Boundary element and finite element coupling for aeroacoustics simulations (original) (raw)
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A High-Order Immersed Boundary Technique for Computational Aeroacoustics
HAL (Le Centre pour la Communication Scientifique Directe), 2022
Finite difference methods are widely employed for numerical simulation in aeroacoustics, a domain in which high-order, low-dispersive and low-dissipative methods are widespread. However, finite differences are restricted to Cartesian grids. When solids of arbitrary shape are present in the simulation, it is possible to use immersed boundary methods (IBM) to avoid boundary-fitted grids. The order of IBM methods is often restricted to 2, even if several high-order IBM methods have been presented in the literature for aeroacoustics. However, we have found these methods to be rather unstable. In this work we seek for a stable, high-order immersed boundary method, for use in the Navier Stokes equations. The technique treats the immersed boundaries as a sharp interface by enforcing boundary conditions through ghost points. These are computed using characteristics and extrapolation along the normal direction to the interface. The method is tested on convective and diffusive problems, and has been applied to benchmark problems for the linearized Euler equations. High orders of convergence could be observed on model problems, with little change in time-step size, without filtering playing an essential role.
Comparison of outflow boundary conditions for subsonic aeroacoustic simulations
2012
Aeroacoustics simulations require much more precise boundary conditions than classical aerodynamics. Two classes of non-reflecting boundary conditions for aeroacoustics are compared in the present work: characteristic analysis based methods and Tam and Dong approach. In characteristic methods, waves are identified and manipulated at the boundaries while Tam and Dong use modified linearized Euler equations in a buffer zone near outlets to mimic a non-reflecting boundary. The principles of both approaches are recalled and recent characteristic methods incorporating the treatment of transverse terms are discussed. Three characteristic techniques (the original NSCBC formulation of Poinsot and Lele and two versions of the modified method of Yoo and Im) are compared to the Tam and Dong method for four typical aeroacoustics problems: vortex convection on a uniform flow, vortex convection on a shear flow, acoustic propagation from a monopole and from a dipole. Results demonstrate that the Tam and Dong method generally provides the best results and is a serious alternative solution to characteristic methods even though its implementation might require more care than usual NSCBC approaches.
Computers & Fluids, 2022
In this work, we address the finite element computation of flow noise in the presence of arbitrarily slowly moving rigid bodies at low Mach numbers, by means of hybrid and direct computational aeroacoustics (CAA) strategies. As regards the former, the problem could be dealt with by means of the Ffowcs Williams-Hawkings acoustic analogy. That reduces to Curle's analogy for a static body, which is analogous to a problem of diffraction of sound waves generated by flow eddies in the vicinity of the body. Acoustic analogies in CAA first demand computing the flow motion to extract an acoustic source term from it and then use the latter to calculate the acoustic pressure field. However, in the case of low Mach number flows, the Ffowcs Williams-Hawkings and Curle analogies present a problem as they require knowing the total pressure distribution on the body's boundary (i.e. the aerodynamic pressure plus the acoustic one). As incompressible computational fluid dynamics (CFD) simulations are usually performed to determine the flow motion, the acoustic pressure distribution on the body surface is unavoidably missing, which can yield acoustic analogies inaccurate. In a recent work, it was proposed to tackle that problem for static and rigid surfaces, by keeping the incompressible CFD and then splitting the acoustic pressure into direct and diffracted components. Two separate wave equations were solved for them, in the framework of the finite element method (FEM). In this article, we extend that work to compute the aerodynamic sound generated by a flow interacting with a slowly moving rigid body. The incompressible Navier-Stokes equations are first solved in an arbitrary Lagrangian-Eulerian (ALE) frame of reference to obtain the acoustic source term. Advantage is then taken from the same computational run to separately solve two acoustic ALE wave equations in mixed form for the incident and diffracted acoustic pressure components. For validation of the total acoustic pressure field, an ALE formulation of a direct CAA approach consisting of a unified solver for a compressible isentropic flow in primitive variables is considered. The performance of the exposed methods is illustrated for the aeroacoustics of flow past a slowly oscillating two-dimensional NACA airfoil and for flow exiting a duct with a moving teeth-shaped obstacle at its termination.
Towards a Generic Non-Reflective Characteristic Boundary Condition for Aeroacoustic Simulations
22nd AIAA/CEAS Aeroacoustics Conference, 2016
A blended zonal characteristic boundary condition is proposed following a quantitative investigation of the performance of several non-reflective boundary conditions. Two test cases are considered that investigate the effects of acoustic and vortical plane waves impinging on the domain outflow region. A third test case investigates the effects of broadband turbulent flow impinging on a non-reflective outflow boundary condition. From these studies, two non-reflective boundary conditions based on a zonal characteristic method are found to provide a minimal acoustic response for impinging acoustic and vortical disturbances, respectively. These methods both make use of the transverse characteristic terms to improve performance, although each method uses a different inclusion of these terms. A final boundary condition is proposed that blends the performance of the two zonal characteristic methods. A blending function is used that switches the characteristic boundary condition smoothly between regions dominated by acoustic, or vortical, disturbances. The feasibility of this novel method is demonstrated on a test case where broadband turbulence impinges on a small section of an outflow region.
Acoustic radiation and scattering by a complex structure can be modelized using a coupling between finite element method (FEM) and boundary element method (BEM). This coupling between ATILA (FEM code) and EQI (BEM code) is efficient in the low or intermediate frequency range. Specific techniques have been developed in the case of the steady-state problem: frequency interpolation, decomposition of the fields in Fourier series, frequency derivative approach of the resonances. In the time-domain problem, efficiency of the Helmholtz Kirchhoff integral equation (HKIE) for scattering by axisymmetric rigid bodies is discussed.
Domain decomposition technique for aeroacoustic simulations
Applied Numerical Mathematics, 2004
A computational tool for the simulation of time harmonic sound propagation in open domains is proposed. It consists of a two step technique. In the first step the viscous flow field is calculated, solving the incompressible Navier-Stokes equations. In the second step the acoustic field is obtained solving the Lighthill's wave equation. The two calculations are performed on two different grids, both formed by non-conforming subdomains. The Lighthill's wave equation is solved in the frequency domain, with a high order accurate compact finite difference scheme. To test the acoustic solver, the phenomenon of wave diffraction past an obstacle is calculated. The results confirm that the interface transmission conditions as well the non-reflecting boundary conditions do not affect the accuracy of the scheme. The complete aeroacoustic technique is applied to the simulation of the noise radiation from a cavity with a grazing subsonic laminar boundary layer. The flow field presents a periodic vortex shedding past the cavity, the vortical flow being a noise source. The numerical results show the existence of the directivity character of the acoustic radiation.
Computer Methods in Applied Mechanics and Engineering, 2007
An algebraic subgrid scale finite element method formally equivalent to the Galerkin Least-Squares method is presented to improve the accuracy of the Galerkin finite element solution to the two-dimensional convected Helmholtz equation. A stabilizing term has been added to the discrete weak formulation containing a stabilization parameter whose value turns to be the key for the good performance of the method. An appropriate value for this parameter has been obtained by means of a dispersion analysis. As an application, we have considered the case of aerodynamic sound radiated by incompressible flow past a two-dimensional cylinder. Following Lighthill's acoustic analogy, we have used the time Fourier transform of the double divergence of the Reynolds stress tensor as a source term for the Helmholtz and convected Helmholtz equations and showed the benefits of using the subgrid scale stabilization.
A boundary element method for aerodynamics and aeroacoustics of bodies in arbitrary motions
International Journal of Aeroacoustics, 2003
The objective of this paper is to validate a potential-flow formulation for the aerodynamic and aeroacoustic analysis of a streamlined body -typically an aircraft -in arbitrary motion, through applications to helicopter rotors in hover and forward flight, for which several approaches are available, some of them already validated in the past.