| dc.description.abstract | 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. | en_US |
