Preliminary Design of a SMA Bending Vortex Generator

The paper introduces the preliminary activities carried out within the RADAR project (ContRollo Attivo Del flusso AeRdinamico, in Italian, or Active Control of the Aerodynamic Flow), funded by the (Italian) Aerospace Research Program (PRORA), DM 662. Its main objective is to enhance the aerodynamic efficiency of a small-medium range aircraft through turbulent flow control techniques, for the environmental impact alleviation in terms of both gas and acoustic emissions. A key innovation involves the design of an adaptive vortex generator to mitigate tip stall and facilitate span-wise load control operations. This concept entails a compact metallic plate, flush with the wing skin if stowed, and a Shape Memory Alloy (SMA) active layer, enabling plate deflection upon heating, and consequently modifying the aerodynamic field. The study herein reported presents a theoretical framework for the preliminary modeling of a 2-layer SMA bending plate. The approach is based on: momentum equilibrium between the SMA actuator and an aluminum plate working as elastic recovery element; stress-induced SMA phase transformation by bending loads. The behavior of the SMA plate is described through the elastic line equation, formulated in terms of deflection angle versus the curvilinear abscissa (wide deflection range). Additionally, by knowing the constitutive law of the SMA material, the resulting load-unload curves for the SMA are computed in terms of applied moment vs resulting deflection at various temperatures. These curves are then compared to the moment-deflection profile of the antagonistic elastic aluminum plate. Under specific assumptions herein adopted, the diagram allows to identify specific points representing the pre-load/ stowed condition of the vortex generator device, and its fully deployed configuration.