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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物理学报64 224702]
[5] 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]
[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物理学报64 224702]
[5] 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]
[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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