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).

A circular cylinder is a geometrically simple bluff body that occurs in various practical applications. As with any bluff body, it exhibits large drag forces and a strong fluctuating lift force, both related to the strong shedding of vortices from the body, which is commonly referred to as the Karman Street. Rigid splitter plates in the wake of the cylinder are known to suppress shedding from the body, and thereby result in reduced drag and fluctuating lift forces, the latter being important to reduce flow-induced vibrations of the body. In the present work, the flow past a cylinder with a downstream flexible splitter plate/flap is studied, the length (L) and flexural rigidity (EI) of the flap being the main parameters besides the flow speed (U). Two flaps length to cylinder diameter ratios (L/D), namely, a short (L/D = 2) and a long (L/D = 5) flaps have been studied, the shorter one being smaller than the recirculation zone, while the larger is longer than the recirculation zone. In both these cases, the flexural rigidity (EI) and the flow speed are systematically varied. In all cases, the flaps motion are directly visualized, the lift and drag forces are measured with a force balance, and the wake velocity field is measured using PIV. In both the long and short flaps cases, the flexural rigidity (EI) of the flexible flap has been varied over a large range of values, and it has been found that the results for flaps tip motion and forces collapse well when plotted with a non-dimensional bending stiffness (K∗), which is defined as K∗ = EI/(1/2ρU2L3). This collapse occurs across flexible flaps with different values of EI, as long as Re > 5000. The collapse is not found to be good for Re < 5000. This difference appears to be related to the large reduction in fluctuating lift for a bare cylinder in the Re range between approximately 1600 and 5000 discussed by Norberg[41]. In the long flap case, the existence of two types of periodic modes is found within the range of K∗ values from 5 × 10−6 to 1 × 10−1 studied. The first one corresponds to a local peak in amplitude at K∗ ≈ 1.5 × 10−3 that is referred to as mode I, and the second that occurs at low values of K∗ (K∗ < 3 × 10−5) that is referred to as mode II. The fluctuating lift is found to be minimum for the mode I oscillation. The mean drag is also found to reach a broad minimum that starts at K∗ corresponding to mode I and continues to be at the same low level of approximately 65% of the bare cylinder drag for all higher K∗ values, representing an approximately 35% decrease in mean drag of the cylinder. The wake measurements also show significant changes with K∗. The formation length (lf /D) obtained from the closure point of the mean separation bubble is found to continuously increase with K∗, reaching values of approximately 2.6 at mode I and thereafter only small increases are seen as K∗ is increased to large values corresponding to the rigid splitter plate case, consistent with the observed variations in the mean drag. The stream wise and cross-stream turbulent intensities and the Reynolds shear stress are all found to be strikingly lower in the mode I case compared to the bare cylinder case, and more importantly, these values are even lower than the rigid splitter plate case. This is consistent with the shedding of weaker vortices and with the minimum in fluctuating lift found in the mode I case. The results for this flap length show that the mode I flap oscillation, corresponding to K∗ ≈ 1.5 × 10−3, may be useful to reduce lift, drag, velocity fluctuations in the wake and the strength of the shed vortices. In particular, the wake fluctuations corresponding to this mode are found to be significantly lower than the rigid splitter plate case. In the short flap case (L/D = 2), it is found that there exists a richer set of flapping modes compared to the long flap, with these modes being dependent on K∗. At low K∗ values, the flap exhibits large amplitude symmetric flap motion that is referred to as mode A, while clearly asymmetric flaps motion are seen at higher K∗ values corresponding to modes B and C. Mode B corresponds to asymmetric large amplitude flapping motion, while mode C is also asymmetric with the flap clearly deflected off to one side, but having small oscillation amplitudes. At even higher K∗ values, corresponding to mode D, symmetric flaps motion are again seen with the amplitudes being smaller than in mode A. Apart from the flap tip amplitude, the non-dimensional frequency of flap tip motion also changes as the flap changes modes. In this case, there is a minimum in the fluctuating lift corresponding to mode B and C oscillation. The mean drag is found to reach a minimum again corresponding to mode C, which corresponds to an approximately 35% decrease in mean drag of the cylinder. In this case, there is a large increase in fluctuating lift (approximately 150% of the bare cylinder case) at higher values of K∗ that appears to correspond to a “resonant” condition between the structural natural frequency of the flexible splitter plate/flap and the wake shedding frequency of the bare cylinder. The wake measurements show that the formation length (lf /D) is the largest for mode C (deflected flap state), which is consistent with the observed minimum in mean drag observed for this mode. The stream wise and cross-stream turbulent intensities and the Reynolds shear stress are all found to be strikingly lower in the mode C case compared to the bare cylinder case, with the values for the Reynolds shear stress being lower than the rigid splitter plate case. This is again consistent with the minimum in fluctuating lift found in the mode C case. The results for this flap length show that the mode C flap oscillation, corresponding to K∗ ≈ 5 × 10−2 that correspond to a deflected flap state with very small oscillation may be useful to reduce lift, drag, velocity fluctuations in the wake and the strength of the shed vortices. The results from the present study show that the flexible flap/splitter plate down-stream of the cylinder exhibits a variety of mode shapes depending on the effective bending rigidity of the flap K∗ for both the long and short flaps cases. The forces and the wake are also found to be strongly dependent on this parameter K∗ with the wake fluctuations, lift fluctuations and the drag being very effectively suppressed at an intermediate value of K∗ that is found to be dependent on the plate/flap length.

The flow around a finite square prism has not been studied extensively when compared with an “infinite” (or two-dimensional) square prism. In the present study, the effect of a wake-mounted splitter plate on the flow around a surface-mounted square prism of finite height was investigated experimentally using a low-speed wind tunnel. Of specific interest were the combined effects of the splitter plate length and the prism’s aspect ratio on the vortex shedding, mean drag force coefficient, and the mean wake. Four square prisms of aspect ratios AR = 9, 7, 5 and 3 were tested at a Reynolds number of Re = 7.4×104 and a boundary layer thickness of /D = 1.5. Splitter plate lengths of L/D = 1, 1.5, 2, 3, 5, and 7, were tested, with all plates having the same height as the prism. Measurements of the mean drag force were obtained with a force balance, and measurements of the vortex shedding frequency were obtained with a single-component hot-wire probe. A seven-hole pressure probe was used to measure the time-averaged wake velocity at a Reynolds number of Re = 3.7×104 for AR = 9 and 5 with splitter plates of lengths L/D = 1, 3, 5, and 7. These measurements were carried out to allow for a better understanding of how the splitter plate affects the mean wake of the finite prism. The results show that the splitter plate is a less effective drag-reduction, but more effective vortex-shedding-suppression, device for finite square prisms than it is for infinite square prisms. Significant reduction in the mean drag coefficient was realized only for short prisms (of AR ≤ 5) when long splitter plates (of L/D ≥ 5) were used. A splitter plate of length L/D = 3 was able to suppress vortex shedding for all aspect ratios tested. However, for square prisms of aspect ratios AR ≤ 7, the splitter plate is a less effective vortex-shedding-suppression device when compared to its use with finite circular cylinders, i.e. longer splitter plates are needed for vortex shedding suppression with square prisms. Wake measurements showed distinct wake velocity fields for the two prisms tested. For the prism of AR = 9, a strong downwash flow in the upper part of the wake became weaker towards the ground plane. For the prism of AR = 5, the downwash remained strong close to the ground plane. With splitter plates installed, the downwash became weaker for both prisms. The splitter plate was found to narrow the wake width, especially close to the ground plane, and led to the stretching of the streamwise vortex structures in the vertical direction, and increased entrainment towards the wake centreline in the cross-stream direction.

Splitter plates are passive flow control devices for reducing drag and suppressing vortex shedding from bluff bodies. Most studies of splitter plates involve the flow around an “infinite” circular cylinder, however, in the present study the flow around a surface-mounted finite-height circular cylinder, with a wake-mounted splitter plate, was studied experimentally in a low-speed wind tunnel using a force balance and single-component hot-wire anemometry. Four circular cylinders of aspect ratios AR = 9, 7, 5 and 3 were tested for a Reynolds number range of Re = 1.9×10^4 to 8.2×10^4. The splitter plates had lengths, relative to the cylinder diameter, of L/D = 1, 1.5, 2, 3, 5 and 7, thicknesses ranging from T/D = 0.10 and 0.15, and were the same height as the cylinder being tested. The cylinders were partially immersed in a flat-plate turbulent boundary layer, where the range of boundary layer thickness relative to the cylinder diameter was δ/D = 1.4 to 1.5. Measurements were made of the mean drag force coefficient, the Strouhal number at the mid-height position, and the Strouhal number and power spectra along the cylinder height. For all four finite circular cylinders, the splitter plates were effective at reducing the magnitude of the Strouhal number, and weakening or even suppressing vortex shedding, depending on the specific combination of AR and L/D. Compared to the case of an infinite circular cylinder, the splitter plate is less effective at reducing the mean drag force coefficient of a finite circular cylinder. The largest drag reduction was obtained for the cylinder of AR = 9 and splitter plates of L/D = 1 to 3, while negligible drag reduction occurred for the shorter cylinders.