Frequency Analysis of Vortex Shedding in Wake Area behind the NACA0012 Airfoil via Fully-Lagrangian Vortex Element Method

Abstract

Shedding frequency of the vortices of the low-pressure area behind NACA0012 airfoil cross-section is provided for a laminar flow of an incompressible viscose fluid using Lagrangian vortex elements scheme. In the current work, only those areas of the solution domain were modeled where there are velocity gradients. It was done by the vorticity transfer equation that was obtained by calculating the cross product of the sides of the momentum equation. According to the Fractional Step method, the vorticity transfer equation was separated into two different equations that were solved sequentially in each time step: non-linear convection equation and the linear diffusion equation. Vorticity field in the physical domain was separated by the sheet and bubble vortices and each of the vortex elements in the solving field moved according to Biot-Savar Law and diffused according to the random walk method. The flow around the airfoil was obtained using Joukowsly mapping of the solution of the flow around a circle. This work was validated by comparing the aerodynamics force coefficients obtained from the vortex elements method with those obtained from analytical methods. Vortex shedding frequencies were calculated using the Fourier transform of the time response of the changes in the aerodynamic forces, being compared to the experimental results under the same conditions.