An immersed boundary method for fluid-structure-acoustics interactions involving large deformations and complex geometries

This paper presents an immersed boundary (IB) method for fluid-structure-acoustics interactions involving large deformations and complex geometries. In this method, the fluid dynamics is solved by a finite difference method where the temporal, viscous and convective terms are respectively discretized by the third-order Runge-Kutta scheme, the fourth-order central difference scheme and a fifth-order W/TENO (Weighted/Targeted Essentially Non-oscillation) scheme. Without loss of generality, a nonlinear flexible plate is considered here, and is solved by a finite element method based on the absolute nodal coordinate formulation. The no-slip boundary condition at the fluid-structure interface is achieved by using a diffusion-interface penalty IB method. With the above proposed method, the aeroacoustics field generated by the moving boundaries and the associated flows are inherently solved. In order to validate and verify the current method, several benchmark cases are conducted: acoustic waves scattered from a stationary cylinder in an inviscid quiescent flow, sound generation by a stationary and a rotating cylinder in a uniform flow, sound generation by an insect in hovering flight, deformation of a red blood cell induced by acoustic waves and acoustic waves scattered by a stationary sphere. The comparison of the sound scattered by a cylinder shows that the present IB-WENO scheme, a simple approach, has an excellent performance which is even better than the implicit IB-lattice Boltzmann method. For the sound scattered by a sphere, the IB-TENO scheme has a lower dissipation compared with the IB-WENO scheme. Applications of this technique to model fluid-structure-acoustics interactions of flapping foils mimicking an insect wing section during forward flight and flapping foil energy harvester are also conducted, considering the effects of foil shape and flexibility. The difference of the force and sound generations of the foils are compared. For wing during forward flight, the results show that flexible wing generates larger thrust with higher acoustic pressure. In terms of the energy harvester, the current results show that the geometrical shape has no significant effects on the force and sound generation, and the flexibility of the plate tends to deteriorate the power extraction efficiency. The flexible plate also induces larger fluctuating pressure at the frequency of 2f (f is the flapping frequency) and weaker sound at the frequencies of f and 3f. The successful validations and applications show that the IB method handled by delta function, whose accuracy is generally lower than that of the internal flow solver, is accurate for predicting the dilatation and acoustics, and thus is an attractive alternative for modeling fluid-structure-acoustics interactions involving large deformations and complex geometries. (C) 2020 Elsevier Ltd. All rights reserved.