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.

Time-resolved wake dynamics of finite wall-mounted circular cylinders submerged in a turbulent boundary layer

“…2004; Krajnović 2011; Yauwenas et al . 2019), the wake structure for AR10 and AR25 is akin to a dipole while that of AR50, AR75 and AR100 is similar to a quadrupole. The critical aspect ratio in this study, (AR50) is consistent with values of reported in these previous studies on circular cylinders (Kawamura et al .…”

“…This phenomenon of different shedding behaviour along the entire span of a cylinder has been observed in previous FWMC studies (Okamoto & Yagita 1973; Farivar 1981; Lee 1997; Yauwenas et al . 2019), and is often referred to as cellular shedding. This cellular shedding behaviour will be investigated in detail using the tallest cylinder (AR100) in § 3.4.2.…”

“…Several experimental and numerical studies have been conducted in the past to investigate the wake structure of FWMCs using geometries such as circular cylinders (Sumner, Heseltine & Dansereau 2004;Pattenden, Turnock & Zhang 2005;Krajnović 2011;Tang et al 2016;Heidari et al 2017;Hamed & Peterlein 2020) and cylinders with sharp edges (Balachandar & Tachie 2001;Wang et al 2006;Wang & Zhou 2009;Bourgeois, Sattari & Martinuzzi 2011;Nasif, Balachandar & Barron 2015;Yauwenas et al 2019). While most of the previous studies examined the FWMC in a uniform flow (Farivar 1981;Okamoto & Yagita 1973;Fox, Apelt & West 1993) or thin turbulent boundary layer (TBL) (δ h, where δ is the boundary layer thickness and h is the cylinder height) (Pattenden et al 2005;Wang & Zhou 2009;Krajnović 2011;Yauwenas et al 2019), a FWMC that is fully immersed in a thick TBL (δ > h as illustrated in figure 1) has received less attention, though encountered in many of the aforementioned practical applications. For δ > h, the FWMC encounters stronger mean shear and higher turbulence intensity in the approach flow, which can further complicate the unsteady flow separation and wake dynamics of the cylinder compared to its counterpart in a uniform flow or thin TBL.…”

“…2006; Wang & Zhou 2009; Bourgeois, Sattari & Martinuzzi 2011; Nasif, Balachandar & Barron 2015; Yauwenas et al . 2019). While most of the previous studies examined the FWMC in a uniform flow (Farivar 1981; Okamoto & Yagita 1973; Fox, Apelt & West 1993) or thin turbulent boundary layer (TBL) (, where δ is the boundary layer thickness and h is the cylinder height) (Pattenden et al .…”

“…2005; Wang & Zhou 2009; Krajnović 2011; Yauwenas et al . 2019), a FWMC that is fully immersed in a thick TBL ( δ > h as illustrated in figure 1) has received less attention, though encountered in many of the aforementioned practical applications. For δ > h , the FWMC encounters stronger mean shear and higher turbulence intensity in the approach flow, which can further complicate the unsteady flow separation and wake dynamics of the cylinder compared to its counterpart in a uniform flow or thin TBL.…”