Numerical Investigation of Tonal Noise on a Transitional Airfoil under Varying Conditions

The generation of discrete acoustic tones is a problem of interest in transitional airfoils. Such tones exist for moderate Re below 2,000,000 and for low to moderate angles of attack. The purpose of this study is to use linear stability theory to study the growth of instabilities on the pressure and suction surfaces of airfoils for varying Re between 144,000 and 468,000 and angles of attack between 0˚ and 12˚. High accuracy 2D simulations based on an Implicit Large Eddy Simulation (ILES) code are conducted for a NACA0012 airfoil for varied conditions, and linear stability analysis is performed to predict amplification rates of disturbances within the boundary layers. The acoustic spectra and surface root mean square (RMS) pressure obtained from the high accuracy simulations are analyzed in conjunction with the stability results in order to explain the process of tone generation. Our results indicate that the growth of instability waves in the flow-separation region is a necessary condition for the generation of tones, but the selected tonal frequencies are governed not only by vortex shedding, but also through a feed-back loop that is determined, in addition to the flow instability, by the trailing-edge scattering and the receptivity mechanisms. The predicted tonal frequency coincides with that of the shedding frequency and is lower than that predicted by Linear Stability Theory (LST) for maximum amplifications. The tones disappear at higher incidence angles because the separation region on the suction side decreases. This leads to weaker instability-wave amplification and its dependency on frequency weakens, thus disrupting the feed-back loop mechanism. Additionally, flow unsteadiness at the trailing edge inhibits consistent trailing edge scattering of acoustic waves. At lower Re and moderate angles of attack, the suction surface is the primary surface responsible for the tones because of its larger separation bubble and stronger instability waves. As the Re increase, the separation region on the suction side diminishes, while instability growth on the pressure surface becomes stronger. Thus, the role of the suction side relative to that of the pressure in tone formation decreases with increasing Re