Characterization of flow contributions to drag and lift of a circular cylinder using a volume expression of the fluid force

A 2D numerical simulation of the flow around a circular cylinder is investigated during the onset of unsteadiness within the range of Reynolds numbers between 50 and 400. Using the recent formulation of Wu et al. [J.-Z. Wu, X.-Y. Lu, L.-X. Zhuang, Integral force acting on a body due to local flow structures, J. Fluid Mech. 576 (2007) 265–286], the fluid force is successfully approximated by a volume integral of a force density over a small flow domain surrounding the cylinder. The domain does not contain either the detached vortices in the wake or the vortex formation region. Using the vorticity laplacian, the domain is dynamically divided into two regions: the external flow region containing the two separated vortex layers and the back-flow region between these two vortex layers. The integration of the force density on both separated vortex layers and on the back-flow region gives two instantaneous contributions to the total force. For the mean drag it is found that the back-flow contribution increases from almost 0%0% of the total drag at Re=50%–20%Re=50%–20% of the total drag at Re=400Re=400. The separated vortex layer contribution is found to decrease as (a+bRe−1/2)(a+bRe−1/2). With regard to the force fluctuations, both regions contribute similarly to the lift oscillations, while only the back-flow region is responsible for the drag oscillations. This alternative comprehension of the fluid force origin is discussed and compared to that of the classical pressure/viscous formulation.