When placed ih a fluid stream, some bodies generate separated flow over a substantial proportion of their surface and hence can be classified as bluff. On sharp-edged bluff bodies, separation is fixed at the salient edges, whereas on bluff bodies with continuous surface curvature the location of separation depends both on the shape of the body and the state of the boundary layer. At low Reynolds numbers, when separation first occurs, the flow around a bluff body remains stable, but as the Reynolds number is increased a critical value is reached beyond which instabilities develop. These instabilities can lead to organized unsteady wake motion, dis­ organized motion, or a combination of both. Regular vortex shedding, the subject of this article, is a dominant feature of two-dimensional bluff-body wakes and is present irrespective of whether the separating boundary layers are laminar or turbulent. It has been the subject of research for more than a century, and many hundreds of papers have been written. In recent years vortex shedding has been the topic of Euromech meetings reported on by Mair & Maull (1971) and Bearman & Graham (1980), and a comprehensive review has been undertaken by Berger & Wille (1972). Vortex shedding and general wake turbulence induce fluctuating pres­ sures on the surface of the generating bluff body, and if the body is flexible this can cause oscillations. Oscillations excited by vortex shedding are usually in a direction normal to that of the free stream, and amplitudes as large as 1.5 to 2 body diameters may be recorded. In addition to the generating body, any other bodies in its wake may be forced into oscillation. Broad-band force fluctuations, induced by turbulence produced in the flow around a bluff body, rarely lead to oscillations as severe as those caused by vortex shedding. Some form of aerodynamic instability, such that move-

Vortex shedding from oscillating bluff bodies

Drag reduction strategies for the turbulent flow around a D-shaped body are examined experimentally and theoretically. A reduced-order vortex model describes the interaction between the shear layer and wake dynamics and guides a path to an efficient feedback control design. The derived feedback controller desynchronizes shear-layer and wake dynamics, thus postponing vortex formation. This actuation is tested in a wind tunnel. The Reynolds number based on the height of the body ranges from 23000 to 70000. We achieve a 40% increase in base pressure associated with a 15% drag reduction employing zero-net-mass-flux actuation. Our controller outperforms other approaches based on open-loop forcing and extremum-seeking feedback strategies in terms of drag reduction, adaptivity, and the required actuation energy.

Feedback shear layer control for bluff body drag reduction

Unsteady aerofoil flows are often characterized by leading-edge vortex (LEV) shedding. While experiments and high-order computations have contributed to our understanding of these flows, fast low-order methods are needed for engineering tasks. Classical unsteady aerofoil theories are limited to small amplitudes and attached leading-edge flows. Discrete-vortex methods that model vortex shedding from leading edges assume continuous shedding, valid only for sharp leading edges, or shedding governed by ad-hoc criteria such as a critical angle of attack, valid only for a restricted set of kinematics. We present a criterion for intermittent vortex shedding from rounded leading edges that is governed by a maximum allowable leading-edge suction. We show that, when using unsteady thin aerofoil theory, this leading-edge suction parameter (LESP) is related to the term in the Fourier series representing the chordwise variation of bound vorticity. Furthermore, for any aerofoil and Reynolds number, there is a critical value of the LESP, which is independent of the motion kinematics. When the instantaneous LESP value exceeds the critical value, vortex shedding occurs at the leading edge. We have augmented a discrete-time, arbitrary-motion, unsteady thin aerofoil theory with discrete-vortex shedding from the leading edge governed by the instantaneous LESP. Thus, the use of a single empirical parameter, the critical-LESP value, allows us to determine the onset, growth, and termination of LEVs. We show, by comparison with experimental and computational results for several aerofoils, motions and Reynolds numbers, that this computationally inexpensive method is successful in predicting the complex flows and forces resulting from intermittent LEV shedding, thus validating the LESP concept.

Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding

We investigate the problem of a heaving and pitching hydrofoil in an inflow that consists of a uniform velocity field and a staggered array of vortices. The foil can exploit the energy in such a Karman vortex street for efficient propulsion of animals or submarines. Through a two-dimensional inviscid analysis, we find that the phase between foil motion and the arrival of inflow vortices is a critical parameter. Everything else being equal, the highest efficiency is seen when this phase is such that the foil moves in close proximity to the oncoming vortices. Different modes of vortex interaction in the wake results from a variation in this phase, and we show that the flow downstream of the foil is related to the foil input power.

Efficient Foil Propulsion Through Vortex Control

A potential flow model of two-dimensional vortex shedding behind an inclined plate is developed. The free shear layers which emanate from the sides of the plate are represented by discrete vortices through the use of the appropriate complex-velocity potential, the Kutta condition and the Joukowsky transformation between a circle and the plate cross-section. The analysis is then applied to predict the kinematic and dynamic characteristics of the flow for various angles of attack. The results compare favourably with the available experimental data as far as the form of vortex shedding and the Strouhal number are concerned. The calculated normal-force coefficients are 20−25% yo larger than those measured by Fage & Johansen (1927).

An inviscid model of two-dimensional vortex shedding for transient and asymptotically steady separated flow over an inclined plate

An inviscid model of two-dimensional vortex shedding behind a square-based section is developed. The model uses a discrete-vortex approximation for the free shear layers. The motion of the shear layers is computed from the velocities of the discrete vortices, which in turn are derived through a Schwartz-Christoffel transformation of the section. The flow round the body is impulsively started from rest and initially develops symmetrically. The introduction of a small asymmetric disturbance results in asymmetric interaction of the shear layers amplifying into steady vortex-shedding motion.The model is shown to predict the form of vortex shedding, the Strouhal number and some other flow quantities to a good degree of agreement with experimental results.

R. R. Clements

Papers

An inviscid model of two-dimensional vortex shedding