Frequency-Domain Linearized Euler Model for Turbomachinery Noise Radiation Through Engine Exhaust

A numerical model for the exhaust noise radiation problem is presented. In the model, it is assumed that an incoming wave is propagating through the exhaust nozzle, or the fan duct, and radiating outside. The near-field propagation is based on the solution of the linearized Euler equations in the frequency domain: for each wave number, a linearized Euler problem is solved using a finite element method on unstructured grids for arbitrarily shaped axisymmetric geometries. The frequency-domain approach enables the suppression of the Kelvin-Helmholtz instability waves. Moreover, each single calculation, limited to a single frequency, is well suited to the exhaust noise radiation problem in which the incoming wave can be treated as a superposition of elementary duct modes. To reduce the memory requirements, a continuous Galerkin formulation with linear triangular and quadrangular elements is employed and the global matrix inversion is performed with a direct solver based on a parallel memory distributed multifrontal algorithm for sparse matrices. The acoustic near field is then radiated in the far field using the formulation of Ffowcs Williams and Hawkings. Numerical calculations for a validation test case, the Munt problem, and two turbomachinery configurations are compared with analytical solutions and experimental data.