Aerodynamic lift and moment fluctuations of a sphere

Abstract

Measurements are reported of the fluctuating lift acting on a sphere and the moment acting about the centre of a sphere at supercritical Reynolds numbers (R > 4 × 105). The lift and moment fluctuations are random functions of time which scale with the free-stream dynamic pressure and sphere dimensions. The power spectra of the lift and moment also scale with the above parameters and with the Strouhal number, nd/U. The spectra contain a maximum spectral density at very low frequencies (nd/U < 0·0003) and do not reveal appreciable effects of vortex shedding at discrete frequencies.Hot wire anemometers were placed near the surface but outside the boundary layer along a great circle in the meridian plane in which the lift was measured. The fluctuating velocity component near the surface on the upstream hemisphere in this meridian plane is highly correlated with the fluctuating lift in the same meridian plane. The correlation betweeen the lift and tangential velocity near the surface suggests that the fluctuating lift is produced by the component of fluctuating bound vorticity about the sphere that is normal to the meridian plane in which the lift force is measured. The fluctuating moment measured about an axis passing through the centre of the sphere and perpendicular to the above meridian plane is almost perfectly correlated with the fluctuating lift (the measured correlation coefficients were 0·99 and 1·00). The fluctuating moment coefficient is very small ($\sqrt{C^2_m}\simeq 5\times 10^{-4}$) compared to the fluctuating lift coefficient ($\sqrt{C^2_L}\simeq 6\times 10^{-2}$). The exceptional correlation between the random lift and moment suggests that the unsteady moment about the sphere centre (which can be produced only by shear stress fluctuations) is caused by the fluctuations of bound vorticity (residing in the boundary layer and wake) that are responsible for the unsteady lift.

Unsteady Lift Force on a Towed Sphere

“…The data presented for the unsteady side forces are thus in a range of Strouhal numbers that has received very little attention in the past. The only other comparable data for this problem are presented by Willmarth & Enlow (1969). They determined unsteady sphere side forces and moments at Reynolds numbers greater than 4)8;10, and for Strouhal numbers between approximately 10\ and 0)2.…”

“…The dimensionless (lift) force spectra of the current investigation at high Strouhal numbers are compared to similarly normalized sphere lift spectra measured by Willmarth & Enlow (1969) at low Strouhal numbers. They performed these measurements on a spherical model operating in a wind tunnel at supercritical Reynolds numbers (4)84;104Re41)67;10).…”

Magnus effect on a rotating sphere at high Reynolds numbers

“…One study that has been cited in almost all studies of the flow around non-rotating spheres is the one of Achenbach (1972) who was originally interested in the pneumatic transportation of spherical fuel elements in high-pressure tubes where high Reynolds numbers were expected. Contrary to the numerous studies on non-rotating spheres (Achenbach, 1972(Achenbach, , 1974a(Achenbach, , 1974bArakeri and Ram, 1984;Bakic, 2002;Calvert, 1972;Choi et al, 2006;Chomaz et al, 1993;Hoerner, 1935;Jang and Lee, 2008;Jeon et al, 2004;Kim and Durbin, 1988;Leder and Geropp, 1993;Maxworthy, 1969;Provansal et al, 2004;Quadflieg, 1975;Raithby and Eckert, 1968;Sakamoto and Haniu, 1990;Sawada et al, 2004;Suryanarayana et al, 1993;Suryanarayana and Meier, 1995;Suryanarayana and Prabhu, 2000;Taneda, 1978;Vlajinac and Covert, 1972;Willmarth and Enlow, 1969), the studies on rotating spheres focus on subcritical Reynolds numbers. Large Eddy Simulation (LES) of the flow over a rotating sphere was performed by Gora et al (2006) at Re D ¼1 Â 10 4 .…”

Lift exerted on stationary spheres in turbulent flow

“…Variations with time of lift forces have been inferred by several investigators and measured by Willmarth & Enlow (1969). They have been linked with perturbations of the separation line and with wake structure, in recent studies by Taneda (1978).…”