A fully developed turbulent flow in a rotating straight square duct is simulated by direct numerical simulations at Reτ = 300 and 0 ≤ Roτ ≤ 40. The rotating axis is parallel to two opposite walls of the duct and normal to the main flow. Variations of the turbulence statistics with the rotation rate are presented, and a comparison with the rotating turbulent channel flow is discussed. Rich secondary flow patterns in the cross section are observed by varying the rotation rate. The appearance of a pair of additional vortices above the pressure wall is carefully examined, and the underlying mechanism is explained according to the budget analysis of the mean momentum equations.
REFERENCES
1.
J. P.
Johnston
, R.
Halleen
, and D. K.
Lezius
, “Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow
,” J. Fluid Mech.
56
(3
), 533
–557
(1972
).2.
D. K.
Lezius
and J. P.
Johnston
, “Roll-cell instabilities in rotating laminar and trubulent channel flows
,” J. Fluid Mech.
77
(01
), 153
–174
(1976
).3.
R.
Kristoffersen
and H. I.
Andersson
, “Direct simulations of low-Reynolds-number turbulent flow in a rotating channel
,” J. Fluid Mech.
256
, 163
–197
(1993
).4.
O.
Grundestam
, S.
Wallin
, and A. V.
Johansson
, “Direct numerical simulations of rotating turbulent channel flow
,” J. Fluid Mech.
598
, 177
–200
(2008
).5.
H.
Wu
and N.
Kasagi
, “Effects of arbitrary directional system rotation on turbulent channel flow
,” Phys. Fluids (1994-present)
16
(4
), 979
–990
(2004
).6.
A.
Mehdizadeh
and M.
Oberlack
, “Analytical and numerical investigations of laminar and turbulent Poiseuille–Ekman flow at different rotation rates
,” Phys. Fluids (1994-present)
22
(10
), 105104
(2010
).7.
L.
Prandtl
, Essentials of Fluid Dynamics: With Applications to Hydraulics Aeronautics, Meteorology, and Other Subjects
(Hafner Publishing Company
, 1952
).8.
F. B.
Gessner
, “The origin of secondary flow in turbulent flow
,” J. Fluid Mech.
58
(01
), 1
–25
(1972
).9.
S.
Gavrilakis
, “Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct
,” J. Fluid Mech.
244
, 101
–129
(1992
).10.
A.
Huser
and S.
Biringen
, “Direct numerical simulation of turbulent flow in a square duct
,” J. Fluid Mech.
257
, 65
–95
(1993
).11.
A.
Pinelli
, “Reynolds number dependence of mean flow structure in square duct turbulence
,” J. Fluid Mech.
644
, 107
(2010
).12.
J. E.
Hart
, “Instability and secondary motion in a rotating channel flow
,” J. Fluid Mech.
45
(02
), 341
–351
(1971
).13.
J.
Pallares
and L.
Davidson
, “Large-eddy simulations of turbulent heat transfer in stationary and rotating square ducts
,” Phys. Fluids (1994-present)
14
(8
), 2804
–2816
(2002
).14.
J.
Pallares
, F.
Grau
, and L.
Davidson
, “Pressure drop and heat transfer rates in forced convection rotating square duct flows at high rotation rates
,” Phys. Fluids (1994-present)
17
(7
), 075102
(2005
).15.
H. S.
Kheshgi
and L. E.
Scriven
, “Viscous flow through a rotating square channel
,” Phys. Fluids (1958-1988)
28
(10
), 2968
–2979
(1985
).16.
C. G.
Speziale
, “Numerical study of viscous flow in rotating rectangular ducts
,” J. Fluid Mech.
122
, 251
–271
(1982
).17.
G. H.
Lee
and J. H.
Baek
, “A numerical study of the similarity of fully developed turbulent flows in orthogonally rotating square ducts and stationary curved square ducts
,” Int. J. Numer. Methods Heat Fluid Flow
12
(3
), 241
–257
(2002
).18.
Z.
Qin
and R. H.
Pletcher
, “The velocity field and instability of rotating duct flow
,” Phys. Fluids (1994-present)
19
(5
), 104106
(2007
).19.
A.
Habip
, “A computational study of laminar and turbulent flows in rotating rectangular ducts
,” Ph.D. dissertation (Texas Tech University
, 1993
).20.
J.
Pallares
and L.
Davidson
, “Large-eddy simulations of turbulent flow in a rotating square duct
,” Phys. Fluids (1994-present)
12
(11
), 2878
–2894
(2000
).21.
G.
Karniadakis
and S.
Sherwin
, Spectral/hp Element Methods for Computational Fluid Dynamics
(Oxford University Press
, 2005
).22.
H. M.
Blackburn
, Using Semtex, version 7.1, Monash University, 5 October 2013, source code is available at http://users.monash.edu.au/~bburn/semtex.html.23.
G. E.
Karniadakis
, M.
Israeli
, and S. A.
Orszag
, “High-order splitting methods for the incompressible Navier-Stokes equations
,” J. Comput. Phys.
97
(2
), 414
–443
(1991
).24.
J.
Kim
, P.
Moin
, and R.
Moser
, “Turbulence statistics in fully developed channel flow at low Reynolds number
,” J. Fluid Mech.
177
, 133
–166
(1987
).25.
H.
Iacovides
and B.
Launder
, “Parametric and numerical study of fully developed flow and heat transfer in rotating rectangular ducts
,” J. Turbomachinery
113
(3
), 331
–338
(1991
).26.
P.
Bradshaw
, “The analogy between streamline curvature and buoyancy in turbulent shear flow
,” J. Fluid Mech.
36
(01
), 177
–191
(1969
).27.
K.
Alvelius
, Studies of Turbulence and Its Modelling Through Large Eddy- and Direct Numerical Simulation
(Royal Institute of Technology
, 1999
).© 2015 AIP Publishing LLC.
2015
AIP Publishing LLC
You do not currently have access to this content.
