Lock-on characteristics behind two side-by-side cylinders of diameter ratio two at small gap ratio

Abstract

The lock-on characteristics, the detailed interactions and downstream evolutions of the wakes behind side-by-side cylinders of unequal diameter (D/d = 2), spaced by a gap ratio 0.75 (G/D = 0.75), are investigated at Reynolds number 600 by the dye flow visualization, laser Doppler anemometry (LDA) and particle image velocimeter (PIV) velocity measurements. The lock-on frequency bands are studied by LDA and PIV at Reynolds number 2,000. The D, d and G are the diameters of the large, the small cylinders and the net gap between two cylinders, respectively. Periodic excitations, in form of rotary oscillation about the cylinder center, are applied to the large cylinder with the same amplitude. It is found that while the large cylinder is excited, two lock-on frequency bands of the wake behind the large cylinder are detected. These two lock-on frequency bands correspond to the primary and the one-third sub-harmonic lock-on of the wake behind large cylinder, respectively. These two lock-on frequency bands distribute symmetrically about the fundamental and the third superharmonic of the natural shedding frequency behind a single cylinder at the same Reynolds number. The left-shifted frequency band (1.8 ≤ fe/fos ≤ 2.0) is not considered as a locked-on frequency band because the phase difference between two excitation frequencies across fe/fos = 2.0 vary significantly. While the wake behind the large cylinder is locked-on at fe/3 (or fos), the gap flow becomes unbiased and the frequency of the wake behind small cylinder remains around the natural shedding frequency. Thus, the frequency band of 3.0 ≤ fe/fos ≤ 3.22 is also not locked-on because the phase difference in the narrow wake excited at fe/fos = 2.93 and 3.07 changes significantly. Note fe and fos denote the excitation frequency and the natural shedding frequency behind a single large cylinder, respectively.