COBEM-2017-0139 What Does Linear Instability Tell Us About Airfoil Tonal Noise?

Several studies spanning since the 1970s to the present, considering turbulent flows at realistic conditions for aircraft flight, have amassed evidence on the dominance of a far-field tonal noise, usually associated with vortex-shedding from the trailing edge. Furthermore, the appearance of multiple tones has been documented for increasing values of the angle of attack and Mach number, which exhibit a ladder-like pattern in terms of the variation of the frequencies with increasing free-stream velocity. Different explanations have been suggested for the origin of the (i) single tone, (ii) multiple tones evenly spaced in frequency and (iii) the ladder-like behavior as free-stream is increased, most of them based on the instability properties of the underlying flow. This contribution presents a comprehensive study of the linear mechanisms possibly acting on a NACA 0012 airfoil, at different Reynolds numbers, angles of attack and Mach numbers. Local and global analyses are performed, on the purpose of extracting all the possible information and eliminating biases associated to the choice of a single methodology. In this sense, ad hoc absolute/convective, multiple-scales analyses, parabolized stability equations and biglobal stability analyses are applied and combined, with the objective of ascertaining if and how airfoil tonal noise can be fully explained, characterized and predicted by linear instability mechanisms. A positive answer to this question would have a tremendous impact regarding flow control and airfoil noise reduction.