On the Thrust Generation from an Elliptic Airfoil in Plunging and Translating Motion at Low Reynolds Numbers

Abstract

In this paper, numerical simulation elliptic airfoil model, which mimics the biological locomotion, is studied. Elliptic airfoil undergoes a combined plunging and translating at low Reynolds number is simulated by using body fitted coordinate system. The moving mesh in the physical domain is mapped to a regular fixed mesh in the computational domain through a time dependent transformation between the physical and computational co-ordinates. The governing equations of laminar incompressible flow are transformed in the computational plane by incorporating the time dependent transformation, which naturally accounts for the mesh velocities. The transformed equations are discretized on the structured, collocated, o-type elliptic grid using the finite difference methodology. The unsteady equations are marched in time by using a semi-implicit pressure correction (projection) scheme. Along with the time marching of the governing equations, utilizing the mesh velocities and the forward Eulertime integration also moves the mesh points. The effect of Reynolds number (Re) is investigated on the flapping flight propulsion is investigated. It is found that there exists a critical Reynolds number (Rec) for every frequency after which there exists a thrust force. The effect of Rec is related to transformation of neutral wake to thrust generating wake. It is also found that the optimal frequency corresponds to a reduced frequency parameter of 0.7 where a lock in exists. It is also found that this Stc is independent of Re and the mode of vortex shedding is same at Re = 100 and 200 for Stc = 0.7. Further, it is shown that the mode of vortex shedding present is always helpful in thrust generation.