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边界层感受性问题是层流向湍流转捩的初始阶段，在转捩过程中起关键性作用，尤其是三维边界层流动.因此，研究三维边界层感受性问题对进一步理解层流向湍流转捩机理以及湍流成因具有重要的理论意义.采用数值方法研究自由来流湍流与三维壁面局部粗糙相互作用下三维边界层的感受性问题，确定是否能在三维边界层内寻找一种新的横流失稳模态；确定在何种条件下三维边界层内能诱导出定常、非定常的横流失稳模态；探索自由来流湍流的强度、展向波数和法向波数以及三维壁面局部粗糙的大小和结构类型等因素在自由来流湍流与三维壁面局部粗糙作用下三维边界层内被激发出的感受性过程中有何影响，并确定何种横流失稳模态在三维边界层感受性过程中占据何种地位.对自由来流湍流与三维壁面局部粗糙作用激发三维边界层内感受性问题的深入研究，将有助于完善流动稳定性与湍流理论，为层流向湍流转捩过程的预测与控制提供合理的理论依据.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]
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[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物理学报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物理学报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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