P.W. Bearman

Investigation of the flow behind a two-dimensional model with a blunt trailing edge and fitted with splitter plates

The flow in the wake of a two-dimensional model with a blunt trailing edge was examined at Reynolds numbers (based on model chord) between 1·4 × 10 5 and 2·56 × 10 5 . The ratio of total boundary-layer thickness at the trailing edge to model base height was approximately 0·5. Measurements were taken of base pressure and vortex shedding frequency together with traverses of the wake using a hot-wire anemometer. Traverses carried out along the wake showed a peak in the root-mean-square velocity-fluctuation at a distance equal to one base height from the model rear face. The position of the peak is referred to as the position of the fully formed vortex. The investigation was extended to a model fitted with splitter plates up to four base heights long. For each plate tested, a position of the fully formed vortex was found, and its distance from the model base was discovered to be inversely proportional to the base pressure coefficient. The flow about the model with splitter plates is described as being separated into five regimes of flow.

ASPECT RATIO AND END PLATE EFFECTS ON VORTEX SHEDDING FROM A CIRCULAR CYLINDER

Aspect ratio effects on the vortex shedding flow from a circular cylinder have been studied by using moveable end plates. Experiments were carried out to measure fluctuating forces, shedding frequency and spanwise correlation whilst varying end plate separation and Reynolds number. The aspect ratio (0.25-12) was found to have a most striking effect on the fluctuating lift. Within a certain range of Reynolds number an increase of the sectional fluctuating lift was obtained for reduced aspect ratio, and showed a maximum for an aspect ratio of 1, where the fluctuating lift could be almost twice the value for very large aspect ratios. This increase of the lift amplitude was found to be accompanied by enhanced spanwise correlation of the flow. The measurements were carried out over the Reynolds number range 8 > 103 < Re < 1.4 x 105. The strong increase in fluctuating lift with small aspect ratio did not occur at the lower and upper boundaries of this range. In the lower Reynolds number range (Re < 2 x 104) the trend could be reversed, i.e. the fluctuating lift decreased with decreasing aspect ratio. Also, with small aspect ratio, a shedding breakdown was found in the upper Reynolds number range (Re = 1.3 x 105). The main three dimensional feature observed was a spanwise variation in the phase of vortex shedding, accompanied by amplitude modulation in the lift signal. However, the level of three-dimensionality can be reduced by using a small aspect ratio. Three-dimensional vortex shedding features are discussed and comparison of the results with those from both two-dimensional numerical simulations and other experiments using large aspect ratios are presented.

On vortex street wakes

The flow in the wake of a two-dimensional blunt-trailing-edge body was investigated in the Reynolds number range, Reynolds number being referred to base height, 1·3 × 10 4 to 4·1 × 10 4 . The effects of splitter plates and base bleed on the vortex street were examined. Measurements were made of the longitudinal spacing between vortices and the velocity of the vortices, and compared with values predicted by von Karmans potential vortex street model. The lateral spacing was estimated by using both the von Karman and Kronauer stability criteria. A new universal wake Strouhal number is devised, using the value of lateral spacing predicted by the Kronauer stability condition as the length dimension. A correlation of bluff-body data was found when pressure drag coefficient times Strouhal number was plotted against base pressure.

A VISUAL STUDY OF THE FLOW AROUND AN OSCILLATING CIRCULAR CYLINDER AT LOW KEULEGAN-CARPENTER NUMBERS AND LOW STOKES NUMBERS

The structures of the flow induced by a circular cylinder performing sinusoidal oscillations in a fluid at rest are investigated by means of flow visualisation. The experiments are carried out at Keulegan-Carpenter numbers between 1.6 and 15 and at Stokes numbers between 5 and 160. Above a certain value of Keulegan-Carpenter number, depending on the Stokes number, some asymmetry appears in the flow separation and the associated vortex development behind the cylinder. The two vortices which are developed in a half cycle differ in strength and may be convected in different directions. This results in a fascinating set of flow patterns. Eight different regimes of flow can be identified within the ranges of Keulegan-Carpenter number and Stokes number studied. Furthermore, most of the resulting flows show a three-dimensional instability along the axis of the cylinder. Measurements of the wavelength of these disturbances are presented.

A study of forces, circulation and vortex patterns around a circular cylinder in oscillating flow

Measurements of sectional and total forces and the spanwise correlation of vortex shedding are presented for a circular cylinder in planar oscillatory flow at Keulegan-Carpenter numbers, KC , in the range from about 4 to 55. The viscous parameter β is in the range from around 100 to 1665. Circulation measurements around a circuit close to and enclosing the cylinder, are also presented. A mode-averaging technique was used for both sectional forces and circulation measurements and this gave, for typical modes of vortex shedding, time histories over an average cycle. The transverse force and the circulation tend to fluctuate in sympathy with each other, except around the instant of flow reversal when the force changes sign but the circulation remains high. Values of the strength of shed vortices, estimated from the measured circulation, are found to be comparable with steady-flow results. For KC [lsim ] 30, modes of vortex shedding occur over distinct ranges of KC with spanwise correlation high at the centre of a KC -range for a particular mode of shedding but low at the boundaries. Above KC ≈ 30 the correlation is no longer very sensitive to KC and the correlation length is estimated to be equal to 4.65 cylinder diameters. In the transverse vortex-street regime (8 [lsim ] KC [lsim ] 15) the cylinder was found to experience a steady transverse force, the coefficient of which is estimated to be about 0.5 at KC = 14.

Near wake flows behind two- and three-dimensional bluff bodies

The flow in the near wake region behind a bluff body, incorporating the vortex formation region, plays an important role in determining the steady and unsteady forces acting on the body. Even behind two-dimensional geometries this flow exhibits certain strong three-dimensional properties. A brief review is presented of the characteristic three-dimensional features found in the wakes of bluff bodies. In the case of three-dimensional bluff bodies a distinction is made between bodies where the geometry is mildly three-dimensional and strongly three-dimensional. The behaviour of the vortex formation length behind a mildly three-dimensional body is discussed. Results from a two-dimensional numerical simulation are used to show how the vortex formation length varies through the lock-in range for a circular cylinder oscillating transverse to a flow. Finally, velocity fields are presented for the wake of complex bluff form, a car model, obtained by using particle image velocimetry which show that the instantaneous flow is quite different to the time-average flow.

A model equation for the transverse forces on cylinders in oscillatory flows

Abstract A quasi-steady model is presented to predict the transverse force on cylinders in waves and oscillating flows. The model assumes that the Strouhal number, based on the instantaneous flow velocity, is constant, taking a value of 0.2. It is also assumed that the lift coefficient, based on the instantaneous dynamic pressure of the flow, is constant over a half cycle of the flow. The predictions of the model are compared with measurements taken on a circular cylinder in planar oscillatory flow over the Keulegan Carpenter number, KC, range from 5 to 53. The agreement between predicted and measured transverse forces is good at high KC but deteriorates at low KC. For high KC, it is shown that the model can be further improved if additional variables are introduced into the model equation.

The effects of three-dimensional imposed disturbances on bluff body near wake flows

Abstract Wind tunnel and water flume experiments have been carried out on a half ellipse model with a blunt trailing edge, the aim being to study the three-dimensional nature of vortex shedding. The trailing edge of the model can be either straight or mildly wavy. Introducing waviness reduces base drag, with the reduction higher at the peaks of the waves, corresponding to where the chord is a maximum, than at valleys. Two vortex shedding frequencies are observed and there are two main modes of shedding, one where it is symmetric about a peak and the other where it is antisymmetric. Vortex splitting is a common feature observed in the flow and this occurs in order to accommodate changes in shedding frequency along the span. Behind a straight trailing edge vortex splitting occurs at random positions whereas superimposed waviness tends to fix where the splitting take place.

An investigation of the effect on vortex shedding of a sudden transverse disturbance applied to a circular cylinder

The effect on vortex shedding of a sudden transverse movement of a circular cylinder or a sudden change of flow direction for a fixed cylinder is investigated numerically in this paper. The near-wake structure and force coefficients are presented for different values of amplitude of this disturbance. Large amplitudes of rapid movement are simulated in order to investigate how the original vortex wake re-establishes itself after a sudden movement has occurred. The work presented here is part of a series of numerical investigations in which the main objective is to study in closer detail the effect of general, externally applied, disturbances on vortex shedding. In this paper the simulations are carried out using a discrete vortex method which models viscous diffusion.