Improved Finite Element Modeling of the Turbofan Engine Inlet Radiation Problem

Abstract

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.

Impedance Eduction with an Extended Search Procedure

“…Nondimensional acoustic pressure and acoustic potential at frequency ! are related by the acoustic momentum equation [18] p r i Mu (1) in which is nondimensional frequency !R c 0 , M U c 0 is nondimensional mean flow velocity based on reference conditions 0 and c 0 at the source plane, and R is the reference duct height at the source plane. Acoustic pressure p is nondimensional with respect to 0 c 2 0 , nondimensional particle velocity u is referenced to c 0 , and nondimensional potential is referenced to Rc 0 .…”

“…This would be the case in a duct with a varying height or curvature (not the case in the current investigation), in an acoustically treated section, and in unlined sections due to scattering near transitions from hard walls to lined walls. To allow for possible nonuniform duct models (area variation or curved), the acoustic field equations are written in a potential formulation [18]. The termination plane is represented by a natural boundary condition describing the contribution of termination impedance.…”

Flow and geometry induced scattering of high frequency acoustic duct modes.

“…The multiple-scales approach has a number of distinct advantages over full numerical methods as it is ideally suited to handle higher frequencies and the computational complexity is only marginally more than calculating the eigenmodes inside a straight parallel duct. The accuracy and usefulness of the multiple scales approach has been validated against finite-element methods [6] for realistic aeroengine configurations and acoustic frequencies [7,8].…”