Numerical Prediction Method for Turbomachinery Noise Radiation Through the Engine Exhaust

Abstract

In this paper we present a numerical method for the prediction of the noise propagating and then radiating out of a turbofan engine. The method is based on the solution of the linearized Euler Equations in the frequency domain: for each wave number, an associated linearized Euler problem is solved using a finite element technique over structured as well as unstructured grids of both triangular and quadrilateral elements in axisymmetric geometries. This is particularly useful when dealing with complicated geometries like the exhaust nozzle of a turbofan engine. The frequency-domain approach makes also possible to treat each wave number separately. The acoustic near field, obtained from the solution of the linearized Euler equations, is then radiated in the far field using the formulation of Ffowcs Williams and Hawkings. Several calculations for a validation test case and a turbo-machinery configuration are presented and compared with analytical solutions and experimental data. Although in the last decades the noise emission from aircraft engines has been considerably reduced, further reduction is needed to meet the more and more stringent environmental targets. While recent research programmes brought to significant progress in reducing both the turbomachinery noise generation and the radiation of noise from the intake, there is still a lack of knowledge and accurate predictions about the more complicated exhaust noise radiation problem. This problem represents a challenge for Computational Aeroacoustics, due to the fact that the sound propagates through the shear layers separating the core, bypass and free-stream fields. In this work a numerical model for propagation and radiation of turbomachinery noise prediction is presented. The aim of the model is to provide a deeper insight and understanding of the aeroacoustic behavior of engine exhaust systems, and improve turbomachinery and exhaust aeroacoustic design and control. We assume that an incoming modulated wave is propagating through the exhaust nozzle or the fan duct and radiating at infinity as a small perturbation of a steady mean flow field, therefore entropy fluctuations and viscous effects are negligible. Under these assumptions, the numerical model is based on the solution of the linearized Euler equations in the near field and on the Ffowcs Williams and Hawkings integral formulation for evaluating the acoustic propagation in the far field. Both the linearized Euler equations and the Ffowcs Williams and Hawkings formulation are solved in the frequency domain. The present frequency-domain model, presented in section II, makes possible to treat separately the elementary duct modes, constituting the tonal noise propagating downstream the turbine and the fan, and to evaluate their propagation in the core and fan ducts, and the radiation in the near field, under real mean-flow conditions, and in the far field, under uniform mean-flow conditions. The single-wave analysis property is particularly useful for fast design