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层流向湍流转捩的预测与控制一直是研究的前沿热点问题之一，其中感受性阶段是转捩过程中的初始阶段，它决定着湍流产生或形成的物理过程.但是有关三维边界层内感受性问题的数值和理论研究都比较少；实际工程问题中大部分转捩过程都是发生在三维边界层流中，所以研究三维边界层中的感受性问题显得尤为重要.本文以典型的后掠角45°无限长平板为例，数值研究了在三维壁面局部粗糙作用下的三维边界层感受性问题，探讨了三维边界层感受性问题与三维壁面局部粗糙长、宽和高之间的关系；然后，考虑在后掠平板上设计不同的三维壁面局部粗糙的分布状态、几何形状、距离后掠平板前缘的位置以及流向和展向设计多个三维壁面局部粗糙对三维边界层感受性问题有何影响；最后，讨论两两三维壁面局部粗糙中心点之间的距离以及后掠角的改变对三维边界层感受性的物理过程将会发生何种影响等.这一问题的深入研究将为三维边界层流中层流向湍流转捩过程的认识和理解提供理论依据.The prediction and control of the laminar-turbulent transition are always one of the most concerned frontiers and hot topics.Receptivity is the initial stage of the laminar-turbulent transition process in the boundary layer,which decides the physical process of the turbulent formation.To date,the researches of receptivity in the three-dimensional boundary layer are much less than those in the two-dimensional boundary layer;while most of the real laminar-turbulent transition in practical engineering occurs in three-dimensional boundary layers.Therefore,receptivity under the threedimensional wall local roughness in a typical three-dimensional boundary layer,i.e.,a 45° back swept infinite flat plate, is numerically studied.And a numerical method for direct numerical simulation (DNS) is constructed in this paper by using fourth order modified Runge-Kutta scheme for temporal march and high-order compact finite difference schemes based on non-uniform mesh for spatial discretization:the convective term is discretized by fifth-order upwind compact finite difference schemes;the pressure term is discretized by sixth-order compact finite difference schemes;the viscous term is discretized by fifth-order compact finite difference schemes;and the pressure equation is solved by third-order finite difference schemes based on non-uniform mesh.As a result,the excited steady cross-flow vortices are observed in the three-dimensional boundary layer.In addition,the relations of three-dimensional boundary-layer receptivity with the length,the width,and the height of three-dimensional wall localized roughness respectively are also ascertained.Then, the influences of the different distributions,the geometrical shapes,and the location to the flat-plate leading-edge of the three-dimensional wall local roughness,and multiple three-dimensional wall local roughness distributed in streamwise and spanwise directions on three-dimensional boundary-layer receptivity are considered.Finally,the effect of the distance between the midpoint of the three-dimensional wall localized roughness and the back-swept angle on three-dimensional boundary-layer receptivity is studied.The intensive research of receptivity in the three-dimensional boundary-layer receptivity will provide the basic theory for awareness and understanding of the laminar-turbulent transition.
[1] Saric W S, Reed H L, White E B 2003 Annu. Rev. Fluid. Mech. 35 413
[2] Shen L Y, Lu C G 2016 Appl. Math. Mech. 37 349
[3] Shen L Y, Lu C G 2016 Appl. Math. Mech. 37 929
[4] Lu C G, Shen L Y 2015 Acta Phys. Sin. 64 224702 （in Chinese)[陆昌根, 沈露予2015 64 224702]
[5] Lu C G, Shen L Y 2016 Acta Phys. Sin. 65 194701 （in Chinese)[陆昌根, 沈露予2016 65 194701]
[6] Shen L Y, Lu C G 2016 Appl. Math. Mech. 37 1145(in Chinese)[沈露予, 陆昌根2016应用数学与力学37 1145]
[7] Xu G L, Fu S 2012 Adv. Mech. 42 262 （in Chinese)[徐国亮, 符松2012力学进展42 262]
[8] Bippes H, Nitschke-Kowsky P 1990 AIAA J. 28 1758
[9] Radeztsky Jr R H, Reibert M S, Saric W S 1994 AIAA P. 2373
[10] Radeztsky R H, Reibert M S, Saric W S 1999 AIAA J. 37 1370
[11] Deyhle H, Bippes H 1996 J. Fluid. Mech. 316 73
[12] Reibert M S, Saric W S, Carrillo Jr R B, et al. 1996 AIAA P. 0184
[13] Reibert M S, Saric W S 1997 AIAA P. 1816
[14] Fedorov A V 1988 J. Appl. Mech. Tech. Phys. 29 643
[15] Manuilovich S V 1989 Fluid. Dyn. 24 764
[16] Crouch J D 1993 AIAA P. 0074
[17] Choudhari M 1994 Theor. Comp. Fluid. Dyn. 6 1
[18] Ng L L, Crouch J D 1999 Phys. Fluid. 11 432
[19] Bertolotti F P 2000 Phys. Fluid. 12 1799
[20] Collis S S, Lele S K 1999 J. Fluid. Mech. 380 141
[21] Schrader L U, Brandt L, Henningson D S 2009 J. Fluid. Mech. 618 209
[22] Schrader L U, Brandt L, Mavriplis C, et al. 2010 J. Fluid. Mech. 653 245
[23] Tempelmann D, Schrader L U, Hanifi A, et al. 2012 J. Fluid. Mech. 711 516
[24] Kurz H B E, Kloker M J 2014 J. Fluid. Mech. 755 62
[25] Shen L Y, Lu C G, Wu W G, Xue S F 2015 Add. Appl. Math. Mech. 7 180
[26] Lu C G, Cao W D, Zhang Y M, Guo J T 2008 P. Nat. Sci. 18 873
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[1] Saric W S, Reed H L, White E B 2003 Annu. Rev. Fluid. Mech. 35 413
[2] Shen L Y, Lu C G 2016 Appl. Math. Mech. 37 349
[3] Shen L Y, Lu C G 2016 Appl. Math. Mech. 37 929
[4] Lu C G, Shen L Y 2015 Acta Phys. Sin. 64 224702 （in Chinese)[陆昌根, 沈露予2015 64 224702]
[5] Lu C G, Shen L Y 2016 Acta Phys. Sin. 65 194701 （in Chinese)[陆昌根, 沈露予2016 65 194701]
[6] Shen L Y, Lu C G 2016 Appl. Math. Mech. 37 1145(in Chinese)[沈露予, 陆昌根2016应用数学与力学37 1145]
[7] Xu G L, Fu S 2012 Adv. Mech. 42 262 （in Chinese)[徐国亮, 符松2012力学进展42 262]
[8] Bippes H, Nitschke-Kowsky P 1990 AIAA J. 28 1758
[9] Radeztsky Jr R H, Reibert M S, Saric W S 1994 AIAA P. 2373
[10] Radeztsky R H, Reibert M S, Saric W S 1999 AIAA J. 37 1370
[11] Deyhle H, Bippes H 1996 J. Fluid. Mech. 316 73
[12] Reibert M S, Saric W S, Carrillo Jr R B, et al. 1996 AIAA P. 0184
[13] Reibert M S, Saric W S 1997 AIAA P. 1816
[14] Fedorov A V 1988 J. Appl. Mech. Tech. Phys. 29 643
[15] Manuilovich S V 1989 Fluid. Dyn. 24 764
[16] Crouch J D 1993 AIAA P. 0074
[17] Choudhari M 1994 Theor. Comp. Fluid. Dyn. 6 1
[18] Ng L L, Crouch J D 1999 Phys. Fluid. 11 432
[19] Bertolotti F P 2000 Phys. Fluid. 12 1799
[20] Collis S S, Lele S K 1999 J. Fluid. Mech. 380 141
[21] Schrader L U, Brandt L, Henningson D S 2009 J. Fluid. Mech. 618 209
[22] Schrader L U, Brandt L, Mavriplis C, et al. 2010 J. Fluid. Mech. 653 245
[23] Tempelmann D, Schrader L U, Hanifi A, et al. 2012 J. Fluid. Mech. 711 516
[24] Kurz H B E, Kloker M J 2014 J. Fluid. Mech. 755 62
[25] Shen L Y, Lu C G, Wu W G, Xue S F 2015 Add. Appl. Math. Mech. 7 180
[26] Lu C G, Cao W D, Zhang Y M, Guo J T 2008 P. Nat. Sci. 18 873
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