By employing particle image velocimetry, the response of a Mach 2.95 turbulent boundary layer to the concave curvature is experimentally investigated. The radius of the concave wall is 350 mm, and the turning angle is 20∘. Logarithmic law is well preserved in the profile of streamwise velocity at all streamwise positions despite the impact of curvature. The varying trend of principal strain rate is found to be different at different heights within the boundary layer, which cannot be explained by the suggestion given by former researchers. Based on the three-layer model proposed in this paper, distribution of the principal strain rate is carefully analyzed. The streamwise increase of wall friction is suggested to be brought by the increase of velocity gradient in the thin subsonic layer. Increases of the static temperature and the related sound speed are responsible for that. Larger correlated turbulent motions could be introduced by the concave curvature. The probability density histograms of streamwise velocity reveal that the large scale hairpin packets are statistically well organized. The concave curvature is found to have the potential of reinforcing the organization, which explains the increase of turbulent level in the supersonic concave boundary layer.
REFERENCES
1.
R.
Mukund
, R.
Viswanath
, R.
Narasimha
, A.
Prabhu
, and J. D.
Crouch
, “Relaminarization in highly favourable pressure gradients on a convex surface
,” J. Fluid Mech.
566
, 97
(2006
).2.
Tandiono
, S. H.
Winoto
, and D. A.
Shah
, “On the linear and nonlinear development of Görtler vortices
,” Phys. Fluids
20
, 094103
(2008
).3.
J. D.
Swearingen
and R. F.
Blackwelder
, “The growth and breakdown of streamwise vortices in the presence of a wall
,” J. Fluid Mech.
182
, 255
(1987
).4.
D. R.
Smith
and A. J.
Smits
, “A study of the effects of curvature and a supersonic turbulent boundary layer
,” Exp. Fluids
18
, 363
(1995
).5.
P.
Hall
and Y.
Fu
, “On the Görtler vortex instability mechanism at hypersonic speeds
,” Theor. Comput. Fluid Dyn.
1
, 125
(1989
).6.
P.
Hall
, “The linear development of Görtler vortices in growing boundary layers
,” J. Fluid Mech.
130
, 41
(1983
).7.
P.
Hall
, “Taylor-görtler vortices in fully developed or boundary-layer flows: Linear theory
,” J. Fluid Mech.
124
, 475
(1982
).8.
W. S.
Saric
, “Görtler vortices
,” Annu. Rev. Fluid Mech.
26
, 379
(1994
).9.
J. M.
Floryan
, “On the Görtler instability of boundary layers
,” Prog. Aerospace Sci.
28
, 235
(1991
).10.
T.
Tandiono
, S. H.
Winoto
, and D. A.
Shah
, “Spanwise velocity component in nonlinear region of Görtler vortices
,” Phys. Fluids
25
, 104104
(2013
).11.
L.-u.
Schrader
, L.
Brandt
, and T. A.
Zaki
, “Receptivity, instability and breakdown of Görtler flow
,” J. Fluid Mech.
682
, 362
(2011
).12.
F.
Li
and M. R.
Malik
, “Fundamental and subharmonic secondary instabilities of Görtler vortices
,” J. Fluid Mech.
297
, 77
(1995
).13.
J.
Ren
and S.
Fu
, “Secondary instabilities of Görtler vortices in high-speed boundary layer flows
,” J. Fluid Mech.
781
, 388
(2015
).14.
P.
Bradshaw
, “Effects of streamline curvature on turbulent flow,” AGARDograph No. 169, 16 (1973).15.
P.
Bradshaw
, “The effect of mean compression or dilatation on the turbulence structure of supersonic boundary layers
,” J. Fluid Mech.
63
, 449
(1974
).16.
P. H.
Hoffmann
, K. C.
Muck
, and P.
Bradshaw
, “The effect of concave surface curvature on turbulent boundary layers
,” J. Fluid Mech.
161
, 371
(1985
).17.
M.
Jayaram
, M. W.
Taylor
, and A. J.
Smits
, “The response of a compressible turbulent boundary layer to short regions of concave surface curvature
,” J. Fluid Mech.
175
, 343
(1987
).18.
J. F.
Donovan
, E. F.
Spina
, and A. J.
Smits
, “The structure of a supersonic turbulent boundary layer subjected to concave surface curvature
,” J. Fluid Mech.
259
, 1
(1994
).19.
W.
Flaherty
and J. M.
Austin
, “Scaling of heat transfer augmentation due to mechanical distortions in hypervelocity boundary layers
,” Phys. Fluids
25
, 106106
(2013
).20.
Y. X.
Zhao
, S. H.
Yi
, L. F.
Tian
, and Z. Y.
Cheng
, “Supersonic flow imaging via nanoparticles
,” Sci. China, Ser. E: Technol. Sci.
52
, 3640
(2009
).21.
S.
Scharnowski
, R.
Hain
, and C. J.
Kahler
, “Reynolds stress estimation up to single-pixel resolution using PIV-measurements
,” Exp. Fluids
52
, 985
(2012
).22.
R. J.
Adrian
, C. D.
Meinhart
, and C. D.
Tomkins
, “Vortex organization in the outer region of the turbulent boundary layer
,” J. Fluid Mech.
422
, 1
(2000
).23.
A. J.
Smits
and D. H.
Wood
, “The response of turbulent boundary layers to sudden pertubations
,” Annu. Rev. Fluid Mech.
17
, 321
(1985
).24.
E. F.
Spina
, A. J.
Smits
, and S. K.
Robinson
, “The physics of supersonic turbulent boundary layers
,” Annu. Rev. Fluid Mech.
26
, 287
(1994
).25.
R. A.
Humble
, S. J.
Peltier
, and R. D. W.
Bowersox
, “Visualization of the structural response of a hypersonic turbulent boundary layer to convex curvature
,” Phys. Fluids
24
, 106103
(2012
).26.
A.
Kendall
and M.
Koochesfahani
, “A method for estimating wall friction in turbulent wall-bounded flows
,” Exp. Fluids
44
, 773
(2008
).27.
S. E.
Guarini
, R. D.
Moser
, K.
Shariff
, and A.
Wray
, “Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5
,” J. Fluid Mech.
414
, 1
(2000
).28.
S.
Pirozzoli
, F.
Grasso
, and T. B.
Gatski
, “Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M = 2.25
,” Phys. Fluids
16
, 530
(2004
).29.
H. H.
Fernholzh
and P. J.
Finley
, “A critical commentary on mean flow data for two dimensional compressible turbulent boundary layers,” AGARDograph No. 253, 198 (1980).30.
D. B.
Spalding
, “A single formula for the law of the wall
,” J. Appl. Mech.
28
, 455
(1961
).31.
N. R.
Tichenor
, R. A.
Humble
, and R. D. W.
Bowersox
, “Response of a hypersonic turbulent boundary layer to favourable pressure gradients
,” J. Fluid Mech.
722
, 187
(2013
).32.
Q. C.
Wang
and Z. G.
Wang
, “Structural characteristics of the supersonic turbulent boundary layer subjected to concave curvature
,” Appl. Phys. Lett.
108
, 114102
(2016
).33.
G. E.
Elsinga
, R. J.
Adrian
, B. W. V.
Oudheusden
, and F.
Scarano
, “Three-dimensional vortex organization in a high-Reynolds-number supersonic turbulent boundary layer
,” J. Fluid Mech.
644
, 35
(2010
).34.
B.
Ganapathisubramani
, E. K.
Longmire
, and I.
Marusic
, “Characteristics of vortex packets in turbulent boundary layers
,” J. Fluid Mech.
478
, 35
(2003
).35.
K. P.
Nolan
, E. J.
Walsh
, and D. M.
McEligot
, “Quadrant analysis of a transitional boundary layer subject to free-stream turbulence
,” J. Fluid Mech.
658
, 310
(2010
).36.
S. S.
Lu
and W. W.
Willmarth
, “Measurements of the structure of the Reynolds stress in a turbulent boundary layer
,” J. Fluid Mech.
60
, 481
(1973
).© 2016 Author(s).
2016
Author(s)
You do not currently have access to this content.
