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An empirical diffusion model for acoustic prediction in rooms with mixted specular and diffuse refections ; ; Billon, Alexis et al in Acta Acustica United with Acustica (2009), 95(1), 97-105 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 ... [more ▼] 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 wall’s scattering coefficient, the diffusion constant that allows the stationary sound field to be governed by a diffusion process, regardless of the room’s 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. [less ▲] Detailed reference viewed: 51 (2 ULg)Introducing atmospheric attenuation within a diffusion model room-acoustic predictions Billon, Alexis ; ; et al in Journal of the Acoustical Society of America (2008), 123(6), 4040-4043 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 42 (2 ULg)On the use of diffusion equations to model the acoustics of coupled rooms Billon, Alexis ; ; et al in Journal of the Acoustical Society of America (2008), 123(5), 3910-3910 he acoustics of coupled rooms are characterized by energy exchanges through apertures and/or partition walls. The use of systems of diffusion equations allows to predict the temporal and spatial energy ... [more ▼] he acoustics of coupled rooms are characterized by energy exchanges through apertures and/or partition walls. The use of systems of diffusion equations allows to predict the temporal and spatial energy distributions in these configurations quite accurately. In this presentation, the diffusion formalism for room acoustics-prediction is summarized. The systems of equations to be solved in the case of coupling through an aperture and through a partition wall are presented. For two rooms coupled through an aperture (two classrooms connected through an open door), the results obtained with the diffusion model are compared to experimental data, in terms of sound pressure levels and sound decays. On the other hand, for the case of two classrooms connected through a partition wall, the diffusion model is compared to experimental data in terms of sound pressure level difference only. Finally, an engineering application is presented in the configuration involving a workroom including multiple sound sources (e.g., machines) connected to offices through open and closed doors. [less ▲] Detailed reference viewed: 31 (1 ULg)Modeling the sound transmission coupled through partition walls using a diffusion model Billon, Alexis ; ; et al in Journal of the Acoustical Society of America (2008), 123(6), 4261-4271 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 25 (1 ULg)Diffusion-based models for predicting sound fields in rooms with mixed specular and diffuse reflection ; Billon, Alexis ; et al Conference (2007, September) A diffusion model, based on the numerical solution of a diffusion equation, was developed in the past to give accurate predictions of the sound-pressure level and of the sound decay at any location in a ... [more ▼] A diffusion model, based on the numerical solution of a diffusion equation, was developed in the past to give accurate predictions of the sound-pressure level and of the sound decay at any location in a single enclosure or in coupled rooms. However, this model is limited to rooms with diffusely reflecting walls. In this study, two methods are presented to extend this model to rooms with mixed specular and diffuse reflections, defined by the classical room-acoustics scattering coefficient. The first method models the reverberant field by using a modified diffusion process, with an empirical diffusion constant departing from the theoretical one based on the mean free path. The set of these coefficients, which depend on the scattering coefficient, has been found empirically to fit the results given by a ray-tracing program. The second method is a hybrid approach. The reverberant sound field due to the diffuse reflections is first obtained with the original diffusion model. Then the sound field due to the specular reflections is modelled with an image-source model. The results given by the two approaches are compared to experimental data obtained for several types of rooms (a classroom, an office and some long rooms). [less ▲] Detailed reference viewed: 41 (3 ULg)Modelling the sound transmission through separation walls using a diffusion model Billon, Alexis ; ; et al Conference (2007, September) The diffusion model has been used successfully to evaluate the acoustic behaviour of a system of coupled rooms connected through a coupling aperture. In this paper, an extension of this model is proposed ... [more ▼] The diffusion model has been used successfully to evaluate the acoustic behaviour of a system of coupled rooms connected through a coupling aperture. In this paper, an extension of this model is proposed to deal with the propagation of sound energy through a partition wall. The diffusion model can be considered as an extension of the statistical theory to none diffuse sound fields. Numerical comparisons with the statistical theory are then carried out. The following parameters are varied: its transmission loss of the separation wall, its surface, the coupled room’s absorption coefficient and the coupled room’s volume. The agreement between the statistical theory and the diffusion model is very good. [less ▲] Detailed reference viewed: 47 (1 ULg)Différentes estimations du libre parcours moyen en acoustique des salles : influence sur l’estimation de l’énergie acoustique par un modèle de diffusion ; Billon, Alexis ; et al Conference (2006, April) La plupart des outils de prévision en acoustique des salles sont basés sur le principe du tir de rayons. La précision des résultats dépend alors du nombre de rayons choisi, nécessairement important quand ... [more ▼] La plupart des outils de prévision en acoustique des salles sont basés sur le principe du tir de rayons. La précision des résultats dépend alors du nombre de rayons choisi, nécessairement important quand la géométrie simulée est grande et/ou disproportionnée, ce qui implique alors des temps de calcul élevés. Pour ce type de géométrie, une méthode alternative, basée sur la résolution numérique d’une équation de diffusion, permet en revanche de réaliser des prévisions acoustiques au prix d’un coût numérique modeste. Ce modèle repose en particulier sur un coefficient de diffusion caractérisant la pièce. Ce coefficient est théoriquement proportionnel au libre parcours moyen (LPM) du local considéré, vérifiant classiquement l’expression 4V/S (V étant le volume de la salle, S la surface des parois). Il est souvent admis que cette valeur est valide pour une salle de dimensions homogènes et dans le cas d’un champ réverbéré diffus. Néanmoins, dans la présente étude nous montrons que pour des locaux particulièrement allongés ou plats, l’atténuation sonore, directement dépendante du coefficient de diffusion, est surestimée par ce modèle. Il en est de même pour des locaux dont la loi de réflexion aux parois s’écarte d’une loi de Lambert. Ainsi, afin d’améliorer les performances du modèle de diffusion, la solution envisagée consiste d’une part, à réaliser un calcul numérique préliminaire du LPM et d’autre part, à considérer les approches analytiques alternatives du LPM rencontrées dans la littérature. La méthode numérique retenue est basée sur le suivi de particules sonores, et permet d’établir le LPM à partir de l’ensemble des distances de collision entre deux parois, pour des conditions de réflexion quelconques. Les résultats de ces approches analytiques et numériques sont présentés en terme d’atténuation sonore pour un local plat et un local allongé, et sont comparés à ceux issus d’autres méthodes numériques. [less ▲] Detailed reference viewed: 223 (2 ULg)Validation of a numerical diffusion equation-based modelling of the reverberated sound field in long rooms ; Billon, Alexis ; et al Conference (2005, July) Many applications as corridors, railways tunnels or tube stations present a long room geometry. A fast and reliable modelling of such sound fields could be helpful for designers. In fact, the classical ... [more ▼] Many applications as corridors, railways tunnels or tube stations present a long room geometry. A fast and reliable modelling of such sound fields could be helpful for designers. In fact, the classical statistical theory based on the assumptions of diffuse sound field is not applicable in such cases because the reverberant sound energy along the room is not uniform. In this study, several models assuming diffuse reflections of sound by walls are used for predicting the reverberant sound field in long rooms. Two models based on a diffusion equation for the energy density (one numerical and one analytical based on an image approach for describing the sound reflection at the corridor extremity) are compared with a radiosity model, and with a ray tracing software. Predictions are compared in terms of sound attenuation and reverberation time with measured data. The long rooms considered in this study were two rectangular corridors of lengths 20.3m and 47.3m. All models overestimate the attenuation, reaching 6dB for the numerical diffusion based model. When a part of specular reflection (30%) is added in the ray tracing model, the predicted sound attenuation matches with the measured one: even in case of rough surfaces, specular reflections cannot be totally excluded. For reverberation time, the agreement between predictions and experiments is good with fewer than 15% of discrepancy. The best predictions of the reverberation time were given by the diffusion models, with discrepancy less than 2% for the numerical model. So, it could be concluded that it is difficult to find a prediction method which is consistent both in terms of steady state and sound decay for the acoustics of long halls. [less ▲] Detailed reference viewed: 73 (1 ULg) |
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