Numerical Modelling of Flexible Heaving Foils

Abstract

Abstract-We consider the effects of chordwise flexibility on the aerodynamic performance of flapping wings using numerical simulation. The twodimensional Navier-Stokes equations are solved using a Fourier pseudo-spectral method with no-slip boundary conditions imposed by the volume penalization method. The flexible wing is modelled with a non-linear beam equation. Our numerical simulations of heaving plates show that the maximum thrust is achieved at a stroke frequency lower than resonant, which is in agreement with experiments. The oscillatory part of the force only increases in amplitude when the frequency increases. We also consider aerodynamic interactions between two heaving foils. IndexTerms-Flapping flight, fluid-structure interaction, spectral method, volume penalization method.I.

Volume penalization for inhomogeneous Neumann boundary conditions modeling scalar flux in complicated geometry

“…For sufficiently large |k| in the sense that |k| |m|, Eqs. (15) and (16) show that |v k | decays proportional to k −2 for odd wave numbers k, whereas it decays as O(k −3 ) only for even k and odd m. Fig. 3 shows the decay of |v k | for η = 10 −2 .…”

“…Mathematically, it was shown that the solution of the penalized Navier-Stokes equations converges towards the solution of the Navier-Stokes equations with no-slip boundary conditions, as η → 0 [10,11]. This VP method has been applied to various flows, e.g., confined hydrodynamic turbulence [12], confined magnetohydrodynamic turbulence [6,13], fluid-structure interaction for moving obstacles [14] and for flexible beams [15], and the aerodynamics of insect flight [16].…”

Four-Winged Flapping Flyer in Forward Flight

“…A full flow field reconstruction around the wings is certainly desirable to compare different points in the parameter space with different performances and clearly identify the aerodynamic mechanisms at play. Experimentally this can be challenging, and numerical simulations such as a 3D version of the fluid-structure simulations of Kolomenskiy et al (2013) can be an interesting option to define robust aerodynamic models.…”

Numerical simulation of vortex-induced drag of elastic swimmer models

“…For example, Ramananarivo et al [14] state * Corresponding author: kai.schneider@univ-amu.fr optimal performance around f /f 0 = 0.7. Two-dimensional data [10] points in the same direction, although the difference to the resonant is smaller. Yeh and Alexeev [20] found two regimes which maximize cruising speed and efficiency at f /f 0 ≈ 1.1 and 1.6, respectively.…”