# Rod-Airfoil Interaction Noise Reduction Using Gradient Distributed Porous Leading Edges
## 1 Introduction
They found that the size of the upstream shed vortices increases with increasing rod diameter, and the rod shed vortices gradually miss the airfoil leading edge as the cross-stream position increases. [PERSON] et al. [13] investigated the effects of the attack angle of the downstream airfoil on the characteristics of aerodynamic noise and the wake structure of the rod-airfoil configuration. They reported that both the peak SPL and peak frequency of the rod-airfoil interaction noise decrease with increasing attack angle of the downstream airfoil due to the larger vortex scale but weaker vortex entrainment, which is caused by the blocking effect produced by the downstream airfoil. To reduce rod-airfoil interaction noise, researchers have proposed several noise control methods. [PERSON] et al. [10] applied boundary layer suction or blowing near the leading edge on both sides of the downstream airfoil to control rod-airfoil interaction noise. They found that the peak SPL in the far field could be significantly reduced by blowing (up to 7.2 dB), whereas it is slightly increased by the application of suction (about 2.7 dB). Both a soft-vane leading edge on the downstream airfoil and the air blowing out of the sides of the upstream rod were investigated by [PERSON] et al. [12] to reduce rod-airfoil interaction noise. Their comparison of sound pressure spectra showed that both concepts can be applied to effectively attenuate the broadband noise around the peak frequency (up to 6 dB). A hybrid computational aeroacoustics model (2D URANS + FW-H equation) was introduced by [PERSON] et al. [14] to prove the potential of a rotating cylinder as a noise reduction technique. The numerical simulation results illustrated that a cylinder with rotational frequencies higher than the vortex shedding frequency of the nonrotating case can notably reduce noise. In recent years, inspired by the three special feather adaptations of the silent flying owl (i.e., leading edge serrations, trailing edge fringes, and soft downy coating surface), researchers have developed a number of innovative bio-inspired noise reduction solutions [4] to reduce rod-airfoil interaction noise. LES and FW-H acoustic analogy methods were applied by [PERSON] et al. [15] to investigate the effect of leading edge serrations on rod-airfoil interaction noise. Their numerical results showed that leading edge serrationsin the form of sinusoidal profiles achieve a noise reduction of about 2.4 dB at the vortex shedding frequency and a significant noise attenuation (up to 10 dB) over a quite wide frequency range above the vortex shedding frequency. Subsequently, [PERSON] et al. [2] experimentally investigated the effect of the amplitude and wavelength of the leading edge serrations on rod-airfoil interaction noise. Their experimental results demonstrated that the noise reduction effects increase with increasing amplitude and decreasing wavelength, and the nondimensional amplitude-to-wavelength ratio is a key parameter for reducing rod-airfoil interaction noise. Porous leading edges have also been used to reduce turbulence-interaction noise in the past few years. Three-dimensional third-octave band sound maps by [PERSON] et al. [16] showed that the noise produced by the leading edge of the porous airfoils that interacts with the grid-generated turbulence is below than that produced by the nonporous leading edges. Moreover, turbulence-interaction noise reduction increases with the (on average) larger pores of the porous leading edges. [PERSON] et al. [17] demonstrated that a porous airfoil (a thin, rigid, flat-plate core covered with metallic porous materials and a wiremesh skin) reduces turbulence-interaction noise, but less efficiently than the airfoil with tubercle-like serrations at the leading edge. [PERSON] et al. [18] found that a single row of pores downstream of the leading edge significantly reduces turbulence-interaction noise, and a source cutoff radiation effect was proposed to explain the observed behavior. A lattice Boltzmann method was employed by [PERSON] et al.