The instability and transition of flow past two circular cylinders arranged in tandem are investigated numerically. A steady symmetric flow is realized at small Reynolds numbers, but the flow becomes unstable above a critical Reynolds number and makes a transition to an oscillatory flow. We obtained the symmetric flow numerically and analyze its stability by applying linear stability theory. The nonlinear oscillatory flow arising from the instability is obtained not only by numerical simulation but also by direct numerical calculation of the equilibrium solution, and the bifurcation diagram for the nonlinear equilibrium solution is depicted. We focused our attention on the effect of the gap spacing between the two cylinders on the stability and transition of the flow. The transition of the flow from a steady state to an oscillatory state is clarified to occur due to a supercritical or subcritical Hopf bifurcation depending upon the gap spacing. We found that there is a certain range of the gap spacing where physical quantities such as the drag and lift coefficients and the Strouhal number show an abrupt change when the gap spacing is continuously changed. We identified the origin of the abrupt change as the existence of multiple stable solutions for the flow.

1.
I.
Peschard
and
P.
Le Gal
, “
Coupled wakes of cylinder
,”
Phys. Rev. Lett.
77
,
3122
(
1996
).
2.
P.
Le Gal
,
M. P.
Chauve
,
R.
Lima
, and
J.
Rezende
, “
Coupled wakes behind two circular cylinders
,”
Phys. Rev. A
41
,
4566
(
1990
).
3.
M. M.
Zdravkovich
, “
Review of flow interference between two circular cylinders in various arrangement
,”
J. Fluids Eng.
99
,
618
(
1977
).
4.
Y.
Ohya
,
A.
Okajima
, and
M.
Hayashi
, “
Wake interference and vortex shedding
,”
Encyclopedia of Fluid Mechanics
, edited by
N. P.
Cheremisinoff
(
Gulf
, Houston,
1988
), Vol.
8
, pp.
323
389
.
5.
S.
Ishigai
,
E.
Nishikawa
,
K.
Nishimura
, and
K.
Cho
, “
Experimental study on structure of gas flow in tube banks with tube axes normal to flow
,”
Bull. JSME
15
,
949
(
1972
).
6.
A.
Okajima
, “
Flows around two tandem circular cylinders at very high Reynolds number
,”
Bull. JSME
22
,
504
(
1979
).
7.
M.
Arie
,
M.
Kiya
,
M.
Moriya
, and
H.
Mori
, “
Pressure fluctuations of the surface of two circular cylinders in tandem arrangement
,”
J. Fluids Eng.
105
,
161
(
1983
).
8.
G.
Xu
and
Y.
Zhou
, “
Strouhal numbers in the wake of two inline cylinders
,”
Exp. Fluids
37
,
248
(
2004
).
9.
T.
Igarashi
, “
Characteristics of the flow around two circular cylinders arranged in tandem (1st report)
,”
Bull. JSME
24
,
323
(
1981
).
10.
W.
Eissler
,
P.
Drtina
, and
A.
Frohn
, “
Cellular automata simulation of flow around chains of cylinders
,”
Int. J. Numer. Methods Fluids
34
,
773
(
1992
).
11.
S.
Mittal
,
V.
Kumar
, and
A.
Raghuvanshi
, “
Unsteady incompressible flows past two cylinders in tandem and staggered arrangement
,”
Int. J. Numer. Methods Fluids
25
,
1315
(
1997
).
12.
J. R.
Meneghini
,
F.
Saltara
,
C. L.R.
Siqueira
, and
J. A.
Ferrari
, Jr.
, “
Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements
,”
J. Fluids Struct.
15
,
327
(
2001
).
13.
B.
Sharman
,
F. S.
Lien
,
L.
Davidson
, and
C.
Norberg
, “
Numerical predictions of low Reynolds number flows over two tandem circular cylinders
,”
Int. J. Numer. Methods Fluids
47
,
423
(
2005
).
14.
Y.
Tanida
,
A.
Okajima
, and
Y.
Watanabe
, “
Stability of circular cylinder oscillating in uniform or in wake
,”
J. Fluid Mech.
61
,
769
(
1973
).
15.
K.
Ohmi
and
K.
Imaichi
, “
Vortex wake visualization of two circular cylinders
,” in
Flow Visualization IV: Proc. 6th Int. Symp.
, Yokohama, Japan, 5-9 October 1992, pp.
322
326
.
16.
D.
Biermann
and
W. H.
Herrnstein
, Jr.
, “
The interference between struts in various combination
,”
National Advisory Commitee for Aeronautics, Tech. Rep.
468
,
515
(
1933
).
17.
J. F.
Thompson
,
F. C.
Thames
, and
C. W.
Mastin
, “
Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies
,”
J. Comp. Physiol.
15
,
299
(
1974
).
18.
J. L.
Steger
and
R. L.
Sorenson
, “
Automatic mesh-point clustering near a boundary in grid generation with elliptic partial differential equations
,”
J. Comp. Physiol.
33
,
405
(
1979
).
19.
C.
Mathis
,
M.
Provansal
, and
L.
Boyer
, “
The Benard-von Karman instability: an experimental study near the threshold
,”
J. Phys. Lett.
45
,
L
483
(
1984
).
20.
C. P.
Jackson
, “
A finite-element study of onset of vortex shedding in flow past variously shaped bodies
,”
J. Fluid Mech.
182
,
23
(
1987
).
21.
J.
Dušek
,
P.
Le Gal
, and
P.
Fraunie
, “
A numerical and theoretical study of the first Hopf bifurcation in a cylinder wake
,”
J. Fluid Mech.
264
,
59
(
1994
).
You do not currently have access to this content.