Numerical and experimental study of the flow around a 4:1 rectangular cylinder at moderate Reynolds number
Introduction
The aerodynamics of detached flows around bluff bodies is of primary importance in wind engineering. It is needed to understand and control various undesirable wind-induced phenomena, such as vortex induced vibrations of tall towers or long-span bridge decks (Irwin, 2008; Li et al., 2017), and should be numerically modeled in a reliable way (Rigo et al., 2018).
Rectangular cylinders are considered as a canonical geometry that allows the study of several elongated civil engineering structures. Despite the simple two-dimensional geometries involved, the flow around bodies of elongated rectangular cross section are highly complex because of the three-dimensional nature of turbulence and the unsteady separation and reattachment dynamics characterizing bluff bodies. Rectangular cylinders at zero incidence have been extensively studied, first experimentally (e.g. Nakaguchi et al., 1968; Nakamura and Mizota, 1975; Washizu et al., 1978; Okajima, 1983; Stokes and Welsh, 1986) and then numerically (e.g. Tamura et al., 1993; Yu and Kareem, 1998; Shimada and Ishihara, 2002). These authors have shown that the flow dynamics around such cross sections is mainly influenced by the ratio of the chord c to the deph d of the cross section. In particular, Shimada and Ishihara (2002) investigated the impact of the ratio at zero incidence through Unsteady Reynolds-Average Navier-Stokes (urans) simulations at , this Reynolds number being defined as , where and ν are the freestream velocity and the kinematic viscosity, respectively. Shimada and Ishihara (2002) divided the aerodynamic behavior into three main categories based on the dynamics of the shear layer. For short cylinders with , flow separation occurs at the leading edges and the rectangular cross section is too short to allow shear layer reattachment. The flow is thus fully separated and vortices are periodically shed from the leading edges of the cylinder. On rectangular cross sections with a ratio , the shear layer reattaches periodically and vortex shedding occurs from both the leading and trailing edges. Finally, for longer rectangular cylinders with , the flow is able to fully reattach and vortices are shed from the trailing edges.
In this context, the Benchmark on the Aerodynamics of a Rectangular Cylinder (barc) (Bartoli et al., 2008) provides experimental and numerical contributions to the study of a 5:1 rectangular cylinder. Bruno et al. (2014) compared more than 70 studies in terms of bulk parameters, flow and pressure statistics, as well as spanwise correlations. Among the principal conclusions, Bruno et al. (2014) reported a narrow distribution of results obtained for the Strouhal number and the time-averaged drag coefficient while those collected for the standard deviation of the lift coefficient are significantly dispersed. It was argued that this scattering is caused by the high sensitivity of the flow along the upper and lower surfaces of the rectangular cylinder to small differences in the wind tunnel setup and in the simulation parameters. In particular, the significant effect of the oncoming flow turbulence level (Shirato et al., 2010; Mariotti et al., 2016; Ricci et al., 2017) or of the cross-sectional edge sharpness (Carassale et al., 2014) have been highlighted, and the impacts of the cfd domain's spanwise length and grid density have been demonstrated (Mannini et al., 2011; Bruno et al., 2012).
Within the framework of the barc, Schewe (2013) investigated experimentally the impact of Reynolds number in the range between and on the aerodynamic coefficients. He showed that the Reynolds number has a minor influence on both the drag coefficient and the Strouhal number, but significantly impacts the lift coefficient and particularly the lift curve slope. Schewe (2013) argued that an increase in the Reynolds number could correspond to an increase in the turbulence level which would cause a shift downstream of the time-averaged reattachment point on the lower surface (for a cylinder at positive angle of attack). This would lead to a modification of the flow topology that could impact the pressure coefficient distribution and therefore the lift. The need for the wind engineering community to capture accurately the slope of the lift coefficient is obvious: it appears (i) in the calculation of the critical wind speed in the quasi-steady theory of galloping and (ii) in the calculation of the buffeting response of structures subject to turbulent wind flows. More recently, Patruno et al. (2016) performed urans and Large Eddy Simulations (les) at three angles of attack. They reported large discrepancies between urans and les results for the different incidences. Moreover, they showed that urans is not able to correctly estimate the internal organization of the recirculation bubble, which impacts the estimation of the spatio-temporal pressure coefficient and subsequently the load coefficients. Additionally, Mannini et al. (2017) used pressure and load measurements to investigate the effects of the incidence, Reynolds number and turbulent intensity on the flow and the subsequent bulk parameters. In particular, the Reynolds-number dependence of force coefficients and the effect of the incoming turbulence on the vortex-shedding mechanism were highlighted. Finally, Cimarelli et al. (2018) reported the first Direct Numerical Simulation (dns) of the flow around a 5:1 rectangular cylinder at .
Despite the significant number of studies that have been conducted on the aerodynamics of rectangular cylinders, this topic is still of interest because of the high sensitivity of the flow to a number of parameters (Bruno et al., 2014). Additionally, testing the ability of computationally affordable cfd approaches to provide sufficiently accurate estimation of such flow remains useful in an industrial perspective. For these reasons, the present work investigates both experimentally and numerically the flow around a rectangular cylinder of aspect ratio , i.e., slightly shorter that in the context of the barc but exhibiting similar dynamics. The spatio-temporal pressure distribution along a cross section of the cylinder is acquired by carrying out unsteady pressure measurements at different incidences and for . The flow is also investigated through Computational Fluid Dynamics (cfd) using both two-dimensional urans and three-dimensional Delayed-Detached Eddy Simulation (ddes) approaches. The comparison of their predictions is of particular interest for determining if the increase in computational cost required by ddes to circumvent some of the urans limitations results in a significantly better estimation of the flow. The present study extends thus the work of Patruno et al. (2016) and Mannini et al. (2017), as it considers a different Reynolds number range, other cfd approaches and a different cylinder geometry. The objective is two-fold: i) to determine the effects of the rectangle incidence and freestream velocity on the variation of the flow topology and the aerodynamic loads, and ii) to assess the capability of urans and ddes to provide a sufficiently accurate estimation of the flow and the subsequent aerodynamic loads for different incidences.
Section snippets
Methodology
Sections 2.1 Experimental approach, 2.2 Computational approaches are dedicated to the description of the experiments and the setup of the cfd simulations, respectively. Both setups aim at reproducing an unconfined two-dimensional flow and were designed following the standards and guidelines suggested in the context of the barc (Bruno et al., 2014), and detailed in the ercoftac qnet-cfd Knowledge Base Wiki (Bruno and Salvetti, 2017). An extensive description of the experimental setup can be
Results
This section presents and discusses the results obtained experimentally and numerically. Statistics computed on load and pressure coefficients are discussed and compared in Secs. 3.1 and 3.2, respectively. Section 3.3 aims to understand the dynamics of the flow by analysing the time response of the pressure distribution. Finally, Sec. 3.4 studies the effects of the Reynolds number on the flow and the subsequent aerodynamic loads.
Conclusions
The flow around a 4:1 rectangular cylinder at several angles of attack has been studied numerically and experimentally. In particular, dynamic pressure measurements have been performed to obtain the time response of the pressure coefficient along a cross section of the cylinder. The pressure distribution was used to compute and study the aerodynamic loads on the body and to analyze the flow dynamics. The sensitivity of the solution on the Reynolds number has been quantified by considering
Acknowledgement
Computational resources have been provided by the Consortium des Équipements de Calcul Intensif (CCI), funded by the Fonds de la Recherche Scientifique de Belgique (F.R.S.-FNRS) under No. 2.5020.11.
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2021, International Journal of Mechanical SciencesCitation Excerpt :Compendiums of the circular, and square cylinder wakes can be found in Williamson [14] and Bai and Alam [9], respectively. A review on the wakes of different bluff body shapes, made by Derakhshandeh and Alam [10], points up that the investigations on the flow over a rectangular cylinder are very limited, especially at low Reynolds numbers (< 200) [13,25–27] compared to high Reynolds numbers (> 200) [8,28–34]. Kumar and Tiwari [35] have investigated the 3D wake flow dependence on impinging shear, cross-sectional aspect ratio W/D (= 0.5–2), and Re (=150–250) for a surface mounted rectangular cylinder.