维结构特征及其电磁力的控制效应的系统研究,得到了回转体绕流流场的结构特征及其电磁力控制参数。研究结果对减少航行器的阻力、抑制旋涡脱落等方面具有一定的应用价值,对于提升航行器的推进效率、减少燃料消耗、稳定性和机动性等方面的研究工作具有一定的意义和作用。
The electromagnetic force (i.e. Lorentz force) generated by the electromagnetic field in the electrically conducive fluid can modify the flow boundary layer, which is an effective flow control method. The Electromagnetic Flow Control (EMFC) can be categorized into two groups, Magnetic Hydrodynamics (MHD) and Electromagnetic Hydrodynamics (EMHD) according to the control method adopted. The flow of fluid with certain conductivity, especially weakly conductive fluids such as seawater and weak electrolyte solutions, can be controlled utilizing the electromagnetic force by reconstructing and adjusting the boundary layer. This flow control method represents the comprehensive effects of nonlinear control, belonging to the category of EMHD. This flow control technique may reduce the drag, enhance or suppress vortex, and have broad application prospect in improving propulsive efficiency, maneuverability and stability of the underwater vehicles (e.g. submarines and ships).
The objective of this dissertation is to investigate numerically the three-dimensional structures of the flow field around three types of bodies of revolutions, i.e. cylinder, sphere and submarine, and the control effects of the electromagnetic force on the flow field. The Navier-Stokes equations considering the source term of electromagnetic body force are solved by finite volume method based on the hierarchical structured mesh.
Main conclusions are as follows:
(1)In the process of vortex shedding from the circular cylinder, the spanwise Karman vortex loses stability gradually and the small scale streamwise vortex is formed. Base on the spanwise scale of the streamwise vortex, two typical instability modes are mode A and mode B. The spanwise length of the mode A instability is to be around3.3-5times the cylinder diameter, and the spanwise length of the mode B instability is about0.83time the diameter. When the boundary layer of the flow around cylinder is controlled by Lorentz force, the vortex shedding is suppressed efficiently. The pressure in the region around the rear stagnation point is increased and the drag is reduced.
(2)Unlike the flow past the circular cylinder, which the separation bubble lose symmetry and turn into unsteady flow, the wake of the sphere transforms from vortex ring to double filaments vortex, and the double filaments vortex loses stability leading to the shedding of the hairpin vortex during the wake transition process. When the flow around sphere is unsteady plane-symmetrical, the drag and lift coefficients oscillate periodically with the same frequency and phase as the hairpin vortex shedding. When the Reynolds number is about400, the vortex shedding and the time history of force coefficients become quasi-periodic. When the Lorentz force is applied on the sphere boundary layer, the formation and shedding of the hairpin vortex is suppressed. The region of favorable pressure gradients near the rear stagnation point is reduced and the fluctuation of the force is suppressed.
(3)Aimed at the submarine model with complex appendages, the disturbance caused by the appendage to the flow field around the submarine is analyzed. The flow field structure around the submarine at different Reynolds numbers and attitudes are also investigated. By control the local flow field around the fairwater utilizing the Lorentz force, the overall flow field and the hydrodynamic characteristics are improved. The results show that the effect of disturbance caused by the vortex shed from the fairwater on the flow around submarine increase as the magnitude of Reynolds number increase. With all other flow parameters being equal, the flow around submarine at yaw is more stable than the flow around submarine at straight course, and the flow around submarine at pitch down attitude is more stable than the flow around submarine at pitch up attitude. The vortex shed from the fairwater are suppressed by applying the Lorentz force in the near-wall region of the fairwater. For the flow around the body of revolution with hydrofoils, the Lorentz force may also suppress the vortex shedding around the hydrofoil, improving the maneuverability of the aircraft.
By systematic study on the three-dimensional structures of the flow field around typical bodies of revolution and the control effect of the electromagnetic force on the flow field, the structure characteristics of the flow field around the submarine and the control parameters of the Lorentz force are obtained. The results have certain practical value in drag reduction and vortex shedding suppression, and will promote the research work in improving propulsive efficiency, maneuverability and stability of the underwater vehicles.
本文采用层次结构网格下的有限体积法求解带电磁力源项的Navier-Stokes方程,对圆柱绕流、圆球绕流和潜艇及其附体流场的三维结构特征及其电磁力控制效应的问题进行了数值模拟研究。
主要的研究结果如下：
(1)圆柱绕流在卡门涡街脱落过程中,随着雷诺数增大,展向的卡门涡逐渐失去稳定性,两种典型的三维不稳定性模式为模式A和模式B。研究结果表明,模式A流场不稳定性的展向波长约为3.3至5倍圆柱直径,模式B流场不稳定性的展向波长约为0.83倍圆柱直径。在圆柱绕流边界层区域内施加电磁力后,卡门涡的脱落得到有效抑制,圆柱后滞点附近的压力得到提升,阻力减小且升力的波动被抑制。
(2)与圆柱绕流的分离泡失去对称性变为非定常流动不同,圆球绕流在三维转捩过程中,尾迹从涡环变为双线涡,双线涡失稳后变为发夹涡脱落。在圆球绕流为非定常面对称流动过程中,随着发夹涡的脱落升阻力具有相同的变化频率和相位角。随着雷诺数继续增大至400左右,涡结构和受力曲线均呈现准周期性变化。通过在圆球边界层施加电磁力后,抑制了发夹涡的形成和脱落,缩小了圆球后滞点周围的最小压力区域,圆球在流向和垂直于流向方向的受力波动被抑制。
(3)针对具有复杂附体结构的潜艇模型,分析了由于附体的扰动对潜艇主体流场的影响,分析了不同雷诺数和航行姿态下潜艇主体及其附体流场的结构变化规律；通过利用电磁力对潜艇附体的局部流场进行控制,改善了潜艇的整体流场和动力学特性。结果表明,在潜艇及其附体流场中,随着雷诺数量级的增大,围壳后尾涡的脱落对流场的扰动作用越来越大。在其他参数相同且航行姿态不同时,偏航时的流场较直航时稳定,下俯时的流场较上仰时的流场稳定。通过在围壳边界层施加电磁力控制后,围壳后的尾涡被抑制为稳定的线状涡。对于带尾舵和鳍翼的潜艇流场,电磁力也可以有效抑制翼型后尾涡的脱落,具有较好的减阻控制效果。
通过对圆柱、圆球和潜艇等典型回转体的流场三维结构特征及其电磁力的控制效应的系统研究,得到了回转体绕流流场的结构特征及其电磁力控制参数。研究结果对减少航行器的阻力、抑制旋涡脱落等方面具有一定的应用价值,对于提升航行器的推进效率、减少燃料消耗、稳定性和机动性等方面的研究工作具有一定的意义和作用。
The electromagnetic force (i.e. Lorentz force) generated by the electromagnetic field in the electrically conducive fluid can modify the flow boundary layer, which is an effective flow control method. The Electromagnetic Flow Control (EMFC) can be categorized into two groups, Magnetic Hydrodynamics (MHD) and Electromagnetic Hydrodynamics (EMHD) according to the control method adopted. The flow of fluid with certain conductivity, especially weakly conductive fluids such as seawater and weak electrolyte solutions, can be controlled utilizing the electromagnetic force by reconstructing and adjusting the boundary layer. This flow control method represents the comprehensive effects of nonlinear control, belonging to the category of EMHD. This flow control technique may reduce the drag, enhance or suppress vortex, and have broad application prospect in improving propulsive efficiency, maneuverability and stability of the underwater vehicles (e.g. submarines and ships).
The objective of this dissertation is to investigate numerically the three-dimensional structures of the flow field around three types of bodies of revolutions, i.e. cylinder, sphere and submarine, and the control effects of the electromagnetic force on the flow field. The Navier-Stokes equations considering the source term of electromagnetic body force are solved by finite volume method based on the hierarchical structured mesh.
Main conclusions are as follows:
(1)In the process of vortex shedding from the circular cylinder, the spanwise Karman vortex loses stability gradually and the small scale streamwise vortex is formed. Base on the spanwise scale of the streamwise vortex, two typical instability modes are mode A and mode B. The spanwise length of the mode A instability is to be around3.3-5times the cylinder diameter, and the spanwise length of the mode B instability is about0.83time the diameter. When the boundary layer of the flow around cylinder is controlled by Lorentz force, the vortex shedding is suppressed efficiently. The pressure in the region around the rear stagnation point is increased and the drag is reduced.
(2)Unlike the flow past the circular cylinder, which the separation bubble lose symmetry and turn into unsteady flow, the wake of the sphere transforms from vortex ring to double filaments vortex, and the double filaments vortex loses stability leading to the shedding of the hairpin vortex during the wake transition process. When the flow around sphere is unsteady plane-symmetrical, the drag and lift coefficients oscillate periodically with the same frequency and phase as the hairpin vortex shedding. When the Reynolds number is about400, the vortex shedding and the time history of force coefficients become quasi-periodic. When the Lorentz force is applied on the sphere boundary layer, the formation and shedding of the hairpin vortex is suppressed. The region of favorable pressure gradients near the rear stagnation point is reduced and the fluctuation of the force is suppressed.
(3)Aimed at the submarine model with complex appendages, the disturbance caused by the appendage to the flow field around the submarine is analyzed. The flow field structure around the submarine at different Reynolds numbers and attitudes are also investigated. By control the local flow field around the fairwater utilizing the Lorentz force, the overall flow field and the hydrodynamic characteristics are improved. The results show that the effect of disturbance caused by the vortex shed from the fairwater on the flow around submarine increase as the magnitude of Reynolds number increase. With all other flow parameters being equal, the flow around submarine at yaw is more stable than the flow around submarine at straight course, and the flow around submarine at pitch down attitude is more stable than the flow around submarine at pitch up attitude. The vortex shed from the fairwater are suppressed by applying the Lorentz force in the near-wall region of the fairwater. For the flow around the body of revolution with hydrofoils, the Lorentz force may also suppress the vortex shedding around the hydrofoil, improving the maneuverability of the aircraft.
By systematic study on the three-dimensional structures of the flow field around typical bodies of revolution and the control effect of the electromagnetic force on the flow field, the structure characteristics of the flow field around the submarine and the control parameters of the Lorentz force are obtained. The results have certain practical value in drag reduction and vortex shedding suppression, and will promote the research work in improving propulsive efficiency, maneuverability and stability of the underwater vehicles.
引文
1. Choi H, Jeon W P, Kim J. Control of flow over a bluff body. Annu Rev Fluid Mech,2008, 40:113-139
2. Cattafesta L N, Sheplak M. Actuators for Active Flow Control. Annu Rev Fluid Mech,2011, 43:247-272
3. Zhou Y, Bai H. Recent advances in active control of turbulent boundary layers. Science China Physics, Mechanics and Astronomy,2011,54(7):1289-1295
4. Zdravkovich M. Flow Around Circular Cylinders, vol.1. Fundamentals. J Fluid Mech, 1997,350:377-378
5. Williamson C H K. Vortex dynamics in the cylinder wake. Annu Rev Fluid Mech,1996,28: 477-539
6. Williamson C H K. Three-dimensional wake transition. J Fluid Mech,1996,328:345-407
7. Roshko A. On the drag and shedding frequency of two-dimensional bluff bodies. DTIC Document,1954.
8. Taneda S. Downstream development of the wake behind cylinders. Journal of the Physics Society of Japan,1959,14:843-848
9. Williamson C H K. Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. J Fluid Mech,1989,206:579-627
10. Eisenlohr H, Eckelmann H. Vortex splitting and its consequences in the vortex street wake of cylinders at low Reynolds number. Physics of Fluids A:Fluid Dynamics,1989,1:189
11. Barkley D, Henderson R D. Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J Fluid Mech,1996,322:215-241
12. Blackburn H, Lopez J. On three-dimensional quasiperiodic Floquet instabilities of two-dimensional bluff body wakes. Phys Fluids,2003,15:L57
13. Rajani B N, Kandasamy A, Majumdar S. Numerical simulation of laminar flow past a circular cylinder. Applied Mathematical Modelling,2009,33:1228-1247
14. Mittal S, Kottaram J J, Kumar B. Onset of shear layer instability in flow past a cylinder. Phys Fluids,2008,20(054102)
15. Behara S, Mittal S. Wake transition in flow past a circular cylinder. Phys Fluids,2010, 22(114104)
16. Behara S, Mittal S. Flow past a circular cylinder at low Reynolds number:Oblique vortex shedding. Phys Fluids,2010,22:054102
17. Labbe D, Wilson P. A numerical investigation of the effects of the spanwise length on the 3-D wake of a circular cylinder. J Fluid Struct,2007,23(8):1168-1188
18. Taneda S. Experimental investigation of the wake behind a sphere at low Reynolds numbers. J Phys Soc Japan,1956,11(10):1104-1108
19. Magarvey R, Bishop R L. Transition ranges for three-dimensional wakes. Canadian Journal of Physics,1961,39:1418
20. Sakamoto H, Haniu H. The formation mechanism and shedding frequency of vortices from a sphere in uniform shear flow. J Fluid Mech,1995,287:151-172
21. Fornberg B. Steady viscous flow past a sphere at high Reynolds numbers. J Fluid Mech, 1988,190:471-489
22. Kurose R, Komori S. Drag and lift forces on a rotating sphere in a linear shear flow. J Fluid Mech,1999,384(4):183-206
23. Hanazaki H. A numerical study of three-dimensional stratified flow past a sphere. J Fluid Mech,1988,192(1):393-419
24. Tomboulides A G, Orszag S A. Numerical investigation of transitional and weak turbulent flow past a sphere. J Fluid Mech,2000.416(1):45-73
25. Johnson T, Patel V. Flow past a sphere up to a Reynolds number of 300. J Fluid Mech, 1999,378(1):19-70
26. Gushchin V, Matyushin R. Vortex formation mechanisms in the wake behind a sphere for 200< Re< 380. Fluid Dynamics,2006,41(5):795-809
27. Mittal R, Wilson J, Najjar F. Symmetry properties of the transitional sphere wake. AIAA journal,2002,40(3):579-582
28. Wu J, Faeth G. Sphere wakes in still surroundings at intermediate Reynolds numbers. AIAA journal,1993,31(8):1448-1455
29. Lee S. A numerical study of the unsteady wake behind a sphere in a uniform flow at moderate Reynolds numbers. Computers & Fluids,2000,29(6):639-667
30. Kim D, Choi H. Laminar flow past a hemisphere. Phys Fluids,2003,15(8):2457
31. Kim D, Choi H, Choi H. Characteristics of laminar flow past a sphere in uniform shear. Phys Fluids,2005,17(10):103602
32. Ploumhans P, Winckelmans G S, Salmon J K, et al. Vortex Methods for Direct Numerical Simulation of Three-Dimensional Bluff Body Flows:Application to the Sphere at Re=300, 500, and 1000. Journal of Computational Physics,2002,178(2):427-463
33. Gumowski K, Miedzik J. Transition to a time-dependent state of fluid flow in the wake of a sphere. Physical Review E,2008,77(5)
34. Pier B. Local and global instabilities in the wake of a sphere. J Fluid Mech,2008,603
35. Giacobello M, Ooi A, Balachandar S. Wake structure of a transversely rotating sphere at moderate Reynolds numbers. J Fluid Mech,2009,621:103
36. Stewart B E, Thompson M C, Leweke T, et al. Numerical and experimental studies of the rolling sphere wake. J Fluid Mech,2010,643:137
37. Stewart B E, Leweke T, Hourigan K, et al. Wake formation behind a rolling sphere. Phys Fluids,2008,20(7):071704
38. Ou K, Castonguay P, Jameson A. Computational Sports Aerodynamics of a Moving Sphere:Simulating a Ping Pong Ball in Free Flight.2011,
39.邹建锋,任安禄,邓见.圆球绕流场的尾涡分析和升阻力研究.空气动力学学报,2004,22(3)：303-308
40. Jeon S, Choi J I N, Jeon W-P, et al. Active control of flow over a sphere for drag reduction at a subcritical Reynolds number. J Fluid Mech,2004,517:113-129
41. Choi J, Jeon W P, Choi H. Mechanism of drag reduction by dimples on a sphere. Phys Fluids,2006,18:041702
42. Jeon S, Choi H. Suboptimal feedback control of flow over a sphere. International Journal of Heat and Fluid Flow,2010,31(2):208-216
43. Bluemink J J, Lohse D, Prosperetti A, et al. A sphere in a uniformly rotating or shearing flow. J Fluid Mech,2008,600
44. Niazmand H. Surface effects on transient three-dimensional flows around rotating spheres at moderate Reynolds numbers. Computers & Fluids,2003,32(10):1405-1433
45. Kim D, Choi H. Laminar flow past a sphere rotating in the stream wise direction. J Fluid Mech,2002,461:365-386
46. Kim D. Laminar flow past a sphere rotating in the transverse direction. Journal of Mechanical Science and Technology,2009,23(2):578-589
47. Garrett S J, Peake N. The stability and transition of the boundary layer on a rotating sphere. J Fluid Mech,2002,456
48. Provansal M. From the double vortex street behind a cylinder to the wake of a sphere. European Journal of Mechanics-B/Fluids,2004,23(1):65-80
49. Sheard G J. Thompson M C. Hourigan K. From spheres to circular cylinders: non-axisymmetric transitions in the flow past rings. J Fluid Mech,2004,506:45-78
50. Liu H L, Huang T T. Summary of DARPA SUBOFF experimental program data. DTIC Document,1998.
51. Alin N. Fureby C, Svennberg S, et al. Large Eddy Simulation of the Transient Flow Around A Submarine During A Maneuver.45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada,2007.
52. Yang C, Lohner R. Prediction of flows over an axisymmetric body with appendages. The 8th International Conference on Numerical Ship Hydrodynamics, Busan, Korea,2003.
53. Alin N, Fureby C, Svennberg U, et al.3D Unsteady Computations for Submarine-Like Bodies.43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada,2005. AIAA
54. Alin N, Bensow R, Fureby C, et al. Current Capabilities of DES and LES for Submarines at Straight Course. Journal of Ship Research,2010,54(3):184-196
55. Liefvendahl M, Fureby C, Persson T. LES and DES of high Reynolds Number Wall Bounded Flows.44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada,2006. AIAA.
56. Liefvendahl M, Alin N, Chapuis M, et al. Ship and propulsor hydrodynamics. V European Conference on Computational Fluid Dynamics, Lisbon, Portugal,2010. ECCOMAS CFD 2010.
57. Bridges D H, Cash A C, Freudenthal J L. Investigation of Scaling Effects in Submarine Flows.44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada,2006.
58. Yalcin L, Ilgaz M, Erdem B. Hydrodynamic analysis of DARPA Suboff model. International Conference on Subsea Technologies, St.Petersburg, Russia,2007.
59. Toxopeus S. Viscous-flow calculations for bare hull DARPA SUBOFF submarine at incidence. International Shipbuilding Progress,2008,55(3):227-251
60. Toxopeus S, Vaz G. Calculation of Current or Manoeuvring Forces using a Viscous-Flow Solver. Proceedings of OMAE2009, Honolulu, Hawaii, USA, June,2009,
61. Jimenez J M, Hultmark M, Smits A. The intermediate wake of a body of revolution at high Reynolds numbers. J Fluid Mech,2010,659(1):516-539
62. Jimenez J M, Reynolds R T, Smits A J. The effects of fins on the intermediate wake of a submarine model. Journal of Fluids Engineering,2010,132:031102
63. Jimenez J M, Smits A J. Tip and Junction Vortices Generated by the Sail of a Yawed Submarine Model at Low Reynolds Numbers. Journal of Fluids Engineering,2011,133: 034501
64. Vaz G, Toxopeus S, Holmes S. Calculation of manoeuvring forces on submarines using two viscous-flow solvers. Proceedings of the ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering, Shanghai,2010. ASME.
65. Phillips A B, Turnock S R, Furlong M. Influence of turbulence closure models on the vortical flow field around a submarine body undergoing steady drift. J Mar Sci Technol,2010. 15:201-217
66. Gross A, Kremheller A, Fasel H F. Simulation of Flow over Suboff Bare Hull Model.49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, Florida,2011.
67.张楠,沈泓萃,姚惠之.潜艇阻力与流场的数值模拟与验证及艇型的数值优化研究.船舶力学,2005,9(1-13)
68.张楠,沈泓萃,姚惠之.用雷诺应力模型预报不同雷诺数下的潜艇绕流.船舶力学,2009,13(5)：688-696
69.张楠,沈泓萃,姚惠之,等.水下航行体壁面脉动压力的大涡模拟研究.水动力学研究与进展,2010,25(1)：106-112
70.王博,姚惠之,张楠.指挥台围壳对潜艇尾流影响的计算研究.船舶力学,2009,13(2)：196-202
71.操盛文,吴方良.尺度效应对全附体潜艇阻力数值计算结果的影响.中国舰船研究,2009,4(1)：33-42
72.孙睿智,吴方良,许建.基于雷诺应力方程模型的全附体潜艇尾部伴流场三维粘性数值计算.船海工程,2008,37(5)：1-5
73.吴方良,吴晓光,马运义,等.基于雷诺应力方程模型的全附体潜艇尾部伴流场三维粘性数值计算.中国舰船研究,2007,2(6)：4-8
74.吴方良,吴晓光,马运义,等.潜艇指挥台围壳对阻力和伴流场影响数值研究.海洋工程,2009,27(3)：91-99
75.邱辽原,石仲堃,周凌,等.回转体三维绕流场数值计算.中国造船,2006,47(4)：1-7
76.黄振宇,缪国平.大涡模拟在水下航行体周围黏性流场计算中的初步应用.水动力学研究与进展,2006,21(2)：190-197
77. Gailitis A, Lielausis O. On a possibility to reduce the hydrodynamic resistance of a plate in an electrolyte. Applied Magnetohydrodynamics,1961,12:143-146
78. Henoch C, Stace J. Experimental investigation of a salt water turbulent boundary layer modified by an applied streamwise magnetohydrodynamic body force. Phys Fluids,1995,7: 1371
79. Nosenchuck D M, Brown G L. Discrete spatial control of wall shear stress in a turbulent boundary layer. Near-wall turbulent flows,1993:689-698
80. Nosenchuck D M, Brown G L. Electromagnetic device and method for boundary layer control. Google Patents.1994.
81. Nosenchuck D, Brown G, Culver H, et al. Spatial and temporal characteristics of boundary layers controlled with the Lorentz force.1995.
82. Nosenchuck D M, Brown G L. Multiple electromagnetic tiles for boundary layer control. 1995-.
83. Nosenchuck D. Boundary layer control using the Lorentz force.1996.
84. Weier T, Gerbeth G, Mutschke G, et al. Experiments on cylinder wake stabilization in an electrolyte solution by means of electromagnetic forces localized on the cylinder surface. Exp Therm Fluid Sci,1998,16(1):84-91
85. Weier T, Fey U, Gerbeth G, et al. Boundary layer control by means of electromagnetic forces. ERCOFTAC bulletin,2000,44:36-40
86. Weier T, Gerbeth G, Mutschke G, et al. Control of flow separation using electromagnetic forces. Flow, Turbulence and Combustion,2003,71(1):5-17
87. Weier T, Gerbeth G, Mutschke G, et al. Separation control by stationary and time periodic Lorentz forces. SFB-Preprint SFB609-03-2004, Sonderforschungsbereich,2004,609
88. Weier T, Huller J, Gerbeth G, et al. Lorentz force influence on momentum and mass transfer in natural convection copper electrolysis. Chemical Engineering Science,2005,60(1): 293-298
89. Weier T. Control of separated flows by time periodic Lorentz forces. European Journal of Mechanics - B/Fluids,2004,23(6):835-849
90. Weier T, Cierpka C, Gerbeth G. Coherent structure eduction from PIV data of an electromagnetically forced separated flow. J Fluid Struct,2008,24(8):1339-1348
91. Weier T, Fey U, Gerbeth G, et al. Control of flow separation from a Hydrofoil using Lorentz Forces. Division of fluid dynamics meeting, New Orleans, LA,1999. American physical society.
92. Weier T, Fey U, Gerbeth G, et al. Boundary layer control by means of wall parallel Lorentz forces. Magnetohydrodynamics,2001,37(1/2):177-186
93. Mutschke G, Gerbeth G, Albrecht T, et al. Separation control at hydrofoils using Lorentz forces. European Journal of Mechanics-B/Fluids,2006,25(2):137-152
94. Shatrov V, Mutschke G, Gerbeth G. Three-dimensional linear stability analysis of lid-driven magnetohydrodynamic cavity flow. Phys Fluids,2003,15(8):2141
95. Shatrov V, Gerbeth G. Electromagnetic flow control leading to a strong drag reduction of a sphere. Fluid Dyn Res,2005,36(3):153-173
96. Shatrov V, Gerbeth G. Magnetohydrodynamic drag reduction and its efficiency. Phys Fluids,2007,19(3):035109
97. Shatrov V, Gerbeth G. Marginal turbulent magnetohydrodynamic flow in a square duct. Phys Fluids,2010,22(8):084101
98. Kim S J, Lee C M. Investigation of the flow around a circular cylinder under the influence of an electromagnetic force. Experiments in Fluids,2000,28(3):252-260
99. Kim S J, Lee C M. Control of flows around a circular cylinder: suppression of oscillatory lift force. Fluid Dyn Res,2001,29(1):47-63
100. Berger T W, Kim J, Lee C, et al. Turbulent boundary layer control utilizing the Lorentz force. Phys Fluids,2000,12:631
101. Rossi L, Thibault J P. Investigation of wall normal electromagnetic actuator for seawater flow control. J Turbul,2002,3
102. Rossi L, Vassilicos J C, Hardalupas Y. Electromagnetically controlled multi-scale flows. J Fluid Mech,2006,558:207-242
103. Thibault J P, Rossi L. Electromagnetic flow control:characteristic numbers and flow regimes of a wall-normal actuator. Journal of Physics D:Applied Physics,2003,36: 2559-2568
104. Park J, Henoch C, Mccamley M, et al. Lorentz force control of turbulent channel flow. AIAA Paper,2003,4157
105. Breuer K S, Park J, Henoch C. Actuation and control of a turbulent channel flow using Lorentz forces. Phys Fluids,2004,16(4):897
106. Breuer K. Lorentz Force Control of Turbulence. DTIC Document,2005.
107. Breuer K. Active Control of Turbulent Boundary Layers for Drag and Noise Reduction in Naval Applications. DTIC Document,2005.
108. Crawford C H, Karniadakis G E. Reynolds stress analysis of EMHD-controlled wall turbulence. Part I. Streamwise forcing. Phys Fluids,1997,9:788
109. Donovan J F, Kral L D, Cary A W. Characterization of a Lorentz force actuator. AIAA, 1997,1997-1918
110. O'sullivan P L, Biringen S. Direct numerical simulations of low Reynolds number turbulent channel flow with EMHD control. Phys Fluids,1998,10:1169
111. O'sullivan P L, Biringen S. Numerical experiments on feedback EMHD control of large scale coherent structures in channel turbulence. Acta mechanica,2001,152(1):9-17
112. Posdziech O, Grundmann R. Electromagnetic control of seawater flow around circular cylinders. European Journal of Mechanics-B/Fluids,2001,20(2):255-274
113. Du Y. Suppressing Wall Turbulence by Means of a Transverse Traveling Wave. Science, 2000,288(5469):1230-1234
114. Du Y, Symeonidis V, Karniadakis G E. Drag reduction in wall-bounded turbulence via a transverse travelling wave. J Fluid Mech,2002,457
115. Spong E, Reizes J, Leonardi E. Efficiency improvements of electromagnetic flow control. International Journal of Heat and Fluid Flow,2005,26(4):635-655
116. Subramanian N, Kral L D. Investigation of an Isolated Lorentz Force Actuator in a Turbulent Flow. AIAA 2000-2560,2000,
117. Pang J, Choi K-S. Turbulent drag reduction by Lorentz force oscillation. Phys Fluids, 2004,16(5):L35
118. Pang J, Choi K S, Aessopos A, et al. Control of near-wall turbulence for drag reduction by Spanwise oscillating Lorentz force.2004.
119. Dattarajan S, Johari H. Boundary layer separation control by Lorentz force actuators. 36th AIAA Fluid Dynamics Conference and Exhibit,2006.
120. Dattarajan S, Johari H. Control of a separating boundary layer with Lorentz force actuators. Phys Fluids,2008,20(4):045107
121.蒋小勤,刘巨斌,魏中磊.电磁力对湍流边界层相干结构的影响.水动力学研究与进展,2005,20(4)：458-462
122.罗世东,许春晓,崔桂香.圆管湍流减阻电磁力控制的直接数值模拟.力学学报,2007,39(3)：311-319
123.周本谋,范宝春,陈志华,等.流体边界层上电磁力的控制效应研究.力学学报,2004,36(4)：472-478
124.周本谋,范宝春,陈志华,等.电磁体积力作用下的圆柱绕流实验研究.工程力学,2006,23(4)：172-176
125. Popinet S. Gerris:a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J Comput Phys,2003,190(2):572-600
126. Popinet S. An accurate adaptive solver for surface-tension-driven interfacial flows. J Comput Phys,2009,228(16):5838-5866
127. Popinet S, Smith M, Stevens C. Experimental and numerical study of the turbulence characteristics of airflow around a research vessel. Journal of Atmospheric and Oceanic Technology,2004,21(10):1575-1589
128. Popinet S, Rickard G. A tree-based solver for adaptive ocean modelling. Ocean Modelling,2007,16(3-4):224-249
129. Rickard G, O'callaghan J, Popinet S. Numerical simulations of internal solitary waves interacting with uniform slopes using an adaptive model. Ocean Modelling,2009,30(1): 16-28
130. Fuster D, Agbaglah G, Josserand C, et al. Numerical simulation of droplets, bubbles and waves:state of the art. Fluid Dyn Res,2009,41:065001
131. Fuster D, Bague A, Boeck T, et al. Simulation of primary atomization with an octree adaptive mesh refinement and VOF method. Int J Multiphas Flow,2009,35(6):550-565
132. Bague A, Fuster D, Popinet S, et al. Instability growth rate of two-phase mixing layers from a linear eigenvalue problem and an initial-value problem. Phys Fluids,2010,22:092104
133. Popinet S. Quadtree-adaptive tsunami modelling. Ocean Dynamics,2011:1-25
134. Agbaglah G, Delaux S, Fuster D, et al. Parallel simulation of multiphase flows using octree adaptivity and the volume-of-fluid method. Comptes Rendus Mecanique,2011,
135. Sun X. Closed-loop control of vortex shedding by means of Lorentz force. PhD dissertation,2003, UMI No.3118445
136. Aiaa. Guide for the verification and validation of computational fluid dynamics simulations. AIAA 1998, G-077-1998
137. Kim J, Kim D, Choi H. An immersed-boundary finite-volume method for simulations of flow in complex geometries. Journal of Computational Physics,2001,171(1):132-150
138. Zhang J, Dalton C. A three-dimensional simulation of a steady approach flow past a circular cylinder at low Reynolds number. International journal for numerical methods in fluids,1998,26(9):1003-1022
139. Mittal R. A Fourier-Chebyshev spectral collocation method for simulating flow past spheres and spheroids. International journal for numerical methods in fluids,1999,30(7): 921-937
140. Groves N C, Huang T T, Chang M S. Geometric characteristics of DARPA SUBOFF models. David Taylor Research Center, Ship Hydromechanics Dept Report DTRC/SHD-1298-01,1989,
141. Hunt J, Hussain F. A note on velocity, vorticity and helicity of inviscid fluid elements. J Fluid Mech,1991,229:569-587
142. Jeong J, Hussain F. On the identification of a vortex. J Fluid Mech,1995,285(1):69-94
143. Verma A, Mittal S. A new unstable mode in the wake of a circular cylinder. Phys Fluids, 2011,23(121701)
144. Blackburn H M, Marques F, Lopez J M. Symmetry breaking of two-dimensional time-periodic wakes. J Fluid Mech,2005,522:395-411
145. Zhang H Q, Fey U, Noack B R, et al. On the transition of the cylinder wake. Phys Fluids, 1995,7:779
146.熊俊.圆柱尾迹三维转捩特性研究.北京,清华大学,2003.
147. Fadlun E, Verzicco R, Orlandi P, et al. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. Journal of Computational Physics, 2000,161(1):35-60
148. Zhang N, Zheng Z. An improved direct-forcing immersed-boundary method for finite difference applications. Journal of Computational Physics,2007,221(1):250-268
149. Blanco A, Magnaudet J. The structure of the axisymmetric high-Reynolds number flow around an ellipsoidal bubble of fixed shape. Phys Fluids,1995,7:1265
150. Masliyah J H, Epstein N. Numerical study of steady flow past spheroids. J Fluid Mech, 1970,44(3):493-512
151. Constantinescu G S, Squires K D, Aeronautics A Ⅰ O, et al. LES and DES investigations of turbulent flow over a sphere. AIAA,2000,2000-0540
152. Sakamoto H, Haniu H. A study on vortex shedding from spheres in a uniform flow. ASME, Transactions, Journal of Fluids Engineering,1990,112:386-392
153. Brown P P, Lawler D F. Sphere drag and settling velocity revisited. Journal of Environmental Engineering,2003,129:222-231
2. Cattafesta L N, Sheplak M. Actuators for Active Flow Control. Annu Rev Fluid Mech,2011, 43:247-272
3. Zhou Y, Bai H. Recent advances in active control of turbulent boundary layers. Science China Physics, Mechanics and Astronomy,2011,54(7):1289-1295
4. Zdravkovich M. Flow Around Circular Cylinders, vol.1. Fundamentals. J Fluid Mech, 1997,350:377-378
5. Williamson C H K. Vortex dynamics in the cylinder wake. Annu Rev Fluid Mech,1996,28: 477-539
6. Williamson C H K. Three-dimensional wake transition. J Fluid Mech,1996,328:345-407
7. Roshko A. On the drag and shedding frequency of two-dimensional bluff bodies. DTIC Document,1954.
8. Taneda S. Downstream development of the wake behind cylinders. Journal of the Physics Society of Japan,1959,14:843-848
9. Williamson C H K. Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. J Fluid Mech,1989,206:579-627
10. Eisenlohr H, Eckelmann H. Vortex splitting and its consequences in the vortex street wake of cylinders at low Reynolds number. Physics of Fluids A:Fluid Dynamics,1989,1:189
11. Barkley D, Henderson R D. Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J Fluid Mech,1996,322:215-241
12. Blackburn H, Lopez J. On three-dimensional quasiperiodic Floquet instabilities of two-dimensional bluff body wakes. Phys Fluids,2003,15:L57
13. Rajani B N, Kandasamy A, Majumdar S. Numerical simulation of laminar flow past a circular cylinder. Applied Mathematical Modelling,2009,33:1228-1247
14. Mittal S, Kottaram J J, Kumar B. Onset of shear layer instability in flow past a cylinder. Phys Fluids,2008,20(054102)
15. Behara S, Mittal S. Wake transition in flow past a circular cylinder. Phys Fluids,2010, 22(114104)
16. Behara S, Mittal S. Flow past a circular cylinder at low Reynolds number:Oblique vortex shedding. Phys Fluids,2010,22:054102
17. Labbe D, Wilson P. A numerical investigation of the effects of the spanwise length on the 3-D wake of a circular cylinder. J Fluid Struct,2007,23(8):1168-1188
18. Taneda S. Experimental investigation of the wake behind a sphere at low Reynolds numbers. J Phys Soc Japan,1956,11(10):1104-1108
19. Magarvey R, Bishop R L. Transition ranges for three-dimensional wakes. Canadian Journal of Physics,1961,39:1418
20. Sakamoto H, Haniu H. The formation mechanism and shedding frequency of vortices from a sphere in uniform shear flow. J Fluid Mech,1995,287:151-172
21. Fornberg B. Steady viscous flow past a sphere at high Reynolds numbers. J Fluid Mech, 1988,190:471-489
22. Kurose R, Komori S. Drag and lift forces on a rotating sphere in a linear shear flow. J Fluid Mech,1999,384(4):183-206
23. Hanazaki H. A numerical study of three-dimensional stratified flow past a sphere. J Fluid Mech,1988,192(1):393-419
24. Tomboulides A G, Orszag S A. Numerical investigation of transitional and weak turbulent flow past a sphere. J Fluid Mech,2000.416(1):45-73
25. Johnson T, Patel V. Flow past a sphere up to a Reynolds number of 300. J Fluid Mech, 1999,378(1):19-70
26. Gushchin V, Matyushin R. Vortex formation mechanisms in the wake behind a sphere for 200< Re< 380. Fluid Dynamics,2006,41(5):795-809
27. Mittal R, Wilson J, Najjar F. Symmetry properties of the transitional sphere wake. AIAA journal,2002,40(3):579-582
28. Wu J, Faeth G. Sphere wakes in still surroundings at intermediate Reynolds numbers. AIAA journal,1993,31(8):1448-1455
29. Lee S. A numerical study of the unsteady wake behind a sphere in a uniform flow at moderate Reynolds numbers. Computers & Fluids,2000,29(6):639-667
30. Kim D, Choi H. Laminar flow past a hemisphere. Phys Fluids,2003,15(8):2457
31. Kim D, Choi H, Choi H. Characteristics of laminar flow past a sphere in uniform shear. Phys Fluids,2005,17(10):103602
32. Ploumhans P, Winckelmans G S, Salmon J K, et al. Vortex Methods for Direct Numerical Simulation of Three-Dimensional Bluff Body Flows:Application to the Sphere at Re=300, 500, and 1000. Journal of Computational Physics,2002,178(2):427-463
33. Gumowski K, Miedzik J. Transition to a time-dependent state of fluid flow in the wake of a sphere. Physical Review E,2008,77(5)
34. Pier B. Local and global instabilities in the wake of a sphere. J Fluid Mech,2008,603
35. Giacobello M, Ooi A, Balachandar S. Wake structure of a transversely rotating sphere at moderate Reynolds numbers. J Fluid Mech,2009,621:103
36. Stewart B E, Thompson M C, Leweke T, et al. Numerical and experimental studies of the rolling sphere wake. J Fluid Mech,2010,643:137
37. Stewart B E, Leweke T, Hourigan K, et al. Wake formation behind a rolling sphere. Phys Fluids,2008,20(7):071704
38. Ou K, Castonguay P, Jameson A. Computational Sports Aerodynamics of a Moving Sphere:Simulating a Ping Pong Ball in Free Flight.2011,
39.邹建锋,任安禄,邓见.圆球绕流场的尾涡分析和升阻力研究.空气动力学学报,2004,22(3)：303-308
40. Jeon S, Choi J I N, Jeon W-P, et al. Active control of flow over a sphere for drag reduction at a subcritical Reynolds number. J Fluid Mech,2004,517:113-129
41. Choi J, Jeon W P, Choi H. Mechanism of drag reduction by dimples on a sphere. Phys Fluids,2006,18:041702
42. Jeon S, Choi H. Suboptimal feedback control of flow over a sphere. International Journal of Heat and Fluid Flow,2010,31(2):208-216
43. Bluemink J J, Lohse D, Prosperetti A, et al. A sphere in a uniformly rotating or shearing flow. J Fluid Mech,2008,600
44. Niazmand H. Surface effects on transient three-dimensional flows around rotating spheres at moderate Reynolds numbers. Computers & Fluids,2003,32(10):1405-1433
45. Kim D, Choi H. Laminar flow past a sphere rotating in the stream wise direction. J Fluid Mech,2002,461:365-386
46. Kim D. Laminar flow past a sphere rotating in the transverse direction. Journal of Mechanical Science and Technology,2009,23(2):578-589
47. Garrett S J, Peake N. The stability and transition of the boundary layer on a rotating sphere. J Fluid Mech,2002,456
48. Provansal M. From the double vortex street behind a cylinder to the wake of a sphere. European Journal of Mechanics-B/Fluids,2004,23(1):65-80
49. Sheard G J. Thompson M C. Hourigan K. From spheres to circular cylinders: non-axisymmetric transitions in the flow past rings. J Fluid Mech,2004,506:45-78
50. Liu H L, Huang T T. Summary of DARPA SUBOFF experimental program data. DTIC Document,1998.
51. Alin N. Fureby C, Svennberg S, et al. Large Eddy Simulation of the Transient Flow Around A Submarine During A Maneuver.45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada,2007.
52. Yang C, Lohner R. Prediction of flows over an axisymmetric body with appendages. The 8th International Conference on Numerical Ship Hydrodynamics, Busan, Korea,2003.
53. Alin N, Fureby C, Svennberg U, et al.3D Unsteady Computations for Submarine-Like Bodies.43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada,2005. AIAA
54. Alin N, Bensow R, Fureby C, et al. Current Capabilities of DES and LES for Submarines at Straight Course. Journal of Ship Research,2010,54(3):184-196
55. Liefvendahl M, Fureby C, Persson T. LES and DES of high Reynolds Number Wall Bounded Flows.44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada,2006. AIAA.
56. Liefvendahl M, Alin N, Chapuis M, et al. Ship and propulsor hydrodynamics. V European Conference on Computational Fluid Dynamics, Lisbon, Portugal,2010. ECCOMAS CFD 2010.
57. Bridges D H, Cash A C, Freudenthal J L. Investigation of Scaling Effects in Submarine Flows.44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada,2006.
58. Yalcin L, Ilgaz M, Erdem B. Hydrodynamic analysis of DARPA Suboff model. International Conference on Subsea Technologies, St.Petersburg, Russia,2007.
59. Toxopeus S. Viscous-flow calculations for bare hull DARPA SUBOFF submarine at incidence. International Shipbuilding Progress,2008,55(3):227-251
60. Toxopeus S, Vaz G. Calculation of Current or Manoeuvring Forces using a Viscous-Flow Solver. Proceedings of OMAE2009, Honolulu, Hawaii, USA, June,2009,
61. Jimenez J M, Hultmark M, Smits A. The intermediate wake of a body of revolution at high Reynolds numbers. J Fluid Mech,2010,659(1):516-539
62. Jimenez J M, Reynolds R T, Smits A J. The effects of fins on the intermediate wake of a submarine model. Journal of Fluids Engineering,2010,132:031102
63. Jimenez J M, Smits A J. Tip and Junction Vortices Generated by the Sail of a Yawed Submarine Model at Low Reynolds Numbers. Journal of Fluids Engineering,2011,133: 034501
64. Vaz G, Toxopeus S, Holmes S. Calculation of manoeuvring forces on submarines using two viscous-flow solvers. Proceedings of the ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering, Shanghai,2010. ASME.
65. Phillips A B, Turnock S R, Furlong M. Influence of turbulence closure models on the vortical flow field around a submarine body undergoing steady drift. J Mar Sci Technol,2010. 15:201-217
66. Gross A, Kremheller A, Fasel H F. Simulation of Flow over Suboff Bare Hull Model.49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, Florida,2011.
67.张楠,沈泓萃,姚惠之.潜艇阻力与流场的数值模拟与验证及艇型的数值优化研究.船舶力学,2005,9(1-13)
68.张楠,沈泓萃,姚惠之.用雷诺应力模型预报不同雷诺数下的潜艇绕流.船舶力学,2009,13(5)：688-696
69.张楠,沈泓萃,姚惠之,等.水下航行体壁面脉动压力的大涡模拟研究.水动力学研究与进展,2010,25(1)：106-112
70.王博,姚惠之,张楠.指挥台围壳对潜艇尾流影响的计算研究.船舶力学,2009,13(2)：196-202
71.操盛文,吴方良.尺度效应对全附体潜艇阻力数值计算结果的影响.中国舰船研究,2009,4(1)：33-42
72.孙睿智,吴方良,许建.基于雷诺应力方程模型的全附体潜艇尾部伴流场三维粘性数值计算.船海工程,2008,37(5)：1-5
73.吴方良,吴晓光,马运义,等.基于雷诺应力方程模型的全附体潜艇尾部伴流场三维粘性数值计算.中国舰船研究,2007,2(6)：4-8
74.吴方良,吴晓光,马运义,等.潜艇指挥台围壳对阻力和伴流场影响数值研究.海洋工程,2009,27(3)：91-99
75.邱辽原,石仲堃,周凌,等.回转体三维绕流场数值计算.中国造船,2006,47(4)：1-7
76.黄振宇,缪国平.大涡模拟在水下航行体周围黏性流场计算中的初步应用.水动力学研究与进展,2006,21(2)：190-197
77. Gailitis A, Lielausis O. On a possibility to reduce the hydrodynamic resistance of a plate in an electrolyte. Applied Magnetohydrodynamics,1961,12:143-146
78. Henoch C, Stace J. Experimental investigation of a salt water turbulent boundary layer modified by an applied streamwise magnetohydrodynamic body force. Phys Fluids,1995,7: 1371
79. Nosenchuck D M, Brown G L. Discrete spatial control of wall shear stress in a turbulent boundary layer. Near-wall turbulent flows,1993:689-698
80. Nosenchuck D M, Brown G L. Electromagnetic device and method for boundary layer control. Google Patents.1994.
81. Nosenchuck D, Brown G, Culver H, et al. Spatial and temporal characteristics of boundary layers controlled with the Lorentz force.1995.
82. Nosenchuck D M, Brown G L. Multiple electromagnetic tiles for boundary layer control. 1995-.
83. Nosenchuck D. Boundary layer control using the Lorentz force.1996.
84. Weier T, Gerbeth G, Mutschke G, et al. Experiments on cylinder wake stabilization in an electrolyte solution by means of electromagnetic forces localized on the cylinder surface. Exp Therm Fluid Sci,1998,16(1):84-91
85. Weier T, Fey U, Gerbeth G, et al. Boundary layer control by means of electromagnetic forces. ERCOFTAC bulletin,2000,44:36-40
86. Weier T, Gerbeth G, Mutschke G, et al. Control of flow separation using electromagnetic forces. Flow, Turbulence and Combustion,2003,71(1):5-17
87. Weier T, Gerbeth G, Mutschke G, et al. Separation control by stationary and time periodic Lorentz forces. SFB-Preprint SFB609-03-2004, Sonderforschungsbereich,2004,609
88. Weier T, Huller J, Gerbeth G, et al. Lorentz force influence on momentum and mass transfer in natural convection copper electrolysis. Chemical Engineering Science,2005,60(1): 293-298
89. Weier T. Control of separated flows by time periodic Lorentz forces. European Journal of Mechanics - B/Fluids,2004,23(6):835-849
90. Weier T, Cierpka C, Gerbeth G. Coherent structure eduction from PIV data of an electromagnetically forced separated flow. J Fluid Struct,2008,24(8):1339-1348
91. Weier T, Fey U, Gerbeth G, et al. Control of flow separation from a Hydrofoil using Lorentz Forces. Division of fluid dynamics meeting, New Orleans, LA,1999. American physical society.
92. Weier T, Fey U, Gerbeth G, et al. Boundary layer control by means of wall parallel Lorentz forces. Magnetohydrodynamics,2001,37(1/2):177-186
93. Mutschke G, Gerbeth G, Albrecht T, et al. Separation control at hydrofoils using Lorentz forces. European Journal of Mechanics-B/Fluids,2006,25(2):137-152
94. Shatrov V, Mutschke G, Gerbeth G. Three-dimensional linear stability analysis of lid-driven magnetohydrodynamic cavity flow. Phys Fluids,2003,15(8):2141
95. Shatrov V, Gerbeth G. Electromagnetic flow control leading to a strong drag reduction of a sphere. Fluid Dyn Res,2005,36(3):153-173
96. Shatrov V, Gerbeth G. Magnetohydrodynamic drag reduction and its efficiency. Phys Fluids,2007,19(3):035109
97. Shatrov V, Gerbeth G. Marginal turbulent magnetohydrodynamic flow in a square duct. Phys Fluids,2010,22(8):084101
98. Kim S J, Lee C M. Investigation of the flow around a circular cylinder under the influence of an electromagnetic force. Experiments in Fluids,2000,28(3):252-260
99. Kim S J, Lee C M. Control of flows around a circular cylinder: suppression of oscillatory lift force. Fluid Dyn Res,2001,29(1):47-63
100. Berger T W, Kim J, Lee C, et al. Turbulent boundary layer control utilizing the Lorentz force. Phys Fluids,2000,12:631
101. Rossi L, Thibault J P. Investigation of wall normal electromagnetic actuator for seawater flow control. J Turbul,2002,3
102. Rossi L, Vassilicos J C, Hardalupas Y. Electromagnetically controlled multi-scale flows. J Fluid Mech,2006,558:207-242
103. Thibault J P, Rossi L. Electromagnetic flow control:characteristic numbers and flow regimes of a wall-normal actuator. Journal of Physics D:Applied Physics,2003,36: 2559-2568
104. Park J, Henoch C, Mccamley M, et al. Lorentz force control of turbulent channel flow. AIAA Paper,2003,4157
105. Breuer K S, Park J, Henoch C. Actuation and control of a turbulent channel flow using Lorentz forces. Phys Fluids,2004,16(4):897
106. Breuer K. Lorentz Force Control of Turbulence. DTIC Document,2005.
107. Breuer K. Active Control of Turbulent Boundary Layers for Drag and Noise Reduction in Naval Applications. DTIC Document,2005.
108. Crawford C H, Karniadakis G E. Reynolds stress analysis of EMHD-controlled wall turbulence. Part I. Streamwise forcing. Phys Fluids,1997,9:788
109. Donovan J F, Kral L D, Cary A W. Characterization of a Lorentz force actuator. AIAA, 1997,1997-1918
110. O'sullivan P L, Biringen S. Direct numerical simulations of low Reynolds number turbulent channel flow with EMHD control. Phys Fluids,1998,10:1169
111. O'sullivan P L, Biringen S. Numerical experiments on feedback EMHD control of large scale coherent structures in channel turbulence. Acta mechanica,2001,152(1):9-17
112. Posdziech O, Grundmann R. Electromagnetic control of seawater flow around circular cylinders. European Journal of Mechanics-B/Fluids,2001,20(2):255-274
113. Du Y. Suppressing Wall Turbulence by Means of a Transverse Traveling Wave. Science, 2000,288(5469):1230-1234
114. Du Y, Symeonidis V, Karniadakis G E. Drag reduction in wall-bounded turbulence via a transverse travelling wave. J Fluid Mech,2002,457
115. Spong E, Reizes J, Leonardi E. Efficiency improvements of electromagnetic flow control. International Journal of Heat and Fluid Flow,2005,26(4):635-655
116. Subramanian N, Kral L D. Investigation of an Isolated Lorentz Force Actuator in a Turbulent Flow. AIAA 2000-2560,2000,
117. Pang J, Choi K-S. Turbulent drag reduction by Lorentz force oscillation. Phys Fluids, 2004,16(5):L35
118. Pang J, Choi K S, Aessopos A, et al. Control of near-wall turbulence for drag reduction by Spanwise oscillating Lorentz force.2004.
119. Dattarajan S, Johari H. Boundary layer separation control by Lorentz force actuators. 36th AIAA Fluid Dynamics Conference and Exhibit,2006.
120. Dattarajan S, Johari H. Control of a separating boundary layer with Lorentz force actuators. Phys Fluids,2008,20(4):045107
121.蒋小勤,刘巨斌,魏中磊.电磁力对湍流边界层相干结构的影响.水动力学研究与进展,2005,20(4)：458-462
122.罗世东,许春晓,崔桂香.圆管湍流减阻电磁力控制的直接数值模拟.力学学报,2007,39(3)：311-319
123.周本谋,范宝春,陈志华,等.流体边界层上电磁力的控制效应研究.力学学报,2004,36(4)：472-478
124.周本谋,范宝春,陈志华,等.电磁体积力作用下的圆柱绕流实验研究.工程力学,2006,23(4)：172-176
125. Popinet S. Gerris:a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J Comput Phys,2003,190(2):572-600
126. Popinet S. An accurate adaptive solver for surface-tension-driven interfacial flows. J Comput Phys,2009,228(16):5838-5866
127. Popinet S, Smith M, Stevens C. Experimental and numerical study of the turbulence characteristics of airflow around a research vessel. Journal of Atmospheric and Oceanic Technology,2004,21(10):1575-1589
128. Popinet S, Rickard G. A tree-based solver for adaptive ocean modelling. Ocean Modelling,2007,16(3-4):224-249
129. Rickard G, O'callaghan J, Popinet S. Numerical simulations of internal solitary waves interacting with uniform slopes using an adaptive model. Ocean Modelling,2009,30(1): 16-28
130. Fuster D, Agbaglah G, Josserand C, et al. Numerical simulation of droplets, bubbles and waves:state of the art. Fluid Dyn Res,2009,41:065001
131. Fuster D, Bague A, Boeck T, et al. Simulation of primary atomization with an octree adaptive mesh refinement and VOF method. Int J Multiphas Flow,2009,35(6):550-565
132. Bague A, Fuster D, Popinet S, et al. Instability growth rate of two-phase mixing layers from a linear eigenvalue problem and an initial-value problem. Phys Fluids,2010,22:092104
133. Popinet S. Quadtree-adaptive tsunami modelling. Ocean Dynamics,2011:1-25
134. Agbaglah G, Delaux S, Fuster D, et al. Parallel simulation of multiphase flows using octree adaptivity and the volume-of-fluid method. Comptes Rendus Mecanique,2011,
135. Sun X. Closed-loop control of vortex shedding by means of Lorentz force. PhD dissertation,2003, UMI No.3118445
136. Aiaa. Guide for the verification and validation of computational fluid dynamics simulations. AIAA 1998, G-077-1998
137. Kim J, Kim D, Choi H. An immersed-boundary finite-volume method for simulations of flow in complex geometries. Journal of Computational Physics,2001,171(1):132-150
138. Zhang J, Dalton C. A three-dimensional simulation of a steady approach flow past a circular cylinder at low Reynolds number. International journal for numerical methods in fluids,1998,26(9):1003-1022
139. Mittal R. A Fourier-Chebyshev spectral collocation method for simulating flow past spheres and spheroids. International journal for numerical methods in fluids,1999,30(7): 921-937
140. Groves N C, Huang T T, Chang M S. Geometric characteristics of DARPA SUBOFF models. David Taylor Research Center, Ship Hydromechanics Dept Report DTRC/SHD-1298-01,1989,
141. Hunt J, Hussain F. A note on velocity, vorticity and helicity of inviscid fluid elements. J Fluid Mech,1991,229:569-587
142. Jeong J, Hussain F. On the identification of a vortex. J Fluid Mech,1995,285(1):69-94
143. Verma A, Mittal S. A new unstable mode in the wake of a circular cylinder. Phys Fluids, 2011,23(121701)
144. Blackburn H M, Marques F, Lopez J M. Symmetry breaking of two-dimensional time-periodic wakes. J Fluid Mech,2005,522:395-411
145. Zhang H Q, Fey U, Noack B R, et al. On the transition of the cylinder wake. Phys Fluids, 1995,7:779
146.熊俊.圆柱尾迹三维转捩特性研究.北京,清华大学,2003.
147. Fadlun E, Verzicco R, Orlandi P, et al. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. Journal of Computational Physics, 2000,161(1):35-60
148. Zhang N, Zheng Z. An improved direct-forcing immersed-boundary method for finite difference applications. Journal of Computational Physics,2007,221(1):250-268
149. Blanco A, Magnaudet J. The structure of the axisymmetric high-Reynolds number flow around an ellipsoidal bubble of fixed shape. Phys Fluids,1995,7:1265
150. Masliyah J H, Epstein N. Numerical study of steady flow past spheroids. J Fluid Mech, 1970,44(3):493-512
151. Constantinescu G S, Squires K D, Aeronautics A Ⅰ O, et al. LES and DES investigations of turbulent flow over a sphere. AIAA,2000,2000-0540
152. Sakamoto H, Haniu H. A study on vortex shedding from spheres in a uniform flow. ASME, Transactions, Journal of Fluids Engineering,1990,112:386-392
153. Brown P P, Lawler D F. Sphere drag and settling velocity revisited. Journal of Environmental Engineering,2003,129:222-231