Graphical Abstract Figure
Graphical Abstract Figure
Close modal

Abstract

A numerical study based on steady Reynolds-averaged-Navier–Stokes (RANS) with the shear stress transport (SST) turbulence model was performed to investigate the flow and heat transfer in a ribbed U-duct with a rectangular cross section that converges linearly in the radially outward direction and diverges linearly in the radially inward direction under rotating and nonrotating conditions. Parameters examined include rotation number (Roi = 0, 0.0219, 0.0336, 0.0731), Reynolds number (Rei = 46,000, 100,000, and 154,000), and the duct's taper angle (α = 0 deg and 1.41 deg) under conditions relevant to gas turbines used for electric power generation. Results obtained show that increasing the taper angle from 0 deg to 1.41 deg, which appears negligibly small, significantly increases both the friction coefficient and the Nusselt number whether there is rotation or not. With rotation at Roi = 0.0336 and Rei = 100,000, the maximum increase in the average friction coefficient and Nusselt number was found to be 41.7% and 36.6%, respectively. Without rotation at Rei = 46,000, those are 11.5% and 14.7%, respectively.

References

1.
Chandra
,
P. R.
,
Han
,
J. C.
, and
Lau
,
S. C.
,
1988
, “
Effect of Rib Angle on Local Heat Mass Transfer Distribution in a Two-Pass Rib-Roughened Channel
,”
ASME J. Turbomach.
,
110
(
2
), pp.
233
241
.
2.
Dutta
,
S.
,
Han
,
J. C.
, and
Lee
,
C. P.
,
1995
, “
Experimental Heat Transfer in a Rotating Triangular Duct Effect of Model Orientation
,”
ASME Trans.
,
117
(
4
), pp.
1058
1061
.
3.
Dutta
,
S.
,
Han
,
J. C.
,
Zhang
,
Y.
, and
Lee
,
C. P.
,
1996
, “
Local Heat Transfer in a Rotating Two-Pass Triangular Duct With Smooth Walls
,”
ASME J. Turbomach.
,
118
(
3
), pp.
435
443
.
4.
Dutta
,
S.
, and
Han
,
J. C.
,
1996
, “
Local Heat Transfer in Rotating Smooth and Ribbed Two-Pass Square Channels With Three Channel Orientations
,”
ASME J. Heat Transfer
,
118
(
3
), pp.
578
584
.
5.
Azad
,
G. S.
,
Uddin
,
M. J.
,
Han
,
J. C.
,
Moon
,
H. K.
, and
Glezer
,
B.
,
2002
, “
Heat Transfer in a Two-Pass Rectangular Rotating Channel With 45-Deg Angled Rib Turbulators
,”
ASME J. Turbomach.
,
124
(
2
), pp.
251
259
.
6.
Wright
,
L. M.
,
Fu
,
W.-L.
, and
Han
,
J. C.
,
2004
, “
Thermal Performance of Angled, V-Shaped, and W-Shaped Rib Turbulators in Rotating Rectangular Cooling Channels (AR=4:1)
,”
ASME J. Turbomach.
,
126
(
4
), pp.
604
614
.
7.
Alkhamis
,
N. Y.
,
Rallabandi
,
A. P.
, and
Han
,
J.-C.
,
2011
, “
Heat Transfer and Pressure Drop Correlations for Square Channels With V-Shaped Ribs at High Reynolds Numbers
,”
ASME J. Heat Transfer
,
133
(
11
), p.
111901
.
8.
Lei
,
J.
,
Han
,
J. C.
, and
Huh
,
M.
,
2012
, “
Effect of Rib Spacing on Heat Transfer in a Two Pass Rectangular Channel (AR=2:1) at High Rotation Numbers
,”
ASME J. Heat Transfer
,
134
(
9
), p.
091901
.
9.
Huh
,
M.
,
Lei
,
J.
, and
Han
,
J. C.
,
2012
, “
Influence of Channel Orientation on Heat Transfer in a Two-Pass Smooth and Ribbed Rectangular Channel (AR=2:1) Under Large Rotation Numbers
,”
ASME J. Turbomach.
,
134
(
1
), p.
011022
.
10.
Mhetras
,
S.
,
Han
,
J.-C.
, and
Huh
,
M.
,
2014
, “
Heat Transfer and Pressure Loss Measurements in a Turbulated High Aspect Ratio Channel With Large Reynolds Number Flows
,”
ASME J. Therm. Sci. Eng. Appl.
,
6
(
4
), p.
041001
.
11.
Chen
,
A. F.
,
Shiau
,
C. C.
,
Han
,
J. C.
, and
Krewinkel
,
R.
,
2019
, “
Heat Transfer in a Rotating Two-Pass Rectangular Channel Featuring Reduced Cross-Sectional Area After Tip Turn (Aspect Ratio=4:1 to 2:1) With Profiled 60 Deg Angled Ribs
,”
ASME J. Turbomach.
,
141
(
7
), p.
071008
.
12.
Chen
,
I. L.
,
Sahin
,
I.
,
Wright
,
L. M.
,
Han
,
J. C.
, and
Krewinkel
,
R.
,
2022
, “
Heat Transfer in a Rotating, Blade-Shaped, Two-Pass Cooling Channel With a Variable Aspect Ratio
,”
ASME J. Turbomach.
,
144
(
2
), p.
021011
.
13.
Alsaleem
,
S. M.
,
Wright
,
L. M.
, and
Han
,
J. C.
,
2023
, “
Heat Transfer and Friction in a Rectangular Channel With Varying Numbers of Walls Roughened With 90-Deg Transverse or 45-Deg V-Shaped Ribs
,”
ASME J. Heat Transfer.
,
145
(
2
), p.
023901
.
14.
Wagner
,
J. H.
,
Johnson
,
B. V.
, and
Hajek
,
T. J.
,
1991
, “
Heat Transfer in Rotating Passages With Smooth Walls and Radial Outward Flow
,”
ASME J. Turbomach.
,
113
(
1
), pp.
42
51
.
15.
Wagner
,
J. H.
,
Johnson
,
B. V.
, and
Kopper
,
F. C.
,
1991
, “
Heat Transfer in Rotating Serpentine Passages With Smooth Walls
,”
ASME J. Turbomach.
,
113
(
3
), pp.
321
330
.
16.
Wagner
,
J. H.
,
Johnson
,
B. V.
,
Graziani
,
R. A.
, and
Yeh
,
F. C.
,
1992
, “
Heat Transfer in Rotating Serpentine Passages With Trips Normal to the Flow
,”
ASME J. Turbomach.
,
114
(
4
), pp.
847
857
.
17.
Johnson
,
B. V.
,
Wagner
,
J. H.
,
Steuber
,
G. D.
, and
Yeh
,
F. C.
,
1994
, “
Heat Transfer in Rotating Serpentine Passages With Selected Model Orientations for Smooth or Skewed Trip Walls
,”
ASME J. Turbomach.
,
116
(
4
), pp.
738
744
.
18.
Johnson
,
B. V.
,
Wagner
,
J. H.
,
Steuber
,
G. D.
, and
Yeh
,
F. C.
,
1994
, “
Heat Transfer in Rotating Serpentine Passages With Trips Skewed to the Flow
,”
ASME J. Turbomach.
,
116
(
1
), pp.
113
123
.
19.
Stephens
,
M. A.
,
Shih
,
T. I.-P.
, and
Civinskas
,
K. C.
,
1996
, “Computations of Flow and Heat Transfer in a Rotating U-shaped Square Duct,” AIAA Paper 96-3161.
20.
Stephens
,
M. A.
, and
Shih
,
T. I.-P.
,
1997
, “Computation of Compressible Flow and Heat Transfer in a Rotating Duct With Inclined Ribs and a 180-Degree Bend,” ASME Paper 97-GT-192.
21.
Shih
,
T. I.-P.
,
Lin
,
Y.-L.
,
Stephens
,
M. A.
,
Chyu
,
M. K.
, and
Civinskas
,
K. C.
“Flow and Heat Transfer in a Ribbed U-Duct under Typical Engine Conditions,” ASME Paper 98-GT-213.
22.
Stephens
,
M. A.
, and
Shih
,
T. I.-P.
,
1999
, “
Flow and Heat Transfer in a Smooth U-Duct With and Without Rotation
,”
AIAA J. Propul. Power
,
15
(
2
), pp.
272
279
.
23.
Lin
,
Y.-L.
,
Shih
,
T. I.-P.
,
Stephens
,
M. A.
, and
Chyu
,
M. K.
,
2001
, “
A Numerical Study of Flow and Heat Transfer in a Smooth and Ribbed U-Duct With and Without Rotation
,”
ASME J. Heat Transfer
,
123
(
2
), pp.
219
232
.
24.
Shih
,
T. I.-P.
,
Lin
,
Y.-L.
, and
Stephens
,
M. A.
,
2001
, “
Fluid Flow and Heat Transfer in an Internal Coolant Passage
,”
Int. J. Rotating Mach.
,
7
(
5
), pp.
351
364
.
25.
Hu
,
S.-Y.
,
Chi
,
X.
,
Shih
,
T. I.-P.
,
Bryden, Chyu
,
M. K.
,
Ames
,
R.
, and
Dennis
,
R. A.
,
2011
, “Flow and Heat Transfer in the Tip-Turn Region of a U-Duct under Rotating and Non-Rotating Conditions,” ASME GT-2011-46013.
26.
Hu
,
S.-Y.
, and
Shih
,
T. I.-P.
,
2018
, “Large-Eddy and RANS Simulations of Heat Transfer in a U-Duct With a High-Aspect Ratio Trapezoidal Cross Section,” ASME GT-2018-75535.
27.
Hu
,
S.-Y.
,
Chi
,
X.
,
Shih
,
T. I.-P.
,
Chyu
,
M. K.
, and
Crawford
,
M.
,
2019
, “
Steady RANS of Flow and Heat Transfer in a Smooth and Pin-Finned U-Duct With a Trapezoidal Cross Section
,”
ASME J. Eng. Gas Turbines Power
,
141
(
6
), p.
061009
.
28.
Taslim
,
M. E.
,
Rahman
,
A.
, and
Spring
,
S. D.
,
1991
, “
An Experimental Investigation of Heat Transfer Coefficients in a Spanwise Rotating Channel With Two Opposite Rib-Roughened Walls
,”
ASME J. Turbomach.
,
113
(
1
), pp.
75
82
.
29.
Taslim
,
M. E.
,
Bondi
,
L. A.
, and
Kercher
,
D. M.
,
1991
, “
An Experimental Investigation of Heat Transfer in an Orthogonally Rotating Channel Roughened With 45 Deg Criss-Cross Ribs on Two Opposite Walls
,”
ASME J. Turbomach.
,
113
(
3
), pp.
346
353
.
30.
El-Husayni
,
H. A.
,
Taslim
,
M. E.
, and
Kercher
,
D. M.
,
1994
, “
Experimental Heat Transfer Investigation of Stationary and Orthogonally Rotating Asymmetric and Symmetric Heated Smooth and Turbulated Channels
,”
ASME J. Turbomach.
,
116
(
1
), pp.
124
132
.
31.
Korotky
,
G. J.
, and
Taslim
,
M. E.
,
1998
, “
Rib Heat Transfer Coefficient Measurements in a Rib-Roughened Square Passage
,”
ASME J. Turbomach.
,
120
(
2
), pp.
376
385
.
32.
Taslim
,
M. E.
,
Li
,
T.
, and
Spring
,
S. D.
,
1998
, “
Measurements of Heat Transfer Coefficients and Friction Factors in Passages Rib-Roughened on All Walls
,”
ASME J. Turbomach.
,
120
(
3
), pp.
564
570
.
33.
Taslim
,
M. E.
, and
Lengkong
,
A.
,
1998
, “
45 Deg Staggered Rib Heat Transfer Coefficient Measurements in a Square Channel
,”
ASME J. Turbomach.
,
120
(
3
), pp.
571
580
.
34.
Taslim
,
M. E.
, and
Korotky
,
G. J.
,
1998
, “
Low-Aspect-Ratio Rib Heat Transfer Coefficient Measurements in a Square Channel
,”
ASME J. Turbomach.
,
120
(
4
), pp.
831
838
.
35.
Taslim
,
M. E.
, and
Lengkong
,
A.
,
1999
, “
45 Deg Round-Corner Rib Heat Transfer Coefficient Measurements in a Square Channel
,”
ASME J. Turbomach.
,
121
(
2
), pp.
272
280
.
36.
Lamont
,
J.
,
Ramesh
,
S.
,
Ekkad
,
S. V.
,
Tolpadi
,
A.
,
Kaminski
,
C.
, and
Salamah
,
S.
,
2013
, “
Heat Transfer Enhancement in Narrow Diverging Channels
,”
ASME J. Turbomach.
,
135
(
4
), p.
041017
.
37.
Saha
,
K.
, and
Acharya
,
S.
,
2013
, “
Bend Geometries in Internal Cooling Channels for Improved Thermal Performance
,”
ASME J. Turbomach.
,
135
(
3
), p.
031028
.
38.
Saha
,
K.
, and
Acharya
,
S.
,
2013
, “
Effect of Bend Geometry on Heat Transfer and Pressure Drop in a Two-Pass Coolant Square Channel for a Turbine
,”
ASME J. Turbomach.
,
135
(
2
), p.
021035
.
39.
Li
,
H.
,
You
,
R.
,
Deng
,
H.
,
Tao
,
Z.
, and
Zhu
,
J.
,
2016
, “
Heat Transfer Investigation in a Rotating U-Turn Smooth Channel With Irregular Cross-Section
,”
Int. J. Heat Mass Transfer
,
96
, pp.
267
277
.
40.
Bohn
,
D. E.
,
Becker
,
V. J.
,
Kusterer
,
K. A.
,
Otsukl
,
Y.
,
Sugimoto
,
T.
, and
Tanaka
,
R.
,
1999
, “3-D Internal Flow and Conjugate Calculations of a Convective Cooled Turbine Blade With Serpentine-Shaped and Ribbed Channels,” ASME Paper 99-GT-220.
41.
Chyu
,
M. K.
,
1991
, “
Regional Heat Transfer in Two-Pass and Three-Pass Passages With 180-Deg Sharp Turns
,”
ASME J. Heat Transfer
,
113
(
1
), pp.
63
70
.
42.
Dowd
,
C.
, and
Tafti
,
D.
,
2016
, “Regional Heat Transfer in Two-Pass and Three-Pass Passages With 180-Deg Sharp Turns,” ASME HT-2016-7348.
43.
Zhang
,
Y. M.
,
Han
,
J. C.
,
Parsons
,
J. A.
, and
Lee
,
C. P.
,
1995
, “
Surface Heating Effect on Local Heat Transfer in a Rotating Two-Pass Square Channel With 60 Deg Angled Rib Turbulators
,”
ASME J. Turbomach.
,
117
(
2
), pp.
272
280
.
44.
Menter
,
F. R.
,
1993
, “Zonal Two-Equation k-ω Turbulence Models for Aerodynamic Flows,” AIAA Paper 93-2906.
45.
Lee
,
C.-S.
, and
Shih
,
T. I-P.
,
2021
, “
Effects of Heat Loads on Flow and Heat Transfer in the Entrance Region of a Cooling Duct With a Staggered Array of Pin Fins
,”
Int. J. Heat Mass Transfer
,
175
, 121302.
46.
Lee
,
C.-S.
,
Shih
,
T. I.-P.
,
Straub
,
D.
,
Weber
,
J. M.
, and
Robey
,
E. H.
,
2023
, “
Computational and Experimental Study of Film-Cooling Effectiveness With and Without Downstream Vortex Generators
,”
ASME J. Turbomach.
,
145
(
2
), p.
021007
.
47.
Straub
,
D.
,
Weber
,
J.
,
Roy
,
A.
,
Lee
,
C.-S.
, and
Shih
,
T. I.-P.
,
2024
, “
Effects of Downstream Vortex Generators on Film Cooling of a Flat Plate Fed by Crossflow
,”
ASME J. Turbomach.
,
146
(
5
), p.
051011
.
48.
Hu
,
K. S.
, and
Shih
,
T. I.-P.
,
2024
, “
Large-Eddy vs Reynolds-Averaged Navier-Stokes Simulations of Flow and Heat Transfer in a U-Duct With Unsteady Flow Separation
,”
Energies
,
17
(
10
), p.
2414
.
49.
Fu
,
W. L.
,
Wright
,
L. M.
, and
Han
,
J. C.
,
2005
, “
Heat Transfer in Two-Pass Rotating Channels (AR = 1:2 and AR = 1:4) With Smooth Walls
,”
ASME J. Heat Transfer
,
127
(
3
), pp.
265
277
.
You do not currently have access to this content.