Lock-on characteristics of a cavity shear layer

Abstract

This investigation focuses on defining the lock-on regions of a cavity shear layer subject to local periodic excitations. A circular cylinder of small diameter ( d=4 mm), located very close to the upstream edge of cavity, is used to generate the local periodic excitations in the form of oscillatory rotation about its center with various angular amplitudes (Δ θ) and frequencies ( f e ). All the experiments were conducted in a recirculating water channel at three different Reynolds numbers that are based on the momentum thickness at the upstream edge of cavity (Re θ 0 =152, 216 and 278). The LDV system and the laser-sheet technique are employed to perform the quantitative velocity measurements and the qualitative flow visualization, respectively. For cavity flows at three Reynolds numbers studied, the resonant lock-on is found to be the primary lock-on region within the range of frequency ratio ( f e / f 0=0.28–2.0). Here f 0 denotes the natural instability frequency of an unexcited cavity shear layer. The frequency bandwidth of resonant lock-on region does increase with increasing excitation amplitudes (Δ θ). While the excitation amplitudes are smaller than 5° (Δ θ⩽5°), the resonant lock-on region, at Reynolds numbers 216 and 278, distributes asymmetrically about f e / f 0=1.0 and biases to the high frequency (or large f e / f 0) side. However, the sidewise expansion of resonant lock-on region is enlarged and the degree of asymmetric distribution is alleviated at large excitation amplitudes (Δ θ>5°). The amount of sidewise expansion of the resonant lock-on region biased toward the high-frequency side is more significant at the lowest Reynolds number (152) than those at two higher Reynolds numbers (216 and 278). Besides, there exists a sub-harmonic lock-on region only at the lowest Reynolds number 152. The existence of a sub-harmonic lock-on region clearly reveals that the differential equation governing the self-excited oscillation within a cavity contains the quadratic nonlinear term. Further, at the lowest Reynolds number (152), the sidewise expansion of the sub-harmonic lock-on region is much narrower than that of the resonant lock-on region.