State-space representation of the unsteady aerodynamics of flapping flight

Authors

• Haithem E. Taha, Virginia Polytechnic Institute and State UniversityFollow
• Muhammad R. Hajj, Virginia Polytechnic Institute and State UniversityFollow
• Philip S. Beran, Wright-Patterson Air Force BaseFollow

Document Type

Article

Date of this Version

2014

Citation

Aerospace Science and Technology 34 (2014)

Comments

U S. Government work.

Abstract

A state-space formulation for the aerodynamics of flapping flight is presented. The Duhamel's principle, applied in linear unsteady flows, is extended to non-conventional lift curves to capture the LEV contribution. The aspect ratio effects on the empirical formulae used to predict the static lift due to a stabilized Leading Edge Vortex (LEV) are provided. The unsteady lift due to arbitrary wing motion is generated using the static lift curve. Then, state-space representation for the unsteady lift is derived. The proposed model is validated through a comparison with direct numerical simulations of Navier-Stokes on hovering insects. A comparison with quasi-steady models that capture the LEV contribution is also performed to assess the role of unsteadiness. Similarly, a comparison with classical unsteady approaches is presented to assess the LEV dominance. Finally, a reduced-order model that is more suitable for flight dynamics and control analyses is derived from the full model.