Noise reduction by the streamwise-decreasing impedance trailing edges of a NACA-0012 airfoil: insights based on the Kutta condition

We investigate the noise reduction performance of a NACA-0012 airfoil at a low subsonic Mach number and a moderate Reynolds number. Noise suppression at the trailing edge is targeted by minimising the wall-pressure jump, which is stipulated by the unsteady Kutta condition. Guided by this principle, we propose an effective trailing-edge configuration capable of significantly suppressing the radiated noise. Numerical results reveal that a pure streamwise-decreasing impedance trailing edge fails to provide effective noise reduction across a broad range of characteristic frequencies; in some cases, it even leads to a significant increase in noise radiation levels. Therefore, we develop an extended trailing-edge (ETE) configuration, which achieves a notable noise reduction of 3.62 dB. This performance is further improved to 4.22 dB with the incorporation of an impedance design, forming an extended impedance trailing edge (EITE). The reduction in radiated noise is accompanied by modifications in the local flow near the EITE, primarily characterised by a decrease of the streamwise and spanwise Reynolds stresses and a rapid decay of coherent structures. With the aid of high-fidelity near-wall data, the distribution patterns of acoustic sources in the wavenumber–frequency space are analysed in detail with insights derived from the Kutta condition, thereby isolating the distinct role of different elements in achieving the desired noise reduction. For the ETE, it is found that noise suppression is attributed to two primary effects: (i) enhanced destructive interference between sound waves scattered by wall sources near the trailing edges, and (ii) a significant suppression of the vortex shedding process, particularly as evidenced by the distribution of near-field longitudinal process sources. Furthermore, extra noise attenuation is attained by the use of EITE, as the impedance surface leads to a lower convective velocity of pressure fluctuations and reduced energy within the supersonic phase speed region, consequently contributing to a lower scattering efficiency.