Alternative drag coefficient in the wake of an isolated bluff body

Abstract

An alternative drag coefficient C[sub d][sup a] [=F̄∕(1/2ρU²[sub ∞]U[sub ∞]T[sub s])], is proposed for an isolated bluff-body wake, where F̅ is the drag force on the body per unit length, U[sub ∞] is the free-stream velocity, ρ is the density of fluid, and T[sub s] is the vortex shedding period. Theoretical analysis presently conducted indicates that, while the conventional drag coefficient C[sub d] [=F̄∕(1/2ρU²[sub ∞] d)] may be interpreted as the intensity of the mean kinetic energy deficit distributed over the characteristic length of cylinder height d, C[sup a] [sub d] is the intensity of the mean kinetic energy deficit distributed over the characteristic length of the Karman vortex wavelength U[sub ∞]T[sub s]. Therefore, C[sup a] [sub d] may be considered to be a drag coefficient with the characteristic length given by U[sub ∞]T[sub s], instead of d. As long as a bluff body is isolated, without energy exchange between the cylinder and its support, this drag coefficient is invariant, as confirmed by our experimental data as well as those in the literature, with respect to the bluff-body geometry, angle of attack, and Reynolds number, with a caveat of limited cases examined presently.