Inspired by the design of the ribbed structure of shark skin, passive drag reduction methods using stream-wise riblet surfaces have previously been developed and tested over a wide range of flow conditions. Such textures aligned in the flow direction have been shown to be able to reduce skin friction drag by 4%–8%. Here, we explore the effects of periodic sinusoidal riblet surfaces aligned in the flow direction (also known as a “wrinkled” texture) on the evolution of a laminar boundary layer flow. Using numerical analysis with the open source Computational Fluid Dynamics solver OpenFOAM, boundary layer flow over sinusoidal wrinkled plates with a range of wavelength to plate length ratios ( λ / L ), aspect ratios ( 2 A / λ ), and inlet velocities are examined. It is shown that in the laminar boundary layer regime, the riblets are able to retard the viscous flow inside the grooves creating a cushion of stagnant fluid that the high-speed fluid above can partially slide over, thus reducing the shear stress inside the grooves and the total integrated viscous drag force on the plate. Additionally, we explore how the boundary layer thickness, local average shear stress distribution, and total drag force on the wrinkled plate vary with the aspect ratio of the riblets as well as the length of the plate. We show that riblets with an aspect ratio of close to unity lead to the highest reduction in the total drag, and that because of the interplay between the local stress distribution on the plate and stream-wise evolution of the boundary layer the plate has to exceed a critical length to give a net decrease in the total drag force.

1.
Bacher
,
E. V.
and
Smith
,
C. R.
, “
Turbulent boundary-layer modification by surface riblets
,”
AIAA J.
24
,
1382
1385
(
1985
).
2.
Bechert
,
D.
,
Hoppe
,
G.
, and
Reif
,
W.-E.
, “
On the drag reduction of the shark skin
,” AIAA Paper No. 85-0546,
1985
.
3.
Bechert
,
D.
,
Bruse
,
M.
,
Hage
,
W.
,
Van der Hoeven
,
J. T.
, and
Hoppe
,
G.
, “
Experiments on drag-reducing surfaces and their optimization with an adjustable geometry
,”
J. Fluid Mech.
338
,
59
87
(
1997
).
4.
Bechert
,
D. W.
,
Bruse
,
M.
, and
Hage
,
W.
, “
Experiments with three-dimensional riblets as an idealized model of shark skin
,”
Exp. Fluids
28
,
403
412
(
2000
).
5.
Blackwell
,
J. A.
, “
Preliminary study of effects of Reynolds number and boundary-layer transition location on shock-induced separation
,” Report No. NASA-TN-D-5003,
1969
.
6.
Chan
,
E. P.
,
Smith
,
E. J.
,
Hayward
,
R. C.
, and
Crosby
,
A. J.
, “
Surface wrinkles for smart adhesion
,”
Adv. Mater.
20
,
711
716
(
2008
).
7.
Chen
,
X.
and
Hutchinson
,
J. W.
, “
Herringbone buckling patterns of compressed thin films on compliant substrates
,”
J. Appl. Mech.
71
,
597
(
2004
).
8.
Choi
,
K.
,
Gadd
,
G.
,
Pearcey
,
H.
,
Savill
,
A.
, and
Svensson
,
S.
, “
Tests of drag-reducing polymer coated on a riblet surface
,”
Appl. Sci. Res.
46
,
209
216
(
1989
).
9.
Choi
,
H.
,
Moin
,
P.
, and
Kim
,
J.
, “
Direct numerical simulation of turbulent flow over riblets
,”
J. Fluid Mech.
255
,
503
539
(
1993
).
10.
Chu
,
D. C.
and
Karniadakis
,
G. E.
, “
A direct numerical simulation of laminar and turbulent flow over riblet-mounted surfaces
,”
J. Fluid Mech.
250
,
1
42
(
1993
).
11.
Dinkelacker
,
A.
,
Nitschke-Kowsky
,
P.
, and
Reif
,
W.-E.
, “
On the possibility of drag reduction with the help of longitudinal ridges in the walls
,” in
Turbulence Management and Relaminarisation
(
Springer
,
1988
), pp.
109
120
.
12.
Djenidi
,
L.
,
Liandrat
,
J.
,
Anselmet
,
F.
, and
Fulachier
,
L.
, “
Numerical and experimental investigation of the laminar boundary layer over riblets
,”
Appl. Sci. Res.
46
,
263
270
(
1989
).
13.
Djenidi
,
L.
,
Squire
,
L.
, and
Savill
,
A.
, “
High resolution conformal mesh computations for V, U or L groove riblets in laminar and turbulent boundary layers
,” in
Recent Developments in Turbulence Management
(
Springer
,
1991
), pp.
65
92
.
14.
Drela
,
M.
,
Flight Vehicle Aerodynamics
(
MIT Press
,
2014
).
15.
El-Samni
,
O.
,
Chun
,
H.
, and
Yoon
,
H.
, “
Drag reduction of turbulent flow over thin rectangular riblets
,”
Int. J. Eng. Sci.
45
,
436
454
(
2007
).
16.
Ferziger
,
J. H.
and
Peric
,
M.
,
Computational Methods for Fluid Dynamics
(
Springer Science & Business Media
,
2012
).
17.
Furuya
,
Y.
,
Nakamura
,
I.
,
Miyata
,
M.
, and
Yama
,
Y.
, “
Turbulent boundary-layer along a streamwise bar of a rectangular cross section placed on a flat plate
,”
Bull. JSME
20
,
315
322
(
1977
).
18.
Goldstein
,
D.
,
Handler
,
R.
, and
Sirovich
,
L.
, “
Direct numerical simulation of turbulent flow over a modeled riblet covered surface
,”
J. Fluid Mech.
302
,
333
376
(
1995
).
19.
Hager
,
W.
, “
Blasius: A life in research and education
,”
Exp. Fluids
34
,
566
571
(
2003
).
20.
Hooshmand
,
D.
,
Youngs
,
R.
,
Wallace
,
J.
, and
Balint
,
J.
, “
An experimental study of changes in the structure of a turbulent boundary layer due to surface geometry changes
,” AlAA Paper No. 83-0230,
1983
.
21.
Hunt
,
J. C.
,
Wray
,
A. A.
, and
Moin
,
P.
, “
Eddies, streams, and convergence zones in turbulent flows
,” in
Studying Turbulence Using Numerical Simulation Databases, 2. Proceedings of the 1988 Summer Program
(
Stanford University
,
1988
), pp.
193
208
.
22.
Kennedy
,
J. F.
,
Hsu
,
S.-T.
, and
Lin
,
J.-T.
, “
Turbulent flows past boundaries with small streamwise fins
,”
J. Hydraul. Div.
99
,
605
616
(
1973
).
23.
Khan
,
M.
, “
A numerical investigation of the drag reduction by riblet-surfaces
,” AIAA Paper No. 86-1127,
1986
.
24.
Kim
,
H. T.
,
Kline
,
S. J.
, and
Reynolds
,
W. C.
, “
The production of turbulence near a smooth wall in a turbulent boundary layer
,”
J. Fluid Mech.
50
,
133
(
1971
).
25.
Kim
,
J.
,
Moin
,
P.
, and
Moser
,
R.
, “
Turbulence statistics in fully developed channel flow at low Reynolds number
,”
J. Fluid Mech.
177
,
133
166
(
1987
).
26.
Lee
,
S.-J.
and
Lee
,
S.-H.
, “
Flow field analysis of a turbulent boundary layer over a riblet surface
,”
Exp. Fluids
30
,
153
166
(
2001
).
27.
Narasimha
,
R.
and
Prasad
,
S.
, “
Leading edge shape for flat plate boundary layer studies
,”
Exp. Fluids
17
,
358
360
(
1994
).
28.
Neumann
,
D.
and
Dinkelacker
,
A.
, “
Drag measurements on V-grooved surfaces on a body of revolution in axial flow
,”
Appl. Sci. Res.
48
,
105
114
(
1991
).
29.
Park
,
S.-R.
and
Wallace
,
J. M.
, “
Flow alteration and drag reduction by riblets in a turbulent boundary layer
,”
AIAA J.
32
,
31
38
(
1994
).
30.
Patankar
,
S. V.
and
Spalding
,
D. B.
, “
A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows
,”
Int. J. Heat Mass Transfer
15
,
1787
1806
(
1972
).
31.
Raayai-Ardakani
,
S.
,
Yagüe
,
J. L.
,
Gleason
,
K. K.
, and
Boyce
,
M. C.
, “
Mechanics of graded wrinkling
,”
J. Appl. Mech.
83
,
121011
(
2016
).
32.
Schlichting
,
H.
,
Gersten
,
K.
, and
Gersten
,
K.
,
Boundary-Layer Theory
(
Springer
,
2000
).
33.
Simpson
,
R. L.
,
An Investigation of the Spatial Structure of the Viscous Sublayer
(
Max-Planck-Institut für Strömungsforschung
,
1976
).
34.
Tardu
,
S. F.
, “
Coherent structures and riblets
,”
Appl. Sci. Res.
54
,
349
385
(
1995
).
35.
Terwagne
,
D.
,
Brojan
,
M.
, and
Reis
,
P.
, “
Smart morphable surfaces for aerodynamic drag control
,”
Adv. Mater.
26
,
6608
6611
(
2014
).
36.
Van De Vooren
,
A.
and
Dijkstra
,
D.
, “
The Navier-Stokes solution for laminar flow past a semi-infinite flat plate
,”
J. Eng. Math.
4
,
9
27
(
1970
).
37.
Versteeg
,
H.
and
Malalasekera
,
W.
,
An Introduction to Computational Fluid Dynamics
(
Pearson
,
1995
).
38.
Viswanath
,
P. R.
, “
Aircraft viscous drag reduction using riblets
,”
Prog. Aerosp. Sci.
38
,
571
600
(
2002
).
39.
Walsh
,
M.
, “
Drag characteristics of V-groove and transverse curvature riblets
,” in , Progress in Astronautics and Aeronautics (
AIAA
,
1980
), pp.
168
184
.
40.
Walsh
,
M. J.
, “
Riblets as a viscous drag reduction technique
,”
AIAA J.
21
,
485
486
(
1983
).
41.
Walsh
,
M. J.
, “
Riblets
,” in
Viscous Drag Reduction in Boundary Layers
, edited by
D. M.
Bushnell
(
AIAA
,
1990
), Vol. 1, pp.
203
261
.
42.
Walsh
,
M.
and
Lindemann
,
A.
, “
Optimization and application of riblets for turbulent drag reduction
,” AIAA Paper No. 84-0347,
1984
.
43.
Walsh
,
M. J.
and
Weinstein
,
L.
, “
Drag and heat-transfer characteristics of small longitudinally ribbed surfaces
,”
AIAA J.
17
,
770
771
(
1979
).
44.
Wen
,
L.
,
Weaver
,
J.
, and
Lauder
,
G.
, “
Biomimetic shark skin: Design, fabrication and hydrodynamic function
,”
J. Exp. Biol.
217
,
1656
1666
(
2014
).
45.
Yin
,
J.
,
Yagüe
,
J. L.
,
Eggenspieler
,
D.
,
Gleason
,
K. K.
, and
Boyce
,
M. C.
, “
Deterministic order in surface micro-topologies through sequential wrinkling
,”
Adv. Mater.
24
,
5441
5446
(
2012
).
You do not currently have access to this content.