Numerical analysis on transitions and symmetry-breaking in the wake of a flapping foil

Abstract

Flying and marine animals often use flapping wings or tails to generate thrust. In this paper, we will use the simplest flapping model with a sinusoidal pitching motion over a range of frequency and amplitude to investigate the mechanism of thrust generation. Previous work focuses on the Karman vortex street and the reversed Karman vortex street but the transition between two states remains unknown. The present numerical simulation provides a complete scenario of flow patterns from the Karman vortex street to reversed Karman vortex street via aligned vortices and the ultimate state is the deflected Karman vortex street, as the parameters of flapping motions change. The results are in agreement with the previous experiment. We make further discussion on the relationship of the observed states with drag and thrust coefficients and explore the mechanism of enhanced thrust generation using flapping motions.

On the forced flow around a rigid flapping foil

“…The results shown that the distance between the tail of the foil and the point of deflection seems to decrease as StA increases, in agreement with the numerical simulations made by Deng and Caulfield (2015) (see figures 5(b), (c), (f) and (g)). For Re = 255, the performed simulations shown that the wake deflects when StA > 0.23, in good agreement with the 3D experimental observations of Godoy-Diana et al (2008) and the numerical simulations of He et al (2012) and Deng and Caulfield (2015).…”

Numerical Simulation of the Wake Structure and Thrust/Lift Generation of a Pitching Airfoil at Low Reynolds number via an Immersed Boundary Method

“…The effects of both amplitude and frequency on the drag/ thrust coefficient are shown in Fig. 24 and compared to the results reported by He et al (2012). The drag coefficient for the corresponding motionless airfoil is C D0 = 0.86.…”

“…Schnipper et al (2009) have provided information regarding the effects of the wake pattern on aerodynamic forces for a flapping airfoil. He et al (2012) have studied transition and symmetry-breaking in the wake of a flapping airfoil by an immersed boundary method (IBM). They have presented results that show flow patterns from the KVS regime to the RKVS one.…”

Analysis of Deflected Vortex Street Produced by an Oscillating Airfoil

“…PIV experiments by Godoy-Diana et al 9 for a pitching foil indicated a deflected wake at high Strouhal numbers (St ∈ (0.33, 0.44)). Many other computational 10,11 and experimental [12][13][14][15] investigations have reported the onset for deflection around the same range.…”

“…We can choose an optimal number of modes for reconstruction by looking at the relative energy contained by the basis of dimension d. This relative energy content is denoted by I(d) and found using Eq. (10). I(d) should be close to one for a good reconstruction of the velocity field.…”