NUMERICAL ANALYSIS FOR THE IMPROVEMENT OF A SPECIAL REVERBERATION TEST ROOM

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1 NUMERICAL ANALYSIS FOR THE IMPROVEMENT OF A SPECIAL REVERBERATION TEST ROOM Davide Borelli and Corrado Schenone Dipartimento di Ingegneria Meccanica, Energetica, della Produzione, dei Trasporti e dei Modelli Matematici, Università degli Studi di Genova, Italy [email protected] A cuboid-shaped special reverberation test room, based on the requirements defined by ISO 3743-:009 standard and usually utilized as the termination of an experimental apparatus for insertion-loss measurements, was tested in terms of reverberating time and sound energy density. Tests were made in accordance with the EN ISO 338 standard and showed that the behavior of the room, albeit being an acceptable terminal for the insertion-loss measurements mentioned above, is below the standard. Various actions were then analyzed to the aim of improving the acoustical behavior of the room. To predict the effects on sound reverberation of these actions a numerical model of the room was implemented by means of a simulation software based on pyramid-tracing algorithm, which is able to solve the three-dimensional sound propagation in enclosures under the assumptions of geometrical acoustics. Tested improvements were based both on the addition of elements inside the room (wall diffusion panels, suspended diffusion panels, semicylindrical diffusers) as well as on the change of the shape of the room itself. The numerical model was calibrated and then used to analyze and compare the effects of each action. Numerical simulations showed that, due also to the small size of the room, a really effective solution does not exist: interventions which increase the reverberation time usually have a bad impact on the sound energy density distribution, and vice-versa. The least unsatisfactory, also considering the economical point of view, would be using suspended diffusion panels, since they give a little increment of the reverberating time at the highest frequencies and they make the sound field more evenly distributed. 1. Introduction Numerical analysis has been proved in recent years to be a very effective way to predict acoustical phenomena 1. Different approaches are available, e.g. finite element method, boundary element method 3, statistical energy analysis 4, ray tracing 5 and so on: every one of them addresses different aims and scopes. From a design/engineering point of view, the ray tracing technique is an accurate and fast way to achieve excellent results in the simulations of close environments such as rooms, auditoriums or musical spaces, with a very small computational cost in terms of hardware requirements, if compared to other methods such as FEM or BEM. In this research, by means of the pyramid tracing method, i.e. a variation of the ray tracing technique, several alternative configurations of a special reverberating room have been modelized, with the aim of improving the performance of the room in terms of reverberation time and sound ICSV19, Vilnius, Lithuania, July 8-1, 01 1

2 energy density distribution. This way, after the calibration of the model, it has been possible to simulate all the hypothesized improvement actions avoiding expensive in-situ experimental tests.. Description of DIME s reverberating room The reverberating test room of Department of Mechanical Engineering of the University of Genoa (DIME) is a cuboid-shaped room and it has a square plant of 4x4 m, while the height of the room is 3 m. The room was born as a thermal chamber to perform tests on heat transfer and to analyze thermo hygrometric behaviour in confined areas (ventilation, heating and cooling). The room, made of reinforced concrete partition walls and bricks 300 mm thick, rests on a metal scaffold. The structure is box-like, and consists of two enclosures separated by a cavity wall about 600 mm width, the outer covering the test environment and protecting it to ensure adequate insulation during the execution of the tests, while the more internal one is the measurement volume. The walls are vertical and confer the room a rectangular parallelepiped shape, which greatly influences its acoustical behaviour. The room was later readapted as a terminal for acoustic measurements of insertion loss in lined ducts and parallel baffle silencers. Its reverberating behaviour was not fully satisfactory, in particular at high frequency, so that the present study has been implemented to find a way to enhance the acoustical performance of the room in terms of reverberation time and sound energy density distribution. To be defined as a reverberating room, compliant for example with ISO 3741:010 or ISO 354:003, the room should have a greater volume, of about 00 m 3. Exceptions exist, and are provided for example in the Annex C of the ISO 3741:010 for rooms smaller than 70 m 3, or by the so called alpha cabins 6,7 which are about 6.4 m 3 and are certified according to ISO 354:003 or ASTM C43-09a. None of these two cases applies to the 48 m 3 room subject of this study, and the chamber has solely been used as a terminal, in the form of a hard-walled special reverberation test room as described in ISO :010 and ISO 3743-:1994, for measurements of insertion loss of ducted silencers without flow according to ISO 11691: Experiments To experimentally evaluate the reverberating behaviour of the room, measurements according to ISO 338-:008 standard were carried out. The standard describes the measurement procedure, the equipment required, and the methods for measuring the reverberation time in confined environments, which can follow two different procedures: the interrupted noise method. the integrated impulse response method. In this study, the integrated impulse response method was chosen, which is to evaluate the response of the room to an impulsive noise, for a frequency range of 15 Hz to 8000 Hz. ISO 338- specifies that no microphone-position shall be too close to any source position in order to avoid too strong influence from the direct sound, so that the minimum distance can be calculated from the following Eq. (1): V d = min ctˆ (1) where V is the volume of the room, c is the speed of sound and Tˆ is an estimate of the expected reverberation time. Assuming an estimated reverberation time of seconds, and given that the volume of the room is 48 m 3, the distance d min resulted to be equal to about 530 mm. The measuring positions for microphones and the sound source (a pistol shot) were then taken according to this value: the distance

3 Sound source (pistol shot) Microphone Room entrance Position 1 Position Position 3 Position 4 Position 5 Position 6 Figure 1. Sketch of the measuring positions. from microphone to source was at least m; the distance from any microphone or source position to the nearest wall was taken equal to 1 m, and the minimum number of measurement positions was taken according to the Engineering Method described in the standard, with 6 source-microphone combinations (3 microphone positions and source positions) and decays in each position.the source was at m from the floor, while the microphone was at 1.5 m from the floor. The measurements were taken with a Larson-Davis model 84 sound level meter equipped with a Larson Davis 560 ½ inch random incidence microphone. The thermo-hygrometric conditions of the test environment in which the experimental measurements were carried out were an average temperature of 17.5 C and a relative humidity of 4%. Figure. Example of decay curve and reverberation time calculation. 3

4 Table 1. Measured reverberation times T 30 [s] for the whole spectrum of interest. Position Frequency [Hz] Average The software, after the selection of the measurement-file to be analyzed, asks for three parameters: Dynamic: indicates the dynamic range used for the calculation; the reverberation time T 60 is defined for a decay of 60 db, but since this is very hard to get on the field, the calculation can be performed on a smaller dynamic (e.g. 30 db) and extrapolated to 60 db. The value must be proportionate to the dynamic conditions of the measurement and the expected maximum dynamic range. Offset: indicates the gap from the highest integrated value down to the initial point of the decay slope. It must be used to skip the first part of decay where usually the slope of the decay is not linear. Also in this case must be proportionate to the conditions of the measurement. Backward integration: in this field the type of backward integration which will be used in the calculation can be chosen. Backward integration is a method to address the fluctuations of the signal: the signal source is integrated from the end and going towards the start, then the integrated signal is used for the calculation. The software offers three choices. The first method (used in this study) is called the "Standard Schroeder" and implements the classic method of Schroeder 8, the second method is called "Squared Schroeder" and is a variation of the Standard Schroeder to lose less dynamic, while the third method is called "Drop Down" and is the simplest method and also the least precise, and should be used only in conditions of very low dynamic signal. The calculation was performed for all twelve experimental tests (two shots in six source-microphone combinations) by setting a dynamic value of 35 db and an offset of 5 db (according to ISO 338): in this way the T 30 was evaluated (see Fig. 4) for each of the six sourcemicrophone positions (making an average for the two shots in every position) and results are illustrated in Table 1. As it can be noticed, the values are not high as it should be for a reverberating room, especially at high frequencies. Therefore diverse improvement actions have been considered in order to achieve a better performance of the room. These actions have been analyzed by means of numerical modeling, to get a precise description of their effects and to identify the optimal solution. 4. Computer aided design and room improvement To predict the effects on sound reverberation of the diverse possible actions, a numerical model of the room was implemented by means of RAMSETE Classic 9,10, a simulation software based on pyramid-tracing algorithm 11,1,13. The pyramid-tracing is an evolution of ray/beam tracing, where triangular beams are generated at the sound source. This way is avoided the problem which occurs in the cone tracing method, since the cones do not fully cover a spherical surface: if they are adjacent some parts remain uncovered, while if they are overlapped, there are parts covered twice 4

5 so that is necessary to create an algorithm for the avoidance of multiple detections or that weights the energy in such a way that the multiple contributions produce the proper sound level. This is not a problem with the pyramid-tracing, since adjacent pyramids perfectly cover a spherical surface; the subdivision of the sphere in any number of triangles is achieved with the algorithm of Tenenbaum et al. 14, subdividing the sphere in 8 octants: this way the number of the generated pyramids can be a power of (8* N ), and moreover all of these have the same base area, thereby generating an isotropic sound source. The central axis of each pyramid is traced as usual in the ray tracing algorithms, being specularly reflected when it hits on a surface. The three corners of the pyramid follow the axis, being reflected from the same plane where it hits, also if the intersection point is outside the facet where the axis hits. A detection occurs when this a receiver (which is a point) is inside the pyramid being traced. In this case, a pseudo-intensity contribution I is recorded (along with the time elapsed since pyramid emission) for each octave band: P Q (1 α ) I' e 4π x wr ϑ i i γ x = () in which x is path length, Q ϑ is the directivity factor, P wr is the acoustic power of the source and the frequency-dependent extinction coefficient γ is computed taking into account only the percent relative humidity of the air φ % : f γ = ϕ% (3) where f is the frequency. In order to calibrate the model, the absorption coefficient of the plaster α p to be inserted in the model has been reversely obtained from the experimental values of T 30 for each frequency band, in order to substitute the default absorption coefficient of the software, using Eq. (4): V 0.16 A 4 β V f T30 α p = S where A is the total area of all non-plastered surfaces, V is the volume of the room, S p is the area of all the plastered surfaces and β is the volumic extinction coefficient 15. To the aim of validating the numerical model, experimental and calculated values of T 30 have been compared. Fig. 3 shows this comparison, which refers to T 30 mean value for the different measurement positions.. Both numerical results from RAMSETE model and theoretical results from Sabine s theory have been considered. Fig. 3a shows the reverberation time curves before the calibration of the model, while Fig. 3b shows the reverberation time curves after the calibration. This comparison indicate that numerical model can be used to simulate the acoustical behaviour of the room. In respect of Sabine s model, numerical modelling allows to take into consideration the the spatial distribution of reverberating time and sound energy density, as well as a) 10 Sabine b) 10 8 Experimental 8 6 Ramsete 6 T30 (s) Frequency (Hz) p T30 (s) Frequency (Hz) Sabine Experimental Ramsete Figure 3. Reverberation time curves: a) before calibration; b) after calibration. (4) 5

6 diffusion effect of the panels. Both these elements cannot be taken into consideration in Sabine s approach, whereas they deeply influence the actual acoustical behaviour of the room. It can be noticed that the calibration of the model is very effective, so that almost no difference can be seen between experimental and predicted values. Four different kinds of room improvement were then modelled: diffusion metal sheet panels in different positions (vertical, tilted at 45 and tilted at ); semicylindrical plastered diffusers (with a fixed radius of 50 mm or variable radii of 50, 500 and 750 mm); commercial wall diffusion panels 16,17,18,19 (four different kinds); lastly, a change in the shape of the room has been hypothesized, changing the floor and the ceiling shape to a right trapezium with bases of 5 m and 4 m. The reason of such a small change in the shape of the room is due to the physical limits of the laboratory, which doesn t allow more relevant and maybe effective changes. For simulations, an omni-directional sound source, placed in the centre of the room at m of height, and an array of 48 receiver points at three different heights (1 m, 1.5 m and 1.75 m) were used to obtain spatial accurate results. In Fig. 4 sketches of the different configurations of the room for the simulations are represented. The simulated commercial diffusion panels were made of different materials, varying from pinewood to high-density polyethylene to expanded polystyrene. Overall, 11 different configurations have been tested. The acoustical characteristics of these commercial diffusion panels were inserted in the RAMSETE Material Manager, creating in this way four new materials which have been alternately assigned to two of the walls of the room for the simulations. This way, the mean reverberation time T 30 has been evaluated, as well as the sound energy density D, by means of the sound pressure, at each receiver position. The sound energy density was evaluated in order to avoid that a potential improvement in terms of reverberation time could have as a side-effect a worse spatial sound distribution. Mean sound energy density D was then calculated averaging, for each one octave frequency band, the values of D at all the different receiver positions for all three measuring heights. The percentage ratio of standard deviation x was then calculated with Eq. (5): σ x = 100 D where σ represents the standard deviation. It must be highlighted that sound density is definitely well distributed in the present configuration, but insertion of reflecting panels can worsen it sharply. Results of simulations are showed in Fig. 5 and Fig. 6. As it can be seen, there are various reverberating behaviours for the different tested interventions. Concerning the reverberation time (Fig. 5), all the commercial diffusion panels, being also in part absorbent, significantly worsen the reverberating performance of the room, and the same happens for the semicylindrical diffusers. Finally, the intervention of demolition and lateral spreading of the back wall of the reverberation chamber, in figure indicated like trapezoid base, remains an actual hypothesis of design: from the analysis of the diagram this solution seems to have a certain positive effect in terms of reverberation, since an oblique side wall provides an irregular shape to the room that slightly rises the average reverberation time for each frequency, therefore improving the acoustic performance of the room itself. The aim of generating a sound field as uniform as possible in the space within the test volume, evaluated by means of the percentage ratio of standard deviation of the mean sound energy density x (Fig. 6), leads to the conclusion that the commercial diffusion panels give good results concerning this issue, the semicylindical diffusers with radius equal to 50 mm provide a slight improvement in terms of sound energy density distribution, while the multiple radii solution gives high deviations in (5) 6

7 Room with vertical diffusion panels Room with 45 tilted diffusion panels Room with tilted diffusion panels Room with semicylindrical diffusers (single radius) Room with semicylindrical diffusers (multiple radii) Room with trapezoid floor and ceiling Figure 4. Sketches of the different simulated configurations. terms of sound energy density, confirming that this kind of solution is only suitable for big confined spaces like auditoriums or theaters and not for small rooms. Considering the effects of the room enlargement on the distribution of the sound field, is evident in Fig. 6 that the curves are fairly constant and there are not significant differences from the present configuration. In the end, reverberation time remains low despite the simulated solutions: there is no improvement action which may obtain the expected result, since all the actions that do not include the increasing of room s volume are just ameliorative but not resolutive. The less worst and more economically affordable solution seems to be the use of suspended reflective panels made of metal sheets: as it can be seen from the graphs, this action provides a small increase of the average reverberation time in the high frequencies and, at the same time, makes the sound field evenly distributed. Beyond the improving solutions, which are not really satisfactory, the modeling technique seems to work well: by its means, with low time and cost, useful information has been obtained, that are able to guide design to an effective improvement. 4,0 3,0 T 30 (s),0 1,0 0, Frequency (Hz) Figure 5. Results of the simulations: reverberation time T 30. % Frequency (Hz) Figure 6. Results of the simulations: standard deviation over sound energy density. 7

8 5. Conclusions A numerical model implemented by a pyramid-tracing commercial code was created, and was validated by measuring the reverberation times of the interior of a special reverberating room. The numerical model was then used to simulate the effects of 11 different actions aimed to improve the acoustical performance of the room, increasing reverberation and equalizing acoustical density. Despite all the solutions considered, it has been found that it is not possible to achieve both the goals at the same time because of physical and structural limitations of the chamber and because of the regulatory constraints that must be met: when reverberation time improves, reductions and unevenness in the spatial distribution of the sound energy density occur, and vice versa, when the sound field appears to be evenly distributed in space, the reverberation times fell significantly. The solution that is the more feasible is the application of diffusion panels hanging from the ceiling of the room, solution which is favourable especially since the panels can be made by common materials (metal sheets, poly-methyl methacrylate, glass, etc ) that absolutely must be reflective and characterized by low absorption coefficients. Instead, the adopted numerical modeling technique resulted to be very useful in guiding the design, providing useful information in a fast and costeffective way. REFERENCES Marburg, S. and Nolte, B. Computational Acoustics of Noise Propagation in Fluids. Springer-Verlag, Berlin, Germany, (008). Tomiku, R., Otsuru, T., Azuma, D. and Takahashi, Y. Use of finite element method for comparison of sound field diffuseness in reverberation rooms with and without absorption materials, Acoustical Science and Technology, 6 (), 5-8, (005). Kirkup, S. M. The boundary element method in acoustic. Integrated Sound Software, Heptonstall, U.K., (1998). Lyon, R. H. Statistical Energy Analysis of Dynamical Systems. M.I.T. Press, Cambridge, U.S.A., (1975). Toyoda, E., Sakamoto, S. and Tachibana, H. Effects of room shape and diffusing treatment on the measurement of sound absorption coefficient in a reverberation room, Acoustical Science and Technology, 5 (4), 55-65, (004). Veen, J., Pan, J. and Saha, P. Standardized Test Procedures for Small Reverberation Rooms, Sound and Vibration, 39 (1), 18 0, (005). Duval, A., Rondeau, J. F., Dejeager, L., Sgard, F. and Atalla, N. Diffuse field absorption coefficient simulation of porous materials in small reverberant rooms: finite size and diffusivity issues, Actes du 10ème Congrès Français d'acoustique, 010, Lyon, France, 1 16 April, (010). Schroeder, M. R. New method of measuring reverberation time, Journal of the Acoustical Society of America, 37 (3), , (1965). Farina, A. Aurora Listens to the Traces of Pyramid Power, Noise & Vibration Worldwide, 6 (6), 6-9, (1995). Farina, A. RAMSETE - a new Pyramid Tracer for medium and large scale acoustic problems, Proceedings of EURO-NOISE 95 Conference, 1995, Lyon, France, 1 3 March, (1995). Lewers, T. A combined beam tracing and radiant exchange computer model of room acoustics, Applied Acoustics, 38 (-4), (1993). Farina, A. Pyramid Tracing vs. Ray Tracing for the simulation of sound propagation in large rooms, in Brebbia, C. A. Ed., Computational Acoustics and its Environmental Applications, Computational Mechanics Publications, Southampton (GB), , (1995). Farina, A. Validation of the pyramid tracing algorithm for sound propagation outdoors: comparison with experimental measurements and with the ISO DIS 9613 standards, Advances in Engineering Software, 31 (4), 41-50, (000). Tenenbaum, R. A., Slama, J. G. and Ballesteros, M. L. Numerical simulation of room acoustics: a new approach for source modelling, Proceedings of the 14 th International Congress on Acoustics, 199, Beijing, China, (199). Wenmaekers, R. H. C., Hak, C. C. J. M., Martin, H. J. and Van Luxemburg L. C. J. Air Absorption Error in Room Acoustical Modeling, Journal of the Acoustical Society of America, 13 (5), 3355, (008)