The effect of aspect ratio on the wake structure of finite wall-mounted square cylinders

Abstract

This paper presents a combined experimental and large-eddy simulation study to characterise the effect of aspect ratio on the near-wake structure of a square finite wall-mounted cylinder (FWMC). The cylinder aspect ratios (span $L$ to width $W$) investigated in the experiments were $1.4\leqslant L/W\leqslant 21.4$ and the oncoming boundary-layer thicknesses were $1.3W$ and $0.9W$ at a Reynolds number based on cylinder width of $1.4\times 10^{4}$ and $1.1\times 10^{4}$, respectively. In complementary simulations, the cylinder aspect ratios investigated were 1.4, 4.3, 10 and 18.6. The cylinder wake structure was visualised in three-dimensional space using a vortex core detection method and decomposed to its oscillation modes using the spectral proper orthogonal decomposition (SPOD) technique. A parametric diagram is proposed to predict whether the time-averaged wake structure is a dipole or a quadrupole pattern, based on oncoming boundary-layer height and aspect ratio. Cellular shedding occurs when the aspect ratio is high with up to three shedding cells occurring across the span for aspect ratios $L/W>18$. Each of these cells sheds at a distinct frequency, as evidenced by the spectral content of the surface pressure measured on the side face and the near-wake velocity. Amplitude modulation is also observed in the vortex shedding, which explains the amplitude modulation of the acoustic pressure emitted by square FWMCs. SPOD is shown to be a viable method to identify the occurrence of cellular shedding in the wake.