The nonlinear inhomogeneous Galbrun-Equation: Derivation and possible Ways to solve numerically

摘要

In recent years, the field of aeroacoustics has gained more attention in engineering developments like low noise ventilators, HVAC systems in electric vehicles, passenger cabins of commercial aircraft as well as novel engine designs of airplanes in general, to fulfill regulations of low level noise exposure. In order to close the gap between expensive prototypes with experimental testing and short development periods under high cost pressure, numerical simulations are state of the art for virtual prototyping. Numerous theories and acoustic analogies have been developed to investigate the effect of flow combined with acoustic radiation and propagation. Important contributions are known as the Linearized Euler Equations (LEE) or the Acoustic Perturbation Equations (APE). A different approach is pursued following the work of Galbrun. His displacement based linear formulation of aeroacoustics is extended to account for nonlinear effects as well as acoustic sources in turbulent flow. Difficulties arise when solving the Galbrun equation numerically. Therefore some already established numerical techniques that can be used to cope with these problems such as the Finite-Element-Method and the Discontinuous-Galerkin-Method are proposed.