How vortex dynamics affects the structural load in step cylinder flow

Abstract

The vortex dynamics and the structural load in a step cylinder (consisting of a small, d, and a large, D, cylinder) flow are investigated numerically at Reynolds number ( $Re_D$ ) 150 for diameter ratios $D/d=2.0, 2.4$ and 2.8. First, the formation mechanism of a non-uniform oblique vortex shedding (the vortex shedding frequency remains unchanged as the oblique shedding angle varies) behind the small cylinder is explained: an increase in the production rate of the vortex strength and a farther downstream movement of the vortex formation position occur simultaneously as the vicinity of the step is approached along the small cylinder. Second, the structural load (the drag and lift) along the step cylinder is investigated, where four local extremes (two local minima and two local maxima) are observed. An in-depth investigation of the vortex dislocation effects on the structural load is provided, showing that the decreased circulation in the near wake and the weakened staggered Kármán vortex shedding pattern cause a major reduction (90 %) of the sectional lift amplitude and a relatively modest reduction (5.7 %) of the sectional drag amplitude, compared with the corresponding sectional force when no vortex dislocation occurs. This new knowledge combined with the three-dimensional effect of the step cylinder wake (caused by the blending of the small and larger cylinder wakes around the step) explain the formation of the four local extremes and the distribution of the structural load between them. Finally, it is found that the increasing $D/d$ amplifies the structural load variation along the step cylinder.