CAA simulation requires the calculation of the propagation of acoustic waves with low numerical dissipation and dispersion error, and to take into account complex geometries. To give, at the same time, an answer to both challenges, a Discontinuous Galerkin Method is developed for Computational AeroAcoustics. Euler's linearized equations are solved with the Discontinuous Galerkin Method using flux splitting technics. Boundary conditions are established for rigid wall, non-reflective boundary and imposed values. A first validation, for induct propagation is realized. Then, applications illustrate: the Chu and Kovasznay's decomposition of perturbation inside uniform flow in term of independent acoustic and rotational modes, Kelvin-Helmholtz instability and acoustic diffraction by an air wing.
The analysis of aeroacoustics propagation is required to solve many practical problems. As an alternative to Euler’s linearized equations, an equation was established by Galbrun in 1931. It assumes the flow verifies Euler’s equations and the perturbation is small and adiabatic. It is a linear second-order vectorial equation based on the displacement. Galbrun’s equation derives from a Lagrangian density and provides conservative expressions of the aeroacoustics intensity and energy density. A (CAA) method dealing with the numerical resolution of Galbrun’s equation using the finite-element method (FEM) is presented. The exact solution for the propagation of acoustic modes inside an axisymmetric straight-lined duct in the presence of a shear flow is known and compared with the FEM solution. Comparisons are found to be in good agreement and validate a first step in the development of a CAA method based on the FEM and Galbrun’s equation. The FEM is then applied to an axisymmetric duct including a varying cross section and a nonuniform flow with respect to both the axial and the radial coordinates. The expression of the aeroacoustics intensity implemented in the FEM provides an accurate in-duct power balance.
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