Numerical Analysis on Aerodynamic Force Generation of Biplane Counter-Flapping Flexible Airfoils

This study explores the effect of chordwise flexible deformation on unsteady aerodynamic characteristics for biplane counter-flapping dual NACA0014 airfoils with various combinations of Reynolds number and reduced frequency. Unsteady laminar viscous flows over duel rigid and flexible airfoils executing counter-plunge motion are computed with time-dependent two-dimensional laminar Reynolds-averaged Navier-Stokes equations coupled with conformal hybrid meshes. The tested Reynolds number with an airfoil characteristic chord length is 10(2), 10(3), and 10(4), and the reduced frequency ranges from 0.5 to 3.5. The dynamic mesh technique is applied to illustrate the flapping deformation modes of the flexible airfoils. To investigate the influence of the chordwise flexure extent on the aerodynamic performance of the flapping airfoils, the present study considers various different curvature deformations of flapping foils with flexure extent ranging from 0 to 0.3 times the chord length at 0.05 intervals. The visualized particle-tracing paths clearly revealed the formation and evolution of leading-edge vortices along the body of the flexible airfoil as it undergoes biplane counter-plunge motion. The generation of thrust-indicative wake structure or the drag-indicated wake structure behind the flexible airfoils depended on the degree of flexure extent of the airfoil at a fixed range of reduced frequency. The thrust force for each airfoil with biplane counter-flapping mode will be enhanced 6.32% more than that for a rigid single flapping airfoil. Present results show that flexible airfoils with flexure extent 0.25 times the chord length in counter-plunge flapping motion could get maximum propulsive efficiency and produce about 64.65% more than that of biplane rigid airfoils. The outcome indicates that appropriate flexible biplane flapping flight could not only increase the thrust force, but also boost the propulsive performance.