Pulsatile flow and mass transport past a circular cylinder

Abstract

The mass transport of a pulsatile free-stream flow past a single circular cylinder is investigated as a building block for an artificial lung device. The free stream far from the cylinder is represented by a time-periodic (sinusoidal) component superimposed on a steady velocity. The dimensionless parameters of interest are the steady Reynolds number (Re), Womersley parameter (α), sinusoidal amplitude (A), and the Schmidt number (Sc). The ranges investigated in this study are 5 ⩽ Re ⩽ 40, 0.25 ⩽ α ⩽ 4, 0.25 ⩽ A ⩽ 0.75, and Sc = 1000. A pair of vortices downstream of the cylinder is observed in almost all cases investigated. These vortices oscillate in size and strength as α and A are varied. For α<αc, where αc = 0.005A−1.13Re1.33, the vortex is always attached to the cylinder (persistent); while for α>αc, the vortex is attached to the cylinder only during part of a time cycle (intermittent). The time-averaged Sherwood number, , is found to be largely influenced by the steady Reynolds number, increasing approximately as Re1/2. For α = 0.25, is less than the steady (α = 0, A = 0) value and decreases with increasing A. For α = 2 and α = 4, is greater than the steady value and increases with increasing A. These qualitatively opposite effects of pulsatility are discussed in terms of quasisteady versus unsteady transport. The maximum increase over steady transport due to pulsatility varies between 14.4% and 20.9% for Re = 10-40, α = 4, and A = 0.75.