Flow Over A Circular Cylinder With A Flexible Splitter Plate

Abstract

Previous work on rigid splitter plates in the wake of a bluff body has shown that the primary vortex shedding can be suppressed for sufficiently long splitter plates. In the present work, we study the problem of a flexible splitter plate in the wake of a circular cylinder. In this case, the splitter plate can deform due to the fluid forces acting on it, and hence the communication between the two sides of the wake is not totally disrupted like in the rigid splitter plate case. In particular, we study two kinds of flexible splitter plates. In the first case, the splitter plate is rigid but is flexibly mounted (hinged) to the cylinder, while in the second case, the entire splitter plate is flexible. We are interested in both the dynamics of the splitter plate, if they do vibrate at all, and in the wake dynamics downstream of the flexible splitter plates. The main parameters in the problem are the splitter plate length (L) to cylinder diameter (D) ratio, the relative mass of the plate, the Reynolds number, and the stiffness and internal damping associated with the flexible plate. In our study, we investigate this problem in the limit where the stiffness and internal damping of the plate are negligible and hence are not parameters of interest. For the hinged-rigid splitter plate case, experiments show that the splitter plate oscillations increase with Reynolds numbers at low values of Re, and are found to reach a saturation amplitude level at higher Re. This type of saturation amplitude level that appears to continue indefinitely with Re, appears to be related to the fact that there is no structural restoring force in this case, and has been seen previously for elastically-mounted cylinders with no restoring force. In the present case, the saturation tip amplitude level can be up to 0.45D,where D is the cylinder diameter. For this hinged-rigid splitter plate case, it is found that the splitter plate length to cylinder diameter (L/D) ratio is crucial in determining the character and magnitude of the oscillations. For small splitter plate lengths (L/D ≤ 3.0), the oscillations appear to be nearly periodic with tip amplitudes of about 0.45D nearly independent of L/D. The non-dimensional oscillation frequencies (fD/U ) on the other hand are found to continuously vary with L/D from fD/U ≈ 0.2at L/D =1 to fD/U ≈ 0.1 at L/D = 3. As the splitter plate length is further increased beyond L/D ≥ 4.0, the character of the splitter plate oscillations suddenly changes. The oscillations become aperiodic with much smaller amplitudes. In this long splitter plate regime, the spectra of the oscillations become broadband, and are reminiscent of the change in character of the wake oscillations seen in the earlier fixed-rigid splitter plate case for L/D ≥ 5.0. It appears that the vortex shedding is nearly inhibited for L/D ≥ 4.0 in the present case. This is also supported by measurements of the wake vorticity field from Particle-Image Velocimetry (PIV). The phase-averaged PIV vorticity fields show that the strength of the shed vortices decreases rapidly as the splitter plate length increases. For longer splitter plates, L/D ≥ 4.0, the plate oscillations are no longer periodic, and hence it appears that the wake vortices are not synchronized with the splitter plate motions. For the entirely-flexible splitter plate case, the splitter plate deformations appear to be in the form of a travelling wave. In this case, the tip amplitudes are significantly larger of the order of 1.1D, and the non-dimensional oscillation frequency (fD/U )is close to 0.2, approximately the same as the Strouhal number for the bare cylinder. In sharp contrast to the hinged-rigid splitter plate case, the non-dimensional amplitude and frequency appear to be nearly independent of the normalized splitter plate length (L/D)even up to L/D =7.0. PIV measurements of the wake vorticity field indicates that there appears to be a nearly continuous sheet of vorticity on both sides of the flexible splitter plate, and the vortex sheet sheds and forms distinct vortices only at the trailing edge of the plate. The strength of these shed vortices appears to be close to that of the bare cylinder at similar Re. The results appear to suggest that in this entirely-flexible case, the vortices form at the same frequency and are of the same strength as in the bare cylinder case, but their formation is just pushed further downstream. This would suggest that in this case, the base suction and drag could be lower than the bare cylinder. Further, the formation of vortices further downstream of the body could imply that this type of flexible splitter plate could be useful to suppress vortex-induced vibrations (VIV).