Computational Aeroacoustics by Coupling the Finite-Element and the Lattice-Boltzmann-Method

Computational aeroacoustics is a relatively young field of engineering. Characteristic application domains are for example the area of aviation and railway, internal flows in pipes or HVAC systems, or even consumer products and household devices, where aerodynamic sound is generated e.g. by fans. Sometimes not only the fluid itself causes sound phenomena, but also vibrations of structures excited by the flow like for example the walls of a pipe or components outside cars, trains or airplanes (mirrors, antennas, pantographs, etc.) lead to further generation of noise. This paper deals with the computation of such fluid-structure coupling effects, considering the interaction of fluid flow, acoustic wave propagation and the structural vibrations of a body lying within or enclosing the flow area.

As computational aeroacoustics requires an accurate, time-dependent calculation of pressure and density fluctuations, it was decided to use the lattice-Boltzmann method, a ‘mesoscopic’ formulation based on a strongly simplified kinetic theory nevertheless approximating the Navier-Stokes equations, for the CFD part of the problem. In contrary to “classical CFD”, where a macroscopic model is used by solving the discretized Navier-Stokes equations, the lattice-Boltzmann method enables a time explicit and - as far as our experience goes - less time expensive computation of compressible flows. It is thus well suited for representing acoustic phenomena, allowing to concurrently approximate both flow and acoustic field. On the structural side, the finite element method was applied to represent the structural dynamics, where flow pressures are applied as loads onto surfaces of structures. The vibrations in turn lead to acoustic wave propagation within the fluid. Data (i.e. flow pressure and vibration velocity) is exchanged via interfaces programmed for this special purpose, taking into account typical differences of finite element mesh and CFD grid. In this way, a bi-directional coupling procedure was generated enabling the calculation of aeroacoustic effects in connection with coupling effects that can occur if structure and fluid influence each other mutually.

As a suitable model for the verification of computational aeroacoustics as well as coupling effects, the flow around a circular cylinder has been chosen. The occurring effects on the fluid as well as on the structure side are well-known and have been the subject of many experiments and simulations. In the wake of the cylinder, for example, the “v. Kármàn vortex streets” are produced which cause narrow-banded sound, the so-called “Aeolian Tones”. This effect, the structural dynamic vibration excited by the flow, as well as the wave propagation caused by the vibrating body were simulated simultaneously.

The application of the method to industrial problems will show the suitability of the approach.