RESOLVENT ANALYSIS OF TRANSITIONAL AND TURBULENT FLOWS AROUND AIRFOILS FOR TRAILING-EDGE NOISE MODEL

Abstract

© TSFP 2024.All rights reserved.We present the results of a physics-based model of the trailing-edge noise radiated by a NACA0012 airfoil at low angle of attack, obtained from resolvent analysis of the turbulent mean flow. Most aeroacoustic models require turbulent spectra of surface pressure fluctuations to reconstruct the acoustic field, which are often derived from empirical models. In our approach, the acoustic model input is reduced to the optimal coherent structures identified by the resolvent. This method has the advantage of isolating the main mechanisms generating noise in the turbulent flow and, unlike empirical models, is applicable to a wide variety of cases. The model is evaluated for two different configurations: (i) an airfoil with a smooth surface at transitional Reynolds number (Re = 5.104), resulting in tonal noise; and (ii) the same airfoil with a zigzag trip near the leading edge at higher Reynolds number (Re = 2.105), resulting in broadband noise. Large eddy simulations (LES) were performed for both cases to obtain the mean flow, which is used to construct the linear operator underlying the resolvent analysis. A spectral proper orthogonal decomposition (SPOD) of the LES snapshots was used to extract the main hydrodynamic and acoustic features of the flow, which served as a reference for the physics-based model. Results for the tonal case show an excellent agreement between the resolvent and the SPOD modes at the frequency of the main tones in terms of dominant coherent structures and acoustic directivity. For the broadband case, a good agreement is also obtained for St < 10, where low-rank dynamics are identified by the SPOD. This match is improved when considering a simple model of eddy viscosity in the resolvent, and even small changes to the mode shapes have a visible influence on the acoustic directivity. This suggests that a resolvent-based model could be a valuable tool in optimisation methods for the control of trailing-edge noise.