Improved Finite Element Modeling of the Turbofan Engine Inlet Radiation Problem

Improvements have been made in the finite element model of the acoustic radiated field from a turbofan engine inlet in the presence of a mean flow. The problem of acoustic radiation from a turbofan engine inlet is difficult to model numerically because of the large domain and high frequencies involved. A numerical model with conventional finite elements in the near field and wave envelope elements in the far field has been constructed. By employing an irrotational mean flow assumption, both the mean flow and the acoustic perturbation problem have been posed in an axisymmetric formulation in terms of the velocity potential; thereby minimizing computer storage and time requirements. The finite element mesh has been altered in search of an improved solution. The mean flow problem has been reformulated with new boundary conditions to make it theoretically rigorous. The sound source at the fan face has been modeled as a combination of positive and negative propagating duct eigenfunctions. Therefore, a finite element duct eigenvalue problem has been solved on the fan face and the resulting modal matrix has been used to implement a source boundary condition on the fan face in the acoustic radiation problem. In the post processing of the solution, the acoustic pressure has been evaluated at Gauss points inside the elements and the nodal pressure values have been interpolated from them. This has significantly improved the results. The effect of the geometric position of the transition circle between conventional finite elements and wave envelope elements has been studied and it has been found that the transition can be made nearer to the inlet than previously assumed

Analysis of acoustic networks including cavities by means of a linear finite volume method

[EN] A procedure allowing for the analysis of complex acoustic networks, including three-dimensional cavities described in terms of zero-dimensional equivalent elements, is presented and validated. The procedure is based on the linearization of the finite volume method often used in gas-dynamics, which is translated into an acoustic network comprising multi-ports accounting for mass exchanges between the finite volumes, and equivalent 2-ports describing momentum exchange across the volume surfaces. The application of the concept to a one-dimensional case shows that it actually converges to the exact analytical solution when a sufficiently large number of volumes are considered. This has allowed the formulation of an objective criterion for the choice of a mesh providing results with a prefixed error up to a certain Helmholtz number, which has been generalized to three-dimensional cases. The procedure is then applied to simple but relevant three-dimensional geometries in the absence of a mean flow, showing good agreement with experimental and other computational results.This work has been partially supported by Ricardo Software, and by Ministerio de Ciencia e Innovacion through Grant DPI2009-14290. The authors thank Dr. F.D. Denia for his kind computational assistance.Torregrosa, AJ.; Broatch, A.; Gil, A.; Moreno Martínez, D. (2012). Analysis of acoustic networks including cavities by means of a linear finite volume method. Journal of Sound and Vibration. 331(20):4575-4586. https://doi.org/10.1016/j.jsv.2012.05.023S457545863312

Aft Fan Duct Acoustic Radiation

A finite element code has been developed for the prediction of the radiated acoustic field from the aft fan duct of a turbofan engine. The acoustic field is modelled based on the assumption that the steady flow in and around the nacelle is irrotational as is the acoustic perturbation. The geometry of the nacelle is axisymmetric and the acoustic source is harmonic and decomposed into its angular harmonics. The steady flow is computed on the acoustic mesh and provides data for the acoustic calculations. The jet is included in the steady flow potential flow model by separating the interior and exterior flow outside the aft fan duct with a thin barrier created by disconnecting the computational domain. The jet and exterior flow are allowed to merge at a defined distance downstream. In the acoustic radiation model continuity of acoustic particle velocity is implicitly satisfied across the shear layer by careful treatment of the surface integral which appears in the finite element method (FEM) formulation. Pressure continuity is enforced by using a penalty constraint on the shear layer. A model for locally reacting acoustic treatment provides a boundary condition on the duct walls. An attempt has been made to limit reflections on the artificial baffle introduced to limit the computational domain, but this is only moderately successful. An old, but reliable frontal solution routine has been updated with considerable impact on computational time. Example calculations are given which show the success achieved in satisfying the complicated interface conditions on the shear layer and the characteristics of the solutions at relatively high frequencies where the refinement of the mesh becomes a limiting consideration for practical computations. © 1998 Academic Press Limited