A direct numerical simulation is made for the incompressible turbulent flow in the 180 deg curved channel with a long straight portion connected to its exit port. An examination is made for how the organized coherent vortex grows and decays in the curved channel: the radius ratio of 0.92, the aspect ratio of 7.2, and the succeeding straight section length of 75 times the channel half width. The 1552 × 91 × 128 ( = 18,427,136) grids are allocated to the computational domain. The frictional-velocity-based Reynolds number is kept at 150 to resolve the long domain including curved and straight regions. In contrast to that the coherent vortex grows along the concave wall, the vortex remains strong in the convex-wall side after the curvature accompanying a tail of the small-scale turbulence near the convex wall. The dissimilarity between the onset and disappearing of the coherent vortex essentially comes from the mean pressure gradient, which aids or averts the near-wall fluid oppositely between the curvature inlet and the exit. The mean flow is decelerated near the inlet of the convex wall to destabilize the flow and to trigger the onset of the coherent vortex. Contrary, the mean flow is accelerated near the exit of the convex wall to weaken the coherent vortex, and is decelerated near the exit of the concave wall to enhance the turbulence. Therefore, the turbulence enhancement and attenuation occurs oppositely between the inlet and exit of the curvature, and the coherent vortex draws a wake in the convex-side rather than the concave-side where it starts.

References

References
1.
Ligrani
,
P. M.
, and
Niver
,
R. D.
,
1988
, “
Flow Visualization of Dean Vortices in a Curved Channel With 40 to 1 Aspect Ratio
,”
Phys. Fluids A
,
31
, pp.
3605
3617
.10.1063/1.866877
2.
Ligrani
,
P. M.
,
Finlay
,
W. H.
,
Field
,
W. A.
,
Fuqua
,
S. J.
, and
Subramanian
,
C. S.
,
1992
, “
Features of Wavy Vortices in a Curved Channel From Experimental and Numerical Studies
,”
Phys. Fluids A
,
4
, pp.
695
709
.10.1063/1.858289
3.
Bland
,
S. B.
, and
Finlay
,
W. H.
,
1991
, “
Transitions Toward Turbulence in a Curved Channel
,”
Phys. Fluids A
,
3
, pp.
106
114
.10.1063/1.857870
4.
Guo
,
Y.
, and
Finlay
,
W. H.
,
1991
, “
Splitting, Merging and Wavelength Selection of Vortices in Curved and/or Rotating Channel Flow Due to Eckhaus Instability
,”
J. Fluid Mech.
,
228
, pp.
661
691
.10.1017/S0022112091002859
5.
Ligrani
,
P. M.
,
Skogerboe
,
P.
,
Schallert
,
A. R.
, and
Skogerboe
,
P.
,
1996
, “
Effects of Dean Vortex Pairs on Surface Heat Transfer in Curved Channel Flow
,”
Int. J. Heat Mass Transfer
,
39
, pp.
27
37
.10.1016/S0017-9310(96)85003-4
6.
Ligrani
,
P. M.
, and
Hedlund
,
C. R.
,
1998
, “
Transition to Turbulent Flow in Curved and Straight Channels With Heat Transfer at High Dean Numbers
,”
Int. J. Heat Mass Transfer
,
41
, pp.
1739
1748
.10.1016/S0017-9310(97)00264-0
7.
Kobayashi
,
M.
,
Maekawa
,
H.
,
Takano
,
T.
, and
Hayakawa
,
S.
,
1991
, “
An Experimental Study on a Turbulent Flow in a Two-Dimensional Curved Channel (Time-Mean Velocity and Multiple Velocity Correlations in the Entrance Section)
,”
Trans. Jpn. Soc. Mech. Eng., Ser. B
,
57
, pp.
4064
4071
.10.1299/kikaib.57.4064
8.
Kobayashi
,
M.
,
Maekawa
,
H.
,
Shimizu
,
Y.
, and
Uchiyama
,
K.
,
1992
, “
An Experimental Study on a Turbulent Flow in a Two-Dimensional Curved Channel (Space-Time Correlation and Spectra of Velocity Fluctuations)
,”
Trans. Jpn. Soc. Mech. Eng., Ser. B
,
58
, pp.
119
126
.10.1299/kikaib.58.119
9.
Moser
,
R. D.
, and
Moin
,
P.
,
1987
, “
The Effects of Curvature in Wall-Bounded Turbulent Flows
,”
J. Fluid Mech.
,
175
, pp.
479
510
.10.1017/S0022112087000491
10.
Zhang
,
J.
,
Zhang
,
B.
, and
Ju
,
J.
,
2001
, “
Fluid Flow in a Rotating Curved Rectangular Duct
,”
Int. J. Heat Fluid Flow
,
22
, pp.
583
592
.10.1016/S0142-727X(01)00126-6
11.
Nagata
,
M.
, and
Kasagi
,
N.
,
2004
, “
Spatio-Temporal Evolution of Coherent Vortices in Wall Turbulence With Streamwise Curvature
,”
J. Turbul.
,
5
, pp.
17
46
.10.1088/1468-5248/5/1/017
12.
Wu
,
H.
, and
Kasagi
,
N.
,
2004
, “
Effects of Arbitrary Directional System Rotation on Turbulent Channel Flow
,”
Phys. Fluids
,
16
, pp.
979
990
.10.1063/1.1649337
13.
Wu
,
H.
, and
Kasagi
,
N.
,
2004
, “
Turbulent Heat Transfer in a Channel Flow With Arbitrary Directional System Rotation
,”
Int. J. Heat Mass Transfer
,
47
, pp.
4579
4591
.10.1016/j.ijheatmasstransfer.2003.07.034
14.
Ko
,
T. H.
, and
Ting
,
K.
,
2006
, “
Entropy Generation and Optimal Analysis for Laminar Forced Convection in Curved Rectangular Ducts: A Numerical Study
,”
Int. J. Therm. Sci.
,
45
, pp.
138
150
.10.1016/j.ijthermalsci.2005.01.010
15.
Ko
,
T. H.
, and
Wu
,
C. P.
,
2009
, “
A Numerical Study on Entropy Generation Induced by Turbulent Forced Convection in Curved Rectangular Ducts With Various Aspect Ratios
,”
Int. Commun. Heat Mass Transfer
,
36
, pp.
25
31
.10.1016/j.icheatmasstransfer.2008.08.016
16.
Guo
,
J.
,
Xu
,
M.
, and
Cheng
,
L.
,
2011
, “
Second Law Analysis of Curved Rectangular Channels
,”
Int. J. Therm. Sci.
,
50
, pp.
760
768
.10.1016/j.ijthermalsci.2010.12.011
17.
Liu
,
F.
, and
Wang
,
L.
,
2009
, “
Analysis on Multiplicity and Stability of Convective Heat Transfer in Tightly Curved Rectangular Ducts
,”
Int. J. Heat Mass Transfer
,
52
, pp.
5849
5866
.10.1016/j.ijheatmasstransfer.2009.07.019
18.
Xun
,
Q. Q.
,
Wang
,
B. C.
, and
Yee
,
E.
,
2011
, “
Large-Eddy Simulation of Turbulent Heat Convection in a Spanwise Rotating Channel Flow
,”
Int. J. Heat Mass Transfer
,
54
, pp.
698
716
.10.1016/j.ijheatmasstransfer.2010.08.018
19.
Matsubara
,
K.
,
Miura
,
T.
,
Sakurai
,
A.
,
Yamazaki
,
K.
, and
Takeda
,
M.
,
2012
, “
Heat Transfer Characteristics and Reynolds Stress Budget of Spatially Advancing Turbulent Flow in a Curved Channel
,”
Numer. Heat Transfer, Part A
,
60
, pp.
234
253
.10.1080/10407782.2011.588562
20.
Matsubara
,
K.
,
Sakurai
,
A.
,
Yamazaki
,
K.
, and
Takeda
,
M.
,
2011
, “
Spatially Advancing Coherent Structures in Curved Channel Turbulent Flow
,”
Phys. Fluids
,
23
, p.
065102
.10.1063/1.3584126
21.
Kim
,
J.
, and
Moin
,
P.
,
1985
, “
Application of a Fractional Step Method to Incompressible Navier–Stokes Equations
,”
J. Comput. Phys.
,
59
, pp.
308
323
.10.1016/0021-9991(85)90148-2
22.
Matsubara
,
K.
,
Kobayashi
,
M.
, and
Maekawa
,
H.
,
1998
, “
Direct Numerical Simulation of a Turbulent Channel Flow With a Linear Spanwise Mean Temperature Gradient
,”
Int. J. Heat Mass Transfer
,
41
, pp.
3627
3634
.10.1016/S0017-9310(98)00072-6
23.
Matsubara
,
K.
,
Kobayashi
,
M.
,
Sakai
,
T.
, and
Suto
,
H.
,
2001
, “
A Study on Spanwise Heat Transfer in a Turbulent Channel Flow—Eduction of Coherent Structures by a Conditional Sampling Technique
,”
Int. J. Heat Fluid Flow
,
22
, pp.
213
219
.10.1016/S0142-727X(01)00082-0
24.
Sakurai
,
A.
,
Matsubara
,
K.
,
Takakuwa
,
K.
, and
Kanbayashi
,
R.
,
2012
, “
Radiation Effects on Mixed Turbulent Natural and Forced Convection in a Horizontal Channel Using Direct Numerical Simulation
,”
Int. J. Heat Mass Transfer
,
55
, pp.
2539
2548
.10.1016/j.ijheatmasstransfer.2012.01.006
25.
Lele
,
S. K.
,
1992
, “
Compact Finite Difference Scheme With Spectral-like Resolution
,”
J. Comput. Phys.
,
103
, pp.
16
42
.10.1016/0021-9991(92)90324-R
26.
Kasagi
,
N.
,
Tomita
,
Y.
, and
Kuroda
,
A.
,
1992
, “
Direct Numerical Simulation of Passive Scalar Field in a Turbulent Channel Flow
,”
ASME Trans. J. Heat Transfer
,
114
, pp.
598
606
.10.1115/1.2911323
27.
Kim
,
J.
,
Moin
,
P.
, and
Moser
,
R.
,
1987
, “
Turbulence Statistics in Fully Developed Channel Flow at Low Reynolds Number
,”
J. Fluid Mech.
,
177
, pp.
133
166
.10.1017/S0022112087000892
28.
Jeong
,
J.
,
Hussain
,
F.
,
Schoppa
,
W.
, and
Kim
,
J.
,
1997
, “
Coherent Structures Near the Wall in a Turbulent Channel Flow
,”
J. Fluid Mech.
,
332
, pp.
185
214
.
You do not currently have access to this content.