Self-sustained oscillations between two tandem cylinders at Reynolds number 1,000

Abstract

This study focuses on the self-sustained oscillatory flow characteristics between two tandem circular cylinders of equal diameter placed in a uniform inflow. The Reynolds number (ReD), based on the cylinder diameter, was around 1,000 and all experiments were performed in a recirculating water channel. The streamwise distance between two tandem cylinders ranged within 1.5 ≤ Xc/D ≤ 7.0. Here Xc denotes the center-to-center distance between two tandem cylinders. For all experiments studied herein, quantitative velocity measurements were performed using hot-film anemometer and the LDV system. The laser sheet technique was employed for qualitative flow visualization. The wavelet transform was applied to elucidate the temporal variation and phase difference between two spectral components of the velocity signals detected in the flow field. The remarkable finding was that when two tandem circular cylinders were spaced at a distance within 4.5 ≤ Xc/D ≤ 5.5, two symmetrical unstable shear layers with a certain wavelength were observed to impinge onto the downstream cylinder. The responding frequency (fu), measured between these two cylinders, was much higher than the natural shedding frequency behind a single isolated cylinder at the same ReD. This responding frequency decreased as the distance Xc/D increased. Not until Xc/D ≥ 6.0, did it recover to the natural shedding frequency behind a single isolated cylinder. Between two tandem cylinders, the Strouhal numbers (Stc = fu Xc/Uc) maintained a nearly constant value of 3, indicating the self-sustained oscillating flow characteristics with a wavelength Xc/3. Here Uc is the convection speed of the unstable shear layers between two tandem cylinders. At ReD = 1,000, the self-sustained oscillating characteristics between two tandem circular cylinders were proven to exhibit a sustained flow pattern, not just a sporadic phenomenon.