SUMMARY Here we present the first digital particle image velocimetry (DPIV)analysis of the flow field around the wings of an insect (the tobacco hawkmoth Manduca sexta, tethered to a 6-component force-moment balance in a wind tunnel). A leading-edge vortex (LEV) is present above the wings towards the end of the downstroke, as the net upward force peaks. Our DPIV analyses and smoke visualisations match the results of previous flow visualisation experiments at midwing, and we extend the experiments to provide the first analysis of the flow field above the thorax. Detailed DPIV measurements show that towards the end of the downstroke, the LEV structure is consistent with that recently reported in free-flying butterflies and dragonflies: the LEV is continuous across the thorax and runs along each wing to the wingtip, where it inflects to form the wingtip trailing vortices. The LEV core is 2-3 mm in diameter (approximately 10% of local wing chord) both at the midwing position and over the centreline at 1.2 m s-1 and at 3.5 m s-1flight speeds. At 1.2 m s-1 the measured LEV circulation is 0.012±0.001 m2 s-1 (mean ± s.d.) at the centreline and 0.011±0.001 m2 s-1 halfway along the wing. At 3.5 m s-1LEV circulation is 0.011±0.001 m2 s-1 at the centreline and 0.020±0.004 m2 s-1 at midwing. The DPIV measurements suggest that if there is any spanwise flow in the LEV towards the end of the downstroke its velocity is less than 1 m s-1. Estimates of force production show that the LEV contributes significantly to supporting body weight during bouts of flight at both speeds(more than 10% of body weight at 1.2 m s-1 and 35-65% of body weight at 3.5 m s-1).

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Experimental error analysis of a digital angular stereoscopic PIV system is presented. The paper firstly describes an experimental rig which includes the design of a novel PIV test block for in situ calibration. This allowed the user to set up a static seeded flow volume which was translated in and out of plane to record PIV images using two megapixel CCD cameras positioned for angular stereoscopic viewing. PIV data were collected for a range of camera angles up to and for a range of flow displacements and processed by cross correlation into a set of two-dimensional calibration and flow displacement vectors. These 2D data were then processed into three-dimensional data by the use of geometric and bicubic spline interpolation algorithms and an error analysis performed on the predicted displacements. Results from this analysis have shown optimum system performance will be obtained by using camera angles of between 20 and and f numbers of f16 and higher. The results have also shown a theoretical prediction of system performance derived in previous work, which considers the ratio of out of plane to in plane errors, matches to within 8 and 18% of the experimental system performance.

A torsionally driven cavity has been used to examine the influence of elasticity on the swirling flow of constant-viscosity elastic liquids (Boger fluids). A wealth of phenomena is observed as the degree of inertia, elasticity and viscous forces are varied by using a range of low-to high-viscosity flexible polyacrylamide Boger fluids and a semi-rigid xanthan gum Boger fluid. As the inertia is decreased and elasticity increased by using polyacrylamide Boger fluids, the circulation rates for a 'Newtonian-like' secondary flow decreases until flow reversal occurs owing to the increasing magnitude of the primary normal stress difference. For each polyacrylamide fluid, the flow becomes highly unstable at a critical combination of Reynolds number and Weissenberg number resulting in a new time-dependent elastic instability. Each fluid is characterized by a dimensionless elasticity number and a correlation with Reynolds number is found for the occurrence of the instability. In the elasticity dominated flow of the polyacrylamide Boger fluids, the instability disrupts the flow dramatically and causes an increase in the peak axial velocity along the central axis by as much as 400%. In this case, the core vortex spirals with the primary motion of fluid and is observed in some cases at Reynolds numbers much less than unity. Elastic 'reverse' flow is observed for the xanthan gum Boger fluid at high Weissenberg number. As the Weissenberg number decreases, and Reynolds number increases, counter-rotating vortices flowing in the inertial direction form on the rotating lid. The peak axial velocity decreases for the xanthan gum Boger fluid with decreasing Weissenberg number. In addition, several constitutive models are used to describe accurately the rheological properties of the fluids used in this work in shear and extensional flow. This experimental investigation of a complex three-dimensional flow using well-characterized fluids provides the information necessary for the validation of non-Newtonian constitutive models through numerical analysis of the torsionally driven cavity flow.

Some insects use leading-edge vortices to generate high lift forces, as has been inferred from qualitative smoke visualisations of the flow around their wings. Here we present the first Digital Particle Image Velocimetry (DPIV) data and quantitative analysis of an insect's leading-edge vortex and near wake at two flight speeds. This allows us to describe objectively two-dimensional slices through the flow field of a tethered Tobacco Hawkmoth (Manduca sexta). The near-field vortex wake appears to braodly resemble elliptical vortex loops. The presence of a leading-edge vortex towards the end of the downstroke is found to coincide with peak upwards force production measured by a six component force-moment balance. The topology of Manduca's leading-edge vortex differs from that previously described in that late in the downstroke, the structure extends continuously from wingtip across the thorax to the other wingtip.

Actuator disc models of insect flight are concerned solely with the rate of momentum transfer to the air that passes through the disc. These simple models assume that an even pressure is applied across the disc, resulting in a uniform downwash distribution. However, a correction factor, k, is often included to correct for the difference in efficiency between the assumed even downwash distribution, and the real downwash distribution. In the absence of any empirical measurements of the downwash distribution behind a real insect, the values of k used in the literature have been necessarily speculative. Direct measurement of this efficiency factor is now possible, and could be used to compare the relative efficiencies of insect flight across the Class. Here, we use Digital Particle Image Velocimetry to measure the instantaneous downwash distribution, mid-downstroke, of a tethered desert locust (Schistocerca gregaria). By integrating the downwash distribution, we are thereby able to provide the first direct empirical measurement of k for an insect. The measured value of k = 1.12 corresponds reasonably well with that predicted by previous theoretical studies.

A geometric error model for analysis and design of stereoscopic PIV systems is presented. The model allows displacement errors in either translational or angular systems to be analysed for any given angle or camera separation and for any off-axis position. A parameter for the analysis of the system performance is also introduced based on the ratio of out-of-plane to in-plane errors. This is subsequently used to investigate the relative performance of translational and angular PIV systems for camera angles up to and camera separations of half the object distance. Results from this analysis show similar trends in centreline characteristics for both types of stereo systems but different trends in off-axis error ratios due to imaging geometry. The results have also suggested that a CCD-based angular PIV stereo system offers up to 40% greater out-of-plane accuracy for a given field of view and laser power than previous translational systems.

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