Abstract

In this study, a rotating cylinder is placed in a stream of shear-thinning fluids, flowing with a uniform velocity. Detailed investigations are performed for the following range of conditions: Reynolds number 100Re500, power-law index 0.2n1 and rotational velocity 0α5. Flow transitions are observed from steady to unsteady at critical values of the Reynolds number, the rotational velocity, and the power-law index. Critical values of the Reynolds number Rec have been obtained for varying levels of the rotational velocity, and the power-law index. Rec varies nonmonotonically with the rotational velocity. At a particular Reynolds number, an increase of the rotational velocity acts as a vortex suppression technique. For shear-thinning fluids considered here, the vortex suppression occurs at a larger value of the critical rotational velocity αc, relative to Newtonian fluids. For the unsteady flow, the lift coefficient versus time curve exhibits oscillatory behavior, and this has been used to delineate the flow regime as steady or unsteady flow. For unsteady flow regimes, both the amplitude of the lift coefficient and the Strouhal number increase with increasing Reynolds numbers. The results presented in this work for such high Reynolds numbers elucidate the possible complex interplay between the kinematic and rheological parameters of non-Newtonian fluids. This investigation also complements the currently available low Reynolds number results up to ∼ Re=140.

References

1.
Sayers
,
A. T.
,
1979
, “
Lift Coefficient and Flow Visualization on a Leading Edge Rotating Cylinder Rudder
,”
Int. J. Mech. Eng. Educ.
,
7
(
2
), pp.
75
79
.https://jglobal.jst.go.jp/en/detail?JGLOBAL_ID=201002029061727591
2.
Tennant
,
J. S.
,
Johnson
,
W. S.
, and
Krothapalli
,
A.
,
1976
, “
Rotating Cylinder for Circulation Control on an Airfoil
,”
J. Hydronaut.
,
10
(
3
), pp.
102
105
.10.2514/3.48147
3.
Prandtl
,
L.
,
1925
, “
The Magnus Effect and Windpowered Ships
,”
Naturwissenschaften
,
13
(
6
), pp.
93
108
.10.1007/BF01585456
4.
Glauert
,
M. B.
,
1957
, “
The Flow Past a Rapidly Rotating Circular Cylinder
,”
Proc. R. Soc. London A
,
242
(
1228
), pp.
108
115
.10.1098/rspa.1957.0157
5.
Moore
,
D. W.
,
1957
, “
The Flow Past a Rapidly Rotating Circular Cylinder in a Uniform Stream
,”
J. Fluid Mech.
,
2
(
06
), pp.
541
550
.10.1017/S002211205700035X
6.
Swanson
,
W. M.
,
1961
, “
The Magnus Effect: A Summary of Investigations to Date
,”
ASME J. Basic Eng.
,
83
(
3
), pp.
461
470
.10.1115/1.3659004
7.
Tokumaru
,
P. T.
, and
Dimotakis
,
P. E.
,
1993
, “
The Lift of a Cylinder Executing Rotary Motions in a Uniform Flow
,”
J. Fluid Mech.
,
255
(
1
), pp.
1
10
.10.1017/S0022112093002368
8.
Badr
,
H. M.
, and
Dennis
,
S. C. R.
,
1985
, “
Laminar Forced Convection From a Rotating Cylinder
,”
Int. J. Heat Mass Transfer
,
28
(
1
), pp.
253
264
.10.1016/0017-9310(85)90027-4
9.
Badr
,
H. M.
, and
Dennis
,
S. C. R.
,
1985
, “
Time-Dependent Viscous Flow Past an Impulsively Started Rotating and Translating Circular Cylinder
,”
J. Fluid Mech.
,
158
, pp.
447
488
.10.1017/S0022112085002725
10.
Mittal
,
S.
,
Nair
,
M.
, and
Sengupta
,
T.
,
1997
, “
Numerical Simulation of Flow Past Rotating and Translating Circular Cylinder
,”
Seventh Asian Congress of Fluid Mechanics, Chennai (Madras)
, India, Dec. 8–12, pp.
701
704
.http://home.iitk.ac.in/~smittal/publi_&_present/sm_conf_pro/nume_simulation_flow.pdf
11.
Chou
,
M.-H.
,
2000
, “
Numerical Study of Vortex Shedding From a Rotating Cylinder Immersed in a Uniform Flow Field
,”
Int. J. Numer. Methods Fluids
,
32
(
5
), pp.
545
567
.10.1002/(SICI)1097-0363(20000315)32:5<545::AID-FLD948>3.0.CO;2-2
12.
Ece
,
M. C.
,
Walker
,
J. D. A.
, and
Doligalski
,
T. L.
,
1984
, “
The Boundary Layer on an Impulsively Started Rotating and Translating Cylinder
,”
Phys. Fluids
,
27
(
5
), pp.
1077
1089
.10.1063/1.864908
13.
Coutanceau
,
M.
, and
Menard
,
C.
,
1985
, “
Influence of Rotation on the Near-Wake Development Behind an Impulsively Started Circular Cylinder
,”
J. Fluid Mech.
,
158
, pp.
399
446
.10.1017/S0022112085002713
14.
Badr
,
H. M.
,
Coutanceau
,
M.
,
Dennis
,
S. C. R.
, and
Menard
,
C.
,
1990
, “
Unsteady Flow Past a Rotating Circular Cylinder at Reynolds Numbers 103 and 104
,”
J. Fluid Mech.
,
220
, pp.
459
484
.10.1017/S0022112090003342
15.
Ingham
,
D. B.
,
1983
, “
Steady Flow Past a Rotating Cylinder
,”
Comput. Fluids
,
11
(
4
), pp.
351
366
.10.1016/0045-7930(83)90020-8
16.
Ingham
,
D. B.
, and
Tang
,
T.
,
1990
, “
A Numerical Investigation Into the Steady Flow Past a Rotating Circular Cylinder at Low and Intermediate Reynolds Numbers
,”
J. Comput. Phys.
,
87
(
1
), pp.
91
107
.10.1016/0021-9991(90)90227-R
17.
Tang
,
T.
, and
Ingham
,
D. B.
,
1991
, “
On Steady Flow Past a Rotating Circular Cylinder at Reynolds Numbers 60 and 100
,”
Comput. Fluids
,
19
(
2
), pp.
217
230
.10.1016/0045-7930(91)90034-F
18.
Kang
,
S.
,
Choi
,
H.
, and
Lee
,
S.
,
1999
, “
Laminar Flow Past a Rotating Circular Cylinder
,”
Phys. Fluids
,
11
(
11
), pp.
3312
3321
.10.1063/1.870190
19.
Kang
,
S.
,
2006
, “
Laminar Flow Over a Steadily Rotating Circular Cylinder Under the Influence of Uniform Shear
,”
Phys. Fluids
,
18
(
4
), p.
047106
.10.1063/1.2189293
20.
Stojković
,
D.
,
Breuer
,
M.
, and
Durst
,
F.
,
2002
, “
Effect of High Rotation Rates on the Laminar Flow Around a Circular Cylinder
,”
Phys. Fluids
,
14
(
9
), pp.
3160
3178
.10.1063/1.1492811
21.
Stojković
,
D.
,
Schön
,
P.
,
Breuer
,
M.
, and
Durst
,
F.
,
2003
, “
On the New Vortex Shedding Mode Past a Rotating Circular Cylinder
,”
Phys. Fluids
,
15
(
5
), pp.
1257
1260
.10.1063/1.1562940
22.
Mittal
,
S.
,
2001
, “
Flow Past Rotating Cylinders: Effect of Eccentricity
,”
ASME J. Appl. Mech.
,
68
(
4
), pp.
543
552
.10.1115/1.1380679
23.
Mittal
,
S.
,
2001
, “
Control of Flow Past Bluff Bodies Using Rotating Control Cylinders
,”
J. Fluids Struct.
,
15
(
2
), pp.
291
326
.10.1006/jfls.2000.0337
24.
Mittal
,
S.
,
2004
, “
Three-Dimensional Instabilities in Flow Past a Rotating Cylinder
,”
ASME J. Appl. Mech
,.,
71
(
1
), pp.
89
95
.10.1115/1.1631032
25.
Mittal
,
S.
, and
Raghuvanshi
,
A.
,
2001
, “
Control of Vortex Shedding Behind Circular Cylinder for Flows at Low Reynolds Numbers
,”
Int. J. Numer. Methods Fluids
,
35
(
4
), pp.
421
447
.10.1002/1097-0363(20010228)35:4<421::AID-FLD100>3.0.CO;2-M
26.
Mittal
,
S.
, and
Kumar
,
B.
,
2003
, “
Flow Past a Rotating Cylinder
,”
J. Fluid Mech.
,
476
, pp.
303
334
.10.1017/S0022112002002938
27.
Kumar
,
S.
,
Cantu
,
C.
, and
Gonzalez
,
B.
,
2011
, “
Flow Past a Rotating Cylinder at Low and High Rotation Rates
,”
ASME J. Fluids Eng.
,
133
(
4
), p.
041201
.10.1115/1.4003984
28.
Padrino
,
J. C.
, and
Joseph
,
D. D.
,
2006
, “
Numerical Study of the Steady-State Uniform Flow Past a Rotating Cylinder
,”
J. Fluid Mech.
,
557
, pp.
191
223
.10.1017/S0022112006009682
29.
Paramane
,
S. B.
, and
Sharma
,
A.
,
2009
, “
Numerical Investigation of Heat and Fluid Flow Across a Rotating Circular Cylinder Maintained at Constant Temperature in 2–D Laminar Flow Regime
,”
Int. J. Heat Mass Transfer
,
52
(
13–14
), pp.
3205
3216
.10.1016/j.ijheatmasstransfer.2008.12.031
30.
Chatterjee
,
D.
, and
Gupta
,
S. K.
,
2015
, “
Numerical Study of the Laminar Flow Past a Rotating Square Cylinder at Low Spinning Rates
,”
ASME J. Fluids Eng.
,
137
(
2
), p.
021204
.10.1115/1.4028500
31.
Pralits
,
J. O.
,
Giannetti
,
F.
, and
Brandt
,
L.
,
2013
, “
Three-Dimensional Instability of the Flow Around a Rotating Circular Cylinder
,”
J. Fluid Mech.
,
730
, pp.
5
18
.10.1017/jfm.2013.334
32.
Navrose
,
Meena
,
J.
, and
Mittal
,
S.
,
2015
, “
Three-Dimensional Flow Past a Rotating Cylinder
,”
J. Fluid Mech.
,
766
, pp.
28
53
.10.1017/jfm.2015.6
33.
Rao
,
A.
,
Radi
,
A.
,
Leontini
,
J. S.
,
Thompson
,
M. C.
,
Sheridan
,
J.
, and
Hourigan
,
K.
,
2015
, “
A Review of Rotating Cylinder Wake Transitions
,”
J. Fluids Struct.
,
53
, pp.
2
14
.10.1016/j.jfluidstructs.2014.03.010
34.
Panda
,
S. K.
, and
Chhabra
,
R. P.
,
2010
, “
Laminar Flow of Power-Law Fluids Past a Rotating Cylinder
,”
J. Non-Newtonian Fluid Mech.
,
165
(
21–22
), pp.
1442
1461
.10.1016/j.jnnfm.2010.07.006
35.
Panda
,
S. K.
, and
Chhabra
,
R. P.
,
2011
, “
Laminar Forced Convection Heat Transfer From a Rotating Cylinder to Power-Law Fluids
,”
Numer. Heat Transfer, Part A
,
59
(
4
), pp.
297
319
.10.1080/10407782.2011.549369
36.
Thakur
,
P.
,
Mittal
,
S.
,
Tiwari
,
N.
, and
Chhabra
,
R. P.
,
2016
, “
The Motion of a Rotating Circular Cylinder in a Stream of Bingham Plastic Fluid
,”
J. Non-Newtonian Fluid Mech.
,
235
, pp.
29
46
.10.1016/j.jnnfm.2016.06.013
37.
Thakur
,
P.
,
Tiwari
,
N.
, and
Chhabra
,
R. P.
,
2019
, “
Forced Convection in a Bingham Plastic Fluid From a Heated Rotating Cylinder
,”
J. Chem. Eng. Jpn.
,
52
(
9
), pp.
730
742
.10.1252/jcej.18we309
38.
Bharti
,
R. P.
,
Chhabra
,
R. P.
, and
Eswaran
,
V.
,
2008
, “
Steady Flow of Power-Law Fluids Across a Circular Cylinder
,”
Can. J. Chem. Eng.
,
84
(
4
), pp.
406
421
.10.1002/cjce.5450840402
39.
Sivakumar
,
P.
,
Bharti
,
R. P.
, and
Chhabra
,
R. P.
,
2006
, “
Effect of Power-Law Index on Critical Parameters for Power-Law Flow Across an Unconfined Circular Cylinder
,”
Chem. Eng. Sci.
,
61
(
18
), pp.
6035
6046
.10.1016/j.ces.2006.05.031
40.
Nirmalkar
,
N.
, and
Chhabra
,
R. P.
,
2014
, “
Momentum and Heat Transfer From a Heated Circular Cylinder in Bingham Plastic Fluids
,”
Int. J. Heat Mass Transfer
,
70
, pp.
564
577
.10.1016/j.ijheatmasstransfer.2013.11.034
41.
Patnana
,
V. K.
,
Bharti
,
R. P.
, and
Chhabra
,
R. P.
,
2010
, “
Two-Dimensional Unsteady Forced Convection Heat Transfer in Power-Law Fluids From a Cylinder
,”
Int. J. Heat Mass Transfer
,
53
(
19–20
), pp.
4152
4167
.10.1016/j.ijheatmasstransfer.2010.05.038
42.
Rao
,
M. K.
,
Sahu
,
A. K.
, and
Chhabra
,
R. P.
,
2011
, “
Effect of Confinement on Power-Law Fluid Flow Past a Circular Cylinder
,”
Polym. Eng. Sci.
,
51
(
10
), pp.
2044
2065
.10.1002/pen.21987
43.
Khan
,
M. B.
,
Sasmal
,
C.
, and
Chhabra
,
R. P.
,
2020
, “
Flow and Heat Transfer Characteristics of a Rotating Cylinder in a FENE-P Type Viscoelastic Fluid
,”
J Non-Newtonian Fluid Mech.
,
282
, pp.
104333
104351
.10.1016/j.jnnfm.2020.104333
44.
Bird
,
R. B.
,
Stewart
,
W. E.
, and
Lightfoot
,
E. N.
,
2002
,
Transport Phenomena
, 2nd ed.,
Wiley
,
New York
.
45.
Thakur
,
P.
,
Tiwari
,
N.
, and
Chhabra
,
R. P.
,
2018
, “
Flow of a Power-Law Fluid Across a Rotating Cylinder in a Confinement
,”
J. Non-Newtonian Fluid Mech.
,
251
, pp.
145
161
.10.1016/j.jnnfm.2017.12.003
46.
Williamson
,
C. H. K.
,
1996
, “
Three-Dimensional Wake Transition
,”
J. Fluid Mech.
,
328
, pp.
345
407
.10.1017/S0022112096008750
47.
Williamson
,
C. H. K.
,
1996
, “
Vortex Dynamics in the Cylinder Wake
,”
Annu. Rev. Fluid Mech.
,
28
(
1
), pp.
477
539
.10.1146/annurev.fl.28.010196.002401
48.
Sohankar
,
A.
,
Norberg
,
C.
, and
Davidson
,
L.
,
1999
, “
Simulation of Three-Dimensional Flow Around a Square Cylinder at Moderate Reynolds Numbers
,”
Phys. Fluids
,
11
(
2
), pp.
288
306
.10.1063/1.869879
49.
Courant
,
R.
,
Friedrichs
,
K.
, and
Lewy
,
H.
,
1928
, “
Über Die Partiellen Differenzengleichungen Der Mathematischen Physik
,”
Math. Ann.
,
100
(
1
), pp.
32
74
.10.1007/BF01448839
50.
D'Alessio
,
S. J. D.
, and
Pascal
,
J. P.
,
1996
, “
Steady Flow of a Power-Law Fluid Past a Cylinder
,”
Acta Mech.
,
117
(
1–4
), pp.
87
100
.10.1007/BF01181039
51.
Zovatto
,
L.
, and
Pedrizzetti
,
G.
,
2001
, “
Flow About a Circular Cylinder Between Parallel Walls
,”
J. Fluid Mech.
,
440
, pp.
1
25
.10.1017/S0022112001004608
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