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Boundary-layer receptivity is the initial stage of the laminar-turbulent transition process, which plays a key role in the transition, especially for the case of three-dimensional boundary-layer flow. The research of the three-dimensional boundary-layer receptivity is theoretically significant for further understanding of the mechanisms of laminar-turbulent transition and turbulence formation. A numerical method is used to study the three-dimensional boundary-layer receptivity under the interaction of the free-stream turbulence and the three-dimensional localized wall roughness. Then whether a new cross-flow instability mode can be found in the three-dimensional boundary layer is studied. Subsequently, investigated are the conditions under which the steady or unsteady cross-flow instability mode can be induced in the three-dimensional boundary layer, the influences of the intensity, spanwise wave number and normal wave number of the free-stream turbulence, and the size and structure of the three-dimensional roughness on the three-dimensional boundary-layer receptivity under the free-stream turbulence interacting with the three-dimensional localized wall roughness, and the instability mode that can be induced and its role in the three-dimensional boundary-layer receptivity. The numerical results show that when the turbulence intensity is low, the steady cross-flow vortex excited by the three-dimensional localized wall roughness dominates the three-dimensional boundary-layer receptivity; on the contrary, when the turbulence intensity is high, the unsteady cross-flow vortex excited by the free-stream turbulence dominates the receptivity; additionally, when the interaction between the three-dimensional localized wall roughness and the free-stream turbulence is existent, three kinds of instability modes are all produced at the same time, namely, the steady cross-flow vortex, the unsteady cross-flow vortex and the new unsteady cross-flow vortex whose dispersion relation is equal to the linear combination of the positive and negative spanwise wave numbers of the first steady cross-flow vortex and the second unsteady cross-flow vortex. The in-depth research on the three-dimensional boundary-layer receptivity under the interaction of the free-stream turbulence and the three-dimensional localized wall roughness is of benefit to accomplishing the hydrodynamic instability theory and the turbulence theory, and providing the theoretical foundation for the prediction and control of the laminar-turbulent transition.
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Keywords:
- receptivity /
- three-dimensional boundary layer /
- localized wall roughness /
- free-stream turbulence
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[2] Xu G L, Fu S 2012 Advances in Mechanics 42 262 (in Chinese)[徐国亮, 符松2012力学进展42 262]
[3] Bippes H 1999 Prog. Aerosp. Sci. 35 363
[4] Bippes H, Nitschke-Kowsky P 1990 AIAA J. 28 1758
[5] Radeztsky Jr. R H, Reibert M S, Saric W S 1994 AIAA P. 2373
[6] Radeztsky R H, Reibert M S, Saric W S 1999 AIAA J. 37 1370
[7] Deyhle H, Bippes H 1996 J. Fluid. Mech. 316 73
[8] Reibert M S, Saric W S, Carrillo Jr. R B, Chapman K 1996 AIAA P. 0184
[9] Reibert M S, Saric W S 1997 AIAA P. 1816
[10] Fedorov A V 1988 J. Appl. Mech. Tech. Phys. 29 643
[11] Manuilovich S V 1989 Fluid. Dyn. 24 764
[12] Crouch J D 1993 AIAA P. 0074
[13] Choudhari M 1994 Theor. Comp. Fluid. Dyn. 6 1
[14] Ng L L, Crouch J D 1999 Phys. Fluid. 11 432
[15] Kurz H B E, Kloker M J 2014 J. Fluid. Mech. 755 62
[16] Shen L Y, Lu C G 2017 Acta. Phys. Sin. 66 014703 (in Chinese)[沈露予, 陆昌根2017 66 014703]
[17] Schrader L U, Brandt L, Henningson D S 2009 J. Fluid. Mech. 618 209
[18] Schrader L U, Brandt L, Mavriplis C, Henningson D S 2010 J. Fluid. Mech. 653 245
[19] Tempelmann D, Schrader L U, Hanifi A, Brandt L, Henningson D S 2011 AIAA P. 3294
[20] Tempelmann D, Schrader L U, Hanifi A, Brandt L, Henningson D S 2012 J. Fluid. Mech. 711 516
[21] Borodulin V I, Ivanov A V, Kachanov Y S, Roschektaev A P 2013 J. Fluid. Mech. 716 487
[22] Shen L Y, Lu C G 2016 Appl. Math. Mech. 37 929
[23] Zhang Y, Zaki T, Sherwin S, Wu X 2011 6th AIAA Theoretical Fluid Mechanics Conference Hawaii, USA, June 27-30, p3292
[24] Luchini P 2013 J. Fluid. Mech. 737 349
[25] Shen L, Lu C 2017 Appl. Math. Mech. 38 1213
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[1] Saric W S, Reed H L, White E B 2003 Annu. Rev. Fluid. Mech. 35 413
[2] Xu G L, Fu S 2012 Advances in Mechanics 42 262 (in Chinese)[徐国亮, 符松2012力学进展42 262]
[3] Bippes H 1999 Prog. Aerosp. Sci. 35 363
[4] Bippes H, Nitschke-Kowsky P 1990 AIAA J. 28 1758
[5] Radeztsky Jr. R H, Reibert M S, Saric W S 1994 AIAA P. 2373
[6] Radeztsky R H, Reibert M S, Saric W S 1999 AIAA J. 37 1370
[7] Deyhle H, Bippes H 1996 J. Fluid. Mech. 316 73
[8] Reibert M S, Saric W S, Carrillo Jr. R B, Chapman K 1996 AIAA P. 0184
[9] Reibert M S, Saric W S 1997 AIAA P. 1816
[10] Fedorov A V 1988 J. Appl. Mech. Tech. Phys. 29 643
[11] Manuilovich S V 1989 Fluid. Dyn. 24 764
[12] Crouch J D 1993 AIAA P. 0074
[13] Choudhari M 1994 Theor. Comp. Fluid. Dyn. 6 1
[14] Ng L L, Crouch J D 1999 Phys. Fluid. 11 432
[15] Kurz H B E, Kloker M J 2014 J. Fluid. Mech. 755 62
[16] Shen L Y, Lu C G 2017 Acta. Phys. Sin. 66 014703 (in Chinese)[沈露予, 陆昌根2017 66 014703]
[17] Schrader L U, Brandt L, Henningson D S 2009 J. Fluid. Mech. 618 209
[18] Schrader L U, Brandt L, Mavriplis C, Henningson D S 2010 J. Fluid. Mech. 653 245
[19] Tempelmann D, Schrader L U, Hanifi A, Brandt L, Henningson D S 2011 AIAA P. 3294
[20] Tempelmann D, Schrader L U, Hanifi A, Brandt L, Henningson D S 2012 J. Fluid. Mech. 711 516
[21] Borodulin V I, Ivanov A V, Kachanov Y S, Roschektaev A P 2013 J. Fluid. Mech. 716 487
[22] Shen L Y, Lu C G 2016 Appl. Math. Mech. 37 929
[23] Zhang Y, Zaki T, Sherwin S, Wu X 2011 6th AIAA Theoretical Fluid Mechanics Conference Hawaii, USA, June 27-30, p3292
[24] Luchini P 2013 J. Fluid. Mech. 737 349
[25] Shen L, Lu C 2017 Appl. Math. Mech. 38 1213
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