In this paper we investigate the interaction of two freely rotatable triangular cylinders that are placed in tandem in a laminar flow. To study how the spacing between the two cylinders may influence the dynamic behavior of the cylinders and vortical structure of the flow, we have performed a series of numerical simulations of the two-cylinder-flow system. In all the simulations, the dimensionless moment of inertia and Reynolds number are fixed to 1.0 and 200, respectively. Four cases with the spacing ratio (L/D) of 2.0, 3.0, 4.0, and 5.0 are studied. With the increase of spacing, three different states of motion of the system are found. At L/D = 2.0, oscillatory rotation (swinging in both directions) is observed. At L/D = 3.0 both cylinders exhibit quasi-periodic autorotations. At L/D = 4.0 and 5.0, a more complicated pattern (irregular autorotation) is observed. For each case, the time history of angular velocity, the phase portrait (angular acceleration versus angular velocity,) and the spectra of the moments of forces on both cylinders are plotted and analyzed. The vortical structures in the near and far wake are visualized. Physical interpretations for various phenomenon observed are presented whenever possible.

References

1.
Maxwell
,
J. C.
, 1853, “
On a Particular Case of the Descent of a Heavy Body in a Resisting Medium
,”
Cambridge Dublin Mathematics Journal
,
9
, pp.
115
118
.
2.
Smith
,
E.
, 1971, “
Autorotating Wing: An Experimental Investigation
,”
J. Fluid Mech.
,
50
, pp.
513
534
.
3.
Iversen
,
J.
, 1979, “
Autorotating Flat-Plate Wings: The Effect of the Moment of Inertia, Geometry and Reynolds Number
,”
J. Fluid Mech.
,
92
, pp.
327
348
.
4.
Lugt
,
H.
, 1980, “
Autorotation of an Elliptic Cylinder About an Axis Perpendicular to the Flow
,”
J. Fluid Mech.
,
99
, pp.
817
840
.
5.
Lugt
,
H.
, 1983, “
Autorotation
,”
Annu. Rev. Fluid Mech.
,
15
, pp.
123
147
.
6.
Skews
,
B.
, 1990, “
Autorotation of Rectangular Plates
,”
J. Fluid Mech.
,
217
, pp.
33
40
.
7.
Skews
,
B.
, 1991, “
Autorotation of Many-Sided Bodies in an Airstream
,”
Nature (London)
,
352
, pp.
512
513
.
8.
Skews
,
B.
, 1998, “
Autorotation of Polygonal Prisms With an Upstream Vane
,”
J. Wind. Eng. Ind. Aerodyn.
,
73
, pp.
145
158
.
9.
Zaki
,
T.
,
Sen
,
M.
, and
el Hak
,
M. G.
, 1994, “
Investigation of Flow Past a Freely Rotatable Square Cylinder
,”
J. Fluids Struct.
,
8
, pp.
555
582
.
10.
Copeland
,
C.
, 1994, “
A Perturbed-Pendulum Model for Flat-Plate Autorotation
,”
J. Fluids Struct.
,
8
, pp.
125
138
.
11.
Mittal
,
R.
,
Seshadri
,
V.
, and
Udaykumar
,
H.
, 2004, “
Flutter, Tumble and Votex Induced Autorotation
,”
Theor. Comput. Fluid Dyn.
,
17
, pp.
165
170
.
12.
Srigrarom
,
S.
, and
Koh
,
A.
, 2008, “
Flow Field of Self-Excited Rotationally Oscillating Equilateral Triangular Cylinder
,”
J. Fluids Struct.
,
24
, pp.
750
755
.
13.
Willmarth
,
W.
, and
Harvey
,
R.
, 1964, “
Steady and Unsteady Motions and Wakes of Freely Falling Disks
,”
Phys. Fluids
,
7
, pp.
197
208
.
14.
Aref
,
H.
, and
Jones
,
S.
, 1993, “
Chaotic Motion of a Solid Through Ideal Fluid
,”
Phys. Fluids A
,
5
, pp.
3026
3028
.
15.
Tanabe
,
Y.
, and
Kaneko
,
K.
, 1994, “
Behavior of a Falling Paper
,”
Phys. Rev. Lett.
,
73
, pp.
1372
1375
.
16.
Mahadevan
,
L.
,
Aref
,
H.
, and
Jones
,
S.
, 1995, “
Comment on Behavior of a Falling Paper
,”
Phys. Rev. Lett.
,
75
, pp.
1420
1420
.
17.
Mahadevan
,
L.
,
Ryu
,
W.
, and
Samuel
,
A.
, 1999, “
Tumbling Cards
,”
Phys. Fluids
,
11
, pp.
1
3
.
18.
Field
,
S.
,
Klaus
,
M.
,
Moore
,
M.
, and
Nori
,
F.
, 1997, “
Chaotic Dynamics of Falling Disks
,”
Nature (London)
,
388
, pp.
252
254
.
19.
Belmonte
,
A.
,
Eisenberg
,
H.
, and
Moses
,
E.
, 1998, “
From Flutter to Tumble: Intertial Drag and Froude Similarity in Falling Paper
,”
Phys. Rev. Lett.
,
81
, pp.
345
348
.
20.
Pesavento
,
U.
, and
Wang
,
Z.
, 2004, “
Falling Paper: Navier-Stokes Solutions, Model of Fluid Forces, and Center of Mass Elevation
,”
Phys. Rev. Lett.
,
93
, p.
144501
.
21.
Andersen
,
A.
,
Pesavento
,
U.
, and
Wang
,
Z.
, 2005, “
Unsteady Aerodynamics of Fluttering and Tumbling Plates
,”
J. Fluid Mech.
,
541
, pp.
65
90
.
22.
Andersen
,
A.
,
Pesavento
,
U.
, and
Wang
,
Z.
, 2005, “
Analysis of Transitions Between Fluttering, Tumbling and Steady Descent of Falling Cards
,”
J. Fluid Mech.
,
541
, pp.
91
104
.
23.
Jones
,
M.
, and
Shelley
,
M.
, 2005, “
Falling Cards
,”
J. Fluid Mech.
,
540
, pp.
393
425
.
24.
Bonisch
,
S.
, and
Heuveline
,
V.
, 2007, “
On the Numerical Simulation of the Instationary Free Fall of a Solid in a Fluid. I. The Newtonian Case
,”
Comput. Fluids
,
36
, pp.
1434
1445
.
25.
Jin
,
C.
, and
Xu
,
K.
, 2008, “
Numerical Study of the Unsteady Aerodynamics of Freely Falling Plates
,”
Comm. Comp. Phys.
,
3
, pp.
834
851
.
26.
Zdravkovich
,
M.
, 1977, “
Review of Flow Interference Between Two Circular Cylinders in Various Arrangements
,”
ASME J. Fluids Eng.
,
69
, pp.
618
633
.
27.
Zdravkovich
,
M.
, 1987, “
The Effects of Flow Interference Between Two Circular Cylinders in Various Arrangements
,”
J. Fluids Struct.
,
1
, pp.
239
261
.
28.
Mittal
,
S.
,
Kumar
,
V.
, and
Raghuvanshi
,
A.
, 1997, “
Unsteady Incompressible Flows Past Two Cylinders in Tandem and Staggered Arrangements
,”
Int. J. Numer. Methods Fluids
,
25
, pp.
1315
1344
.
29.
Meneghini
,
J.
,
Saltara
,
F.
,
Siqueira
,
C.
, and
JR
,
J. F.
, 2001, “
Numerical Simulation of Flow Interference Between Two Circular Cylinders in Tandem and Side-by-Side Arrangements
,”
J. Fluids Struct.
,
15
, pp.
327
350
.
30.
Sharman
,
B.
,
Lien
,
F.
,
Davidson
,
L.
, and
Norberg
,
C.
, 2005, “
Numerical Predictions of Low Reynolds Number Flows Over Two Tandem Circular Cylinders
,”
Int. J. Numer. Methods Fluids
,
47
, pp.
423
447
.
31.
Zhou
,
Y.
, and
Yiu
,
M.
, 2006, “
Flow Structure, Momentum and Heat Transport in a Two-Tandem-Cylinder Wake
,”
J. Fluid Mech.
,
548
, pp.
17
48
.
32.
Alam
,
M.
, and
Zhou
,
Y.
, 2008, “
Strouhal Numbers, Forces and Flows Structures Around Two Tandem Cylinders of Different Diameters
,”
J. Fluids Struct.
,
24
, pp.
505
526
.
33.
Papaioannou
,
G.
,
Yue
,
D.
,
Triantafyllou
,
M.
, and
Karniadakis
,
G.
, 2006, “
Evidence of Holes in the Arnold Tongues of Flow Past Two Oscillating Cylinders
,”
Phys. Rev. Lett.
,
96
, p.
014501
.
34.
Deng
,
J.
,
Shao
,
X.
, and
Yu
,
Z.
, 2007, “
Hydrodynamics Studies on Two Traveling Wavy Foils in Tandem Arrangement
,”
Phys. Fluids
,
19
, p.
113104
.
35.
Papaioannou
,
G.
,
Yue
,
D.
,
Triantafyllou
,
M.
, and
Karniadakis
,
G.
, 2008, “
On the Effect of Spacing on the Vortex-Induced Vibrations of Tandem Cylinders
,”
J. Fluids Struct.
,
24
, pp.
833
854
.
36.
Kim
,
S.
,
Alam
,
M.
,
Sakamoto
,
H.
, and
Zhou
,
Y.
, 2009, “
Flow-Induced Vibrations of Two Circular Cylinders in Tandem Arrangement. Part 1: Characteristics of Vibration
,”
J. Wind. Eng. Ind. Aerodyn.
,
97
, pp.
304
311
.
37.
Ristroph
,
L.
and
Zhang
,
J.
, 2008, “
Anomalous Hydrodynamic Drafting of Interacting Flapping Flags
,”
Phys. Rev. Lett.
,
100
, p.
228104
.
38.
Jia
,
L.
, and
Yin
,
X.
, 2008, “
Passive Oscillations of Two Tandem Flexible Filaments in a Flowing Soap Film
,”
Phys. Rev. Lett.
,
101
, p.
194502
.
39.
Zhu
,
L.
, 2009, “
Interaction of Two Tandem Deformable Bodies in a Viscous Incompressible Flow
,”
J. Fluid Mech
,
635
, pp.
455
475
.
40.
Zhang
,
X.
,
Ni
,
S.
, and
He
,
G.
, 2008, “
A Pressure-Correction Method and Its Applications on an Unstructured Chimera Grid
,”
Comput. Fluids
,
37
, pp.
993
1010
.
41.
Morton
,
K.
, and
Mayers
,
D.
, 1994,
NumericalSsolution of Partial Differential Equations: An Introduction
,
Cambridge University Press
,
Cambridge
.
42.
Cao
,
L.
,
Hong
,
Y.
,
Zhao
,
H.
, and
He
,
G.
, 1995, “
Predicting Chaotic Time Series With Wavelet Networks
,”
Physica D
,
85
, pp.
225
238
.
43.
Kantz
,
H.
, and
Schreiber
,
T.
, 1997,
Nonlinear Time Series Analysis
,
Cambridge University Press
,
Cambridge
.
44.
Hegger
,
R.
,
Kantz
,
H.
, and
Schreiber
,
T.
, 1999, “
Practical Implementation of Nonlinear Time Series Methods: The Tisean Package
,”
Chaos
,
9
, pp.
413
435
.
You do not currently have access to this content.