Thickness Effect on the Thrust Generation of Heaving Elliptic Airfoils

Abstract

The influence of the Reynolds number on the propulsive characteristics of insect wings is investigated by focusing on the aerodynamic transition from drag to thrust. The effect of both the thickness ratio and the Reynolds number on the thrust generation of elliptic airfoils is investigated using a lattice Boltzmann method. Three Reynolds numbers (Re = 50,100, and 185) and two Strouhal numbers (Sr = 0.2 and 0.4) are treated, while the thickness ratio is varied from 0.05 to 1.0. For all investigated Reynolds numbers, it is found that the airfoils oscillating at Sr = 0.2 do not produce thrust. For Sr = 0.4, it is found that thrust is produced at Re = 185. It is found that an airfoil of approximately 10% thickness produces maximum thrust. Thus, it can be said that, for thrust generation, there exists critical Reynolds and Strouhal numbers, and the thickness ratio is also a crucial parameter. By investigating the vortex pattern, velocity profiles, and vorticity intensities of the vortex cores behind the oscillating airfoils, it is found that 1) mushroom vortex patterns indicative of thrust do not completely guarantee the thrust generation, and 2) a phase lag between the thrust-force indicating vortex pattern and the resulting thrust production is observed. The present investigation shows that thrust-producing airfoils should produce strong vortices, enough to overcome the momentum deficit due to the boundary layer. Present results are obtained within the limitation of the laminar flow assumption.