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.