This paper is a brief review of recent research on the streamwise corner boundary layer as it affects the component performance evaluation of both the theoretical and practical aircraft design. Typical examples include aircraft wing–body junction, rectangular air intakes, and turbine-hub flow. The paper addresses the questions of what we know and do not know about the streamwise corner boundary layer. Streamwise corner flows are characterized by the presence of secondary flows in the cross-stream planes, which are driven by the normal and secondary-shear components of the Reynolds stress tensor. Extensive studies of analysis for Prandtl's second kind of secondary flows have promoted the understanding of characteristics and formation of streamwise corner boundary layer. However, compared to the flat plate boundary layer, the research on the streamwise corner boundary layer is still far from enough, especially in the similarity solution, the instability, and transition mechanism. In recent years, a significant progress has been achieved in the study on the streamwise corner boundary layer in turbulent flow through direct numerical simulation and stress ω Reynolds stress model.

1.
P. J.
Erbland
,
Current and Near-Term RLV/Hypersonic Vehicle Programs
(RTO-EN-AVT-116,
2004
), p.
24
.
2.
E.
Thompson
,
K.
Henry
, and
L.
Williams
,
Faster Than a Speeding Bullet: Guinness Recognizes NASA Scramjet
(
NASA
,
2005
).
3.
A.
Viviani
and
G.
Pezzella
, “
Introductory chapter: Hypersonic vehicles—past, present, and future insights
,” in
Hypersonic Vehicles—Past, Present and Future Developments
(
IntechOpen
,
2019
).
4.
S.
Yi
,
Y.
Zhao
,
L.
He
, and
M.
Zhang
,
Supersonic and Hypersonic Nozzle Design
(
National Defense Industry Press
,
Changsha
,
2013
) (in Chinese).
5.
H.
Liu
and
Y.
Zhao
,
Nozzle Design of Rectangular Supersonic Ducts Based on the Characteristics Tracing Method
(
Chinese Aerodynamics Research Society
,
2015
) (in Chinese).
6.
W.-P.
Wang
,
R.-S.
Lin
,
M.
Malik
,
J.
Edwards
,
W.-P.
Wang
,
R.-S.
Lin
,
M.
Malik
, and
J.
Edwards
, “
Control of corner flow vortices by geometry shaping in Mach 2.4 rectangular nozzles
,” AIAA Paper No. 97-2228,
1997
.
7.
M. C.
Davis
and
J. T.
White
, “
X-43A flight-test-determined aerodynamic force and moment characteristics at Mach 7.0
,”
J. Spacecr. Rockets
45
,
472
484
(
2008
).
8.
C. M.
Rondeau
and
T. R.
Jorris
, “
X-51A scramjet demonstrator program: Waverider ground and flight test
,” in
SFTE 44th International SETP Southwest Flight Test Symposium
(Curran Associates Inc.,
2013
), p.
15
.
9.
A.
Pierce
, Aviation Goes Hypersonic (Technology Today,
2015
), Vol. 75, p.
8
.
10.
A. S.
Valerino
,
Effects of Internal Corner Fillets on Pressure Recovery: Mass Flow Characteristics of Scoop-Type Conical Supersonic Inlets
(
NACA
,
Washington D.C.
,
1952
).
11.
L.
Shi
and
R.
Guo
, “
Serpentine inlet design and analysis
,” AIAA Paper No. 2012-0839,
2012
.
12.
J. L.
Mark
,
M. A.
McGarry
, and
P. V.
Reagan
,
Research on a Two-Dimensional Inlet for a Supersonic v/Stol Propulsion System
(
McDonnell Aircraft Company, McDonnell Douglas Corporation
,
1989
).
13.
F.
Wilcox
,
T.
Birch
, and
J.
Allen
, “
Force, surface pressure, and flowfield measurements on a slender missile configuration with square cross-section at supersonic speeds
,” AIAA Paper No. 2004-5451,
2004
.
14.
W. J.
Devenport
,
N. K.
Agarwal
,
M. B.
Dewitz
,
R. L.
Simpson
, and
K.
Poddar
, “
Effects of a fillet on the flow past a wing-body junction
,”
AIAA J.
28
,
2017
2024
(
1990
).
15.
J. L.
Fleming
,
R. L.
Simpson
,
J. E.
Cowling
, and
W. J.
Devenport
, “
An experimental study of a turbulent wing-body junction and wake flow
,”
Exp. Fluids
14
,
366
(
1993
).
16.
R. H.
Liebeck
, “
Design of the blended wing body subsonic transport
,”
J. Aircr.
41
,
10
25
(
2004
).
17.
Q.
Tang
,
Y.
Zhu
,
X.
Chen
, and
C.
Lee
, “
Development of second-mode instability in a Mach 6 flat plate boundary layer with two-dimensional roughness
,”
Phys. Fluids
27
,
064105
(
2015
).
18.
J.
Délery
and
J.-P.
Dussauge
, “
Some physical aspects of shock wave/boundary layer interactions
,”
Shock Waves.
19
,
453
468
(
2009
).
19.
B. C.
Weinberg
and
S. G.
Rubin
, “
Compressible corner flow
,”
J. Fluid Mech.
56
,
753
(
1972
).
20.
W.
Eagle
,
J.
Driscoll
, and
J.
Benek
, “
Experimental investigation of corner flows in rectangular supersonic inlets with 3D shock-boundary layer effects
,” AIAA Paper No. 2011-0857,
2011
.
21.
J. W.
Elder
, “
The flow past a flat plate of finite width
,”
J. Fluid Mech.
9
,
133
(
1960
).
22.
B. E.
Rice
,
N. J.
Bisek
,
S.
Peltier
, and
J. W.
Hofferth
, “
Investigation of secondary motion in high speed flow
,” AIAA Paper No. 2017-0526,
2017
.
23.
L.
Prandtl
, “
Über die ausgebildete turbulenz (Investigations on turbulent flow)
,” in
International Congress on Applied Mechanics
(
ZAMM
,
Zurich
,
1926
).
24.
J.
Nikuradse
, “
Untersuchungen über die geschwindigkeitsverteilung in turbulenten strömungen
,” Ph.D. thesis (
Göttingen
,
1926
).
25.
B.
Stankovic
,
S.
Belosevic
,
N.
Crnomarkovic
,
A.
Stojanovic
,
I.
Tomanovic
, and
A.
Milicevic
, “
Specific aspects of turbulent flow in rectangular ducts
,”
Therm. Sci.
21
,
663
678
(
2017
).
26.
R.
Moissis
, “
The secondary flow in rectangular ducts
,” Ph.D. thesis (
Massachusetts Institute of Technology
,
1957
).
27.
S. G.
Rubin
, “
Incompressible flow along a corner
,”
J. Fluid Mech.
26
,
97
(
1966
).
28.
V. I.
Kornilov
, “
Three-dimensional turbulent near-wall flows in streamwise corners: Current state and questions
,”
Prog. Aerosp. Sci.
94
,
46
81
(
2017
).
29.
D.
Modesti
,
S.
Pirozzoli
, and
F.
Grasso
, “
Direct numerical simulation of developed compressible flow in square ducts
,”
Int. J. Heat Fluid Flow
76
,
130
140
(
2019
).
30.
D.
Davis
and
F.
Gessner
, “
Further experiments on supersonic turbulent flow development in a square duct
,” AIAA Paper No. 1987-1287,
1987
.
31.
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
545
(
2004
).
32.
Q.
Wang
,
Z.
Wang
, and
Y.
Zhao
, “
An experimental investigation of the supersonic turbulent boundary layer subjected to concave curvature
,”
Phys. Fluids
28
,
096104
(
2016
).
33.
G. F.
Carrier
, “
The boundary layer in a corner
,”
Q. Appl. Math.
4
,
367
370
(
1947
).
34.
S. H.
Maslen
, “
Transverse velocities in fully developed flows
,”
Q. Appl. Math.
16
,
173
175
(
1958
).
35.
L. C.
Hoagland
, “
Fully developed turbulent flow in straight rectangular ducts: Secondary flow, its cause and effect on the primary flow
,” Ph.D. thesis (
Massachusetts Institute of Technology
,
1960
).
36.
E.
Brundrett
and
W. D.
Baines
, “
The production and diffusion of vorticity in duct flow
,”
J. Fluid Mech.
19
,
375
(
1964
).
37.
B.
Launder
and
D.
Spalding
,
Lectures in Mathematical Model of Turbulence
(
Academic Press
,
1972
).
38.
F. B.
Gessner
and
J. B.
Jones
, “
On some aspects of fully-developed turbulent flow in rectangular channels
,”
J. Fluid Mech.
23
,
689
(
1965
).
39.
F. B.
Gessner
, “
The origin of secondary flow in turbulent flow along a corner
,”
J. Fluid Mech.
58
,
1
25
(
1973
).
40.
R. A.
Oman
,
The three-dimensional laminar boundary layer along a corner
(
Massachusetts Institute of Technology
,
1959
).
41.
S. G.
Rubin
and
B.
Grossman
, “
Viscous flow along a corner: Numerical solution of the corner layer equations
,”
Q. Appl. Math.
29
,
169
186
(
1971
).
42.
K. N.
Ghia
, “
Incompressible streamwise flow along an unbounded corner
,”
AIAA J.
13
,
902
907
(
1975
).
43.
W. H.
Barclay
and
A. H.
Ridha
, “
Flow in streamwise corners of arbitrary angle
,”
AIAA J.
18
,
1413
1420
(
1980
).
44.
K. N.
Ghia
and
R. T.
Davis
, “
A study of compressible potential and asymptotic viscous flows for comer region
,”
AIAA J.
12
,
355
359
(
1974
).
45.
L.
Prandtl
,
K.
Oswatitsch
, and
K.
Wieghardt
,
Führer Durch Die Strömungslehre
(
Springer-Verlag
,
1981
).
46.
H.
Raiesi
,
A.
Pollard
, and
U.
Piomelli
, “
Direct numerical simulations of turbulence induced secondary motion in square and skewed ducts
,” in
Seventh International Symposium on Turbulence and Shear Flow Phenomena
(
Begel House Inc
.,
2011
), pp.
1
6
.
47.
P.
Orlandi
,
D.
Modesti
, and
S.
Pirozzoli
, “
DNS of turbulent flows in ducts with complex shape
,”
Flow Turbul. Combust.
100
,
1063
1079
(
2018
).
48.
S.
Pirozzoli
,
D.
Modesti
,
P.
Orlandi
, and
F.
Grasso
, “
Turbulence and secondary motions in square duct flow
,”
J. Fluid Mech.
840
,
631
655
(
2018
).
49.
M.
Kh. Ibragimov
,
V. S.
Petrishchev
, and
G. I.
Sabelev
, “
Calculation of secondary flow in a turbulent fluid stream
,”
Fluid Dyn.
4
,
114
116
(
1972
).
50.
R. R.
Morajkar
,
J. F.
Driscoll
, and
M.
Gamba
, “
Experimental study of supersonic turbulent corner flow evolution in a low aspect ratio rectangular channel
,” AIAA Paper No. 2015-0542,
2015
.
51.
R. R.
Morajkar
and
M.
Gamba
, “
Turbulence characteristics of supersonic corner flows in a low aspect ratio rectangular channel
,” AIAA Paper No. 2016-1590,
2016
.
52.
S. J.
Peltier
,
B. E.
Rice
,
N. J.
Bisek
,
C. K.
McKenna
, and
J. W.
Hofferth
, “
Structure of secondary motion in a Mach 2 boundary layer
,” AIAA Paper No. 2018-0583,
2018
.
53.
S.
Levy
,
R. O.
Niemi
, and
R. A.
Fuller
, “
Heat transfer to water in thin rectangular channels
,”
J. Heat Transfer
81
,
129
(
1959
).
54.
R. G.
Deissler
and
M. F.
Taylor
, “
Analysis of turbulent flow and heat transfer in noncircular passages
,” Report No. NACA TN 4384 (
1958
).
55.
H. S.
Choi
and
T. S.
Park
, “
The influence of streamwise vortices on turbulent heat transfer in rectangular ducts with various aspect ratios
,”
Int. J. Heat Fluid Flow
40
,
1
14
(
2013
).
56.
G. M.
Daschiel
,
Strategies to Reduce Friction Losses and Their Implications for the Energy Efficient Design of Internal Flow Domains
(
KIT Scientific Publishing
,
2014
).
57.
A.
Pinelli
,
M.
Uhlmann
,
A.
Sekimoto
, and
G.
Kawahara
, “
Reynolds number dependence of mean flow structure in square duct turbulence
,”
J. Fluid Mech.
644
,
107
122
(
2010
).
58.
S.
Gavrilakis
, “
Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct
,”
J. Fluid Mech.
244
,
101
129
(
1992
).
59.
A.
Noorani
, “
Particle-laden turbulent wall-bounded flows in moderately complex geometries
,” Ph.D. thesis (
KTH Royal Institute of Technology
,
2015
).
60.
A.
Noorani
,
R.
Vinuesa
,
L.
Brandt
, and
P.
Schlatter
, “
Aspect ratio effect on particle transport in turbulent duct flows
,”
Phys. Fluids
28
,
115103
(
2016
).
61.
I.
Nezu
, “
Open-channel flow turbulence and its research prospect in the 21st century
,”
J. Hydraul. Eng.
131
,
229
246
(
2005
).
62.
R. J.
Adrian
and
I.
Marusic
, “
Coherent structures in flow over hydraulic engineering surfaces
,”
J. Hydraul. Res.
50
,
451
464
(
2012
).
63.
M.
Uhlmann
,
A.
Pinelli
,
G.
Kawahara
, and
A.
Sekimoto
, “
Marginally turbulent flow in a square duct
,”
J. Fluid Mech.
588
,
153
162
(
2007
).
64.
B.
Galletti
and
A.
Bottaro
, “
Large-scale secondary structures in duct flow
,”
J. Fluid Mech.
512
,
85
94
(
2004
).
65.
P.
Bradshaw
, “
Turbulent secondary flows
,”
Annu. Rev. Fluid Mech.
19
,
53
74
(
1987
).
66.
H.
Oertel
,
Prandtl's Essentials of Fluid Mechanics
(
Springer
,
2004
).
67.
H. A.
Einstein
and
H.
Li
, “
Secondary currents in straight channels
,”
Eos Trans. Am. Geophys. Union
39
,
1085
1088
(
1958
).
68.
L.
Howarth
, “
Concerning secondary flow in straight pipes
,”
Math. Proc. Cambridge Philos. Soc.
34
,
335
(
1938
).
69.
A. A. R.
Townsend
,
The Structure of Turbulent Shear Flow
,
2nd ed.
(
Cambridge University Press
,
New York
,
1956
).
70.
J. W.
Delleur
and
D. S.
McManus
, “
Secondary flow in straight open channels
,” in
Proceedings of the Sixth Midwest Conference on Fluid Mechanics, Austin Texas (
Cambridge University Press
,
1959
), pp.
81
97
.
71.
A. A. R.
Townsend
,
The Structure of Turbulent Shear Flow
,
2nd ed.
(
Cambridge University Press
,
1980
).
72.
A.
Melling
and
J. H.
Whitelaw
, “
Turbulent flow in a rectangular duct
,”
J. Fluid Mech.
78
,
289
315
(
1976
).
73.
A. O.
Demuren
and
W.
Rodi
, “
Calculation of turbulence-driven secondary motion in non-circular ducts
,”
J. Fluid Mech.
140
,
189
222
(
1984
).
74.
A.
Huser
and
S.
Biringen
, “
Direct numerical simulation of turbulent flow in a square duct
,”
J. Fluid Mech.
257
,
65
95
(
1993
).
75.
H.
Wedin
,
D.
Biau
,
A.
Bottaro
, and
M.
Nagata
, “
Coherent flow states in a square duct
,”
Phys. Fluids
20
,
094105
(
2008
).
76.
A.
Vidal
,
R.
Vinuesa
,
P.
Schlatter
, and
H. M.
Nagib
, “
Turbulent rectangular ducts with minimum secondary flow
,”
Int. J. Heat Fluid Flow
72
,
317
328
(
2018
).
77.
A.
Vidal
,
R.
Vinuesa
,
P.
Schlatter
, and
H. M.
Nagib
, “
Influence of corner geometry on the secondary flow in turbulent square ducts
,”
Int. J. Heat Fluid Flow
67
,
69
78
(
2017
).
78.
A.
Vidal
,
R.
Vinuesa
,
P.
Schlatter
, and
H. M.
Nagib
, “
Impact of corner geometry on the secondary flow in turbulent ducts
,” in
Proceedings of the 10th International Symposium on Turbulence and Shear Flow Phenomena
, TSFP-10, Chicago, USA,
2017
.
79.
P.
Orlandi
, “
Vortex dipole rebound from a wall
,”
Phys. Fluids Fluid Dyn.
2
,
1429
1436
(
1990
).
80.
J. R. A.
Pearson
, “
Homogeneous turbulence and laminar viscous flow
,” Ph.D. thesis (
University of Cambridge
,
1957
).
81.
A.
Pal
and
S. G.
Rubin
, “
Asymptotic features of viscous flow along a corner
,”
Q. Appl. Math.
29
,
91
108
(
1971
).
82.
A. G.
Mikhail
and
K. N.
Ghia
, “
Study of viscous compressible flow along an axial corner
,” in
10th Fluid Plasmadynamics Conference (American Institute of Aeronautics and Astronautics
,
1977
), p.
685
.
83.
A. G.
Mikhail
and
K. N.
Ghia
, “
Viscous compressible flow in the boundary region of an axial corner
,”
AIAA J.
16
,
931
939
(
1978
).
84.
H. A.
El-Gamal
and
W. H.
Barclay
, “
Experiments on the laminar flow in a rectangular streamwise corner
,”
Aeronaut. Q.
29
,
75
97
(
1978
).
85.
A.
Ridha
, “
Flow along streamwise corners revisited
,”
J. Fluid Mech.
476
,
223
(
2003
).
86.
M.
Zamir
, “
Similarity and stability of the laminar boundary layer in a streamwise corner
,”
Proc. R. Soc. Lond. A
377
,
269
288
(
1981
).
87.
P. W.
Duck
,
S. R.
Stow
, and
M. R.
Dhanak
, “
Non-similarity solutions to the corner boundary-layer equations (and the effects of wall transpiration)
,”
J. Fluid Mech.
400
,
125
162
(
1999
).
88.
D. H.
Park
,
S. O.
Park
,
K. J.
Kwon
, and
H. J.
Shim
, “
Particle image velocimetry measurement of laminar boundary layer in a streamwise corner
,”
AIAA J.
50
,
811
817
(
2012
).
89.
H. J.
Leutheusser
, “
Turbulent flow in rectangular ducts
,”
J. Hydraul. Div.
89
,
1
19
(
1963
).
90.
A. J.
Melling
, “
Investigation of flow in non-circular ducts and other configurations by laser doppler anemometry
,” Ph.D. thesis (
University of London
,
1975
).
91.
F.
Gessner
,
S.
Ferguson
, and
C.
Lo
, “
Experiments on supersonic turbulent flow development in a square duct
,” in
4th Joint Fluid Mechanics, Plasma Dynamics and Lasers Conference (American Institute of Aeronautics and Astronautics
,
1986
).
92.
V. I.
Kornilov
and
A. M.
Kharitonov
, “
Interaction between turbulent boundary layers in a right dihedral corner
,”
J. Appl. Mech. Tech. Phys.
19
,
336
341
(
1978
).
93.
V. I.
Kornilov
and
A. M.
Kharitonov
, “
On the part played by the local pressure gradient in forming the flow in a corner
,”
Fluid Dyn.
17
,
242
246
(
1982
).
94.
R.
Morajkar
,
Role of Secondary Flows on Flow Separation Induced by Shock/Boundary-Layer Interaction in Supersonic Inlets
(
University of Michigan
,
2017
).
95.
D. I.
Sebacher
and
L. P.
Lee
, “
Crossflow in two-dimensional asymmetric nozzles
,” Report No. NASA TN D-7999 (
1975
).
96.
A.
Trettel
and
J.
Larsson
, “
Mean velocity scaling for compressible wall turbulence with heat transfer
,”
Phys. Fluids
28
,
026102
(
2016
).
97.
R.
Yang
,
D.
Modesti
,
Y.
Zhao
,
Q.
Wang
,
Z.
Wang
, and
S.
Pirozzoli
, “
Influence of corner angle in streamwise supersonic corner flow
,”
Phys. Fluids
33
,
056108
(
2021
).
98.
R.
Yang
,
R.
Yang
, and
Y.
Zhao
, “
Influence of compressibility on the development of streamwise supersonic corner flow
,”
Phys. Fluids
33
,
116102
(
2021
).
99.
S.
Pirozzoli
and
M.
Bernardini
, “
Turbulence in supersonic boundary layers at moderate Reynolds number
,”
J. Fluid Mech.
688
,
120
168
(
2011
).
100.
K.
Gersten
, “
Corner interference effects
,” Report No. AGARD Report 299 (
1959
).
101.
H. J.
Perkins
,
The Turbulent Corner Boundary Layer
(
University of Cambridge
,
1970
).
102.
M.
Zamir
and
A. D.
Young
, “
Experimental investigation of the boundary layer in a streamwise corner
,”
Aeronaut. Q.
21
,
313
339
(
1970
).
103.
O. O.
Mojola
, “
Transition in a streamwise corner
,”
AIAA J.
15
,
427
429
(
1977
).
104.
O. T.
Schmidt
and
U.
Rist
, “
Numerical investigation of classical and bypass transition in streamwise corner-flow
,”
Procedia IUTAM
14
,
218
226
(
2015
).
105.
W. D.
Lakin
and
M. Y.
Hussaini
, “
Stability of the laminar boundary layer in a streamwise corner
,”
Proc. R. Soc. London A
393
,
101
116
(
1983
).
106.
S. J.
Parker
and
S.
Balachandar
, “
Viscous and inviscid instabilities of flow along a streamwise corner
,”
Theor. Comput. Fluid Dyn.
13
,
231
270
(
1999
).
107.
M. R.
Dhanak
, “
On the instability of flow in a streamwise corner
,”
Proc. R. Soc. Lond. A
441
,
201
210
(
1993
).
108.
S.
Balachandar
and
M. R.
Malik
, “
Inviscid instability of streamwise corner flow
,”
J. Fluid Mech.
282
,
187
201
(
1995
).
109.
I.
Galionis
and
P.
Hall
, “
Spatial stability of the incompressible corner flow
,”
Theor. Comput. Fluid Dyn.
19
,
77
113
(
2005
).
110.
P. J.
Schmid
and
D. S.
Henningson
,
Stability and Transition in Shear Flows
(
Springer
,
New York
,
2001
).
111.
H.
Schlichting
and
K.
Gersten
,
Boundary-Layer Theory
(
Springer Berlin Heidelberg
,
Berlin, Heidelberg
,
2017
).
112.
A.
Bottaro
,
P.
Corbett
, and
P.
Luchini
, “
The effect of base flow variation on flow stability
,”
J. Fluid Mech.
476
,
293
302
(
2003
).
113.
D.
Biau
and
A.
Bottaro
, “
Transient growth and minimal defects: Two possible initial paths of transition to turbulence in plane shear flows
,”
Phys. Fluids
16
,
3515
3529
(
2004
).
114.
F.
Alizard
,
J.-C.
Robinet
, and
U.
Rist
, “
Sensitivity to base-flow variation of a streamwise corner flow
,” in
Seventh IUTAM Symposium on Laminar-Turbulent Transition,
edited by P. Schlatter and D. Henningson (Springer, Dordrecht, 2009), Vol. 18, pp.
69
74
.
115.
F.
Alizard
,
J.-C.
Robinet
, and
U.
Rist
, “
Sensitivity analysis of a streamwise corner flow
,”
Phys. Fluids
22
,
014103
(
2010
).
116.
O.
Schmidt
and
U.
Rist
, “
Viscous and inviscid instabilities of supersonic flow in a streamwise corner
,” AIAA Paper No. 2011-3755,
2011
.
117.
O. T.
Schmidt
and
U.
Rist
, “
Linear stability of compressible flow in a streamwise corner
,”
J. Fluid Mech.
688
,
569
590
(
2011
).
118.
O. T.
Schmidt
and
U.
Rist
, “
Viscid–inviscid pseudo-resonance in streamwise corner flow
,”
J. Fluid Mech.
743
,
327
357
(
2014
).
119.
D. J.
Lusher
and
N. D.
Sandham
, “
Shock-wave/boundary-layer interactions in transitional rectangular duct flows
,”
Flow Turbul. Combust.
105
,
649
670
(
2020
).
120.
E. R. G.
Eckert
and
T. F.
Irvine
, Jr., “
Incompressible friction factor, transition and hydrodynamic entrance length studies of ducts with triangular and rectangular cross-sections
,” Report No. WADC-TR-58-85 (
Minnesota University
,
1957
).
121.
E. R. G.
Eckert
and
T. F.
Irvine
, Jr.
, “
Pressure drop and heat transfer in a duct with triangular cross section
,”
J. Heat Transfer
82
,
125
136
(
1960
).
122.
P. C.
Bandopadhayay
and
J. B.
Hinwood
, “
On the coexistence of laminar and turbulent flow in a narrow triangular duct
,”
J. Fluid Mech.
59
,
775
783
(
1973
).
123.
G.
Daschiel
,
B.
Frohnapfel
, and
J.
Jovanović
, “
Numerical investigation of flow through a triangular duct: The coexistence of laminar and turbulent flow
,”
Int. J. Heat Fluid Flow
41
,
27
33
(
2013
).
124.
H.
Raiesi
, “
Theory and simulation of separated boundary layers and turbulence induced secondary motion
,” Ph.D. thesis (
Queen's University
,
2010
).
125.
P.
Orlandi
and
S.
Pirozzoli
, “
Transitional and turbulent flows in rectangular ducts: Budgets and projection in principal mean strain axes
,”
J. Turbul.
21
,
286
310
(
2020
).
126.
B. E.
Owolabi
,
R. J.
Poole
, and
D. J. C.
Dennis
, “
Experiments on low-Reynolds-number turbulent flow through a square duct
,”
J. Fluid Mech.
798
,
398
410
(
2016
).
127.
J.
Jiménez
and
P.
Moin
, “
The minimal flow unit in near-wall turbulence
,”
J. Fluid Mech.
225
,
213
240
(
1991
).
128.
L. G.
Loitsianskii
, “
Interference of boundary layers
,” Report No. 249 (
CAHI
,
1936
).
129.
B.
Thwaites
, “
Approximate calculation of the laminar boundary layer
,”
Aeronaut. Q.
1
,
245
280
(
1949
).
130.
S.
Wilkinson
and
M.
Zamir
, “
Cross-flow and vorticity patterns in the corner boundary layer at different corner angles
,”
Aeronaut. J.
88
,
309
316
(
1984
).
131.
M. R.
Dhanak
and
P. W.
Duck
, “
The effects of freestream pressure gradient on a corner boundary layer
,”
Proc. R. Soc. Math. Phys. Eng. Sci.
453
,
1793
1815
(
1997
).
132.
V. I.
Vasiliev
, “
Self-similar viscous incompressible flow along an unbounded corner
,”
AIAA J.
34
,
946
952
(
1996
).
133.
F. T.
Smith
, “
Three dimensional stagnation point flow into a corner
,”
Proc. R. Soc. Lond. A
344
,
489
507
(
1975
).
134.
A.
Ridha
, “
On the dual solutions associated with boundary-layer equations in a corner
,”
J. Eng. Math
26
,
525
537
(
1992
).
135.
M. H.
Bloom
and
S.
Rubin
, “
High-speed viscous corner flow
,”
J. Aerosp. Sci.
28
,
145
157
(
1961
).
136.
E. R.
Van Driest
,
Investigation of Laminar Boundary Layer in Compressive Fluids Using the Crocco Method
(
NACA
,
Washington D.C.
,
1952
).
137.
C.
Hung
and
R.
Maccormack
, “
Numerical solution of supersonic laminar flow over a three-dimensional compression corner
,” AIAA Paper No. 1977-0694,
1977
.
138.
C. M.
Hung
and
S. S.
Kurasaki
, “
Thin-layer approximation for three-dimensional supersonic corner flows
,”
AIAA J.
18
,
1544
1546
(
1980
).
139.
J. S.
Shang
and
W. L.
Hankey
, “
Numerical solution of the Navier–Stokes equations for a three-dimensional corner
,”
AIAA J.
15
,
1575
1582
(
1977
).
140.
D. C.
Wilcox
,
Turbulence Modeling for CFD
,
3rd ed.
(
DCW Industries, Inc
.,
Mill Valley, California
,
2006
).
141.
Z.
Zhang
,
G.
Cui
, and
C.
Xu
,
Theory and Application of Numerical Simulation of Turbulent Large Eddy
(
Tsinghua University Press
,
2008
) (in Chinese).
142.
C. G.
Speziale
, “
On turbulent secondary flows in pipes of noncircular cross-section
,”
Int. J. Eng. Sci.
20
,
863
872
(
1982
).
143.
C.
Hung
and
R.
Maccormack
, “
Numerical solution of a three-dimensional shock wave and turbulent boundary-layer interaction
,” AIAA Paper No. 1978-0161,
1978
.
144.
M. P.
Escudier
, “
The distribution of the mixing length in turbulent flows near walls
,” Imperial College Report No. TWF/TN/1 (
Mechanical Engineering Department
,
1965
).
145.
J. S.
Shang
,
W. L.
Hankey
, and
J. S.
Petty
, “
Three-dimensional supersonic interacting turbulent flow along a corner
,”
AIAA J.
17
,
706
713
(
1979
).
146.
T.
Cebeci
,
A. M. O.
Smith
, and
G.
Mosinskis
, “
Calculation of compressible adiabatic turbulent boundary layers
,”
AIAA J.
8
,
1974
1982
(
1970
).
147.
A. G.
Mikhail
and
K. N.
Ghia
, “
Analysis and asymptotic solutions of compressible turbulent corner flow
,”
J. Eng. Power
104
,
571
579
(
1982
).
148.
F. B.
Gessner
and
A. F.
Emery
, “
A length-scale model for developing turbulent flow in a rectangular duct
,”
J. Fluids Eng.
99
,
347
356
(
1977
).
149.
D. O.
Davis
and
G. D.
Kerlick
, “
Experimental and numerical investigation of supersonic turbulent flow through a square duct
,”
AIAA J.
24
,
1508
1515
(
1986
).
150.
M.
Mani
,
D.
Babcock
,
C.
Winkler
, and
P.
Spalart
, “
Predictions of a supersonic turbulent flow in a square duct
,” AIAA Paper No. 2013-0860,
2013
.
151.
P. R.
Spalart
, “
Strategies for turbulence modelling and simulations
,”
Int. J. Heat Fluid Flow
21
,
252
263
(
2000
).
152.
P.
Spalart
, “
Reflections on RANS modeling
,” in Progress in Hybrid RANS-LES Modelling (Springer,
2012
).
153.
K.
Yamamoto
,
K.
Tanaka
, and
M.
Murayama
, “
Effect of a nonlinear constitutive relation for turbulence modeling on predicting flow separation at wing-body juncture of transonic commercial aircraft
,” AIAA Paper No. 2012-2895,
2012
.
154.
H. J.
Nagapetyan
, “
Development and application of quadratic constitutive relation and transitional crossflow effects in the Wray–Agarwal turbulence model
,” Ph.D. thesis (Washington University in St. Louis,
2018
).
155.
B. E.
Launder
and
W. M.
Ying
, “
Prediction of flow and heat transfer in ducts of square cross-section
,” in
Proceedings of the Institution of Mechanical Engineers
(Institution of Mechanical Engineers, 1973), pp.
455
461
.
156.
D.
Modesti
, “
A priori tests of eddy viscosity models in square duct flow
,”
Theor. Comput. Fluid Dyn.
34
,
713
(
2020
).
157.
R.
Pecnik
and
G.
Iaccarino
, “
Predictions of turbulent secondary flows using the v2-f model
,” AIAA Paper No. 2008-3852,
2008
.
158.
S.
Nisizima
and
A.
Yoshizawa
, “
Turbulent channel and Couette flows using an anisotropic k-epsilon model
,”
AIAA J.
25
,
414
420
(
1987
).
159.
F. B.
Gessner
and
A. F.
Emery
, “
A Reynolds stress model for turbulent corner flows. I: Development of the model
,”
J. Fluids Eng.
98
,
261
268
(
1976
).
160.
F. B.
Gessner
and
J. K.
Po
, “
A Reynolds stress model for turbulent corner flows. II. Comparisons between theory and experiment
,”
J. Fluids Eng.
98
,
269
276
(
1976
).
161.
M. S.
Filonovich
,
J. B.
Leal
, and
L. R.
Rojas-Solórzano
, “
Prediction of compound channel secondary flows using anisotropic turbulence models
,” in
Proceedings of the 2014 International Conference on Informatics, Networking and Intelligent Computing (INIC 2014)
, Shenzhen, China, 16–17 November 2014 (
CRC Press
,
2015
), p.
163
.
162.
S. B.
Pope
,
Turbulent Flows
(
Cambridge University Press
,
Cambridge, New York
,
2000
).
163.
M. S.
Vázquez
and
O.
Métais
, “
Large-eddy simulation of the turbulent flow through a heated square duct
,”
J. Fluid Mech.
453
,
201
238
(
2002
).
164.
T.
Kaller
,
S.
Hickel
, and
N.
Adams
, “
LES of an asymmetrically heated high aspect ratio duct at high Reynolds number at different wall temperatures
,” AIAA Paper No. 2018-4287,
2018
.
165.
T.
Kaller
,
V.
Pasquariello
,
S.
Hickel
, and
N. A.
Adams
, “
Turbulent flow through a high aspect ratio cooling duct with asymmetric wall heating
,”
J. Fluid Mech.
860
,
258
299
(
2019
).
166.
Z.
Vane
and
S. K.
Lele
, “
Prediction of turbulent secondary flows in ducts using equilibrium wall-modeled LES
,” AIAA Paper No. 2015-1274,
2015
.
167.
Z. P.
Vane
,
I.
Bermejo-Moreno
, and
S. K.
Lele
, “
Wall-modeled large-eddy simulations of a supersonic turbulent flow in a square duct
,” AIAA Paper No. 2014-2209,
2014
.
168.
R.
Yang
,
Z.
Wang
,
Y.
Zhao
,
Q.
Wang
, and
W.
Feng
, “
Numerical investigation on spatial development of the secondary flow in a supersonic turbulent square duct
,”
Aerosp. Sci. Technol.
100
,
105832
(
2020
).
169.
O.
Marin
,
R.
Vinuesa
,
A. V.
Obabko
, and
P.
Schlatter
, “
Characterization of the secondary flow in hexagonal ducts
,”
Phys. Fluids
28
,
125101
(
2016
).
170.
R.
Vinuesa
,
A.
Noorani
,
A.
Lozano-Durán
,
G. K. E.
Khoury
,
P.
Schlatter
,
P. F.
Fischer
, and
H. M.
Nagib
, “
Aspect ratio effects in turbulent duct flows studied through direct numerical simulation
,”
J. Turbul.
15
,
677
706
(
2014
).
171.
R.
Vinuesa
,
P.
Schlatter
, and
H. M.
Nagib
, “
Secondary flow in turbulent ducts with increasing aspect ratio
,”
Phys. Rev. Fluids.
3
,
054606
(
2018
).
172.
H.
Zhang
,
F. X.
Trias
,
A.
Gorobets
,
Y.
Tan
, and
A.
Oliva
, “
Direct numerical simulation of a fully developed turbulent square duct flow up to Reτ = 1200
,”
Int. J. Heat Fluid Flow
54
,
258
267
(
2015
).
173.
R.
Vinuesa
,
P.
Schlatter
,
J.
Malm
,
C.
Mavriplis
, and
D. S.
Henningson
, “
Direct numerical simulation of the flow around a wall-mounted square cylinder under various inflow conditions
,”
J. Turbul.
16
,
555
587
(
2015
).
174.
M.
Atzori
,
R.
Vinuesa
,
A.
Lozano-Durán
, and
P.
Schlatter
, “
Characterization of turbulent coherent structures in square duct flow
,”
J. Phys. Conf. Ser.
1001
,
012008
(
2018
).
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