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Most of previous studies focused on the boundary-layer receptivity to the convected disturbances in the free stream interacting with localized wall roughness. Whereas the research on the boundary-layer receptivity induced by localized blowing or localized suction is relatively few. In this paper, we investigate two-dimensional boundary-layer receptivity induced by localized blowing/suction within free-stream turbulence through using direct numerical simulation and fast Fourier transformation. High-order compact finite difference schemes in the y-direction, fast Fourier transformation in the x-direction, and a Runge-Kutta scheme in time domain are used to solve the Navier-Stokes equations. The numerical results show that Tollmien-Schlichting (T-S) wave packets are excited by the free-stream turbulence interacting with localized blowing in the two-dimensional boundary layer, which are superposed by a group of stable, neutral and unstable T-S waves. The dispersion relations, growth rates, amplitude distributions and phase distributions of the excited waves accord well with theoretical solutions of the linear stability theory, thus confirming the existence of the boundary-layer receptivity. And the frequencies of the instability waves are between the upper and lower branches of the neutral stability curves. According to the evolutions of the wave packets, the positions of peaks and valleys are tracked over time to calculate the propagation speed by taking the average. The propagation speeds of the wave packets are approximately one-third of the free-stream velocity, which are in accordance with Dietz's measurements. The propagation speeds of wave packets are also close to the phase speeds of the most unstable waves for the numerical results. The relations of the receptivity response to the forcing amplitude, the blowing intensity, and the blowing width are found to be linear, when the forcing amplitude and the blowing intensity are less than 1% free-steam velocity amplitude and 0.01, respectively. And the maximum amplitudes of the T-S waves can be excited while the blowing length is equal to the resonant wavelength /(TS-FS), where TS is the wave-number of the T-S wave, and FS is the wave-number of the forcing disturbance. These results are similar to those given by Dietz [Dietz A J 1999 J. Fluid Mech. 378 291]. Additionally, T-S waves with the same dispersion relations but opposite phases are generated by localized blowing and localized suction respectively, and the amplitudes of the T-S waves excited by localized blowing are nearly 15% greater than those by localized suction under the same condition. According to this theory, an optimal design of localized suction device is able to enhance or delay the laminar-turbulent transition for turbulent control.
[1] Li C B, Fu S 2000 Chin. Phys. 9 508
[2] Gong A L, Li R Q, Li C B 2002 Acta Phys. Sin. 51 1068 (in Chinese) [龚安龙, 李睿劬, 李存标 2002 51 1068]
[3] Chen L, Tang D B 2011 Acta Phys. Sin. 60 094702 (in Chinese) [陈林, 唐登斌 2011 60 094702]
[4] Hu H B, Du P, Huang S H, Wang Y 2013 Chin. Phys. B 22 074703
[5] Wang W, Guan X L, Jiang N 2014 Chin. Phys. B 23 104703
[6] Saric W S, Reed H L, Kerschen E J 2002 Annu. Rev. Fluid Mech. 34 291
[7] Kurz H B E, Kloker M J 2014 J. Fluid Mech. 755 62
[8] Ustinov M V 2013 Fluid Dynam. 48 621
[9] Ustinov M V 2014 Fluid Dynam. 49 468
[10] Morkovin M V 1969 On the Many Faces of Transition Viscous Drag Reduction (New York: Springer) pp1-31
[11] Goldstein M E 1983 J. Fluid Mech. 127 59
[12] Goldstein M E 1985 J. Fluid Mech. 154 509
[13] Ruban A I 1984 Fluid Dynam. 19 709
[14] Kerschen E J 1990 Appl. Mech. Rev. 43 152
[15] Zavol'Skii N A, Reutov V P, Rybushkina G V 1983 J. Appl. Mech. Tech. Phys. 24 355
[16] Duck P W, Ruban A I, Zhikharev C N 1996 J. Fluid Mech. 312 341
[17] Dietz A J 1996 AIAA P. 96 2083
[18] Dietz A J 1998 AIAA J. 36 1171
[19] Dietz A J 1999 J. Fluid Mech. 378 291
[20] Wu X S 2001 J. Fluid Mech. 431 91
[21] Wu X S 2002 J. Fluid Mech. 453 289
[22] Zhang Y, Zaki T, Sherwin S, Wu X 2011 6th AIAA Theortical Fluid Mechanics Conference Hawaii, USA, June 27-30, 2011 p3292
[23] Shen L Y, Lu C G, Wu W G, Xue S F 2015 Add. Appl. Math. Mech. 7 180
[24] Lu C G, Cao W D, Zhang Y M, Guo J T 2008 P. Nat. Sci. 18 873
[25] Zhang Y, Zhou H 2005 Appl. Math. Mech. 26 547
[26] Ricco P 2009 J. Fluid Mech. 638 267
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[1] Li C B, Fu S 2000 Chin. Phys. 9 508
[2] Gong A L, Li R Q, Li C B 2002 Acta Phys. Sin. 51 1068 (in Chinese) [龚安龙, 李睿劬, 李存标 2002 51 1068]
[3] Chen L, Tang D B 2011 Acta Phys. Sin. 60 094702 (in Chinese) [陈林, 唐登斌 2011 60 094702]
[4] Hu H B, Du P, Huang S H, Wang Y 2013 Chin. Phys. B 22 074703
[5] Wang W, Guan X L, Jiang N 2014 Chin. Phys. B 23 104703
[6] Saric W S, Reed H L, Kerschen E J 2002 Annu. Rev. Fluid Mech. 34 291
[7] Kurz H B E, Kloker M J 2014 J. Fluid Mech. 755 62
[8] Ustinov M V 2013 Fluid Dynam. 48 621
[9] Ustinov M V 2014 Fluid Dynam. 49 468
[10] Morkovin M V 1969 On the Many Faces of Transition Viscous Drag Reduction (New York: Springer) pp1-31
[11] Goldstein M E 1983 J. Fluid Mech. 127 59
[12] Goldstein M E 1985 J. Fluid Mech. 154 509
[13] Ruban A I 1984 Fluid Dynam. 19 709
[14] Kerschen E J 1990 Appl. Mech. Rev. 43 152
[15] Zavol'Skii N A, Reutov V P, Rybushkina G V 1983 J. Appl. Mech. Tech. Phys. 24 355
[16] Duck P W, Ruban A I, Zhikharev C N 1996 J. Fluid Mech. 312 341
[17] Dietz A J 1996 AIAA P. 96 2083
[18] Dietz A J 1998 AIAA J. 36 1171
[19] Dietz A J 1999 J. Fluid Mech. 378 291
[20] Wu X S 2001 J. Fluid Mech. 431 91
[21] Wu X S 2002 J. Fluid Mech. 453 289
[22] Zhang Y, Zaki T, Sherwin S, Wu X 2011 6th AIAA Theortical Fluid Mechanics Conference Hawaii, USA, June 27-30, 2011 p3292
[23] Shen L Y, Lu C G, Wu W G, Xue S F 2015 Add. Appl. Math. Mech. 7 180
[24] Lu C G, Cao W D, Zhang Y M, Guo J T 2008 P. Nat. Sci. 18 873
[25] Zhang Y, Zhou H 2005 Appl. Math. Mech. 26 547
[26] Ricco P 2009 J. Fluid Mech. 638 267
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