Experimental control of Tollmien-Schlichting waves using the Wiener-Hopf formalism

• Published in: Physical review fluids 2023-07, Vol.8 (7), Article 073902
• Main Authors: Audiffred, Diego B. S., Cavalieri, André V. G., Brito, Pedro P. C., Martini, Eduardo
• Format: Article
• Language: English
• Subjects: Fluid mechanics; Mechanics; Physics
• ISSN: 2469-990X; 2469-990X
• DOI: 10.1103/PhysRevFluids.8.073902

Reactive flow control has been shown as a promising tool to improve, among other aspects, the aerodynamic characteristics of an aircraft. This paper focuses on the use of reactive flow control to attenuate Tollmien-Schlichting (TS) waves over a wing profile. TS waves are an instability mechanism that is one of the first stages of boundary layer transition to turbulence. The Wiener-Hopf technique was used in this work for the experimental boundary layer control. The approach improves previous wave-cancellation techniques that, by constructing control kernels in the frequency domain, lead to control kernels with a non-causal part, i.e., actuation would need future sensor information to be constructed. In practical applications, it is unfeasible to access this type of information. Ignoring the non-causal part of the kernel leads to suboptimal solutions that might significantly degrade the performance of the controller. The Wiener-Hopf formalism allows us to take into account causality constraints in the formulation of the control problem, leading to an optimal realistic solution and a control kernel that is causal by construction. Moreover, it is possible to construct the control strategy based only on the power and cross-spectra obtained experimentally, in a data-driven approach. The present work shows how to apply experimentally the Wiener-Hopf resolvent-based formalism using signals from a wind tunnel experiment, demonstrating that the Tollmien-Schlichting waves can be effectively attenuated via a Wiener-Hopf based controller, which yielded better results than a typical wave-cancellation approach.