Nicholas J. Lawson

The aerodynamics of Manduca sexta: digital particle image velocimetry analysis of the leading-edge vortex.

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-1 flight 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-1 LEV 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).

Three-dimensional particle image velocimetry: error analysis of stereoscopic techniques

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.

Three-dimensional particle image velocimetry: experimental error analysis of a digital angular stereoscopic system

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.

Swirling flow of viscoelastic fluids. Part 1. Interaction between inertia and elasticity

A torsionally driven cavity, consisting of a fully enclosed cylinder with rotating bottom lid, is used to examine the confined swirling flow of low-viscosity Boger fluids for situations where inertia dominates the flow field. Flow visualization and the optical technique of particle image velocimetry (PIV) are used to examine the effect of small amounts of fluid elasticity on the phenomenon of vortex breakdown. Low-viscosity Boger fluids are used which consist of dilute concentrations of high molecular weight polyacrylamide or semi-dilute concentrations of xanthan gum in a Newtonian solvent. The introduction of elasticity results in a 20% and 40% increase in the minimum critical aspect ratio required for vortex breakdown to occur using polyacrylamide and xanthan gum, respectively, at concentrations of 45 p.p.m. When the concentrations of either polyacrylamide or xanthan gum are raised to 75 p.p.m., vortex breakdown is entirely suppressed for the cylinder aspect ratios examined. Radial and axial velocity measurements along the axial centreline show that the alteration in existence domain is linked to a decrease in the magnitude of the peak in axial velocity along the central axis. The minimum peak axial velocities along the central axis for the 75 p.p.m. polyacrylamide and 75 p.p.m. xanthan gum Boger fluids are 67% and 86% lower in magnitude, respectively, than for the Newtonian fluid at Reynolds number of Re [approximate] 1500–1600. This decrease in axial velocity is associated with the interaction of elasticity in the governing boundary on the rotating base lid and/or the interaction of extensional viscosity in areas with high velocity gradients. The low-viscosity Boger fluids used in this study are rheologically characterized and the steady complex flow field has well-defined boundary conditions. Therefore, the results will allow validation of non-Newtonian constitutive models in a numerical model of a torsionally driven cavity flow.

Digital particle image velocimetry measurements of the downwash distribution of a desert locust Schistocerca gregaria

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.

Swirling flow of viscoelastic fluids. Part 2. Elastic effects

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.

Measurement of shock wave unsteadiness using a high-speed schlieren system and digital image processing

A new method to measure shock wave unsteadiness is presented. Time-resolved visualizations of the flow field under investigation are obtained using a high-speed schlieren optical system and the motion of the shock wave is determined by means of digital image processing. Information on the shocks unsteadiness is subsequently derived with Fourier analysis. A sample study on shock unsteadiness in a shock-wave/turbulent boundary-layer interaction with separation is included. The method presented enables a measure of shock unsteadiness at locations in the imaged flow field not accessible by intrusive methods.

High-speed photogrammetry system for measuring the kinematics of insect wings

We describe and characterize an experimental system to perform shape measurements on deformable objects using high-speed close-range photogrammetry. The eventual application is to extract the kinematics of several marked points on an insect wing during tethered and hovering flight. We investigate the performance of the system with a small number of views and determine an empirical relation between the mean pixel error of the optimization routine and the position error. Velocity and acceleration are calculated by numerical differencing, and their relation to the position errors is verified. For a field of view of approximately 40 mm x 40 mm, a rms accuracy of 30 mum in position, 150 mm/s in velocity, and 750 m/s2 in acceleration at 5000 frames/s is achieved. This accuracy is sufficient to measure the kinematics of hoverfly flight.

Crossflow characteristics of an oscillating jet in a thin slab casting mould

The application of LDA to a transient 1/3 scale (500 mm wide) water model of a mould, typical of steel thin slab casting, is presented. The characteristics of a crossflow, associated with the oscillating jet emerging from a submerged nozzle (internal diameter 33 mm), were analyzed for a range of casting rates (0-2 m/min), nozzle submergences (20-120 mm) and nozzle-mould wall gap widths (0-21 mm). The frequency of oscillation was found to be primarily dependent on the casting rate of the system, independent of nozzle submergence or gap width, whereas the RMS crossflow velocity depended on all three parameters. Additional crossflow was also observed past the jet below the nozzle exit and this allowed the jet to oscillate even with zero gap width

Experimental and computational investigation of an ‘open’ transonic cavity flow

Abstract This paper presents an investigation of a transonic flow (M∞=0.85) over a rectangular cavity having a length-to-depth ratio of 5. Velocities were measured inside the cavity on the central plane and two off-centre planes using a two-component particle image velocimetry system. These measurements were supported by surface flow visualization, and mean and time-varying surface pressure measurements. The flow was also simulated using an unsteady Reynolds-averaged Navier—Stokes code, with a realizable k — ε turbulence model. It is shown that this CFD model does not capture all the characteristics of the flowfield correctly. However, by using this integrated experimental and computational approach we have been able to identify three-dimensional flowfield structures within the cavity. The influence of the thickness of the approaching boundary layer is discussed.