Binary interactions between stationary circular and non-circular cylinders in steady unbounded flow

Abstract

We perform two-dimensional particle resolved direct numerical simulations of the steady cross flow past a pair of interacting circular and non-circular cylinders with the cut-cell method, a sub-class of non-body-conforming methods that provides a sharp description of the boundary, is strictly mass and momentum conservative, and can be easily extended to adaptive grids. We use hierarchically refined Cartesian meshes where we place a reference cylinder (i) at the center of the domain and vary the location of a neighboring cylinder (j). We consider a large parameter space defined by the radius of curvature 2/ζi and 2/ζj ranging from 1 to 0, the angles of incidence αi and αj at values of 0° and 45°, the center-to-center gap ratio G ranging from 1.5 to 20, the alignment angle θ measured between the free-stream flow and the line connecting the centers of the cylinders, ranging from 0° to 360°, and finally the Reynolds number Re varied from 1 to 20. Specifically, we investigate the force and flow disturbances introduced by the neighboring cylinder on the reference cylinder, with a focus on the normalized hydrodynamic drag and lift coefficients and the associated prevailing flow regimes. Our study highlights the substantial impact of both the gap ratio G and the alignment angle θ in delineating distinct flow regimes, each exhibiting distinctive flow characteristics and consistent trends in pressure distributions and variations of the normalized drag and lift coefficients. Generally, the flow and force disturbances become more pronounced when significant interactions between the cylinders occur, whether due to proximity, wake interference, or both. We identify a critical threshold for G, beyond which the flow and force disturbances induced by the neighboring cylinder markedly diminish, except in scenarios dominated by significant wake interactions. Our investigation shows that the documented trends in the flow and force variations exhibit remarkable similarity at Re of 10 and 20, but expectedly deviate at Re=1. Finally, we propose an empirical model to predict the hydrodynamic disturbances between two circular cylinders based on the modulation of the drag Cd,i and lift Cl,i coefficients. Leveraging the periodic nature of Cd,i and Cl,i as a function of the relative angular alignment θ of the neighboring cylinder, we use Fourier series expansions demonstrating accurate reconstruction of the data across a wide parameter space. Furthermore, our model exhibits promising predictive capabilities when applied to unexplored parameter ranges, encompassing scenarios involving non-circular cylinders and interpolated regions of Re and G.