# Rod-Airfoil Interaction Noise Reduction Using Gradient Distributed Porous Leading Edges
## 1 Introduction  
Noise radiated from a rod-airfoil configuration, i.e., rod-airfoil interaction noise, has recently attracted extensive research interest [1, 2, 3, 4] because it is a benchmark well-suited for studying the noise generation mechanisms encountered in several practical industrial and aeronautical applications. Examples of such mechanisms include blade-vortex interaction noise in helicopter rotors and the rotor-stator interaction noise between the rotor wake and the leading edges of the downstream stator blades in turbo-engines. Furthermore, rod-airfoil interaction noise is a simple but relevant test case for theoretical and numerical broadband noise modeling [5]. [PERSON] et al. [5] performed a rod-airfoil experiment in the large anechoic room of the Ecole Centrale de Lyon. In their benchmark experiment, a symmetric airfoil with a NACA-0012 profile (chord length \(c=100\) mm) was placed at a distance of 10 times the rod diameter (\(d=10\) mm, \(d/c=0.1\)) downstream of the rod to avoid feedback of the downstream airfoil onto the vortex shedding of the upstream rod. The results of far-field acoustic measurements and near-field particle image velocimetry (PIV), single hot-wire, and wall pressure coherence measurements of the rod-airfoil configuration at a zero angle of attack of the airfoil provided a detailed database about the main flow statistics and sound pressure spectra of the rod-airfoil interaction noise. These benchmark data were then used to validate the ability of several combined CFD solvers and aeroacoustic modelsto predict broadband noise, such as RANS + FW-H computations [1; 5], LES + FW-H computations [5; 6; 7], and DES + FW-H computations [8; 9]. Following [PERSON] et al. [5], parametric studies of the rod-airfoil interaction noise were further conducted by experimental methods. [PERSON] et al. [10] used a single far-field microphone to measure the sound pressure level (SPL) of the rod-airfoil configuration under several rod diameters ranging from \(d=4\) to 16 mm. The airfoil was also placed 10 times the rod diameter downstream of the cylindrical rod in their experiments. The results showed that the Strouhal frequency is lower and the sound pressure levels are higher in the low frequencies below and around the Strouhal frequency for larger rod diameters. In addition to different rod diameters, [PERSON] and [PERSON] [11] performed microphone array measurements to investigate rod-airfoil interaction noise characteristics for different types of airfoils and different streamwise gaps between the rod and the airfoil. They found that the rod/wake noise and the trailing edge noise of the airfoil are nearly identical, whereas the leading edge noise of the airfoil is considerably less for a bigger and blunter leading airfoil edge. They also found that the emitted rod-airfoil interaction noise depends more on the rod diameter than on the streamwise gap. [PERSON] et al. [12] performed phased microphone array tests on the noise characteristics of a rod-airfoil configuration by changing four parameters: rod type (cylindrical or square), rod diameter, cross-stream position of the rod, and streamwise gap between the airfoil leading edge and the rod. Their acoustic results revealed that the interaction noise at the leading airfoil edge significantly increases as the rod diameter increases. They also found that the intensity and corresponding peak SPL of the rod-airfoil interaction first increase and then decrease as the streamwise gap increases from 30 to 170 mm (rod diameter \(d=15\) mm). The intensity and overall SPL gradually decrease as the cross-stream position of the rod increases. [PERSON] et al. [12] further used a planar PIV system to acquire the instantaneous spanwise vorticity for different rod-airfoil configurations and then to explain the underlying physical mechanisms responsible for the observed noise characteristics.