Fluid-structure interactions of an oscillating cylinder in cross flow in the presence of a neighbouring cylinder

Abstract

The fluid-structure interactions of a single streamwise oscillating circular cylinder and two tandem (including a streamwise oscillating circular cylinder) and side-by-side circular cylinders have been experimentally investigated using methods of LIF (Laser-induced fluorescence) visualization, PIV, laser vibrometer and hot wires. In the case of a single streamwise oscillating cylinder, the wake mode has been studied at relatively large oscillation amplitudes A/d = 0.5 and 0.67 over a range of frequencies fe/fs = 0 ~ 3.1. Five typical flow structures, referred to as S-I, S-II, A-I, A-III and A-IV modes, respectively, are identified. Their occurance is dependent on a combination of A/d and fe/fs. The occurence of the S-II mode has been predicted. The threshold frequency ratio (fe/fs)c for the occurence of the S-II mode is inversely proportional to A/d and dependent on the Reynolds number Re. The Re effect is negligible for Re > 250. The results are in good agreement with available experimental data. Interference between a streamwise oscillating cylinder (A/d = 0.5 and 0.67, fe/fs = 0 ~ 2) wake and that of a downstream stationary cylinder with an identical diameter has been experimentally studied. The center-to-center spacing L/d of two cylinders varies from 2.5 to 4.5. Three distinct flow regimes have been identified. For 0.45 ~ 0.5 < fe/fs < 0.8 ~ 1.0 (depends on A/d), a single antisymmetrical vortex street (A-mode) emerges behind the downstream cylinder. For 0.8 ~ 1.0 < fe/fs < (fe/fs)c which depends on A/d and Re, the flow behind the downstream cylinder is characterized by an antisymmetric-antisymmetric complex street (AA-mode) that consists of two outer rows of binary vortices orginating from the upstream cylinder, and two inner rows of single vortices shed by the downstream cylinder. For fe/fs > (fe/fs)c, the symmetric-antisymmetric complex street (SA-mode) occurs behind the downstream cylinders, respectively. Effects of initial conditions such as L/d, Re, fe/fs and A/d on the flow regimes have been discussed. Analysis has been developed to predict the occurence of the SA-mode flow structure; the analysis is in excellent agreement with the experimental data. Interface between a stationary cylinder wake and that of a downstream streamwise oscillating cylinder (L/d = 2.5 ~ 4.5; A/d = 0.5 and 0.67; fe/fs = 0 ~ 2) has also been studied. Two flow regimes have been identified, i.e., the 'single-cylinder shedding regime' at L/d <= 3.5 and the 'two-cylinder shedding regime' L/d > 3.5. For the 'single-cylinder shedding regime', the upstream cylinder does not appear to shed vortices; vortices are symmetrically formed behind the downstream cylinder as a result of interactions between the shear layers separated from the upstream cylinder and the oscillation of the downstream cylinder. For the 'two-cylinder shedding regime', the vortices are shed alternately from the upstream cylinder; a staggered spatial arrangement of vortices occurs behind the downstream cylinder. Experimental study of the wake structure of two side-by-side cylinders has been conducted at Re = 150 - 14300. The focus is on the effect of Re on the dominant frequency of the wake in the asymmetrical flow regime, i.e., T/d = 1.2 - 1.6 (T is the center-to-center cylinder gap). As Re increases, the flow structure behind the cylinders may change from one single vortex street to two vortex streets with one narrow and one wide for the same T/d. The one-street flow structure is dominated by one frequency f'o = fod/U ~= 0.09, where fo is the dominant frequency and U is the free-stream velocity. Two dominant frequencies of fo' ~ 0.3 and 0.09 characterize the two-street flow structure. The critical Re, at which the transition from single to two streets occurs increases as T/d decreases. The present results help clarify previous scattered reports for 1.2 < T/d < 1.5; detection of one dominant frequency by some but two by others. Finally, vortex induced vibration of a single cylinder in a cross flow was analyzed theoretically by considering the cylinder as an elastic beam. Two-Dimensional coupled and nonlinear dynamics equations were established using Hamilton's principle. The fluid forces were simplified and calculated using related parameters such as the Strouhal number, root-mean-square lift and drag coefficients, and fluid damping ratio, which could be directly determined from previous experimental results. Displacement and strain responses, and the natural frequency of the cylinder have been found analytically using Mathematical (c) software. The results are in agreement with the available experimental data.