On Wake-Induced Flutter of a Circular Cylinder in the Wake of Another

Abstract

Two-dimensional stability of leaward cylinder in the wake of fixed windward cylinder is studied within the framework of quasi-static aerodynamic theory at both subcritical and supercritical flow region. Routh-Hurwitz stability criterion is employed. Two important points are clarified: 1. The wake-induced flutter is symmetric with respect to the horizontal line if there is no xy (refer to Fig. 1) static coupling. When coupled, the wake symmetry preserves provided the sign of static coupling is changed. This finding is supported by recent experimental data [7] and is in contrary with previous results [4–6]. 2. For the uncoupled case, vertical and horizontal frequency coalescence does not necessarily imply no oscillation. This is in variance with previous studies [2, 3, 34]. The region of instability is related to four physical variables: vertical to horizontal natural frequency ratio κ = ωy /ωx = (Kyy /Kxx )1/2 , static coupling coefficient ε = Kxy /Kxx , cylinder spacing to diameter ratio d/c and flow characteristics. Some highlights of numerical results [1] are as follows: (a) The region of instability roughly lies between 0 < |ε| < 0.1 and 0.8 ≤ κ ≤ 1.2. (b) The region of instability enlarges as |ε| increases from zero to 0.8 when everything else is kept fixed. (c) For both subcritical and supercritical flow, the region of instability shrinks as d/c varies from 10–16 when keeping all other factors fixed. (d) The region of instability shrinks as the flow changes from subcritical to supercritical when everything else remains unchanged.