An experimental stability and transition investigation of a centrifugally unstable wall jet blown from a slot over a circular Coandă cylinder was conducted using flow visualization and particle image velocimetry. Clear and unambiguous observations of spontaneously generated stationary streamwise structures, never observed previously, were analyzed using standard image processing techniques. These structures ultimately exhibited a secondary time-dependent wavy instability that was followed by transition to turbulence. A modified Görtler number, based on the slot height, was used as a basis for comparison to linear stability theory and was directly related to the Reynolds number via geometric scaling. Direct observation of the vortices allowed the identification of an upper limit to the critical Görtler number of 6.3 that bracketed the value of 3.5 from the linear stability theory. The vortical shear layer grew exponentially along the azimuth and was characterized by a Reynolds number dependent growth rate parameter. Extrapolation of the growth rate parameter to zero furnished a critical Görtler number of 3.1 ± 1.25 (95% CI) that compared remarkably well with the linear stability theory. The shear layer separation angle did not vary monotonically with the Reynolds number: as the Reynolds number increased, the thicker boundary layer was more susceptible to separation, and thus, the separation angle, relative to the slot, decreased. However, following transition to turbulence at higher Reynolds numbers (≈400), the high-momentum fluid near the wall, resulting from turbulent mixing, produced a subsequent increase in the separation angle.
REFERENCES
1.
T.
Young
, “Outlines of experiments and inquiries respecting sound and light
,” Philos. Trans. R. Soc. London
90
, 106
–150
(1800
).2.
J. D.
Jackson
, “Osborne Reynolds: Scientist, engineer and pioneer
,” Proc. R. Soc. A
451
(1941
), 49
–86
(1995
).3.
H.
Coanda
, “Device for deflecting a stream of elastic fluid projected into an elastic fluid
,” U.S. patent 2,052,869 (1 September 1936
).4.
G. V.
Lachmann
, Boundary Layer and Flow Control: Its Principles and Application
(Pergamon Press
, New York
, 1961
), Vol. 1.5.
G. V.
Lachmann
, Boundary Layer and Flow Control: Its Principles and Application
(Pergamon Press
, New York
, 1961
), Vol. 2.6.
R.
Wille
and H.
Fernholz
, “Report on the first European mechanics colloquium, on the Coanda effect
,” J. Fluid Mech.
23
(4
), 801
–819
(1965
).7.
K. P.
Lo
, C. J.
Elkins
, and J. K.
Eaton
, “Separation control in a conical diffuser with an annular inlet: Center body wake separation
,” Exp. Fluids
53
(5
), 1317
–1326
(2012
).8.
D.
Barros
, J.
Borée
, B. R.
Noack
, A.
Spohn
, and T.
Ruiz
, “Bluff body drag manipulation using pulsed jets and Coanda effect
,” J. Fluid Mech.
805
, 422
–459
(2016
).9.
R. J.
Englar
, “Overview of circulation control pneumatic aerodynamics: Blown force and moment augmentation and modification as applied primarily to fixed-wing aircraft
,” Proceedings of the 2004 NASA/ONR Circulation Control Workshop, NASA CP 2005-213509/PT1June 2005, pp. 37
–100
.10.
G. S.
Jones
and R. D.
Joslin
, Applications of Circulation Control Technology
(American Institute of Aeronautics and Astronautics
, 2006
).11.
S.
Baleriola
, A.
Leroy
, S.
Loyer
, P.
Devinant
, and S.
Aubrun
, “Scaling investigation of plasma-induced flows over curved and flat surfaces: Comparison to the wall jet
,” Int. J. Heat Fluid Flow
76
, 259
–273
(2019
).12.
R. I.
Ahmed
, A. R.
Abu Talib
, A. S.
Mohd Rafie
, and H.
Djojodihardjo
, “Aerodynamics and flight mechanics of MAV based on Coandă effect
,” Aerosp. Sci. Technol.
62
, 136
–147
(2017
).13.
A.
Dumas
, M.
Subhash
, M.
Trancossi
, and J. P.
Marques
, “The influence of surface temperature on Coanda effect
,” Energy Procedia
45
, 626
–634
(2014
).14.
V.
Tesař
and H. C. H.
Bandalusena
, “Bistable diverter valve in microfluidics
,” Exp. Fluids
50
(5
), 1225
–1233
(2011
).15.
16.
G. I.
Fekete
, “Coanda flow of a two-dimensional wall jet on the outside of a cylinder
,” Report No. 63-11, Department of Mechanical Engineering, McGill University
, 1963
.17.
B. G.
Newman
, “The deflection of plane jets by adjacent boundaries—Coanda effect
,” Boundary Layer Flow Control
1
, 232
–264
(1961
).18.
D. E.
Guitton
, “Two-dimensional turbulent wall jets over curved surfaces
,” Report No. 64-7, Department of Mechanical Engineering, McGill University
, 1964
.19.
N.
Fujisawa
and R.
Kobayashi
, “Turbulence characteristics of wall jets along strong convex surfaces
,” J. Mech. Sci.
29
, 311
–320
(1987
).20.
Lord Rayleigh
, “On the dynamics of revolving fluids
,” Proc. R. Soc. London, Ser. A
93
, 148
–154
(1917
).21.
H.
Görtler
, “Instabilität laminarer grenzschichten an konkaven wänden gegenüber gewissen dreidimensionalen störungen
,” Z. Angew. Math. Mech.
21
(4
), 250
–252
(1941
).22.
W. S.
Saric
, “Görtler vortices
,” Annu. Rev. Fluid Mech.
26
(1
), 379
–409
(1994
).23.
J. M.
Floryan
and W. S.
Saric
, “Stability of Gortler vortices in boundary layers
,” AIAA J.
20
(3
), 316
–324
(1982
).24.
R.
Neuendorf
and I.
Wygnanski
, “On a turbulent wall jet flowing over a circular cylinder
,” J. Fluid Mech.
381
, 1
–25
(1999
).25.
O.
Likhachev
, R.
Neuendorf
, and I.
Wygnanski
, “On streamwise vortices in a turbulent wall jet that flows over a convex surface
,” Phys. Fluids
13
(6
), 1822
–1825
(2001
).26.
R.
Neuendorf
, L.
Lourenco
, and I.
Wygnanski
, “On large streamwise structures in a wall jet flowing over a circular cylinder
,” Phys. Fluids
16
(7
), 2158
–2169
(2004
).27.
A.
Gross
and H. F.
Fasel
, “Coanda wall jet calculations using one- and two-equation turbulence models
,” AIAA J.
44
(9
), 2095
–2107
(2006
).28.
R. I.
Ahmed
, A. R.
Abu Talib
, A. S. M.
Rafie
, and H.
Djojodihardjo
, “Aerodynamics and flight mechanics of MAV based on Coandă effect
,” Aerosp. Sci. Technol.
62
, 136
–147
(2017
).29.
S.
Das
, M.
Abdollahzadeh
, J.
Pascoa
, A.
Dumas
, and M.
Trancossi
, “Numerical modeling of Coanda effect in a novel propulsive system
,” Int. J. Multiphys.
8
(2
), 181
–201
(2014
).30.
A.
Dumitrache
, F.
Frunzulica
, and T. C.
Ionescu
, “Mathematical modeling and numerical investigations on the Coandă effect
,” in (InTech
, 2012
), Chap. 5, pp. 101
–132
.31.
F.
Frunzulica
, A.
Dumitrache
, O.
Preotu
, and H.
Dumitrescu
, “Control of two-dimensional turbulent wall jet on a Coandă surface
,” Proc. Appl. Math. Mech.
11
(1
), 651
–652
(2011
).32.
G.
Han
, M.
de Zhou
, and I.
Wygnanski
, “On streamwise vortices and their role in the development of a curved wall jet
,” Phys. Fluids
18
(9
), 095104-1
–095104-14
(2006
).33.
A.
Pandey
, “Streamwise vortices in a convex wall jet
,” Ph.D. dissertation (The Ohio State University
, 2019
).34.
J. K.
Rogenski
, L. F.
de Souza
, and J. M.
Floryan
, “Non-linear aspects of Görtler instability in boundary layers with pressure gradient
,” Phys. Fluids
28
, 124107
(2016
).35.
M.
Méndez
, M. S.
Shadloo
, A.
Hadjadj
, and A.
Ducoin
, “Boundary layer transition over a concave surface caused by centrifugal instabilities
,” Comput. Fluids
171
, 135
–153
(2018
).36.
J. M.
Floryan
, “On the Görtler instability of boundary layers
,” Prog. Aerosp. Sci.
28
(3
), 235
–271
(1991
).37.
O. J. E.
Matsson
, “Görtler vortices in wall jet flow on a rotating cylinder
,” Phys. Fluids
10
(9
), 2238
–2248
(1998
).38.
J. M.
Floryan
, “Görtler instability of boundary layers over concave and convex walls
,” Phys. Fluids
29
(8
), 2380
–2387
(1986
).39.
P.
Hall
, “The linear development of Görtler vortices in growing boundary layers
,” J. Fluid Mech.
130
(1
), 41
–58
(1983
).40.
O. J. E.
Matsson
, “On the curved wall jet influenced by system rotation and self-similar suction or blowing
,” Phys. Fluids
7
(12
), 3048
–3059
(1995
).41.
M. R.
Scott
and H. A.
Watts
, “Computational solution of linear two-point boundary value problems via orthonormalization
,” SIAM J. Numer. Anal.
14
(1
), 40
–70
(1997
), available at www.jstor.org/stable/2156620?seq=1.42.
R.
Danon
, J. W.
Gregory
, and D.
Greenblatt
, “Transient wall-jet flowing over a circular cylinder
,” Exp. Fluids
57
(141
), 1
–14
(2016
).43.
A.
Naim
, D.
Greenblatt
, A.
Seifert
, and I.
Wygnanski
, “Active control of a circular cylinder flow at transitional Reynolds numbers
,” Flow, Turbul. Combust.
78
(3-4
), 383
–407
(2007
). 44.
M. B.
Glauert
, “The wall jet
,” J. Fluid Mech.
1
(6
), 625
–643
(1956
).45.
G. I.
Taylor
, “Stability of a viscous liquid contained between two rotating cylinders
,” Philos. Trans. R. Soc., A
223
(605-615
), 289
–343
(1923
).46.
D.
Coles
, “Transition in circular Couette flow
,” J. Fluid Mech.
21
, 385
–425
(1965
).47.
G. P.
King
, Y. L. W.
Lee
, H. L.
Swinney
, P. S.
Marcus
, and P. S.
Marcus
, “Wave speeds in wavy Taylor-vortex flow
,” J. Fluid Mech.
141
, 365
–390
(1984
).48.
B.
Wang
, X.
Mao
, and T. A.
Zaki
, “Low-frequency selectivity in flat-plate boundary layer with elliptic leading edge
,” J. Fluid Mech.
866
, 239
–262
(2019
).© 2020 Author(s).
2020
Author(s)
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