The hysteresis effect on the vortex induced vibration (VIV) on a circular cylinder is investigated by the numerical solution of the two-dimensional Reynolds averaged Navier-Stokes equations. An upwind and total variation diminishing (TVD) conservative scheme is used to solve the governing equations written in curvilinear coordinates and the k-ɛ turbulence model is used to simulate the turbulent flow in the wake of the body. The cylinder is supported by a spring and a damper and free to vibrate in the transverse direction. In previous work, numerical results for the amplitude of oscillation and vortex shedding frequency were compared to experimental data obtained from the literature to validate the code for VIV simulations. In the present work, results of practical interest are presented for the power absorbed by the system, phase angle, amplitude, frequency, and lift coefficient. The numerical results indicate that the hysteresis effect is observed only when the frequency of vortex shedding gets closer to the natural frequency of the structure in air.

References

References
1.
Wanderley
,
J. B. V.
,
Souza
,
G. H. B.
,
Sphaier
,
S. H.
, and
Levi
,
C. A.
, 2008, “
Vortex-Induced Vibration of an Elastically Mounted Circular Cylinder Using an Upwind TVD Two-Dimensional Numerical Scheme
,”
Ocean Eng.
,
35
, pp.
1533
1544
.
2.
Roe
,
P. L.
, 1984, “
Generalized Formulation of TVD Lax-Wendroff Scheme
,” ICASE Report No. 84–53.
3.
Sweby
,
P. K.
, 1984, “
High Resolution Scheme Using Flux Limiter for Hyperbolic Conservation Laws
,”
SIAM (Soc. Ind. Appl. Math) J. Numer. Anal.
,
21
, pp.
995
1011
.
4.
Boussinesq
,
J.
, 1877, “
Essai Sur La Théorie Des Eaux Courantes
,”
Mem. Presentes Acad. Sci. Paris
,
23
, p.
46
.
5.
Chien
,
K. Y.
, 1982, “
Predictions of Channel and Boundary-Layer Flows With a Low-Reynolds-Number Turbulence Model
,”
AIAA J.
,
20
, pp.
33
38
.
6.
Khalak
,
A.
, and
Williamson
,
C. H. K.
, 1996, “
Dynamics of a Hydroelastic Cylinder With Very Low Mass and Damping
,”
J. Fluids Struct.
,
10
, pp.
455
472
.
7.
Williamson
,
C. H. K.
, and
Roshko
,
A.
, 1979, “
Vortex Formation in the Wake of an Oscillating Cylinder
,”
J. Fluids Struct.
2
, pp.
355
381
.
8.
Wanderley
,
J. B. V.
,
Sphaier
,
S. H.
, and
Levi
,
C. A.
, 2008, “
A Numerical Investigation of Vortex Induced Vibration on an Elastically Mounted Rigid Cylinder
,”
27th International Conference on Offshore Mechanics and Arctic Engineering
,
OMAE–ASME
,
Lisboa
.
9.
van Leer
,
B.
, 1979, “
Towards the Ultimate Conservative Difference Scheme, V: A Second-Order Sequel to Godunov’s Method
,”
J. Comput. Phys.
,
32
, pp.
101
136
.
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