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Pulsed actuation is one of the most fundamental control types to study regularity of flow structures in supersonic mixing layers, which helps to predict the aero-optical effects caused by the supersonic mixing layer where the different-sized vortices dominate the flow field. However, the knowledge about the evolution mechanism of vortices in the supersonic mixing layer which is controlled by the pulsed forcing is limited. Based on the large eddy simulation (LES), the visualized flow field of a supersonic mixing layer controlled by the pulsed forcing is presented and the unique growth mechanism of the vortices in such a case is revealed clearly. The method of position extraction of the vortex core in the supersonic mixing layer, which is a quantitative technique to obtain the instantaneous location of a vortex in flow field, is employed to calculate the dynamic characteristics (e.g., instantaneous convective speed and size) of the vortices quantitatively. The pulsed forcings of different frequencies are imposed on the same supersonic mixing layer respectively, and the instantaneous convective speed and size of the vortices for each pulse frequency considered in this study are then computed. By comparing the dynamic characteristics of the vortices between cases, the evolution mechanism of the vortices in the supersonic mixing layer controlled by the pulsed forcing is revealed.as follows. 1) Growth of the vortices in the supersonic mixing layer controlled by the pulsed forcing no longer depends on the pairing nor merging between adjacent vortices, which is just the growth mechanism of vortices in a free supersonic mixing layer. Actually, the size of a vortex in the controlled supersonic mixing layer is dominated by the imposed pulse frequency, so the size of each vortex in such a flow field is approximately identical. 2) The number of vortices in the controlled supersonic mixing layer is proportional to the pulse frequency, whereas the size of vortex is inversely proportional to the pulse frequency. That is, the higher the pulse frequency, the bigger the number of vortices in the controlled flow field is and the smaller the size of every vortex. 3) The average convective speed of vortices in the controlled supersonic mixing layer gradually decreases with pulse frequency increasing because the pulsed forcing essentially drags on the movement of vortices in flow field. Finally, an equation which describes the quantitative relationship between the dynamic characteristics of a vortex and the pulsed forcing frequency is derived, that is, the product of the average convective speed of vortices in the controlled supersonic mixing layer and the imposed pulse period is approximately equal to the mean diameter of vortices in the flow field.
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Keywords:
- vortex evolution /
- supersonic mixing layer /
- large eddy simulation /
- pulsed forcing
[1] Yin X L 2003 Principle of Aero-Optics (Beijing: China Astronautics Press) p2 (in Chinese) [殷兴良 2003 气动光学原理 (北京: 中国宇航出版社) 第2页]
[2] Shen Q, Yuan X J, Wang Q, Yang W B, Guan F M, Ji F 2012 Adv. Mech. 42 252 (in Chinese) [沈清, 袁湘江, 王强, 杨武兵, 关发明, 纪锋 2012 力学进展 42 252]
[3] Luo J S 2015 Acta Aeronaut. Astronaut. Sin. 36 357 (in Chinese) [罗纪生 2015 航空学报 36 357]
[4] Zhu Y Z, Yi S H, Kong X P, He Lin 2015 Acta Phys. Sin. 64 064701 (in Chinese) [朱杨柱, 易仕和, 孔小平, 何霖 2015 64 064701]
[5] Zhang D D, Tan J G, Lv L 2015 Acta Astronaut. 117 440
[6] Laizet S, Lardeau S, Lamballais E 2010 Phys. Fluids 22 015104
[7] Wang B, Wei W, Zhang Y L, Zhang H Q, Xue S Y 2015 Comput. Fluids 123 32
[8] Zhang Y L, Wang B, Zhang H Q, Xue S Y 2015 J. Propul. Power 31 156
[9] Chen Q, Wang B, Zhang H Q, Zhang Y L, Gao W 2016 Int. J. Hydrogen Energy 41 3171
[10] Jumper E J, Hugo R J 1995 AIAA J. 33 2151
[11] Catrakis H J, Aguirre R C 2004 AIAA J. 42 1973
[12] Dimotaksi P, Catrakis H, Fourguette D 2001 J. Fluid Mech. 433 105
[13] Chew L, Christiansen W 1993 AIAA J. 31 2290
[14] Gan C J, Li L, Ma H D, Xiong H L 2014 Acta Phys. Sin. 63 054703 (in Chinese) [甘才俊, 李烺, 马汉东, 熊红亮 2014 63 054703]
[15] Gan C J, Li L, Ma H D, Xiong H L 2013 Acta Phys. Sin. 62 184701 (in Chinese) [甘才俊, 李烺, 马汉东, 熊红亮 2013 62 184701]
[16] Guo G M, Liu H, Zhang B 2016 Appl. Opt. 55 2708
[17] Jumper E J, Fitagerald E J 2001 Prog. Aerosp. Sci. 37 299
[18] Hugo R J, Jumper E J 2000 Appl. Opt. 39 4392
[19] Visbal M R, Rizzeta D P 2008 AIAA Paper 2008-1074
[20] Rennie R M, Siegenthaler J P, Jumper E J 2006 AIAA Paper 2006-561
[21] Rennie R M, Duffin D A, Jumper E J 2007 AIAA Paper 2007-4007
[22] Freeman A P, Catrakis H J 2009 AIAA J. 47 2582
[23] Rennie R M, Duffin D A, Jumper E J 2008 AIAA J. 46 2787
[24] Guo G M, Liu H, Zhang B, Zhang Z Y, Zhang Q B 2016 Acta Phys. Sin. 65 074702 (in Chinese) [郭广明, 刘洪, 张斌, 张忠阳, 张庆兵 2016 65 074702]
[25] Guo G M, Liu H, Zhang B 2016 J. Astronaut. Aeronaut. Aviat. 48 57
[26] Papamoschou D, Roshko A l988 J. Fluid Mech. 197 1
[27] Aguirre R C, Catrakis H J 2004 AIAA J. 42 10
[28] Papamoschou D 1991 AIAA J. 29 5
[29] Kourta A, Sauvage R 2002 Phys. Fluids 14 3790
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[1] Yin X L 2003 Principle of Aero-Optics (Beijing: China Astronautics Press) p2 (in Chinese) [殷兴良 2003 气动光学原理 (北京: 中国宇航出版社) 第2页]
[2] Shen Q, Yuan X J, Wang Q, Yang W B, Guan F M, Ji F 2012 Adv. Mech. 42 252 (in Chinese) [沈清, 袁湘江, 王强, 杨武兵, 关发明, 纪锋 2012 力学进展 42 252]
[3] Luo J S 2015 Acta Aeronaut. Astronaut. Sin. 36 357 (in Chinese) [罗纪生 2015 航空学报 36 357]
[4] Zhu Y Z, Yi S H, Kong X P, He Lin 2015 Acta Phys. Sin. 64 064701 (in Chinese) [朱杨柱, 易仕和, 孔小平, 何霖 2015 64 064701]
[5] Zhang D D, Tan J G, Lv L 2015 Acta Astronaut. 117 440
[6] Laizet S, Lardeau S, Lamballais E 2010 Phys. Fluids 22 015104
[7] Wang B, Wei W, Zhang Y L, Zhang H Q, Xue S Y 2015 Comput. Fluids 123 32
[8] Zhang Y L, Wang B, Zhang H Q, Xue S Y 2015 J. Propul. Power 31 156
[9] Chen Q, Wang B, Zhang H Q, Zhang Y L, Gao W 2016 Int. J. Hydrogen Energy 41 3171
[10] Jumper E J, Hugo R J 1995 AIAA J. 33 2151
[11] Catrakis H J, Aguirre R C 2004 AIAA J. 42 1973
[12] Dimotaksi P, Catrakis H, Fourguette D 2001 J. Fluid Mech. 433 105
[13] Chew L, Christiansen W 1993 AIAA J. 31 2290
[14] Gan C J, Li L, Ma H D, Xiong H L 2014 Acta Phys. Sin. 63 054703 (in Chinese) [甘才俊, 李烺, 马汉东, 熊红亮 2014 63 054703]
[15] Gan C J, Li L, Ma H D, Xiong H L 2013 Acta Phys. Sin. 62 184701 (in Chinese) [甘才俊, 李烺, 马汉东, 熊红亮 2013 62 184701]
[16] Guo G M, Liu H, Zhang B 2016 Appl. Opt. 55 2708
[17] Jumper E J, Fitagerald E J 2001 Prog. Aerosp. Sci. 37 299
[18] Hugo R J, Jumper E J 2000 Appl. Opt. 39 4392
[19] Visbal M R, Rizzeta D P 2008 AIAA Paper 2008-1074
[20] Rennie R M, Siegenthaler J P, Jumper E J 2006 AIAA Paper 2006-561
[21] Rennie R M, Duffin D A, Jumper E J 2007 AIAA Paper 2007-4007
[22] Freeman A P, Catrakis H J 2009 AIAA J. 47 2582
[23] Rennie R M, Duffin D A, Jumper E J 2008 AIAA J. 46 2787
[24] Guo G M, Liu H, Zhang B, Zhang Z Y, Zhang Q B 2016 Acta Phys. Sin. 65 074702 (in Chinese) [郭广明, 刘洪, 张斌, 张忠阳, 张庆兵 2016 65 074702]
[25] Guo G M, Liu H, Zhang B 2016 J. Astronaut. Aeronaut. Aviat. 48 57
[26] Papamoschou D, Roshko A l988 J. Fluid Mech. 197 1
[27] Aguirre R C, Catrakis H J 2004 AIAA J. 42 10
[28] Papamoschou D 1991 AIAA J. 29 5
[29] Kourta A, Sauvage R 2002 Phys. Fluids 14 3790
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