CAA Approaches for the Duct Regions

A Computational Aeroacoustics (CAA) approach is applied to solve the LEE equation system. A fourth-order Dispersion-Relation-Preserving finite difference scheme is implemented for spatial discretization [Tam & Webb (1993)], and a 2N storage form Low Dissipation and Low Dispersion Runge-Kutta scheme is applied for time integration [Hu et al. (1996)], [Stanescu & Habashi (1998)]. Appropriate boundary conditions are prescribed at different boundary regions. Much attention has been paid to grid generation and far field boundary conditions.

For a full 3D CAA sound propagation simulation, the typical size of an aero-engine intake results in a large problem whose solution is very expensive. It is known, however, that only a limited number of cut-on modes are excited in the source region of the engine and will propagate into the far-field. For restricted geometries like axisymmetric ducts or specific flow physics such as non-swirling mean flow, the problem size can be reduced by transformation and simplification.

Figure 2: Scheme of the Different Approaches

A schematic overview of the different approaches is given in Fig.2.

3D Axisymmetric CAA Approaches

Under the conditions of axisymmetric acoustic boundary conditions and mean flow, the 3D equations can be transformed into a system of complex 2D equations by a Fourier series expansion in the azimuthal direction. The complex equations for each azimuthal mode can then be solved in 2D, and because the azimuthal dependency is given analytically, the 3D sound field can be recomposed from the 2D solutions. Compared to a full 3D solution, this procedure reduces the numerical effort significantly.

Furthermore, a distinction can be made between mean flow with and without swirl for this approach. For the non swirling mean flow such as in the engine intake, the real and imaginary parts of complex 2D equations are decoupled. Therefore, only the real part has to be simulated, with the imaginary part being determined from the real part with a phase shift. This halves the numerical effort compared with the swirling mean flow where real and imaginary parts have to be simulated simultaneously.

Fully 3D CAA Approach

In spite of the advantages of the axisymmetric approach with respect to the numerical effort, a fully 3D approach is required in many cases as the geometry of real engines is not axisymmetric. To investigate the influence of the geometry on the sound propagation of engines with scarfed inlets a fully 3D CAA approach can be used to solves the 3D LEE equations. In addition to the large case size, the grid generation is challenging because the CAA procedure requires block structured meshes. Because the quality of the grid is crucial to the quality of the solutions, the grid should be smooth and locally orthogonal. To this end, the grids can be smoothed with a biharmonic technique developed at TUB [Yan et al. (July 6-9, 1998)].