Numerical investigation of flow over a two-dimensional square cylinder with a synthetic jet generated by a bi-frequency signal

Abstract

The flow around a square cylinder with a synthetic jet positioned at the rear surface is numerically investigated with the unsteady Reynolds-averaged Navier-Stokes (URANS) method. Instead of the typical sinusoidal wave, a bi-frequency signal is adopted to generate the synthetic jet. The bi-frequency signal consists of a basic sinusoidal wave and a high-frequency wave. Cases with various amplitudes of the high-frequency component are simulated. It is found that synthetic jets actuated by bi-frequency signals can realize better drag reduction with lower energy consumption when appropriate parameter sets are applied. A new quantity, i.e., the actuation efficiency Ae, is used to evaluate the controlling efficiency. The actuation efficiency Ae reaches its maximum of 0.266 8 when the amplitude of the superposed high-frequency signal is 7.5% of the basic signal. The vortex structures and frequency characteristics are subsequently analyzed to investigate the mechanism of the optimization of the bi-frequency signal. When the synthetic jet is actuated by a single-frequency signal with a characteristic velocity of 0.112 m/s, the wake is asymmetrical. The alternative deflection of vortex pairs and the peak at half of the excitation frequency in the power spectral density (PSD) function are detected. In the bi-frequency cases with the same characteristic velocity, the wake gradually turns to be symmetrical with the increase in the amplitude of the high-frequency component. Meanwhile, the deflection of the vortex pairs and the peak at half of the excitation frequency gradually disappear as well.