Christian Prax

Experimental localization of an acoustic sound source in a wind-tunnel flow by using a numerical time-reversal technique

The possibility of using the time-reversal technique to localize acoustic sources in a wind-tunnel flow is investigated. While the technique is widespread, it has scarcely been used in aeroacoustics up to now. The proposed method consists of two steps: in a first experimental step, the acoustic pressure fluctuations are recorded over a linear array of microphones; in a second numerical step, the experimental data are time-reversed and used as input data for a numerical code solving the linearized Euler equations. The simulation achieves the back-propagation of the waves from the array to the source and takes into account the effect of the mean flow on sound propagation. The ability of the method to localize a sound source in a typical wind-tunnel flow is first demonstrated using simulated data. A generic experiment is then set up in an anechoic wind tunnel to validate the proposed method with a flow at Mach number 0.11. Monopolar sources are first considered that are either monochromatic or have a narrow or wide-band frequency content. The source position estimation is well-achieved with an error inferior to the wavelength. An application to a dipolar sound source shows that this type of source is also very satisfactorily characterized.

Time-domain delay-and-sum beamforming for time-reversal detection of intermittent acoustic sources in flows

This study focuses on the identification of intermittent aeroacoustic sources in flows by using the time-domain beamforming technique. It is first shown that this technique can be seen as a time-reversal (TR) technique, working with approximate Green functions in the case of a shear flow. Some numerical experiments investigate the case of an array measurement of a generic acoustic pulse emitted in a wind-tunnel flow, with a realistic multi-arm spiral array. The results of the time-domain beamforming successfully match those given by a numerical TR technique over a wide range of flow speeds (reaching the transonic regime). It is shown how the results should be analyzed in a focusing plane parallel to the microphone array in order to estimate the location and emission time of the pulse source. An experimental application dealing with the aeroacoustic radiation of a bluff body in a wind-tunnel flow is also considered, and shows that some intermittent events can be clearly identified in the noise radiation. Time-domain beamforming is then an efficient tool for analyzing intermittent acoustic sources in flows, and is a computationally cheaper alternative to the numerical TR technique, which should be used for complex configurations where the Green function is not available.

A new meshless approach for three dimensional fluid flow and related heat transfer problems

Abstract The mathematical formulation, basic concept and numerical implementation of a meshless method for solving three dimensional fluid flow and related heat transfer problems are presented in this paper. A second order moving least squares approximation is used for the spatial discretization together with an implicit scheme for time marching. The vorticity and vector potential formulation of Navier–Stokes equations is employed to avoid the difficulties associated with pressure–velocity coupling. Two three-dimensional examples of natural convection in a differentially heated cubic cavity and in the annular space between a sphere and a cube are considered and steady-state solutions are obtained for Rayleigh numbers in the range of 10 3 –10 6 . Results show the flexibility of the method and demonstrate its accuracy.

Control of the vorticity mode in the linearized Euler equations for hybrid aeroacoustic prediction

The issue of vorticity mode perturbation in Linearized Euler Equations (LEE) is addressed in this paper. We chose to tackle this question by the point of view of source term formulation. It is numerically shown that the use of a rotational free acoustic source term significantly reduces the development of the hydrodynamic mode. In accordance with the theory, the proposed source term lead to a quasi total absence of vorticity mode in a spatially uniform mean flow, and a strong reduction in a sheared mean flow.

Detection of Non-Stationary Aeroacoustic Sources by Time-Domain Imaging Methods

Imaging methods such as the beamforming technique are widely used to localize and identify aeroacoustic sources. However, so far, existing applications in aeroacoustics have mostly been performed in the frequency domain. To tackle the characterization of nonstationary sources (for example, intermittent sources), time-domain imaging methods are more appropriate. Indeed, the spatio-temporal reconstruction of the acoustic fields allows studying the source structure in “real-time”. In this paper, two aeroacoustic problems are investigated with the help of time-domain inverse methods. First, numerical acoustic data obtained from the simulation of the radiation of a 2D mixing layer are studied through a numerical time-reversal method based on the Linearized Euler Equations. The spatio-temporal maxima of the acoustic energy are then detected by observing successive snapshots of the reconstructed acoustic field. These are assumed to correspond to wave focusing and, hence, to be related to the presence of a source. Finally, vorticity field snapshots are observed at the times at which spatio-temporal maxima are found. A conditional average of the flow fields, assuming large acoustic emission, is thus possible in principle. The global structure of the source is found to be quadripolar and each kind of detected maxima corresponds to a fixed vortical structure. Second, experimental data of the noise produced by a forward-facing step in a wind-tunnel flow are analysed by using the timedomain beamforming technique. The detection of spatio-temporal maxima highlights that the broadband noise source produced by the step can be seen as a succession of short duration events scattered around the step edge.

Modeling the inhomogeneous reverberant sound field within the acoustic diffusion model: A statistical approach

In room acoustics, starting from the sound particle concept, it is now well established that the reverberant field can be modeled from a diffusion equation function of the acoustic density and a gradient equation function of the acoustic intensity. The main works on the development of an acoustic diffusion model have highlighted the major role of a coefficient of the model, the so-called diffusion coefficient. Indeed, the main phenomena influencing the reverberant sound field can be modeled by proposing an appropriate expression of this diffusion coefficient. The work presented here deals with the modeling of inhomogeneous reverberant sound fields induced by geometric disproportions, and investigates, in particular, the case of long rooms. Previously, the ability of the acoustic diffusion to model adequately the spatial variations of the sound field along the room has been demonstrated by considering a diffusion coefficient that is spatially dependent. We propose here to extend this work by determining an empirical law of the diffusion coefficient, depending on both the scattering and absorption coefficients of the walls of the room. The approach proposed here is statistical and is based on the least squares method. Several linear models are proposed, for which a rigorous statistical analysis makes it possible to assess their relevance.

Localization of aeroacoustic sources by using time-reversal and beamforming techniques

The study deals with the localization of aeroacoustic sources in flows by using array processing techniques. In such situations, the source is located in the flow and the propagation model must properly take into account flow effects, with possible temperature gradients. The resolution of the inverse problem can rely: (i) either on the numerical simulation of the propagation by using the time-reversal principle; (ii) or on using the beamforming technique, provided a high-frequency model of the Green function is used, such as that given by a simplified analytical model or by ray-tracing. The advantages and links between the two approaches are discussed. Some comparisons in terms of localization error are then provided, based on simulated data, both in the time and frequency domains. The case of a pulse in a shear flow is considered, showing similar performances for both methods. Then a harmonic source in a shear flow and in a jet flow is studied, with possible temperature gradients, showing the limitations...

A FLUX-BASED CONSERVATION APPROACH FOR ACOUSTIC PROBLEMS

In this paper a Control Volume Finite Element Method for harmonic acoustic problems is presented. A dispersion analysis for control volume constructed on Q1 finite elements is compared to Galerkin FEM. The spatial convergence is also given in an eigenfrequency determination process for a cavity. The application for exterior acoustic problems is also studied by dividing the whole field into inner and outer domains using a fictitious boundary. A control volume formulation is used to compute the inner field of the truncated problem, and several approaches are combined to describe the outer field behavior on the outside of the fictitious boundary. The task of coupling is easily implemented through the balance of local flux through polygonal volumes. A two-dimensional configuration with a circular interface demonstrates the validity of this approach.