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 $$Cd_{1}$$\n \n C\n \n d\n 1\n \n \n (Re) at both distances is similar to that for a single circular cylinder. The development of the drag curves $$Cd_{2}$$\n \n C\n \n d\n 2\n \n \n (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$$\\rightarrow$$\n →\n 10$$^{7}$$\n \n \n 7\n \n , 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$$\\approx$$\n ≈\n 1$$\\times$$\n ×\n 10$$^{6}$$\n \n \n 6\n \n - 7$$\\times$$\n ×\n 10$$^{6}$$\n \n \n 6\n \n , the Strouhal numbers have nearly equal values of St$$\\approx$$\n ≈\n 0.22 - 0.24 for both distances. This is followed by a branching. For Re$$\\rightarrow$$\n →\n 10$$^{7}$$\n \n \n 7\n \n 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.\n Graphic abstract