J. M. R. Graham

Forces on cylinders in viscous oscillatory flow at low Keulegan-Carpenter numbers

This paper presents a comparison between theory and experiment for the in-line forces on cylinders of general cross-section in planar oscillatory flows of small amplitude. The theoretical analysis evaluates corrections to the standard inviscid inertial force at low Keulegan-Carpenter numbers which arise from the presence of viscous laminar boundary layers and from the development of vortex shedding. The boundary-layer contribution due to both skin friction and displacement effects is calculated to first order in the Stokes parameter β −½ . The contribution to the in-line force from separation and vortex shedding, for which the results presented only apply to sharp-edged bodies, is taken from previous work on vortex shedding from isolated edges using the discrete vortex modelling technique. The resulting force has components both in phase with the fluid acceleration (inertia) and in phase with the velocity (drag). The theoretical results are compared to measurements taken in a [xcup ]-tube water channel on a number of cylinders of different cross-section including circular cylinders and sharp-edged sections. The comparisons suggest that the theory is valid for Keulegan–Carpenter numbers below about 3 and for moderately high values of the β parameter.

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.

The forces on sharp-edged cylinders in oscillatory flow at low Keulegan–Carpenter numbers

This paper describes an analysis of the forces induced by separation and vortex shedding from sharp-edged bodies in oscillatory flow at high Reynolds number. The analysis which is valid for the case of small oscillations of the fluid is compared with experimental data obtained at fairly low Keulegan–Carpenter numbers. The main conclusions of this paper were presented at the International Symposium on Wave Induced Forces on Structures at Bristol, 1978.

A free-surface and blockage correction for tidal turbines

The effects of free-surface proximity on the flow field around tidal stream turbines are modelled using actuator disc theory. Theoretical results are presented for a blocked configuration of tidal stream turbines such as a linear array that account for the proximity of the free surface and the seabed. The theoretical results are compared to open channel flow experimental results in which the flow field has been simulated using a porous disc and strip. These results are complemented by more detailed measurements of the performance of a model horizontal-axis turbine carried out in a water flume and a wind tunnel. The two sets of experiments represent highly blocked and effectively unblocked cases, respectively. The theoretical model of the effects of free-surface proximity provides a blockage correction for axial induction that can be incorporated in blade element momentum codes. The performance predictions obtained with such a code are in good agreement with the experimental results for C P and C T at low tip-speed ratios. The agreement weakens with increasing tip-speed ratio, as the wake of turbine enters a reversed flow state. A correction following the philosophy of Maskell is applied to C T in this region, which provides a better agreement.

Vortex shedding from bluff bodies in oscillatory flow: A report on Euromech 119

European Mechanics Colloquium number 119 was held at Imperial College on 16–18 July 1979, when the subject of vortex shedding from bodies in unidirectional flow and oscillatory flow, was discussed. A wide range of experimental work was presented including low-Reynolds-number flows around circular cylinders, the influence of disturbances on bluff body flow, the measurement of fluctuating forces and the influence of oscillations of the stream. About a third of the 33 papers presented concentrated on theoretical aspects and the majority of these were concerned with the ‘method of discrete vortices’.

The lift on an aerofoil in starting flow

An analysis is given of the initial development of the lift on an aerofoil in inviscid starting flow. It is shown that because of the spiral shape of the vortex sheet shed initially from the trailing edge the lift and drag are both singular at the start of impulsive motion. This result is in contrast with the prediction of finite forces by methods that assume the vortex sheet to be initially planar. The effect of a steady rate of change of incidence following the sudden onset of transverse (heaving) motion of an aerofoil in a steady stream is also discussed.

EFFECT OF VORTEX SHEDDING ON THE COUPLED ROLL RESPONSE OF BODIES IN WAVES

Hydrodynamic damping of floating bodies is due mainly to wave radiation and viscous damping. The latter is particularly important in controlling those responses of the the body for which the wave damping is small. The roll response of ship hulls near resonance in beam seas is an example of this. The present paper applies a discrete vortex method as a local solution to model vortex shedding from the bilges of a barge hull of rectangular cross-section and hence provides an analytic method for predicting its coupled motions in three degrees of freedom, including the effects of the main component of viscous damping. The method provides a frequency-domain solution satisfying the full linearised boundary conditions on the free surface.

Wake dynamics of external flow past a curved circular cylinder with the free stream aligned with the plane of curvature

The fundamental mechanism of vortex shedding past a curved cylinder has been investigated at a Reynolds number of 100 using three-dimensional spectral/hp computations. Two different configurations are presented herein:in both cases the main component of the geometry is a circular cylinder whose centreline is a quarter of a ring and the inflow direction is parallel to the plane of curvature.

Turbulent flow past a porous plate

The method of Vickery for calculating the drag of plane lattice structures normal to a turbulent stream is extended to cases of increased solidity. The analysis incorporates an extended version of Taylors theory for the flow through a porous plate, and a simplified version of Hunts analysis of the distortion of a turbulent flow by the mean flow field of a body. Some comparisons are made with experimental data.

Secondary flow in the human common carotid artery imaged by MR angiography.

The blood flow in arteries affects both the biology of the vessels and the development of atherosclerosis. The flow is three-dimensional, unsteady, and difficult to measure or to model computationally. We have used phase-shift-based magnetic resonance angiography to image and measure the flow in the common carotid arteries of a healthy human subject. There was curvature of the vessels and thin-slice dynamic flow imaging showed evidence of the presence of secondary motions. Flexing the cervical spine straightened the vessels and reduced the asymmetry of the flow.