剪切来流下圆柱绕流的电磁控制
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摘要
本文对均匀来流和剪切来流条件下,圆柱绕流及其电磁控制进行了实验和数值研究。实验在转动水槽中进行,电磁激活板由电极条和磁条按一定顺序交错排列而成。通过吊杆将装有电磁激活板的圆柱插在槽内液体中。吊杆上的应变片用于测试圆柱的阻力,注入适当的染料用来显示流场。数值模拟时,基于指数极坐标中考虑场力的Navier-Stokes方程,采用ADI格式和FFT格式。结果表明,实验与计算所描述的流场具有相同的变化趋势。
研究表明,电磁场在圆柱表面附近产生的Lorentz力,可以改变流体边界层的结构,抑制流体分离,其控制效果与构成电磁激活板的电极条和磁条的宽度与强度(即Lorentz力的大小)有关。Lorentz力较小时,流动分离点后移,但不能完全抑制流体的分离。随着Lorentz力的增大,极板窄的电磁激活板首先可以完全抑制流体分离;当Lorentz力的进一步增大时,无论极板宽窄,都可以完全抑制流体分离。随着Lorentz力增大,阻力减小,阻力振动幅度也逐渐减小。
对于均匀来流,涡在圆柱两侧(上、下表面)的周期性脱落导致升力的周期性振荡,其均值为0;Lorentz力作用后,由于流动分离得到抑制,升力不再振荡,其值为0。但对于剪切来流,流场是不对称的,以上侧流速较快,下侧流速较慢的情形为例,此时,圆柱的尾迹向下偏斜,滞止点上移,升力也不再为0,指向下侧;Lorentz力作用后,圆柱的尾迹成一条直线向下侧偏移,升力不再振荡,但其值不为零,Lorentz力越大,升力的绝对值也越大。
In this paper, the experimental and numerical investigations on electro-magnetic control of cylinder wake have been performed in this paper. Experiments are conducted in a rotating annular tank filled with a low-conducting electrolyte, the electro-magnetic actuator is made of staggered magnetic and electro. A cylinder with an electro-magnetic actuator mounted on the surface is placed into the electrolyte. Force measurements have been carried out by strain gages attached to a fixed beam to which the cylinder is suspended and flow fields are visualized by dye markers. Based on the Navier-Stokes equations considering the electromagnetic body force, i.e. Lorentz force, in the exponential-polar coordinates, the numerical investigations are carried out by means of an Alternative-Direction Implicit algorithm and a Fast Fourier Transform algorithm. Experimental results have shown the same tendency with the numerical results.
The research show that with the uniform flow condition, the electromagnetic body forces, which caused by the electromagnetic field can change the cylinder boundary layer structure and suppress the boundary layer separation. However, the control effect of electromagnetic force is different with different value and different actuator width. When Lorentz force is small, the separation points on the cylinder surface will be moved rearward, but it cannot be suppressed completely. When the Lorentz force become large, the flow separation can be suppressed completely by the narrow actuator first. When the Lorentz force become further large, both the wide and narrow actuators can suppress the cylinder wake successfully.The drag and the values of drag vary will reduce when the Lorentz force become larger.
The flow field is symmetrical on the uniform flow condition. Before the application of Lorentz force, the values of lift vary periodically because the vortexes appear and shed periodically from the cylinder. Then, the average value of lift is 0. With the application of Lorentz force, the lift becomes steady because of the suppression of vortex shedding, and its value is 0. However, the shear flow is not symmetrical. If the flow velocity is large on the cylinder upside and small on the cylinder underside, the wake leans to the side of small velocity of flow. The shift of the front stagnation point to the high velocity side, the pressure is large on the high velocity side and small on the low velocity side. The average value of lift is not 0 any longer, and its direction points to the low velocity side. With the action of Lorentz force, the wake becomes a line leaning to the side of low velocity of flow and the lift becomes steady,but the value of lift is not 0. The absolute value of lift becomes larger with the increase of Lorentz force.
研究表明,电磁场在圆柱表面附近产生的Lorentz力,可以改变流体边界层的结构,抑制流体分离,其控制效果与构成电磁激活板的电极条和磁条的宽度与强度(即Lorentz力的大小)有关。Lorentz力较小时,流动分离点后移,但不能完全抑制流体的分离。随着Lorentz力的增大,极板窄的电磁激活板首先可以完全抑制流体分离;当Lorentz力的进一步增大时,无论极板宽窄,都可以完全抑制流体分离。随着Lorentz力增大,阻力减小,阻力振动幅度也逐渐减小。
对于均匀来流,涡在圆柱两侧(上、下表面)的周期性脱落导致升力的周期性振荡,其均值为0;Lorentz力作用后,由于流动分离得到抑制,升力不再振荡,其值为0。但对于剪切来流,流场是不对称的,以上侧流速较快,下侧流速较慢的情形为例,此时,圆柱的尾迹向下偏斜,滞止点上移,升力也不再为0,指向下侧;Lorentz力作用后,圆柱的尾迹成一条直线向下侧偏移,升力不再振荡,但其值不为零,Lorentz力越大,升力的绝对值也越大。
In this paper, the experimental and numerical investigations on electro-magnetic control of cylinder wake have been performed in this paper. Experiments are conducted in a rotating annular tank filled with a low-conducting electrolyte, the electro-magnetic actuator is made of staggered magnetic and electro. A cylinder with an electro-magnetic actuator mounted on the surface is placed into the electrolyte. Force measurements have been carried out by strain gages attached to a fixed beam to which the cylinder is suspended and flow fields are visualized by dye markers. Based on the Navier-Stokes equations considering the electromagnetic body force, i.e. Lorentz force, in the exponential-polar coordinates, the numerical investigations are carried out by means of an Alternative-Direction Implicit algorithm and a Fast Fourier Transform algorithm. Experimental results have shown the same tendency with the numerical results.
The research show that with the uniform flow condition, the electromagnetic body forces, which caused by the electromagnetic field can change the cylinder boundary layer structure and suppress the boundary layer separation. However, the control effect of electromagnetic force is different with different value and different actuator width. When Lorentz force is small, the separation points on the cylinder surface will be moved rearward, but it cannot be suppressed completely. When the Lorentz force become large, the flow separation can be suppressed completely by the narrow actuator first. When the Lorentz force become further large, both the wide and narrow actuators can suppress the cylinder wake successfully.The drag and the values of drag vary will reduce when the Lorentz force become larger.
The flow field is symmetrical on the uniform flow condition. Before the application of Lorentz force, the values of lift vary periodically because the vortexes appear and shed periodically from the cylinder. Then, the average value of lift is 0. With the application of Lorentz force, the lift becomes steady because of the suppression of vortex shedding, and its value is 0. However, the shear flow is not symmetrical. If the flow velocity is large on the cylinder upside and small on the cylinder underside, the wake leans to the side of small velocity of flow. The shift of the front stagnation point to the high velocity side, the pressure is large on the high velocity side and small on the low velocity side. The average value of lift is not 0 any longer, and its direction points to the low velocity side. With the action of Lorentz force, the wake becomes a line leaning to the side of low velocity of flow and the lift becomes steady,but the value of lift is not 0. The absolute value of lift becomes larger with the increase of Lorentz force.
引文
1.Gerrard J H.The mechanics of the formation region of vortices behind bluff bodies.J.Fluid Mech,1966,25,401.
2.Apelt C J,West G S.&Szewczyk A A.The effects of wake splitter plates on the flow past a circular cylinder in the range 10~4＜R＜5x10~4.J.Fluid Mech,1973,61,187.
3.Apelt C J&West G S.The effects of wake,splitter plates on bluff-body flow in the range 10~4＜R＜5x10~4,Part2.J.Fluid Mech,1975,71,145.
4.Unal M F&Rockwell D.On vortex formation from a cylinder.Part2.Control by splitter-plate interference.J.Fluid Mech,1988,190,513.
5.Cimbala J M and Garg S.Flow in the wake of a freely rotatable cylinder with splitter plate.AIAA J,1991,29,1001.
6.Kwon K&Choi H.Control of laminar vortex shedding behind a circular cylinder using splitter plates.Phys.Fluids,1996,8,479.
7.Strykowski P J and Sreenivasan K R.On the formation and suppression of vortex 'shedding' at low Reynolds numbers.J.Fluid Mech,1990,218,71-107
8.Tokumaru P T and Dimotakis P E.Rotary oscillatory control of a cylinder wake.J.Fluid Mech,1991,224,77-90
9.Roussopoulos K.Feedback control of vortex shedding at low Reynolds numbers.J.Fluid Mech,1993,248,267-296
10.Li Z J,Navon I M,Hussaini M Y and Le Dimet F X.Optimal control of cylinder wakes via suction and blowing[J].Computers and Fluids,2003,32:149-171
11.Lecordier L C,Browne L W B,Le Masson S,Dumouchel F and Paranthoen.Control of vortex shedding by thermal effect at low Reyolds numbers.Experimental Thermal and Fluid Science,2000,21:227-237
12.Wu C J,Xie Y Q& Wu J Z."Fluid roller bearing" effect and flow control,Acta.Mechanica Sinica,2003,19:476-484.
13.Wu C J,Wang L&Wu J Z.Suppression of the von Karman vortex street behind a circular cylinder by a traveling,wave generated by a flexible surface,J.Fluid Mech,2007,574:365-391.
14.李椿萱,彭少波,吴子牛.附属小圆柱对主圆柱绕流影响的数值模拟.北京航空航天大学报[J],2003,29(11):951-959
15.Strykowski P J,Sreenivasan K R.On the formation and suppressionof vortex 'shedding' at low Reynolds numbers[J].Fluid Mech,1990,218:71-107
16.Krothapalli A,Shih C,Lourenco L Metal.Drag reduction of acircular cylinder at high Reynolds numbers[R].AIAA,1997,97-0211
17.林长圣.近平板圆柱绕流的边界元分析.重庆建筑大学学报[J],2000,22(6):34-36
18.Davis A M J.O Neill ME.Separation in a slow finear shear flow past a cylinder and a plate[J].J.Fluid Mech,1997,81:551-584
19.Hun Shunfang.An investigation of drag reduction of underwater vehicle by heating Proc of ICECH.China,1988
20.黄为民,游晖,林向群.前驻点加热圆柱绕流场的实验研究[J].上海机械学院学报,1994,16(3):99-102
21.汪箭,陶正文,雷云龙,范维澄.热圆柱绕流的数值模拟.计算物理,1992,9(4):399-401
22.陆夕云,庄扎贤.均匀来流中旋转圆柱粘性绕流数值模拟[J].力学学报,1994,26(2):233-238.
23.贾志刚,吕志咏,邓小刚.均匀来流中旋转振荡圆柱绕流的数值研究[J].航空学报,1999,20(5):389-393
24.Tokumaku P T,Dimotakis P E.Rotary oscillation control of a cylinder wake[J].Fluid Mech,1991,224:77-90
25.赵宇,王薇,鄂学全.旋转振荡圆柱绕流中的频率耦合现象研究.水动力学研究与进展,2001,16(4):435-441
26.刘松,符松.纵向受迫振荡圆柱绕流问题的数值模拟.计算物理,2001,18(2):157-162
27.王志东,周林慧.均匀流中横向振荡圆柱绕流场的数值分析.水动力学研究与进展,2005,20(2):146-151
28.Gailitis A,Lielausis O.On a possibility to reduce the hydrodynamical resistance of a plate in an electrolyte[J].Applied Magnetohydrodynamics,1961,12:143-146
29.Henoch C,Stace J.Experimental investigation of a salt water turbulent boundary larger modified by an applied streamwise magnetohydrodynamic body force[J].Phys.Fluid,1995,7(6):1371-1382
30.Crawford C H,Karniadakis G E.Reynolds Stress Analysis of EMHD-Controlled Wall Turbulence[J].Phys.Fluid,1997,9(3):788-806
31.Weier T,Gerbeth G,Posdziedch O.Experiments on cylinder wake stabilization in an electrolyte solution by means of electromagnetic forces localized on the cylinder surface[J].Experimental Thermal and Fluid Science,1998,16:84-91
32.Oliver Posdziech,Roger Grundmann.Electromagnetic control of seawater flow around circular cylinder[J].Eur.J.Mech.B-Fluids,20(2001):255-274
33.Kim Seong-jae,Lee Choung-mook.Investigation of the flow around a circular cylinder under the influence of an electromagnetic force[J].Experiments in fluids,2000,28:252-260
34.Kim Seong-jae,Lee Choung-mook.Control of flows around a circular cylinder:suppression of oscillatory lift force.[J].Fluid Dynamics Research,29(2001):47-63
35.Rossi L, Thibault J R Electromagnetic forcing in turbulence and flow control analytical definitions of EM parameters and hydrodynamic characterizations of the flow[J].Physics of Fluids,2003,10(2):572-588 :
36.Masch F D and Moore W L.Drag forces in velocity gradient flow.ASCE J Hydraul Div, 1960,86,1-11.
37.Shaw T L and Starr M R.Shear flow past a circular cylinder.ASCE J Hydraul Div,1972,98,461-473.
38.Mukhopadhyay A, Venugopal P and Vanka S P.Oblique vortex shedding from a circular cylinder in linear shear flow.Computers&Fluids, 2002,1-24.
39.Bosch G, Rodi W.Simulation of vortex shedding past a square cylinder near a wall.Int.J.Heat Fluid Flow, 1996,17,267-275.
40.Bhattacharyya S, Maiti D K.Shear flow past a square cylinder near a wall.International Journal of Engineering Science, 2004,42,2119-2134.
41.Chew Y T, Luo S C, Cheng M.Numerical study of a linear shear flow past a rotating cylinder.Journal of Wind Engineering and Industrial Aerodynamics, 1997,66,107-125.
42.Kang S.Uniform-shear flow over a circular cylinder at low Reynolds numbers.Journal of Fluids and Structures 2006,22,541-555
43.Lei C, Cheng L, Kavanagh K.A finite difference solution of the shear flow over a circular cylinder, Ocean Engineering, 2000,27,271-290
2.Apelt C J,West G S.&Szewczyk A A.The effects of wake splitter plates on the flow past a circular cylinder in the range 10~4＜R＜5x10~4.J.Fluid Mech,1973,61,187.
3.Apelt C J&West G S.The effects of wake,splitter plates on bluff-body flow in the range 10~4＜R＜5x10~4,Part2.J.Fluid Mech,1975,71,145.
4.Unal M F&Rockwell D.On vortex formation from a cylinder.Part2.Control by splitter-plate interference.J.Fluid Mech,1988,190,513.
5.Cimbala J M and Garg S.Flow in the wake of a freely rotatable cylinder with splitter plate.AIAA J,1991,29,1001.
6.Kwon K&Choi H.Control of laminar vortex shedding behind a circular cylinder using splitter plates.Phys.Fluids,1996,8,479.
7.Strykowski P J and Sreenivasan K R.On the formation and suppression of vortex 'shedding' at low Reynolds numbers.J.Fluid Mech,1990,218,71-107
8.Tokumaru P T and Dimotakis P E.Rotary oscillatory control of a cylinder wake.J.Fluid Mech,1991,224,77-90
9.Roussopoulos K.Feedback control of vortex shedding at low Reynolds numbers.J.Fluid Mech,1993,248,267-296
10.Li Z J,Navon I M,Hussaini M Y and Le Dimet F X.Optimal control of cylinder wakes via suction and blowing[J].Computers and Fluids,2003,32:149-171
11.Lecordier L C,Browne L W B,Le Masson S,Dumouchel F and Paranthoen.Control of vortex shedding by thermal effect at low Reyolds numbers.Experimental Thermal and Fluid Science,2000,21:227-237
12.Wu C J,Xie Y Q& Wu J Z."Fluid roller bearing" effect and flow control,Acta.Mechanica Sinica,2003,19:476-484.
13.Wu C J,Wang L&Wu J Z.Suppression of the von Karman vortex street behind a circular cylinder by a traveling,wave generated by a flexible surface,J.Fluid Mech,2007,574:365-391.
14.李椿萱,彭少波,吴子牛.附属小圆柱对主圆柱绕流影响的数值模拟.北京航空航天大学报[J],2003,29(11):951-959
15.Strykowski P J,Sreenivasan K R.On the formation and suppressionof vortex 'shedding' at low Reynolds numbers[J].Fluid Mech,1990,218:71-107
16.Krothapalli A,Shih C,Lourenco L Metal.Drag reduction of acircular cylinder at high Reynolds numbers[R].AIAA,1997,97-0211
17.林长圣.近平板圆柱绕流的边界元分析.重庆建筑大学学报[J],2000,22(6):34-36
18.Davis A M J.O Neill ME.Separation in a slow finear shear flow past a cylinder and a plate[J].J.Fluid Mech,1997,81:551-584
19.Hun Shunfang.An investigation of drag reduction of underwater vehicle by heating Proc of ICECH.China,1988
20.黄为民,游晖,林向群.前驻点加热圆柱绕流场的实验研究[J].上海机械学院学报,1994,16(3):99-102
21.汪箭,陶正文,雷云龙,范维澄.热圆柱绕流的数值模拟.计算物理,1992,9(4):399-401
22.陆夕云,庄扎贤.均匀来流中旋转圆柱粘性绕流数值模拟[J].力学学报,1994,26(2):233-238.
23.贾志刚,吕志咏,邓小刚.均匀来流中旋转振荡圆柱绕流的数值研究[J].航空学报,1999,20(5):389-393
24.Tokumaku P T,Dimotakis P E.Rotary oscillation control of a cylinder wake[J].Fluid Mech,1991,224:77-90
25.赵宇,王薇,鄂学全.旋转振荡圆柱绕流中的频率耦合现象研究.水动力学研究与进展,2001,16(4):435-441
26.刘松,符松.纵向受迫振荡圆柱绕流问题的数值模拟.计算物理,2001,18(2):157-162
27.王志东,周林慧.均匀流中横向振荡圆柱绕流场的数值分析.水动力学研究与进展,2005,20(2):146-151
28.Gailitis A,Lielausis O.On a possibility to reduce the hydrodynamical resistance of a plate in an electrolyte[J].Applied Magnetohydrodynamics,1961,12:143-146
29.Henoch C,Stace J.Experimental investigation of a salt water turbulent boundary larger modified by an applied streamwise magnetohydrodynamic body force[J].Phys.Fluid,1995,7(6):1371-1382
30.Crawford C H,Karniadakis G E.Reynolds Stress Analysis of EMHD-Controlled Wall Turbulence[J].Phys.Fluid,1997,9(3):788-806
31.Weier T,Gerbeth G,Posdziedch O.Experiments on cylinder wake stabilization in an electrolyte solution by means of electromagnetic forces localized on the cylinder surface[J].Experimental Thermal and Fluid Science,1998,16:84-91
32.Oliver Posdziech,Roger Grundmann.Electromagnetic control of seawater flow around circular cylinder[J].Eur.J.Mech.B-Fluids,20(2001):255-274
33.Kim Seong-jae,Lee Choung-mook.Investigation of the flow around a circular cylinder under the influence of an electromagnetic force[J].Experiments in fluids,2000,28:252-260
34.Kim Seong-jae,Lee Choung-mook.Control of flows around a circular cylinder:suppression of oscillatory lift force.[J].Fluid Dynamics Research,29(2001):47-63
35.Rossi L, Thibault J R Electromagnetic forcing in turbulence and flow control analytical definitions of EM parameters and hydrodynamic characterizations of the flow[J].Physics of Fluids,2003,10(2):572-588 :
36.Masch F D and Moore W L.Drag forces in velocity gradient flow.ASCE J Hydraul Div, 1960,86,1-11.
37.Shaw T L and Starr M R.Shear flow past a circular cylinder.ASCE J Hydraul Div,1972,98,461-473.
38.Mukhopadhyay A, Venugopal P and Vanka S P.Oblique vortex shedding from a circular cylinder in linear shear flow.Computers&Fluids, 2002,1-24.
39.Bosch G, Rodi W.Simulation of vortex shedding past a square cylinder near a wall.Int.J.Heat Fluid Flow, 1996,17,267-275.
40.Bhattacharyya S, Maiti D K.Shear flow past a square cylinder near a wall.International Journal of Engineering Science, 2004,42,2119-2134.
41.Chew Y T, Luo S C, Cheng M.Numerical study of a linear shear flow past a rotating cylinder.Journal of Wind Engineering and Industrial Aerodynamics, 1997,66,107-125.
42.Kang S.Uniform-shear flow over a circular cylinder at low Reynolds numbers.Journal of Fluids and Structures 2006,22,541-555
43.Lei C, Cheng L, Kavanagh K.A finite difference solution of the shear flow over a circular cylinder, Ocean Engineering, 2000,27,271-290