Direct Numerical Simulation of Inverted Flag

Abstract

flapping motion of an inverted flag having free leading edge and clamped trailing edge behind the bluff body were simulated using the penalty immersed boundary method in a two-dimensional viscous flow. Three parameters were optimized, the Reynold’s number (𝑅𝑒), bending rigidity (𝛾) and the streamwise gap (𝐺𝑥) from the bluff body. These parameters were discussed with flapping modes, flapping amplitude, the power spectra and their vorticity interaction with flapping frequency. By placing the bluff body, the inverted flag showed three flapping modes; flapping mode, deflected mode and biased mode. Inverted flag in the flapping mode having high peak-to-peak amplitude (𝑦𝐿⁄) with high mean drag coefficient (𝐶𝑑) is preferred for energy harvesting as it produces high strain energy (𝐸𝑠). This happened for a finite range of flow speed or 𝑅𝑒 and 𝛾 at a far distance (𝐺𝑥) from the bluff body. Critical 𝑅𝑒 and the range for 𝛾 was found in which flag flapped in the flapping mode keeping the mass ratio unity for all the simulations because, 𝛾 decides the bending momentum magnitude of the non-dimensionalized momentum equation of inverted flag. Vortices shed by the upstream bluff body had a strong effect on the flapping amplitude of downstream inverted flag. Lateral position of inverted flag and its effect on vorticity is discussed in detail with their power spectra to find the maximum amplitude and highest 𝐶𝑑. This research can help in concluding the optimum streamwise position of the inverted flag behind the bluff body.