Numerical investigation on lag mechanism of drag-to-thrust transition for a pitching airfoil

The reverse Bénard-von Kármán (RBvK) vortex street produced by flapping wings is considered to be a thrust-generating wake, but studies have shown that as the Strouhal number increases, the generation of a net thrust for a pitching airfoil at low Reynolds numbers lags significantly behind the appearance of the RBvK wake. To reveal the physical mechanism behind this phenomenon, the flow field of the NACA0012 airfoil undergoing a simple harmonic pitching motion at a Reynolds number of 1000 is numerically studied. Both a surface integration method and a finite control volume based force estimation method are used to investigate the effects of the surface stress distribution and the wake flow variation on the drag-to-thrust transition, respectively. The results indicate that the lag phenomenon exists for all pitching amplitudes considered, and the degree of lag which quantified as the difference between the Strouhal number of the drag-to-thrust transition and that of the neutral wake, decreases as the pitching amplitude gets larger. The distributed force characteristics suggest that when the airfoil oscillation parameters enter into the wake pattern regime corresponding to the RBvK vortex street, the thrust component due to the pressure distribution on the airfoil surface cannot overcome the viscous drag of the shear layer, which is responsible for the lag between the thrust generation and the formation of the RBvK wake. The aerodynamic decomposition based on the flow field indicates that the thrust characteristic is dominated by three terms: the vortex thrust, the momentum induced thrust, and the pressure induced thrust. The variations of the wake flow and the corresponding thrust characteristics show that, although the RBvK wake can produce a "jet effect", it cannot generate enough momentum induced thrust to overcome both the vortex drag of the RBvK vortex itself and the additional drag due to the pressure loss in the wake, when the Strouhal number is small. Therefore, a net thrust cannot be generated even though there exists a RBvK vortex street. The mechanism of the lag phenomenon is further explained from the perspective of the flow field analysis.