Aerodynamic lift and drag fluctuations of a sphere

Abstract

An experimental and theoretical investigation is made of the unsteady lift and drag exerted on a sphere in a nominally steady, high Reynolds number, incompressible flow. The net force on the sphere has previously been ascribed to fluctuations in the bound vorticity in the meridian plane normal to the force, produced by large-scale coherent structures shed into the wake. A simplified model of vortex shedding is proposed that involves coherent eddies in the form of a succession of randomly orientated vortex rings, interconnected by pairs of oppositely rotating line vortices, and shed at quasi-regular intervals with a Strouhal number ∼ 0.19. The rings are rapidly dissipated by turbulence diffusion, but it is shown that only the nascent vortex ring makes a significant contribution to the surface force, and that the force spectrum at Strouhal numbers exceeding unity is effectively independent of the shape of the fully formed vortex. Predictions of the lift and drag spectra at these frequencies are found to be in good accord with new towing tank measurements presented in this paper.

Computations of the flow past a still sphere at moderate reynolds numbers using an immersed boundary method

“…1 The literature provides several examples of both numerical and experimental analysis of the flow around a stationary sphere - Almedeij (2008), Bouchet et al (2006), Ploumhans et al (2002), Howe et al (2001), Kim et al (2001), Fadlun et al (2000), Tomboulides and Orszag (2000), Johnson and Patel (1999), Mittal and Najjar (1999), Fornberg (1988), Shirayama (1992). Despite the geometric symmetry and simplicity of a solid sphere, complex flow patterns can be observed in the wake at moderate large Reynolds numbers, whose characterization constitutes an interesting benchmark for validating Navier-Stokes equations solvers.…”

Dynamic Response of a High-Altitude Tethered Balloon System

“…s (17) and is therefore much more sensitive to the sagging of the tether and, mathematically speaking, to the point of application of the force w t S. In particular, from the response shown in Fig. 7, it appears that the horizontal position of the center of the tether is at 72% of the horizontal position of the aerostat (and not 50% as in the straight line assumption).…”

“…There is also a substantial amount of literature available on sphere aerodynamics (see, for example, the early work in [14] and more recently [15][16][17], just to quote a few examples), and more specific to the case of tethered spheres is the considerable body of research work on their vortex-induced vibrations (see, for example, [18][19][20][21]). However, in all these models, the fluid loading on the tether line and its mass are neglected.…”

Unsteady Lift Produced by a Streamwise Vortex Impinging on an Airfoil

“…The overall lift spectrum is determined by the average spectrum of the lift produced by the uncorrelated structures. This is entirely analogous to the quasi-periodic shedding mechanism that appears to control the spectrum of the unsteady side force experienced by a sphere in a nominally uniform mean stream (Wang & Lauchle 1999;Howe et al 2001). Figure 1 indicates how we intend to model these interactions.…”