Experimental verification of an Oseen flow slender body theory

Abstract

Consider uniform flow past four slender bodies with elliptical cross-section of constant ellipticity along the length of 0, 0.125, 0.25 and 0.375, respectively, for each body. Here, ellipticity is defined as the ratio of the semiminor axis of the ellipse to the semimajor axis. The bodies have a pointed nose which gradually increases in cross-section with a radius of curvature 419 mm to a mid-section which then remains constant up to a blunt end section with semimajor axis diameter 160 mm, the total length of all bodies being 800 mm. The bodies are side-mounted within a low-speed wind tunnel with an operational wind speed of the order 30 m s−1. The side force (or lift) is measured within an angle of attack range of −3° to 3° such that the body is rotated about the major axis of the ellipse cross-section. The lift slope is determined for each body, and how it varies with ellipticity. It is found that this variance follows a straight line which steadily increases with increasing ellipticity. It is shown that this result is predicted by a recently developed Oseen flow slender body theory, and cannot be predicted by either inviscid flow slender body theory or viscous crossflow theories based upon the Allen and Perkins method.

The theory and application of Navier-Stokeslets (NSlets)

“…Furthermore, in the high Reynolds number limit, the Oseenlet tends towards the Eulerlet, in addition we have Figure 6 shows that the slender body theory in Oseen flow 13 gives a close match to experiment for the lift L. Here, ellipticity e is defined as the ratio of the semi-minor axis to the semi-major axis s of the ellipse cross-section and α is the angle of attack. Again, from existing theory this is surprising as the Oseen flow approximation is violated on the surface of the slender body.…”

“…Second, consider uniform flow with Reynoldsy number Re ∼ 10 6 past a slender body whose cross-section is elliptical, and approximate the NSlet by the Eulerlet. It is seen that this is equivalent 5 to the uniform flow past a slender body with elliptical cross-section in Oseen flow given by Chadwick 13 who satisfies the slip body boundary condition for the potential part of the Oseen flow description.…”