Mechanisms of sound amplification and sound reduction in the flapping flight of side-by-side airfoils

The acoustic signature of side-by-side airfoils, subject to small-amplitude harmonic pitching and incoming flow unsteadiness, is investigated. The two-dimensional near-field problem is formulated using thin-airfoil theory, where flow unsteadiness is modeled as a passing line vortex, and wake evolution is calculated via the Brown and Michael formula. Assuming that the setup is acoustically compact, acoustic radiation is obtained by means of the Powell-Howe acoustic analogy. The associated compact Green׳s function is calculated numerically using potential-flow analysis of the fluid-structure flow domain. Results, comparing the acoustic radiation of the double-airfoil system to a reference case of a single airfoil, point to several mechanisms of sound attenuation and sound amplification, caused by airfoil-airfoil and airfoils-wake interactions. It is found that counter-phase pitching of the airfoils results in effective cloaking of the system, which otherwise becomes significantly noisy (as a 5/2-power of the pitching frequency) at large frequencies. In addition, depending on the distance between airfoils, in-phase pitching may result in an acoustic signature equivalent to a single airfoil (when the airfoils are adjacent) or to two separate airfoils (when the airfoils are far apart). In general, flow unsteadiness produces more sound when interacting with a double (compared with a single) airfoil setup. However, airfoils׳ nonlinear wake-wake interactions give rise to a sound reduction mechanism, which becomes most efficient at times when incoming vorticity passes above airfoils׳ leading and trailing edges. The present scheme can be readily extended to consider the acoustic properties of various double-airfoil configurations, as well as multiple (>2) airfoil setups.