Theory Background for the Aeroacoustics Branch
The scientific field of aeroacoustics deals with the interaction between a background mean flow and an acoustic field propagating in this flow. In general, this concerns both the very complex description of the creation of sound by turbulence in the background flow, that is, flow induced noise and the influence the background mean flow has on the propagation of an externally created sound field, that is, flow borne noise or convected acoustics. The computational aeroacoustics (CAA) capabilities of the aeroacoustics interfaces in COMSOL Multiphysics only cover the convected acoustics situation.
Aeroacoustic simulations would ideally involve solving the fully compressible continuity, momentum (Navier-Stokes equations), and energy equations in the time domain. The acoustic pressure waves would then form a subset of the fluid solution. This approach is often impractical for real-world CAA applications due to the required computational time and memory resources. Instead, for solving many practical engineering problems, a decoupled two-step approach is used: first solve for the fluid flow, then the acoustic perturbations of the flow.
For solving the acoustic problem, the governing equations are linearized around the background mean flow and only solved for the acoustic perturbation. Acoustic variables are assumed to be small and perturbation theory can be used, for example, the total pressure
is the sum of the background mean pressure p0 and the acoustic pressure variations p (sometimes labeled p’ or p1).
This section presents the basic mathematical framework for the aeroacoustic equations solved in the aeroacoustic interfaces, starting with the general governing equations for fluid flow, that is, conservation equations, constitutive equations, and equations of state. Then the linearized Navier-Stokes equations, the linearized Euler equations, the linearized potential flow equations, and finally the equations for the compressional potential flow are presented.
In this section the theory background for:
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General Governing Equations
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Linearized Navier-Stokes
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Linearized Euler
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Scattered Field Formulation for LE and LNS
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Linearized Potential Flow
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Compressible Potential Flow