Investigation of the flopping regime with two-, three- and four-cylinder arrays

Abstract

 The variation of the base pressure coefficient (Cp), and the characteristics of the velocity power spectra for arrays of two-, three- and four-cylinders aligned normal to the flow are presented. For the two-cylinder array with s/d=0.750 (where s is the spacing between the top and bottom surfaces of adjacent cylinders and d is the diameter of the cylinder) and Re=2.5×10³, peaks in the power spectra of 145 and 45 Hz which correspond to Strouhal numbers of 0.35 and 0.11 have been observed. For the three-cylinder array with Re=2.5×10³, at 0.338?s/d?0.730, three quasi-stable modes are observed. For 0.730?s/d?0.850, flopping and one quasi-stable mode are observed. For 0.850?s/d?1.202, only one mode is observed. The hot-wire power spectra measured downstream of the cylinder array on the center plane between the top and center cylinder and, also on the plane at s/2 above the top cylinder has three relative peaks that correspond to a wake structure, i.e. a pattern of vortices. For the four-cylinder array, when 0.338?s/d?0.750, four quasi-stable modes are observed. First, a mode can be observed in which the average Cp value of the top cylinder is relatively high, the average Cp value of the bottom cylinder is relatively low, and the average Cp values of the two center cylinders are nearly equal. A second mode is sometimes observed that is similar to the first except that the relatively high and low average Cp values of the outer cylinders are interchanged. A third mode is observed in which the average Cp value of the upper–inner cylinder is relatively high, the average Cp value of the lower–inner cylinder is relatively low, and the average Cp values of the outer cylinders are nearly equal. A fourth mode can be observed that is similar to the third mode except that the relative high and low average Cp values of the two inner cylinders are interchanged. For 0.750?s/d?1.202, only two of these modes are observed.