Three‐dimensional computation for flow‐induced vibrations in in‐line and cross‐flow directions of a circular cylinder

Abstract

SUMMARY We present numerical results for in‐line and cross‐flow vibrations of a circular cylinder, which is immersed in a uniform flow and is elastically supported by damper‐spring systems to compute vibrations of a rigid cylinder. In the case of a circular cylinder with a low Scruton number, it is well‐known that two types of self‐excited vibrations appear in the in‐line direction in the range of low reduced velocities. On the other hand, a cross‐flow vibration of the circular cylinder can be excited in the range of high reduced velocities. Therefore, we compute the flow‐induced vibrations of the circular cylinder in the wide range of the reduced velocities at low and high Scruton numbers and discuss about excitation mechanisms in the in‐line and cross‐flow directions. Copyright © 2011 John Wiley & Sons, Ltd.

Three-dimensional computation for flow-induced vibrations of an upstream circular cylinder in two tandem circular cylinders

“…However, in the case of Ur = 4.0, the wakes become non-symmetrical vortices behind the upstream vibrating cylinder. These results are the same as the wake shed from a vibrating circular cylinder (Kondo 2012). Figure 14 shows cross-flow vibration responses of the upstream circular cylinder and instantaneous vorticity contours of wakes shed from two circular cylinder during one period in the cross-flow vibration amplitudes of the upstream circular cylinder, when the reduced velocity Ur is 6.2.…”

“…Thus the resonance yields the large first-and second-excited vibrations in the in-line direction, as seen in Figure 7. As a result, we could catch the resonance phenomenon of the upstream circular cylinder for two tandem cylinders as well as a single circular cylinder (Kondo 2012). It is also observed that the f cd2 of the downstream stationary cylinder corresponds to the f cd1 of the upstream vibrating cylinder.…”

“…When the Ur exceeds approximately Ur = 5, the amplitude Y 1amp suddenly grows and reaches the maximum amplitude Y 1amp = 0.86 at Ur = 6.2. In the case of a single circular cylinder as seen in Kondo (2012), the lower branch region of the vortex-induced vibration was clearly captured by the numerical computations. However, when two circular cylinders are mounted at the spacing S/D = 3, lower than the critical spacing, the lower branch region of the vortexinduced vibration for the upstream circular cylinder cannot be observed clearly by the numerical computation.…”

“…The spatial discretization of the Navier-Stokes and continuity equations is achieved by the third-order upwind finite element method (see Kondo (1994Kondo ( , 2012 in detail). This procedure is carried out on the basis of the Petrov-Galerkin formulation in which the following modified weighting functionū i is adopted:…”

“…This is due to the fact that the fluid C 2014 Taylor & Francis 2 N. Kondo forces acting on the circular cylinder in the range of supercritical Reynolds numbers are significantly lower in comparison with fluid forces obtained in the range of subcritical Reynolds numbers. In the cases of, respectively, low and high Scruton numbers, Kondo (2012) also showed threedimensional numerical results for in-line and cross-flow vibrations of a circular cylinder at a subcritical Reynolds number and denoted clearly the three-dimensional structures of fluid flow around the vibrating circular cylinder. In numerical computations of the high Reynolds number flow, the three-dimensional computation is required for obtaining accurate solutions of the Navier-Stokes equations, because the two-dimensional computations cannot yield satisfactory solutions of the Navier-Stokes equations.…”