Vincent Valeau

On the use of a diffusion equation for room-acoustic prediction

This paper presents an alternative model for predicting the reverberant sound field in empty rooms with diffusely reflecting boundaries, based on the generalization and the numerical implementation of a diffusion equation for the energy density. The paper focuses on the source term and the boundary conditions of the diffusion equation, both for the steady state and the time-varying state, in order to make computational use of the model. In addition, theoretical analysis of the diffusion equation shows that the diffusion model may be considered as an extension of the classical theory of reverberation to nondiffuse sound fields. The numerical model is first applied to a cubic room and shows a very good agreement with statistical theory. Two numerical applications are also given for a long room and a flat room; results are in good agreement with numerical results from a ray-tracing software. The main advantage of the present model is its capability to be applied regardless of the complexity of the room shape...

On the use of a diffusion model for acoustically coupled rooms

A numerical model is proposed to predict the reverberant sound field in a system of two coupled volumes that are connected through an open aperture. The model is based on the numerical implementation of a diffusion model that has already been applied to predict the sound-energy distribution and the sound decay in single rooms. In comparison with the statistical theory, the proposed approach permits the prediction of the sound field by taking into account the sound source location and the receiver locations as well as the transition from one room to the other at the coupling aperture. Moreover, the diffusion model results match satisfactorily the experimental data in terms of sound-pressure level and reverberation times, both in the room containing the source and in the receiving room. Simulations with a ray-based model are also carried out, leading to results similar to those of the diffusion model, but at a cost of larger computation times.

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.

Modeling the sound transmission between rooms coupled through partition walls by using a diffusion model

In this paper, a modification of the diffusion model for room acoustics is proposed to account for sound transmission between two rooms, a source room and an adjacent room, which are coupled through a partition wall. A system of two diffusion equations, one for each room, together with a set of two boundary conditions, one for the partition wall and one for the other walls of a room, is obtained and numerically solved. The modified diffusion model is validated by numerical comparisons with the statistical theory for several coupled-room configurations by varying the coupling area surface, the absorption coefficient of each room, and the volume of the adjacent room. An experimental comparison is also carried out for two coupled classrooms. The modified diffusion model results agree very well with both the statistical theory and the experimental data. The diffusion model can then be used as an alternative to the statistical theory, especially when the statistical theory is not applicable, that is, when the reverberant sound field is not diffuse. Moreover, the diffusion model allows the prediction of the spatial distribution of sound energy within each coupled room, while the statistical theory gives only one sound level for each room.

Introducing atmospheric attenuation within a diffusion model for room-acoustic predictions

This paper presents an extension of a diffusion model for room acoustics to handle the atmospheric attenuation. This phenomenon is critical at high frequencies and in large rooms to obtain correct acoustic predictions. An additional term is introduced in the diffusion equation as well as in the diffusion constant, in order to take the atmospheric attenuation into account. The modified diffusion model is then compared with the statistical theory and a cone-tracing software. Three typical room-acoustic configurations are investigated: a proportionate room, a long room and a flat room. The modified diffusion model agrees well with the statistical theory (when applicable, as in proportionate rooms) and with the cone-tracing software, both in terms of sound pressure levels and reverberation times.

A numerical investigation of the Fick's law of diffusion in room acoustics

In this paper the validity of the Ficks law of diffusion in room acoustics is investigated in the stationary state. The Ficks law, underlying the room-acoustics diffusion model, assumes a proportionality relationship between the local sound intensity and the energy density gradient, the proportionality constant being the so-called diffusion coefficient. This relationship, based on an analogy with the behavior of real particles in a scattering medium, is assessed by using a numerical tool simulating the actual dynamics of sound particles in a room. Two types of room geometries are considered: rooms with proportionate dimensions and long rooms. Concerning proportionate rooms the numerical analysis highlights the presence of weak variations of the reverberant energy density, generating an intensity vector pattern which is shown to be correctly described by the theoretical Ficks law and homogeneous diffusion. Conversely, inside long rooms, an estimate of the local value of the diffusion coefficient is carried out, showing that the reverberant sound field is well described by a spatially varying diffusion coefficient (non-homogeneous diffusion). The rate of increase of the estimated diffusion coefficient depends on the cross-sectional area of the room and on the boundaries absorption coefficient.

An Empirical Diffusion Model for Acoustic Prediction in Rooms with Mixed Diffuse and Specular Reflections

In this paper, a modification to the room-acoustic diffusion model is proposed to take different amounts of wall scattering into account. An extensive set of numerical simulations using a cone-tracing software has first been carried out, in order to highlight the impact of the scattering coefficient on the diffusion process in rooms, in terms of sound pressure levels. An iterative method is then proposed to identify, for a given value of the walls scattering coefficient, the diffusion constant that allows the stationary sound field to be governed by a diffusion process, regardless of the rooms geometry. Using this method, an empirical law can be proposed between the diffusion constant and the scattering coefficient. The empirical diffusion model is then compared to scale model experiments, as well as to other models from the literature, with a satisfactory agreement for the sound pressure level. However, the empirical diffusion model fails to predict the sound decay for rooms with perfectly specularly reflecting surfaces, due to the inherent concept of a diffusion process.

Development of a time-frequency representation for acoustic detection of buried objects

A recently developed apparatus permits the detection of buried objects, such as landmines, by remotely sensing the variations of ground vibration that occur over the buried object with a laser Doppler vibrometer (LDV), when the ground is insonified by means of acoustic-to-seismic coupling. As it is currently implemented, the LDV scans individual points on the ground. The technique shows much promise, but it is slow when compared to some other techniques. This work demonstrates that mines can be detected as the LDV beam moves continuously across the ground, by using an optimal time-frequency representation of the LDV signals. This improvement has the potential to significantly increase scanning speeds. The vibrometer output signal is analyzed by means of time-frequency representations, which exhibit characteristic acoustic “signatures” when scanning over buried objects. The most efficient representation appears to be the smoothed spectrogram weighted by the time-frequency coherence function. It detects the...

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.