Ocean Engineering 216 (2020) 107865 Available online 23 August 2020 0029-8018/© 2020 Elsevier Ltd. All rights reserved. Reynolds-number effect on fow past a rectangular cylinder in the presence of a free surface Wenjie Zhong a , Solomon C. Yim b , Lu Deng a, c, * a College of Civil Engineering, Hunan University, Changsha, 410082, Hunan, China b School of Civil and Construction Engineering, Oregon State University, Corvallis, 97331, Oregon State, USA c Key Laboratory for Damage Diagnosis of Engineering Structures of Hunan Province, Changsha, 410082, Hunan, China A R T I C L E INFO Keywords: Reynolds number Rectangular cylinder Free surface RANS simulation Vortex shedding ABSTRACT Rectangular cylinders are insensitive to the Reynolds number (Re) due to the geometrically restricted fow separation. The introduction of asymmetry, e.g., inclination, asymmetric cross-section and asymmetric bound- ary, in the fow can signify the role of Re. To date, the effect of Re on rectangular cylinders near a free surface has not been comprehensively investigated. In this study, multiphase simulations of a square located at four depth-to- length ratios (0.3, 0.7, 1.0 and 4.5) over the Re range from 2.0 × 10 4 to 9.9 × 10 4 were conducted. Strong Reynolds-number effect on the fow was observed at the shallow and moderate depths. The surface jet, forming as the result of surface curvature when Re increases, is related to the local Froude number (Fr). The critical Re values for the surface jet formation at the three depth-to-length ratios, i.e., 0.3, 0.7 and 1.0, are 3.0 × 10 4 , 4.0 × 10 4 and 4.5 × 10 4 , respectively. The suppression of vortex shedding at the shallow depths is explained as the detachment of shear layers together with the modifcations of vorticity fuxes. The restoration of vortex shedding when Re is high is due to the surface jet interference which forces the recontact of the shear layers across the sharp corners to couple with each other. 1. Introduction Flow past rectangular cylinders in an infnite medium is one of classical topics in fuid mechanics (Bruno et al., 2010; Norberg, 1993; Okajima, 1982; Shimada and Ishihara, 2002; Sohankar, 2006). The wide applications of this fow contain, but are not limited to, the feld of civil engineering, e.g., buildings, towers and bridges, the feld of mechanical engineering, e.g., turbines and heat exchangers, and the feld of ocean engineering, e.g., offshore platforms, risers and pipes. From the fuid mechanics point of view, the fow over a rectangular cylinder involves plenty of physical phenomena, e.g., fow separation and reattachment, vortex formation and shedding, and unsteady wake. A prominent feature in this type of fow is the fxed point of fow separation at sharp corners, which is quite a contrast to the fow past a circular cylinder. While the curved surface of circular cylinders permits the shift of separation po- sition or laminar-to-turbulent transition relying on the Reynolds num- ber, Re (= UD/ν, where D is the characteristic length), (Bloor, 1964; Catalano et al., 2003; Norberg, 2003; Williamson, 1996; Yokuda and Ramaprian, 1990), the geometrically fxed fow separation of rectan- gular cylinders renders the infuence of Re insignifcant, especially when Re is greater than 2.0 × 10 4 (Franke et al., 1990; Norberg, 1993; Sohankar, 2006; Sohankar et al., 1999). Note that the signifcant Reynolds-number effect on the rectangular cylinder fow at low to moderate Re, e.g., 70 < Re < 2.0 × 10 4 , is associated with the fow transition from laminar to turbulent as observed by Okajima (1982), which is outside the scope of the present study. One way to make the infuence of Re signifcant in the moderate to high range is to incorpo- rate asymmetry in the fow confguration. Mannini et al. (2010) found that when the rectangular cylinder with a width-to-length ratio, w/l (where w and l are the width and length of the rectangular cylinder, respectively), of 5.0 is inclined at an angle of α = 4 ◦ , the fow features change signifcantly and the lift coeffcient rises as Re increases from 2.6 × 10 4 to 1.9 × 10 6 . Schewe (2013) experimentally studied the same fow but at several angles of attack over a range of Re from 4.0 × 10 3 to 6.0 × 10 5 , and reported similar phenomena of strong Reynolds-number effect as Mannini et al. (2010). Schewe (2013) also found that the infuence of Re on the rectangular cylinder with a small w/l (= 0.2) is small due to the lack of fow reattachment. Moreover, when the cross-section of a cyl- inder is asymmetric, e.g., a trapezoidal-shaped bridge section, the strong effect of Re is also exhibited (Larose and D’auteuil, 2006; Schewe, 2001). Apart from using geometric modifcation to gain asymmetric * Corresponding author. College of Civil Engineering, Hunan University, Changsha, 410082, Hunan, China. E-mail address: denglu@hnu.edu.cn (L. Deng). Contents lists available at ScienceDirect Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng https://doi.org/10.1016/j.oceaneng.2020.107865 Received 9 October 2019; Received in revised form 15 June 2020; Accepted 25 July 2020