Fan tones are known to be an important noise component of modern high bypass ratio aero-engines. To accurately evaluate the sound propagation in an aero-engine inlet and the far field radiation there of, the prediction methods must be capable of handling complex geometries, including the spinner, and variable cross-section, and of accounting for basic mean flow effects. In general, fully three dimensional numerical methods[1 2 3 4] are required for the calculation of sound propagation in a duct. The main disadvantage is that 3D methods, especially for high frequency cases, have high costs, both of time consumption as well as of the computational resources demanded.
This paper addresses small amplitude sound propagation in axisymmetric duct flows. The three-dimensional linearized Euler equations in a cylindrical coordinate system (x,r,φ) could be used to describe this problem. However, under the assumption of an axisymmetric mean flow and axisymmetric acoustic boundary conditions, the three-dimensional fluctuating quantities can be decomposed into a Fourier series in the azimuthal direction. This transform of the independent variable φ to the azimuthal mode number m yields a system of independent two-dimensional (x,r) differential equations for each azimuthal mode m of the fluctuations. Since tone noise in the inlet of aircraft engines is generally dominated by only a few components at the blade passing frequency and its harmonics plus harmonics of the shaft frequency (in the case of buzz-saw noise), it is computationally much more efficient to treat these few two-dimensional Fourier components rather than to solve the full three-dimensional system. In fact, the Fourier decomposition technique has found various applications in axisymmetric duct acoustics. For example, it was employed in the Finite Element Method (FEM) of Eversman et al.[5], the Multiple-Scales (MS) method of Rienstra[6].
The approach proposed in this paper is a hybrid numerical procedure. The 2D axisymmetric mean flow is firstly calculated by a low-order computational fluid dynamics (CFD) method through solution of the Euler equations. Then the acoustic field is computed by a high-order computational aeroacoustic (CAA) approach through solution of each component of the derived 3D axisymmetric system. Usually the models of MS[6], FEM[5], boundary element (BE)[7] and finite and infinite element (FE/IE)[8 9] prefer the choice of frequency domain since they are technically easier to deal with for single frequency problems and only the convected Helmholtz equation is considered as the governing equation. However, the time domain method has gained more favour in CAA simulations[1 2] due to the convenience on broadband noise predictions as well as on solving complex equation systems. To develop a more general numerical procedure, a time domain method is chosen to solve the derived governing equations in this paper.
The proposed CFD/CAA numerical procedure is firstly validated by comparison with the analytical solutions in a circular and an annular duct with a uniform mean flow. Then, two typical numerical results are given for an aero-engine inlet duct geometry and benchmarked against the results of FEM and MS methods[10]. In order to show the capability of the CFD/CAA hybrid method, the acoustic hard-walled duct cuton and cutoff transition phenomenon is studied numerically for the same aero-engine duct inlet geometry. Much attention is paid to the sensitivity of the transition plane to the basic mean flow assumptions with a 1D potential flow and a 2D Euler mean flow, respectively. The contents of this website is organized in the following manner: In order to give detailed information of the mathmatical model and the numerical algorithm, use the link to another part of our CFD Website. The numerical validation and investigation cases are detailed in the results and discussion section. Finally a conclusion on the presented results is given.
For more detail, refer to this site: The CAA Methods in use at the HFI.
For more detail, refer to this site: The CAA Methods in use at the HFI.