Stranded cables are widely used in applications where their heat transfer and fluid dynamics are important, but they have not been extensively studied. This paper investigates, using large eddy simulations with the dynamic Smagorinsky sub-grid scale model, a helically wound stranded conductor cable in comparison to a circular cylinder at a Reynolds number of 1000 and Prandtl number of 0.7. The cylinder and the cable were normal to the flow. The triply decomposed heat transport equations were derived, and proper orthogonal decomposition was applied to the fluctuating vorticity and temperature fields to determine the total, coherent, and incoherent terms in the heat transport equations. The results showed that the stranded cable, relative to circular cylinder, has (i) three-dimensional mean flow and heat transfer, especially within and around recirculation region, (ii) 9% higher drag and 8% higher base pressure magnitude, (iii) near-stagnant flow in the gaps between the strands, which results in a significant variation in the local Nusselt number, (iv) ∼15% lower span-wise averaged local Nusselt number in the attached boundary layer, suggesting that surface modifications should be addressed to enhance heat transfer, (v) ∼36° variation in the separation angle along the span, (vi) 12% higher turbulent kinetic energy and 39% higher spanwise normal Reynolds stresses, (vii) insignificant difference in shedding frequency, suggesting similar flow induced vibrations to the cylinder, (viii) asymmetry in the flow and heat fields around the x axis, (ix) significantly different coherent temperature fields and dynamics, and (x) in general, high heat energy transport close to the cable rear side.

1.
IEEE standard for calculating the current-temperature relationship of bare overhead conductors, IEEE Std 738-2012 (Revision of IEEE Std 738-2006–Incorporates IEEE Std 738-2012 Cor 1-2013), 1–72,
2013
.
2.
J.
Nebres
,
S.
Batill
, and
R.
Nelson
, “
Flow about yawed, stranded cables
,”
Exp. Fluids
14
,
49
58
(
1993
).
3.
C.
Morton
and
S.
Yarusevych
, “
Vortex shedding in the wake of a step cylinder
,”
Phys. Fluids
22
,
083602
(
2010
).
4.
C.
Morton
and
S.
Yarusevych
, “
An experimental investigation of flow past a dual step cylinder
,”
Exp. Fluids
52
,
69
83
(
2012
).
5.
C.
Morton
and
S.
Yarusevych
, “
On vortex shedding from low aspect ratio dual step cylinders
,”
J. Fluids Struct.
44
,
251
269
(
2014
).
6.
C.
Morton
,
S.
Yarusevych
, and
F.
Scarano
, “
A tomographic particle image velocimetry investigation of the flow development over dual step cylinders
,”
Phys. Fluids
28
,
025104
(
2016
).
7.
C.
Morton
and
S.
Yarusevych
, “
Vortex shedding from cylinders with two step discontinuities in diameter
,”
J. Fluid Mech.
902
,
A29
(
2020
).
8.
C.
Tian
,
F.
Jiang
,
B.
Pettersen
, and
H. I.
Andersson
, “
Diameter ratio effects in the wake flow of single step cylinders
,”
Phys. Fluids
32
,
093603
(
2020
).
9.
C.
Tian
,
F.
Jiang
,
B.
Pettersen
, and
H. I.
Andersson
, “
Vortex dislocation mechanisms in the near wake of a step cylinder
,”
J. Fluid Mech.
891
,
A24
(
2020
).
10.
A.
Ekmekci
and
D.
Rockwell
, “
Effects of a geometrical surface disturbance on flow past a circular cylinder: A large-scale spanwise wire
,”
J. Fluid Mech.
665
,
120
157
(
2010
).
11.
C.-K.
Chyu
and
D.
Rockwell
, “
Near-wake flow structure of a cylinder with a helical surface perturbation
,”
J. Fluids Struct.
16
,
263
269
(
2002
).
12.
H. H.
Nigim
and
S. M.
Batill
, “
Flow about cylinders with surface perturbations
,”
J. Fluids Struct.
11
,
893
907
(
1997
).
13.
J.
Nebres
and
S.
Batill
, “
Flow about a circular cylinder with a single large-scale surface perturbation
,”
Exp. Fluids
15
,
369
379
(
1993
).
14.
M. R.
Islam
and
A.
Mohany
, “
Vortex shedding characteristics in the wake of circular finned cylinders
,”
Phys. Fluids
32
,
045113
(
2020
).
15.
M. R.
Islam
and
A.
Mohany
, “
On the three-dimensional flow development around circular finned cylinders
,”
Phys. Fluids
32
,
115116
(
2020
).
16.
I.
Rodriguez
,
O.
Lehmkuhl
,
U.
Piomelli
,
J.
Chiva
,
R.
Borrell
, and
A.
Oliva
, “
LES-based study of the roughness effects on the wake of a circular cylinder from subcritical to transcritical Reynolds numbers
,”
Flow, Turbul. Combust.
99
,
729
763
(
2017
).
17.
E.
Achenbach
, “
The effect of surface roughness on the heat transfer from a circular cylinder to the cross flow of air
,”
Int. J. Heat Mass Transfer
20
,
359
369
(
1977
).
18.
R.
Wang
,
S.
Cheng
, and
D. S.-K.
Ting
, “
Numerical study of roundness effect on flow around a circular cylinder
,”
Phys. Fluids
32
,
044106
(
2020
).
19.
M.
Abdelhady
, “
Assessing the accuracy of convective heat transfer from overhead conductor at low wind speed using large eddy simulations (LES)
,” M.S. Dissertation (
University of Calgary
,
Calgary, Alberta, Canada
,
2017
).
20.
J. H.
Jung
and
H. S.
Yoon
, “
Large eddy simulation of flow over a twisted cylinder at a subcritical Reynolds number
,”
J. Fluid Mech.
759
,
579
611
(
2014
).
21.
D. J.
Wei
,
H. S.
Yoon
, and
J. H.
Jung
, “
Characteristics of aerodynamic forces exerted on a twisted cylinder at a low Reynolds number of 100
,”
Comput. Fluids
136
,
456
466
(
2016
).
22.
J.
Moon
and
H. S.
Yoon
, “
Effect of variable pitch on flow around a helically twisted elliptic cylinder
,”
AIP Adv.
10
,
095215
(
2020
).
23.
H. S.
Yoon
,
J.
Moon
, and
M. I.
Kim
, “
Effect of a double wavy geometric disturbance on forced convection heat transfer at a subcritical Reynolds number
,”
Int. J. Heat Mass Transfer
141
,
861
875
(
2019
).
24.
H. S.
Yoon
,
K. J.
Oh
,
H. J.
Kim
,
M. I.
Kim
, and
J.
Moon
, “
Double wavy geometric disturbance to the bluff body flow at a subcritical Reynolds number
,”
Ocean Eng.
195
,
106713
(
2020
).
25.
K.
Zhang
,
D.
Zhou
,
H.
Katsuchi
,
H.
Yamada
,
Z.
Han
, and
Y.
Bao
, “
Bistable states in the wake of a wavy cylinder
,”
Phys. Fluids
32
,
074112
(
2020
).
26.
H. J.
Kim
and
H. S.
Yoon
, “
Reynolds number effect on the fluid flow and heat transfer around a harbor seal vibrissa shaped cylinder
,”
Int. J. Heat Mass Transfer
126
,
618
638
(
2018
).
27.
H. S.
Yoon
,
S. H.
Nam
, and
M. I.
Kim
, “
Effect of the geometric features of the harbor seal vibrissa based biomimetic cylinder on the flow over a cylinder
,”
Ocean Eng.
218
,
108150
(
2020
).
28.
H. S.
Yoon
,
S. H.
Nam
, and
M. I.
Kim
, “
Effect of the geometric features of the harbor seal vibrissa based biomimetic cylinder on the forced convection heat transfer
,”
Int. J. Heat Mass Transfer
159
,
120086
(
2020
).
29.
E.
Firat
,
G. M.
Ozkan
, and
H.
Akilli
, “
Flow past a hollow cylinder with two spanwise rows of holes
,”
Exp. Fluids
60
,
163
(
2019
).
30.
C.
Sun
,
A.
Mohd Azmi
,
T.
Zhou
,
H.
Zhu
, and
Z.
Zang
, “
Experimental study on wake flow structures of screen cylinders using PIV
,”
Int. J. Heat Fluid Flow
85
,
108643
(
2020
).
31.
L.-C.
Hsu
, “
Heat transfer of flow past a cylinder with a slit
,”
Int. J. Therm. Sci.
159
,
106582
(
2021
).
32.
T.
Igarashi
and
Y.
Iida
, “
Fluid flow and heat transfer around a circular cylinder with vortex generators
,”
JSME Int. J., Ser. II
31
,
701
708
(
1988
).
33.
U. O.
Ünal
and
M.
Atlar
, “
An experimental investigation into the effect of vortex generators on the near-wake flow of a circular cylinder
,”
Exp. Fluids
48
,
1059
1079
(
2010
).
34.
D. J.
Richards
, “
Aerodynamic properties of the severn crossing conductor
,” Report RD/L/R 1111,
Central Electricity Research Laboratory
,
Leatherhead, England
,
1962
.
35.
K. J.
Horton
,
C. M.
Ferrer
,
K. P.
Watson
, and
D.
Charovz
, “
Measurement of the hydrodynamic force and strum characteristics of stranded cables
,” Report NCSC TM 471-87,
Naval Coastal Systems Center (NCSC)
,
Panama City, FL
,
1987
.
36.
C. W.
Votaw
and
O. M.
Griffin
, “
Vortex shedding from smooth cylinders and stranded cables
,”
J. Basic Eng.
93
,
457
460
(
1971
).
37.
S. M.
Batill
,
R. C.
Nelson
, and
J. V.
Nebres
, “
An experimental investigation of the flow field around yawed stranded cables
,” Report CR 2210-89-1,
Naval Coastal Systems Center (NCSC)
,
Panama City, FL
,
1989
.
38.
V. T.
Morgan
, “
The heat transfer from bare stranded conductors by natural and forced convection in air
,”
Int. J. Heat Mass Transfer
16
,
2023
2034
(
1973
).
39.
M.
Matsumura
and
R. A.
Antonia
, “
Momentum and heat transport in the turbulent intermediate wake of a circular cylinder
,”
J. Fluid Mech.
250
,
651
668
(
1993
).
40.
A.
Desai
,
S.
Mittal
, and
S.
Mittal
, “
Experimental investigation of vortex shedding past a circular cylinder in the high subcritical regime
,”
Phys. Fluids
32
,
014105
(
2020
).
41.
R.
Perrin
,
M.
Braza
,
E.
Cid
,
S.
Cazin
,
P.
Chassaing
,
C.
Mockett
,
T.
Reimann
, and
F.
Thiele
, “
Coherent and turbulent process analysis in the flow past a circular cylinder at high Reynolds number
,”
J. Fluids Struct.
24
,
1313
1325
(
2008
), part of special issue: Unsteady Separated Flows and their Control.
42.
A.
Vernet
,
G. A.
Kopp
,
J. A.
Ferré
, and
F.
Giralt
, “
Three-dimensional structure and momentum transfer in a turbulent cylinder wake
,”
J. Fluid Mech.
394
,
303
337
(
1999
).
43.
M.
Mohebi
,
D. H.
Wood
, and
R. J.
Martinuzzi
, “
The turbulence structure of the wake of a thin flat plate at post-stall angles of attack
,”
Exp. Fluids
58
,
67
(
2017
).
44.
J. G.
Chen
,
T. M.
Zhou
,
R. A.
Antonia
, and
Y.
Zhou
, “
Comparison between passive scalar and velocity fields in a turbulent cylinder wake
,”
J. Fluid Mech.
813
,
667
694
(
2017
).
45.
L.
Djenidi
and
R. A.
Antonia
, “
Momentum and heat transport in a three-dimensional transitional wake of a heated square cylinder
,”
J. Fluid Mech.
640
,
109
129
(
2009
).
46.
J. G.
Chen
,
Y.
Zhou
,
R. A.
Antonia
, and
T. M.
Zhou
, “
The turbulent Kármán vortex
,”
J. Fluid Mech.
871
,
92
112
(
2019
).
47.
J. G.
Chen
,
R. A.
Antonia
,
Y.
Zhou
, and
T. M.
Zhou
, “
Characteristics of temperature dissipation rate in a turbulent near wake
,”
Exp. Therm. Fluid Sci.
114
,
110050
(
2020
).
48.
S.
Jogee
,
B. V. S. S. S.
Prasad
, and
K.
Anupindi
, “
Large-eddy simulation of non-isothermal flow over a circular cylinder
,”
Int. J. Heat Mass Transfer
151
,
119426
(
2020
).
49.
S.
Karimi
,
P.
Musilek
, and
A. M.
Knight
, “
Dynamic thermal rating of transmission lines: A review
,”
Renewable Sustainable Energy Rev.
91
,
600
612
(
2018
).
50.
M.
Germano
,
U.
Piomelli
,
P.
Moin
, and
W. H.
Cabot
, “
A dynamic subgrid‐scale eddy viscosity model
,”
Phys. Fluids A
3
,
1760
1765
(
1991
).
51.
J.
Smagorinsky
, “
General circulation experiments with the primitive equations I. The basic experiment
,”
Mon. Weather Rev.
91
,
99
(
1963
).
52.
M.
Abdelhady
and
D. H.
Wood
, “
Evaluating the impact of free-stream turbulence on convective cooling of overhead conductors using large eddy simulations
,”
J. Energy Resour. Technol.
141
,
062010
(
2019
).
53.
P.
Beaudan
and
P.
Moin
, “
Numerical experiments on the flow past a circular cylinder at sub-critical Reynolds number
,” Report TF-62,
Standford University
,
1994
.
54.
A. G.
Kravchenko
and
P.
Moin
, “
Numerical studies of flow over a circular cylinder at ReD = 3900
,”
Phys. Fluids
12
,
403
417
(
2000
).
55.
V. T.
Morgan
, “
The thermal rating of overhead-line conductors. Part I. The steady-state thermal model
,”
Electr. Power Syst. Res.
5
,
119
139
(
1982
).
56.
CIGRÉ
, “
Thermal behaviour of overhead conductors
,” CIGRÉ 207, SC 22, WG 22.12,
2002
.
57.
M.
Abdelhady
and
D.
Wood
, “
Effect of thermal boundary condition on forced convection from circular cylinders
,”
Numer. Heat Transfer, Part A
76
,
420
437
(
2019
).
58.
S.
Cao
,
S.
Ozono
,
Y.
Tamura
,
Y.
Ge
, and
H.
Kikugawa
, “
Numerical simulation of Reynolds number effects on velocity shear flow around a circular cylinder
,”
J. Fluids Struct.
26
,
685
702
(
2010
).
59.
W.
Sarwar
and
F.
Mellibovsky
, “
Characterization of three-dimensional vortical structures in the wake past a circular cylinder in the transitional regime
,”
Phys. Fluids
32
,
074104
(
2020
).
60.
H.
Jiang
, “
Separation angle for flow past a circular cylinder in the subcritical regime
,”
Phys. Fluids
32
,
014106
(
2020
).
61.
A.
Žukauskas
, in
Handbook of Single-Phase Convective Heat Transfer
(
Wiley
,
1987
), Chap. 6, p.
7
.
62.
M. M.
Zdravkovich
, “
Conceptual overview of laminar and turbulent flows past smooth and rough circular cylinders
,”
J. Wind Eng. Ind. Aerodyn.
33
,
53
62
(
1990
).
63.
C.
Norberg
, “
Effects of Reynolds number and a low-intensity freestream turbulence on the flow around a circular cylinder
,” Report 87/2,
Chalmers University of Technology
,
1987
.
64.
D. A.
Lysenko
,
I. S.
Ertesvåg
, and
K. E.
Rian
, “
Large-eddy simulation of the flow over a circular cylinder at Reynolds number 3900 using the OpenFOAM toolbox
,”
Flow, Turbul. Combust.
89
,
491
518
(
2012
).
65.
C.
Norberg
, “
LDV-measurements in the near wake of a circular cylinder
,” in
Advances in the Understanding of Bluff Body Wakes and Vortex-Induced Vibrations—BBVIV-1
(
ASME
,
Washington, DC
,
1998
).
66.
R. D.
Henderson
, “
Nonlinear dynamics and pattern formation in turbulent wake transition
,”
J. Fluid Mech.
352
,
65
112
(
1997
).
67.
T. R.
Galloway
and
B. H.
Sage
, “
Local and macroscopic transport from a 1.5-in. cylinder in a turbulent air stream
,”
AIChE J.
13
,
563
570
(
1967
).
68.
V. T.
Morgan
, “
The overall convective heat transfer from smooth circular cylinders
,”
Adv. Heat Transfer
11
,
199
264
(
1975
).
69.
J.-s.
Wang
,
D.
Fan
, and
K.
Lin
, “
A review on flow-induced vibration of offshore circular cylinders
,”
J. Hydrodyn.
32
,
415
440
(
2020
).
70.
H.
Nakamura
and
T.
Igarashi
, “
Variation of Nusselt number with flow regimes behind a circular cylinder for Reynolds numbers from 70 to 30 000
,”
Int. J. Heat Mass Transfer
47
,
5169
5173
(
2004
).
71.
L.
Ong
and
J.
Wallace
, “
The velocity field of the turbulent very near wake of a circular cylinder
,”
Exp. Fluids
20
,
441
453
(
1996
).
72.
Y.
Gao
and
C.
Liu
, “
Rortex and comparison with eigenvalue-based vortex identification criteria
,”
Phys. Fluids
30
,
085107
(
2018
).
73.
L.
Sirovich
, “
Turbulence and the dynamics of coherent structures. I. Coherent structures
,”
Q. Appl. Math.
45
,
561
571
(
1987
).
74.
X.
Ma
,
G.-S.
Karamanos
, and
G. E.
Karniadakis
, “
Dynamics and low-dimensionality of a turbulent near wake
,”
J. Fluid Mech.
410
,
29
65
(
2000
).
75.
B. R.
Noack
,
K.
Afanasiev
,
M.
Morzyński
,
G.
Tadmor
, and
F.
Thiele
, “
A hierarchy of low-dimensional models for the transient and post-transient cylinder wake
,”
J. Fluid Mech.
497
,
335
363
(
2003
).
76.
J. A.
Bourgeois
,
B. R.
Noack
, and
R. J.
Martinuzzi
, “
Generalized phase average with applications to sensor-based flow estimation of the wall-mounted square cylinder wake
,”
J. Fluid Mech.
736
,
316
350
(
2013
).
77.
M. G.
Kindree
,
M.
Shahroodi
, and
R. J.
Martinuzzi
, “
Low-frequency dynamics in the turbulent wake of cantilevered square and circular cylinders protruding a thin laminar boundary layer
,”
Exp. Fluids
59
,
186
(
2018
).
78.
L.-H.
Feng
,
J.-J.
Wang
, and
C.
Pan
, “
Proper orthogonal decomposition analysis of vortex dynamics of a circular cylinder under synthetic jet control
,”
Phys. Fluids
23
,
014106
(
2011
).
79.
A. K. M. F.
Hussain
, “
Coherent structures-reality and myth
,”
Phys. Fluids
26
,
2816
2850
(
1983
).
80.
W. C.
Reynolds
and
A. K. M. F.
Hussain
, “
The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments
,”
J. Fluid Mech.
54
,
263
288
(
1972
).
81.
P.
Kundu
and
I.
Cohen
, in
Fluid Mechanics
, 4th ed. (
Elsevier
,
2010
), Chap. 13, p.
590
.
You do not currently have access to this content.