Transient hydrodynamic blockage of gap flow between separated bodies in low-Reynolds-number regime

Abstract

Hydrodynamic blockage is a distinctive phenomenon governing the flow behavior of distinctly spaced bodies in low-Reynolds-number regimes. As thick shear layers develop around the bodies due to strong viscous diffusion, virtual fluid barriers form within gaps between the bodies, hindering the flow penetration through the gaps. Although previous studies reported that hydrodynamic blockage critically affects the propulsion of animals in the low-Reynolds-number regime, its quantitative effects on the flow behavior remain unclear from the perspective of the unsteady fluid-structure interaction. This study introduces a novel approach to quantitatively examine and characterize the transient development of hydrodynamic blockage. We numerically investigate the transient hydrodynamic blockage using multiple stationary cylinders in a two-dimensional domain, considering wide ranges of the Reynolds number and gap width between the cylinders under diverse accelerating free streams. First, the formation process of a virtual fluid barrier is evaluated in terms of the shear layer development around cylinders. A new parameter is then introduced to quantify the degree of hydrodynamic blockage by comparing the flow rate of free stream to that affected by the blockage. We reveal that, in addition to strong viscous diffusion which initiates hydrodynamic blockage, streamwise convection is also important in characterizing the transient hydrodynamic blockage. By comparing the amount of convection required for the full development of hydrodynamic blockage to the effective gap width that combines the physical gap width and the viscous diffusion length, the regime where the blockage dominates the flow behavior is identified.