Time-domain DGM for turbofan exhaust noise predictions

Over the past fifty years, large strides have been made in reducing aircraft noise pollution. To continue on this trend, and to meet more aggressive noise regulations, higher-fidelity numerical models must be used early in the design process to accurately characterize the noise signature of prospective aircraft and engine designs. Predicting turbofan exhaust noise propagation requires a numerical scheme that can model a highly non-uniform flow-field, has low dispersion and dissipation error, has high computational efficiency, and can handle complex geometries. Time-domain nodal discontinuous Galerkin methods (DGM) have shown success in applications requiring high spatial accuracy, computational efficiency, and complex geometry representation. This thesis further develops the DGM for turbofan exhaust noise applications using a hybrid approach and solving the three-dimensional (3D) linearized Euler equations (LEE) in the time-domain. A parallel, 3D implementation of the above scheme is outlined and the accuracy and efficiency are verified. Challenges in applying the scheme to engineering applications are addressed. The relationship between accuracy and computational cost is investigated using a dispersion analysis of the scheme. Complications involving modeling of the highly non-uniform exhaust flow-field are addressed, including developing a new dispersion analysis of the LEE to study the formation and growth of aliasing-driven instabilities in shear layers, and the impact of the mean flow representation accuracy on the acoustic solution. A mapping procedure used to interface the mean flow solver with the aeroacoustic solver is discussed, and extended to the treatment of mean-flow boundary-layers that are unresolved on the acoustic mesh. Addressing the robustness and efficiency of the method, compact analytical source terms are developed that exploit the numerical flux between elements and band-limited source terms are investigated to reduce the number of computations required for an analysis. The numerical scheme is applied to the problem of scattering of fan tonal noise by noise-reducing chevrons on the bypass duct, considering a realistic geometry and flow-field.