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To investigate the stability and transition control mechanism of supersonic boundary layer, a coupled method of velocity/temperature control based on synthetic cold/hot jet is proposed. Based on the prior dual-synthetic jet actuator, a high performance synthetic cold/hot jet is achieved by adding a cooling/heating module. By placing the actuator under the flat-plate, periodic blow-suction is produced and low momentum jets are injected into the boundary layer to control the transition. Numerical simulations are conducted to study the propagation and evolvement of the unstable waves in the supersonic flat-plate boundary layer with Ma=4.5. Influences of wall blow-suction, synthetic jet temperature, perturbation frequency, and perturbation amplitude on control effect of the unstable wave are mainly studied. The flow field and control effect are analyzed using the temporal mode of linear stability theory. The results show that without jet control, the first and second mode perturbation wave coexist simultaneously with the second mode dominant in the two-dimensional wave. In the effect of the wall blow-suction, the second mode appears to be more unstable while the first mode is suppressed. Under the control of the coupled speed-temperature, the jet temperature has significant influences on the area of the unstable region and the growth rate of the perturbation mode. When the jet temperature is different from the inlet fluid temperature, the fluctuation of temperature accelerates the transition of laminar flow to turbulent flow, and the velocity profile becomes more full, which leads to a more stable flow field. The control effect of high frequency blow-suction disturbance on flow field are better than that of low frequency. When the control frequency is higher than 400 Hz, the imaginary part of the eigenvalue ω _i of the second mode disturbance wave decreases, and the disturbance component accelerates the correction between velocity profile and temperature profile of supersonic boundary layer, thus making a more stable second mode. When the disturbance amplitude decreases to 1% of the main flow speed, only the second mode is detected of low time growth rate, which results in a better control effect. However, as the disturbance amplitude further decreases, the first mode reemerges, and its wave number overlaps with that of the second mode at first, and then, separates from each other. The research results provide a new idea for supersonic boundary layer transition control from laminar flow to turbulent flow.
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Keywords:
- dual-synthetic cold/hot jet /
- boundary layer /
- transition control /
- linear stability theory
[1] Prandtl L 1904 Proceedings of the third International Mathematics Congress Heidelberg, August 3-6 1904 p484
[2] Zhou H, Su C H, Zhang Y M 2015 Transition Mechanism and Prediction of Supersonic/Hypersonic Boundary Layer (Beijng:Science Presss) p4 (in Chinese)[周恒, 苏彩虹, 张永明 2015 超声速/高超声速边界层的转捩机理及预测 (北京:科学出版社) 第4页]
[3] Kim K, Sung H J 2003 AIAA J. 41 484
[4] Kim K, Sung H J 2003 AIAA J. 557 423
[5] Hao G L, Jiang N 2015 J. Mech. Stren. 35 730 (in Chinese)[郝刚立, 姜楠 2015 机械强度 35 730]
[6] Hao G L 2008 M. S. Dissertion (Tianjin:Tianjin University) (in Chinese)[郝刚立 2008 硕士学位论文 (天津:天津大学)]
[7] Lysenko V I, Maslov A A 1984 J. Fluid Mech. 147 39
[8] Stetson K F, Thompson E R, Donaldson J C, Siler L G 1984 AIAA 1984-0006
[9] Stetson K F, Thompson E R, Donaldson J C, Siler L G 1985 AIAA 1985-0492
[10] Stetson K F, Thompson E R, Donaldson J C, Siler L G 1989 AIAA 1989-1895
[11] Zhao G F 2001 Appl. Mech. Rev. 33 519 (in Chinese)[赵耕夫 2001 力学学报 33 519]
[12] Wang S Z, Lei J M, Li C X 2014 Collection in 16th Computational Fluid Dynamics Symposium Xiamen, China February 26-, 2014 p1 (in Chinese)[王锁柱, 雷娟棉, 李椿萱 2014 第十六届全国计算流体力学会议 中国厦门, 2014年 2月26日–2月28日, p1]
[13] Lu C G, Shen L Y 2015 Acta Phys. Sin. 64 224702 (in Chinese)[陆昌根, 沈露予 2015 物理学报 64 224702]
[14] Lu C G, Shen L Y 2016 Acta Phys. Sin. 65 194701 (in Chinese)[陆昌根, 沈露予 2016 物理学报 65 194701]
[15] Shen L Y, Lu C G 2017 Acta Phys. Sin. 66 014703 (in Chinese)[沈露予, 陆昌根 2017 物理学报 66 014703]
[16] Luo Z B, Xia Z X, Liu B 2006 AIAA J. 44 2418
[17] Luo Z B, Xia Z X, Deng X, Wang L, Li Y J, Ma Y, Wang J W, Peng L, Jiang H, Yang S K, Yang R 2017 Acta Aerodyn. Sin. 35 252 (in Chinese)[罗振兵, 夏智勋, 邓雄, 王林, 李玉杰, 马瑶, 王俊伟, 彭磊, 蒋浩, 杨升科, 杨瑞 2017 空气动力学学报 35 252]
[18] Huang Z F, Cao W, Zhou H 2005 Sci. China:Ser. G 48 614
[19] Andrea S 2015 Ph. D. Dissertation (Southampton:University of Southampton)
[20] Mack L M 1975 AIAA J. 13 278
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[1] Prandtl L 1904 Proceedings of the third International Mathematics Congress Heidelberg, August 3-6 1904 p484
[2] Zhou H, Su C H, Zhang Y M 2015 Transition Mechanism and Prediction of Supersonic/Hypersonic Boundary Layer (Beijng:Science Presss) p4 (in Chinese)[周恒, 苏彩虹, 张永明 2015 超声速/高超声速边界层的转捩机理及预测 (北京:科学出版社) 第4页]
[3] Kim K, Sung H J 2003 AIAA J. 41 484
[4] Kim K, Sung H J 2003 AIAA J. 557 423
[5] Hao G L, Jiang N 2015 J. Mech. Stren. 35 730 (in Chinese)[郝刚立, 姜楠 2015 机械强度 35 730]
[6] Hao G L 2008 M. S. Dissertion (Tianjin:Tianjin University) (in Chinese)[郝刚立 2008 硕士学位论文 (天津:天津大学)]
[7] Lysenko V I, Maslov A A 1984 J. Fluid Mech. 147 39
[8] Stetson K F, Thompson E R, Donaldson J C, Siler L G 1984 AIAA 1984-0006
[9] Stetson K F, Thompson E R, Donaldson J C, Siler L G 1985 AIAA 1985-0492
[10] Stetson K F, Thompson E R, Donaldson J C, Siler L G 1989 AIAA 1989-1895
[11] Zhao G F 2001 Appl. Mech. Rev. 33 519 (in Chinese)[赵耕夫 2001 力学学报 33 519]
[12] Wang S Z, Lei J M, Li C X 2014 Collection in 16th Computational Fluid Dynamics Symposium Xiamen, China February 26-, 2014 p1 (in Chinese)[王锁柱, 雷娟棉, 李椿萱 2014 第十六届全国计算流体力学会议 中国厦门, 2014年 2月26日–2月28日, p1]
[13] Lu C G, Shen L Y 2015 Acta Phys. Sin. 64 224702 (in Chinese)[陆昌根, 沈露予 2015 物理学报 64 224702]
[14] Lu C G, Shen L Y 2016 Acta Phys. Sin. 65 194701 (in Chinese)[陆昌根, 沈露予 2016 物理学报 65 194701]
[15] Shen L Y, Lu C G 2017 Acta Phys. Sin. 66 014703 (in Chinese)[沈露予, 陆昌根 2017 物理学报 66 014703]
[16] Luo Z B, Xia Z X, Liu B 2006 AIAA J. 44 2418
[17] Luo Z B, Xia Z X, Deng X, Wang L, Li Y J, Ma Y, Wang J W, Peng L, Jiang H, Yang S K, Yang R 2017 Acta Aerodyn. Sin. 35 252 (in Chinese)[罗振兵, 夏智勋, 邓雄, 王林, 李玉杰, 马瑶, 王俊伟, 彭磊, 蒋浩, 杨升科, 杨瑞 2017 空气动力学学报 35 252]
[18] Huang Z F, Cao W, Zhou H 2005 Sci. China:Ser. G 48 614
[19] Andrea S 2015 Ph. D. Dissertation (Southampton:University of Southampton)
[20] Mack L M 1975 AIAA J. 13 278
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