Wim De Roeck

A multi-domain Fourier pseudospectral time-domain method for the linearized Euler equations

The Fourier pseudospectral time-domain (F-PSTD) method is computationally one of the most cost-efficient methods for solving the linearized Euler equations for wave propagation through a medium with smoothly varying spatial inhomogeneities in the presence of rigid boundaries. As the method utilizes an equidistant discretization, local fine scale effects of geometry or medium inhomogeneities require a refinement of the whole grid which significantly reduces the computational efficiency. For this reason, a multi-domain F-PSTD methodology is presented with a coarse grid covering the complete domain and fine grids acting as a subgrid resolution of the coarse grid near local fine scale effects. Data transfer between coarse and fine grids takes place utilizing spectral interpolation with super-Gaussian window functions to impose spatial periodicity. Local time stepping is employed without intermediate interpolation. The errors introduced by the window functions and the multi-domain implementation are quantified and compared to errors related to the initial conditions and from the time iteration scheme. It is concluded that the multi-domain methodology does not introduce significant errors compared to the single-domain method. Examples of scattering from small scale density scatters, sound reflecting from a slitted rigid object and sound propagation through a jet are accurately modelled by the proposed methodology. For problems that can be solved by F-PSTD, the presented methodology can lead to a significant gain in computational efficiency.

Indirect acoustic impedance determination in flow ducts using a two-port formulation.

A passive acoustic two-port formulation is commonly used to describe the acoustic transmission characteristics and hence the acoustic performance of duct systems. In this paper, the acoustic two-port representation of flow ducts is used for the indirect determination of the acoustic impedance of acoustic absorbent materials under grazing flow conditions. Since the two-port parameters can be easily obtained experimentally, the methodology offers a possible alternative for the low-frequency estimation of the grazing flow impedance in comparison to the direct determination of the acoustic impedance. This paper discusses the theoretical model that is used for the indirect deduction of the grazing flow impedance. This theory is based on the analytical description of the sound field in flow ducts. A numerical validation on a geometry which is similar as the proposed experimental configuration is performed and the preliminary validation of the theory illustrates the capability of the indirect impedance determination technique to obtain a good estimation of the grazing flow impedance of acoustic absorbent materials.

Monopole and Dipole Identification Using Generalized Inverse Beamforming

Aeroacoustic problems pose some challenges to the conventional techniques normally used to source localization and identification. The main difficulties are that sources are normally distributed, with coherent and incoherent regions, and with simultaneous mono and multipole radiation patterns. Among the most recent ones, the Generalized Inverse Beamforming method has the promise to meet these challenges. In this paper, the potential for identification of compact sources in close vicinity, similar to a distributed source, and the potential to identify a dipole center and orientation, induced by two compact sources, are illustrated in two no-flow tests. Results obtained in semi-anechoic room are compared to numerical prediction, and the generalized inverse beamforming performance compared to the conventional beamforming results. This validation is a preparation for the application of the method to aeroacoustic problems.

Towards Accurate Flow and Acoustic Prediction Techniques for Cavity Flow Noise Applications

Nowadays a large variety of difierent hybrid approaches exist difiering from each other in the way the source region is modeled; in the way the equations are used to compute the propagation of acoustic waves in a non-quiescent medium; and in the way the coupling between source and acoustic propagation regions is made. This paper intends to make a comparison between some commonly used methods for aero-acoustic applications. As application, the aerodynamically generated noise by a ∞ow over a rectangular cavity is investigated. Two difierent cavities are studied. In the flrst cavity (L=D = 4, M = 0:5), the sound fleld is dominated by the wake mode of the cavity, originating from the periodical vortex shedding at the cavity leading edge, and its higher harmonics. In the second cavity (L=D = 2, M = 0:6), shear-layer modes, due to ∞ow-acoustic interaction phenomena, generate the major components in the noise spectrum. Source domain modeling is carried out using a second-order flnite-volume Large-Eddy simulation (LES), where the efiect of subgrid scale modeling on the accuracy of the flnal acoustic results is investigated. Propagation equations, taking into account convection and refraction efiects, based on a high-order flnite-difierence formulation of the linearized Euler equations (LEE) and acoustic perturbation equations (APE) are compared with each other using difierent coupling methods between source region and acoustic region. Conventional acoustic analogies and Kirchhofis method are rewritten for the difierent propagation equations and used to obtain near-fleld acoustic results. The accuracy of the difierent coupling methods and their sensitivity to the size of the source region is investigated. In this way, this paper aims at giving more insight in the accuracy and practical use of difierent hybrid CAA techniques to predict the aerodynamically generated sound fleld by a ∞ow over rectangular cavities.

An aerodynamic/acoustic splitting technique for hybrid CAA applications

Hybrid CAA-approaches, where the computational domain is split into an aerodynamic source domain and an acoustic propagation region, are commonly used for aeroacoustic engineering applications and have proven to be of acceptable efficiency and accuracy. The different coupling techniques tend to give erroneous results for a number of applications, which are mainly encountered in confined environments. Acoustic analogies are inaccurate, if the acoustic variables are of the same order of magnitude as the flow variables and an acoustic continuation of the source domain simulation using the latter solution as acoustic boundary conditions is only possible if no vortical outflow is occurring. These inaccuracies can be avoided by using appropriate filtering techniques where the source domain solution is split into an acoustic and an aerodynamic fluctuating part. In this paper, such an aerodynamic/acoustic splitting technique is developed and validated for some simple test cases. The filtering method is valid for low-Mach number applications, assuming that all compressibility effects are caused by the irrotational acoustic field while the incompressible aerodynamic field is responsible for the vortical movement of the flow field. Under these assumptions, it is shown that the aerodynamic and acoustic fields at every time step are obtained by solving a system of Poisson equations driven by the fluctuating expansion ratio and vorticity, obtained form the source domain simulation. For hybrid CAA-approaches this filtering technique, general applicable for both free-field and confined flow applications, is able to provide more accurate coupling information and improves the knowledge of aerodynamic noise generating mechanisms.

Experimental analysis of the aerodynamic noise generating mechanisms in simple expansion chambers.

For the aeroacoustic design of expansion chambers, commonly installed in e.g. HVAC systems or automotive exhaust ducts, the aerodynamic noise generation mechanisms as well as the transmission characteristics of acoustic waves propagating in a non-quiescent medium have to be taken into account. The attenuation of downstream propagating acoustic waves should be maximized with a minimum of additional flow noise generation and often a compromise between these phenomena has to be made. In this paper, these two aeroacoustic properties are experimentally analyzed for a simple expansion chamber carrying a uniform and pulsating mean flow. To determine both the transmission and noise generation characteristics for this type of applications an active bi-port representation is used. The dierent experiments are carried out on an open circuit aeroacoustic wind tunnel where the test objects are located inside a semi-anechoic room. This also allows to determine the noise emission and radiation in free-field environments. The preliminary results, shown in this paper, are in good agreement with previously obtained experimental and theoretical predictions.

Flow noise prediction of confined flows using synthetic turbulence and linearized Euler equations in a hybrid methodology

The goal of this paper is the numerical prediction of broadband noise generated by a low Mach number confined flow using a hybrid methodology. A time domain stochastic solver based on the random particle method has been developed which generates a synthetic pseudo-turbulent unsteady velocity field. This generated velocity field is first validated for the case of convected homogeneous isotropic turbulence with a Gaussian spectrum. The stochastic solver has been coupled to a Linearized Euler discontinuous Galerkin code which is able to calculate the sound propagation in non-uniform mean flows. Secondly the hybrid methodology is validated for its ability to predict acoustic far field pressure in free field conditions. Finally, the methodology is applied to a duct obstructed by a slit.

Acoustic Characterization of a Helmholtz Resonator Under Grazing Flow Conditions Using a Hybrid Methodology

A hybrid methodology is applied to characterize a Helmholtz resonator under a grazing flow. In a first step, the mean flow profile is obtained from a RANS simulation. The acoustic field and its interaction with the hydrodynamic field are calculated in a second step, by solving the linearized Navier-Stokes equations. The impedance of the Helmholtz resonator is obtained using the in-situ measurement technique. Because the method relies on the use of linear governing equations, the validity of the results is limited to the linear regime. Within this region, the computed reactance shows good agreement with an analytical model and experimental observations. Preliminary computations of the resistance show the potential of the method, but the optimal position of the facing sheet measurement point remains an open question.

Combined Numerical and Experimental Study of a Slit Resonator Under Grazing Flow

This study compares two numerical methods based on the Linearized Navier-Stokes equations (LNSE) for the simulation of a resonator in presence of a cold mean flow: a time domain Runge-Kutta Discontinuous Galerkin (RKDG) code and a frequency-domain high-order continuous Finite Element Method (pFEM). The results are compared to experimental data from a dedicated experimental campaign on a slit resonator. It was shown that the simulations predict the correct trends, but some discrepancies have been observed. The origin of these differences has to be investigated further. Different impedance measurement techniques are applied to the numerical and experimental data to obtain the acoustic impedance of the slit resonator. Within their respective range of validity, reasonable agreement is found between the different techniques.

Implementation of a surface based coupling approach in a high-order DG aeroacoustics propagation solver

A surface based coupling approach similar to Curle’s acoustic analogy has been implemented. This method allows for the computation of aerodynamically generated noise propagation accounting for scattering effects produced by surface boundaries. For low Mach number problems with acoustically compact sources of sound, the advantages of choosing a surface based approach to use unsteady sources for acoustics propagation are twofold. On one hand, the computational domain used during CFD simulations can be significantly reduced, and the data for the sources has to be stored uniquely in the noise generating surfaces. On the other hand, no truncation on the sources information is necessary. In this work, the sound propagation produced by the lift and drag forces acting on a tandem cylinders configuration is calculated using a discontinuous Galerkin method to solve the linearized Euler equations. The proposed coupling approach is first verified for the acoustics propagation of the sound generated by the lift and drag dipoles originated by flow passing a single cylinder, where no scattering occurs. After verification, the methodology is applied to the tandem cylinders problem and the scattering effects are investigated.