Hybrid Computational Aeroacoustics (CAA)
The computational aeroacoustic (CAA) method used here is of the so-called hybrid type. It is based on a one way coupling between the turbulent flow sources and the acoustic problem. It is thus assumed that no important back-coupling exists from the acoustic field to the flow. The computational method is based on the finite element method (FEM) discretization of Lighthill’s acoustic analogy (wave equation). This formulation of the equations ensures that any solid (fixed or vibrating) boundaries are implicitly taken into account. The method is also applicable for interior problems (see Ref. 66).
In the frequency domain, the FEM discretization of Equation 2-11, yields a domain and a boundary contribution (in the Pressure Acoustics, Frequency Domain notation), given as
(2-14)
where, the normal mass flow mn definition, is the one given when coupling using the Aeroacoustic Flow Source Coupling. In this way boundary contributions from vibrating surfaces or hard surfaces are included.
The Lighthill acoustic analogy represents the acoustic propagation model from the source region to the exterior of the region. Inside the source region the pressure fluctuations ptot solved in the CFD problem are the ones observed, for example, through measurements. They are the sum of the incompressible hydrodynamic (flow) pressure fluctuations pflow and the compressible acoustic pressure variations pac. The acoustic analogy propagates the acoustic compressible pressure waves from the source region to the exterior.
Figure 2-15: Sketch of the acoustic propagation analogy with source region, structures, and acoustic propagation.
The hybrid method is based on a mapping and time to frequency FFT approach, in order to solve the acoustic problem in the frequency domain and on a mesh appropriate for the acoustic problem. The mesh used to solve the Fluid Flow problem has characteristics necessary to resolve the turbulence as well as the flow boundary layers. The mesh also corresponds to linear discretization for most Fluid Flow methods. The acoustic mesh, on the other hand, has to resolve the wavelength and geometry, and it is typically based on the default second order spatial discretization (see Ref. 66 and Ref. 67).