Numerical investigation of unsteady flow over tandem permeable elliptic and rigid circular cylinders at Reynolds number of 150

Abstract

This study presents a comprehensive numerical investigation of dynamic flows past a permeable elliptic cylinder and a impervious circular cylinder in tandem arrangement employing lattice Boltzmann method with block-structured topology-confined mesh refinement. Simulations are conducted in wide parameter space of spacing ratio ($L/D=1.5-5$), elliptic cylinder aspect ratio ($AR=0.2-1$), and Darcy number ($10^{-4}-0.8$) at Reynolds number of 150 (where $L$ and $D$ are two cylinder’s spacing and cylinder diameter, respectively). In this space, four vortex regimes are identified as overshoot (OS), reattachment (RA), quasi-coshedding (QS), and co-shedding (CS). At small-to-moderate spacing ratios, only OS and RA regimes occurs, signifying proximity effect over aspect ratio in flow instability with varying permeability; while large spacing ratios reveal all four regimes, with QS and CS appearing at small to moderate permeabilities. The shadowing effect significantly alters the impervious cylinder’s pressure distribution, especially at small spacing ratios. The time-averaged drag coefficient rises as the Darcy number increases, approaching single circular cylinder values. Drag and lift coefficient fluctuations are minimal at small-to-moderate spacing ratios but intensify in QS and CS regimes at large spacing ratios due to shadowing. The time-averaged lift coefficient is adjustable at moderate-to-large spacing ratios in RA, QS, and CS regimes, while the Strouhal number, influenced by proximity and permeability, highlights the porous elliptic cylinder’s role in alternating vortex shedding frequency.