Paul Ploumhans

Efficient Discontinuous Galerkin Methods for solving acoustic problems

I Introduction 2II Mathematical model 2A Finite and infinite elements, frequency-domain approach . . . . . . . . . . . . . . . . . . . . . 21 Governing equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Free field boundary condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Coupling with acoustic ducts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Spatial discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4B RK-DGM approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Governing equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Spatial discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Implementation of the space Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Optimization of the computation of surface fluxes . . . . . . . . . . . . . . . . . . . . 75 Convergence properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Time discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10IIIValidation 12A Test case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12B Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12IVLarge-scale applications 15A Parallel implementation of the DG method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15B Test case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15C Test case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17V Conclusions 18VIAcknowledgments 18

Optimal numerical parameterization of discontinuous Galerkin method applied to wave propagation problems

This paper deals with the high-order discontinuous Galerkin (DG) method for solving wave propagation problems. First, we develop a one-dimensional DG scheme and numerically compute dissipation and dispersion errors for various polynomial orders. An optimal combination of time stepping scheme together with the high-order DG spatial scheme is presented. It is shown that using a time stepping scheme with the same formal accuracy as the DG scheme is too expensive for the range of wave numbers that is relevant for practical applications. An efficient implementation of a high-order DG method in three dimensions is presented. Using 1D convergence results, we further show how to adequately choose elementary polynomial orders in order to equi-distribute a priori the discretization error. We also show a straightforward manner to allow variable polynomial orders in a DG scheme. We finally propose some numerical examples in the field of aero-acoustics.

Validation of a CAA formulation based on Lighthill's Analogy using AcuSolve and ACTRAN/LA on an Idealized Automotive HVAC Blower and on an axial fan

The purpose of this work is to evaluate a Computer Aided Engineering (CAE) method in which computational aero acoustics (CAA) techniques are used to predict the noise level from automotive fans. The engineering objective is to ensure that the noise level in an automotive cooling system or an air handling system is sufficiently low for all operating conditions. In fact, automobile manufacturers are placing increased emphasis on the reduction of cabin noise level so that this noise reduction has become a critical design consideration. This has resulted in more stringent noise requirements for air handling systems and other cooling systems. For most operating conditions, the blower is the major noise contributor for the cabin noise level. In this paper we use the extended version of the variational formulation of Lighthill’s analogy, as presented in Caro et al. This formulation is ideally suited to the finite element method (FEM). It accounts for aerodynamic sources through two source terms. The first term accounts for volume sources; the second term accounts for sources defined on control surfaces, i.e., surfaces where the normal flow velocity does not vanish. An important contribution of the present work is an innovative approach for transferring information from the CFD mesh to the CAA one. This problem has a significant practical importance because CFD ∗Contact: robert@pioneersolutionsinc.com †Corresponding author: stephane.caro@fft.be Copyright c

Aeroacoustic Simulation of the Noise radiated by an Helmholtz Resonator placed in a Duct

The quintessential aeroacoustic test case of an Helmholtz resonator was studied, deploying the recently released coupling between the Engineering design tools STAR-CD (a CFD code) and Actran/LA (a CA code). The objective, to accurately model both the frequency and magnitude of the aeroacoustic resonance phenomenon in the geometry as compared with both experimental and analytical data, was achieved. This paper presents the methodology used, demonstrates the importance of accurate representation of compressible effects in CFD, and presents methods to optimise the data transfer between the codes by focusing on the dominant source regions.

A New CAA Formulation based on Lighthill's Analogy applied to an Idealized Automotive HVAC Blower using AcuSolve and Actran/LA

In this paper, we investigate the use of the variational formulation of Lighthill’s analogy, implemented in a Finite/Infinite Element framework. We present an innovative way to handle porous boundaries (or equivalently, control surfaces upon which aerodynamic sources are defined). We show how Lighthill’s analogy can be used to predict broadband blower noise. Infinite elements are used to enforce the Sommerfeld radiation boundary condition. A derivation of the analogy is presented and is compared with the derivation of Curle’s analogy (extended to handle porous boundaries). The implementation is described and is validated on a test case. Preliminary results on a real automotive HVAC blower case are presented.

Comparison between measured and predicted tonal noise from a subsonic fan using a coupled Computational Fluid Dynamics (CFD) and Computational Acoustics (CA) approach

The flow through an HVAC blower fan, typical to the automotive industry, was solved using STAR-CD. Time varying pressure data was then exported to ACTRAN/TM where the CFD results were decomposed into acoustic duct modes, using a multiple plane matching method. These duct modes were then propagated to far field locations and compared with experimental data at the blade passing frequency, obtained in the semi-anechoic chamber at Denso Thermal Systems. Good agreement was attained for microphones located downstream of the inlet and outlet ducts. At the other microphone locations there is doubt that the dominant noise generation mechanism is purely aeroacoustic: vibroacoustic noise sources are present. Since aeroacoustic noise sources alone were modeled, there was a deterioration in the simulation/experimental comparison.

Simulation of three-dimensional bluff-body flows using vortex methods: from direct numerical simulation towards large-eddy simulation modelling

Recent contributions to the three-dimensional vortex method for bluff-body flows are presented. The numerical method a vortex method combined with a boundary element method is briefly reviewed. It is applied to direct numerical simulation of the flow past a sphere (Re = 300 and 1000). The on-going work to extend the method towards vortex-based large-eddy simulation for high Reynolds number flows is also presented. Preliminary results for the flow past a hemisphere are discussed.