Investigation of the steady and unsteady forces acting on a pair of circular cylinders in crossflow up to ultra-high Reynolds numbers

Abstract

Measurements of the steady and unsteady forces acting on a pair of circular cylinders in crossflow are performed from subcritical up to ultra-high Reynolds numbers. The two cylinders with equal diameters d are arranged inline at two centre-to-centre distances: S/d = 2.8 and 4. The trend of the drag curve for the upstream cylinder $$Cd_{1}$$ C d 1 (Re) at both distances is similar to that for a single circular cylinder. The development of the drag curves $$Cd_{2}$$ C d 2 (Re, S/d = 2.8, 4) of the downstream cylinder is inverse to that of the upstream cylinder. For both cylinder spacing values, the drag on the downstream cylinder is negative for subcritical Reynolds numbers, increases abruptly to positive values at the beginning of the supercritical regime, and shows a significant dip at transcritical Reynolds numbers. This drag inversion indicates that the critical distance Sc decreases sharply in the supercritical Reynolds number range. For S/d = 2.8 at Re$$\rightarrow$$ → 10$$^{7}$$ 7 , the downstream cylinder experiences once more a thrust force. The curve of the Strouhal number St(Re) of the downstream cylinder for S/d = 4 is very close to that of a single cylinder. For Reynolds numbers of Re$$\approx$$ ≈ 1$$\times$$ × 10$$^{6}$$ 6 - 7$$\times$$ × 10$$^{6}$$ 6 , the Strouhal numbers have nearly equal values of St$$\approx$$ ≈ 0.22 - 0.24 for both distances. This is followed by a branching. For Re$$\rightarrow$$ → 10$$^{7}$$ 7 and the case S/d = 2.8, the Strouhal numbers dip at St = 0.17. However, for S/d = 4, they increase up to St = 0.27. In the supercritical range, two peaks occur in the power spectra for the large distance S/d = 4. Based on a wavelet analysis, we can conclude that the low-frequency mode, which does not occur for a single cylinder, is an interference effect. Graphic abstract

Experimental and Computational Fluid Dynamics: decades of turbulent EFD/CFD complementarity

“…Increasing the size of wind tunnels is not the only way to increase the Re. One can mention that high-pressure tunnels (among others the 100 bar, Schewe et al [31], Princeton super pipe, for a review see Smits et al [30]) allow for ultra high Re numbers; low-temperature wind tunnels can also reach very high values as is the case with the European Transonic Wind Tunnel (ETW) in Cologne. However, these facilities are very unique and of limited access for academic research.…”

Two identical tandem square prisms with rounded edges and hard marine fouling at incidence in cross-flow: Effect of spacing and Reynolds number on unsteady fluid dynamics

“…Whereas a large amount of studies have been performed in the past regarding the fluid-dynamic behaviour of two 2D (i.e. "infinite") smooth circular cylinders (Zdravkovich, 1977;Okajima, 1979;Igarashi, 1981;Pearcy et al, 1982;Arie et al, 1983;Igarashi, 1984;Zdravkovich, 1985Zdravkovich, , 1987Meneghini et al, 2001;Alam et al, 2003;Zhou and Yiu, 2006;Alam and Zhou, 2007;Carmo et al, 2010;Sumner, 2010;Alam and Meyer, 2011;Alam, 2014;Griffith et al, 2017;Alam et al, 2018;Schewe and Jacobs, 2019;Hosseini et al, 2021;Schewe et al, 2021) or sharp-edged prisms with square cross sections (Reinholds et al, 1977;Shiraishi et al, 1986;Kareem, 1987;Sakamoto et al, 1987;Sakamoto and Haniu, 1988;Luo, 1989;Luo and Teng, 1990;Ohya et al, 1989;Luo and Teng, 1990;Takeuchi and Matsumoto, 1992;Tatsutani et al, 1993;Hangan and Vickery, 1999;Luo et al, 1999;Alam et al, 2002;Liu and Chen, 2002;Kim et al, 2008;Yen et al, 2008;Sohankar and Etminan, 2009;Etminan et al, 2011;…”

Surface Roughness Effects on Flows Past Two Circular Cylinders in Tandem Arrangement at Co-Shedding Regime

“…Of particular interest for this paper, the center-to-center spacing, L, and the Reynolds number value determine if two circular cylinders in tandem arrangement will behave as one extended bluff body or as two bodies, each one generating a von Kármán vortex street [3][4][5]. For small values of L, the downstream cylinder can experiment until negative drag force.…”

“…On the other hand, the downstream cylinder presents a jump to positive drag as L increases, and consequently, there is a critical center-to-center spacing where a signal reverse is clearly identified. These phenomena are complex, and for subcritical Reynolds numbers, they were classified into three flow regimes and viscous wake patterns [4,5]: (i) extended-body regime, (ii) reattachment regime, and (iii) co-shedding regime. It is important to comment that the subcritical regime for Reynolds numbers is characterized when the boundary layer remains laminar, and the transition to turbulence occurs after the flow separation region, i.e., in the near wake region.…”

“…The von Kármántype vortices take place in the gap space between two bodies and will determine the vortex formation regime from the downstream cylinder. The value L/D ≈ 3.5, named as critical spacing, is important to establish the transition from regimes of extended-body and reattachment to co-shedding regime [5]. The literature also reports that a bistable state appears around the critical spacing, where the flow intermittently changes from reattachment regime to co-shedding regime [3].…”