The ready availability of full-field velocity measurements in present-day experiments has kindled interest in using such data for force estimation, especially in situations where direct measurements are difficult. Among the methods proposed, a formulation based on impulse is attractive, for both practical and physical reasons. However, evaluation of the impulse requires a complete description of the vorticity field, and this is particularly hard to achieve in the important region close to a body surface. This paper presents a solution to the problem. The incomplete experimental-vorticity field is augmented by a vortex sheet on the body, with strength determined by the no-slip boundary condition. The impulse is then found from the sum of vortex-sheet and experimental contributions. Components of physical interest can straightforwardly be recognised; for example, the classical ‘added mass’ associated with fluid inertia is represented by an explicit term in the formulation for the vortex sheet. The method is implemented in the context of two-dimensional flat-plate flow, and tested on velocity-field data from a translating wing experiment. The results show that the vortex-sheet contribution is significant for the test data set. Furthermore, when it is included, good agreement with force-balance measurements is found. It is thus recommended that any impulse-based force calculation should correct for (likely) data incompleteness in this way.
The understanding of low Reynolds number aerodynamics is becoming increasingly prevalent with the recent surge in interest in advanced Micro-Air Vehicle (MAV) technology. Research in this area has been primarily stimulated by a military need for smaller, more versatile, autonomous, surveillance aircraft. The mechanism for providing the high lift coe cient required for MAV applications is thought to be largely influenced by the formation of a Leading Edge Vortex (LEV). This paper analyses experimentally, the influence of the LEV e↵ect for a flat plate wing (A = 4) under fast and slow pitch-up motions at Re =10,000 using a combination of dye flow visualisation and PIV measurements. It is found that a fast pitch over 1c shows a flow topology dominant LEV, while for a slow pitch case over 6c, the flow is largely separated. The development of the suction surface flow and the LEV was strongly correlated with the kinematics of the leading edge, suggesting that the e↵ective local angle of incidence at the Leading Edge (LE) is of considerable significance in unsteady pitching motions.
NomenclatureA Aspect Ratio b Wing span, m c Wing chord, m c max Maximum number of chords travelled k Reduced frequency LE Leading Edge LEV Leading Edge Vortex Q Q-criterion vortex detection parameter s Distance travelled in chord lengths, m TE Trailing Edge TEV Trailing Edge Vortex t Time, s U inf Reference velocity, ms 1 ↵ Angle of incidence, ↵ Pitch rate, rad/s ✏ Error ci Swirling Strength ⇢ Density, kg/m 3
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