Two tandem cylinders of different diameters in cross-flow: effect of an upstream cylinder on wake dynamics

Abstract

This work aims to provide a systematic experimental study on the wake of two tandem cylinders of unequal diameters. The fluid dynamics around a circular cylinder of diameter $D$ placed in the wake of another circular cylinder with a smaller diameter of $d$ is investigated, including the time-mean drag coefficient ($C_{D}$), the fluctuating drag and lift coefficients ($C_{D}^{\prime }$ and $C_{L}^{\prime }$), the Strouhal number ($St$) and the flow structures. The Reynolds number based on $D$ is kept constant at $4.27\times 10^{4}$. The ratios $d/D$ and $L/d$ vary from 0.2 to 1.0 and 1.0 to 8.0 respectively, where $L$ is the distance from the upstream cylinder centre to the forward stagnation point of the downstream cylinder. The ratios $d/D$ and $L/d$ are found, based on extensive hotwire, particle imaging velocimetry, pressure and flow visualization measurements, to have a marked influence on the wake dynamics behind the cylinders. As such, the flow is classified into the reattachment and co-shedding flow regimes, the latter being further subdivided into the lock-in, subharmonic lock-in and no lock-in regions. It is found that the critical spacing that divides the two regimes is dictated by the upstream-cylinder vortex formation length and becomes larger for smaller $d/D$. The characteristic flow properties are documented in each regime and subdivided region, including the flow structure, $St$, wake width, vortex formation length and the lateral width between the two gap shear layers. The variations in $C_{D}$, $C_{D}^{\prime }$, $C_{L}^{\prime }$ and the pressure distribution around the downstream cylinder are connected to the flow physics.