Stephane Citherlet <firstname.lastname@example.org>
The acoustical and thermal properties of materials have contradictory behaviour. Constructions, which provide good acoustic absorption usually, have a low thermal inertia and vice versa. It is therefore important to find a balance between acoustic absorption and thermal inertia in order to deliver well designed buildings. This paper presents an integrated solution, developed to assess the room acoustics performance of a building within the ESP-r environment.
The approach used in this work applies the diffuse-sound field theory to calculate the reverberation time via three analytical equations: Sabine, Eyring and Millington approaches. The calculation includes the absorption of the space boundaries, the occupants and furniture. Also included is the air absorption, which takes into account the air temperature and humidity from the thermal simulation.
Within a space, a sound is absorbed due to multiple reflections at the enclosure boundaries during its propagation. At each successive reflection, the enclosure boundaries and the objects within it absorb a fraction of the sound energy. The fraction of absorbed sound energy depends on the frequency of the emitted sound and the capacity of a material to absorb this frequency. For instance, concrete finished with roughcast is a rather poor sound absorber compared to agglomerated fiber wood, as shown in Figure 1.
Figure 1 Acoustic absorption coefficients of three wall typologies.
Contrast the thermal performance, concrete has a higher capacity to store heat (thermal inertia) than the fiber wood, because of a higher density and thermal conductivity. This higher thermal inertia generally increases absorption of solar gains and may improve occupants’ thermal comfort, especially for spaces with no cooling plant and large window areas. To provide a well-designed building, a balance must be found between acoustic absorption and thermal inertia.
In order to perform a simulation with ESP-r, the first step consists in creating the 3D geometry model of the building, based on thermal zones. A thermal zone is a volume of air assumed to have homogeneous thermodynamic properties. A zone is used to represent a room, a portion of a room or a concatenation of several rooms. The geometric description of a zone is composed of an air volume, which is bounded by closed polygons with associated attributes such as orientation and specific multilayer constructions. The construction is defined by its materials and their corresponding thickness. Originally, ESP-r supported thermo-physical properties such as density and thermal conductivity. In order to allow room acoustics simulation, the construction description has been enlarged to include the one-octave band acoustic absorption coefficients. For the room acoustics calculation, the 3D geometry model provides the area of each bounding surface and the construction provides the absorption coefficients.
The reverberation time assessment is based on three versions of the diffuse-field theory. Based on this approach, the reverberation time, for a given frequency f, can be expressed by the following expression:
f frequency under consideration [Hz]
V volume of the enclosure [m³]
T absolute temperature of the air in the enclosure [°K]
total equivalent area of the enclosure for frequency f [m²].
In Eq. (1), the total equivalent area of the enclosure includes the absorption due to the boundaries, furniture, occupants, and air, can be written:
Different expressions have been proposed to assess equivalent absorption area of the enclosure boundaries . To demonstrate the feasibility of the integrated approach in this work, three well-known analytical expressions, Sabine, Millington and Eyring, were implemented in ESP-r to assess the reverberation time.
These methods can be used in a broad range of typical building spaces but each approach has a domain of validity depending on , the average acoustic absorption, as shown in Table 1.
Table 1 Selection criteria for reverberation models.
The theoretical model, from which these equations are derived, requires the decaying sound field to be perfectly diffuse. This idealised condition is sufficiently fulfilled in practice when: (a) no room dimension is markedly different from the others; (b) room dimensions are large compared to the wavelength, which is the case in building acoustics; (c) absorption is distributed almost uniformly over the enclosure boundaries.
The thermodynamic properties of air affect the fraction of sound energy that is absorbed by the air. Air absorption is sensitive to air temperature, air composition, particularly water vapour concentration, and sound frequency. It is particularly necessary to account for air absorption in large spaces, where the distance travelled between two reflections is large. This absorption mechanism may be an important issue during the design of naturally ventilated large spaces, where the acoustical performance is of critical concern. For instance, in the Llewellyn Hall (12750 m³) in Canberra, an inland city with low ambient humidity and cold nights, an extremely low internal relative humidity was obtained (around 25%) when outside air was used to ventilate the concert hall. For occupant comfort, the internal relative humidity had to be maintained at about 55%, which significantly increased the reverberation time. At 4 kHz, the reverberation time increased from 1.25 s to 1.70 s when the relative humidity increased from 25% to 55% . To keep the acoustical quality independent of climate conditions, a mechanical ventilation system was installed. This example illustrates the influence of the thermo-physical properties of air on the room acoustics and demonstrates the need for an integrated assessment of thermal and room acoustics performance.
The equivalent absorption due the enclosed air can be expressed (see for instance ) by 4 m V , where m is the air absorption coefficient [m-1] and V is the volume of the enclosure [m³]. The air absorption coefficient m, can be extracted from published data, for instance the PrEN 12354/6 standard , which is tabled per octave band for several air temperatures and relative humidity ranges.
The integrated approach gives access to the temperature and humidity of the air within the enclosure at any time of the day. Therefore, m can be expressed for specific air conditions and a more detailed formulation can be used, which is derived from  and . This leads to the following expression of the air absorption coefficient m:
f frequency of the sound [Hz]
p air pressure [kPa]
p0 reference air pressure (101.325) [kPa]
T absolute temperature of the air [°K]
T0 reference air temperature (293.15) [°K]
frN relaxation frequencies for Nitrogen [Hz]
frO relaxation frequencies for Oxygen [Hz].
The expression of the relaxation frequencies frO and frN as a function of the air temperature and humidity can be found in ISO 9613/1.
Figure 2 shows the interface of the room acoustics module as implemented in ESP-r. When loaded, this module first reads the geometry representation of the project, followed by the physical properties of each construction itemised within the project and finally the information related to the possible occupants and items of furniture (1 in Figure 2).
Figure 2 Interface of the room acoustics module in ESP-r.
The procedure to perform a reverberation time calculation starts with the selection of one or several adjacent zones to analyse within the list of available zones in the project (2). For each selected zone, its characteristics (Volume, floor area, etc.) and the related surfaces attributes (surface name, composition and net area) are then displayed (3). Before the reverberation time calculation is initiated, several options can be modified in order to select the calculation method and to specify the output format (4).
Once the desired calculation and reporting options have been selected, the reverberation time calculation can be initiated (5). The selected zone(s) are then scanned. For each detected surface, the corresponding absorption coefficient set is used to determine the equivalent surface area according to the selected calculation method. At the end of this process, the total equivalent area of the boundaries is obtained. Then, if occupants and furniture exist in the zone, the corresponding equivalent area is calculated. Finally, the air absorption contribution is included according to the temperature and humidity obtained by the thermal simulation. This total equivalent absorption area, is then converted into the reverberation time.
The headquarters of Energie Ouest Suisse (EOS), Figure 3, a major electricity producing company in Switzerland, was selected as a case study because, first it had been widely monitored on the thermal and lighting side during the European project ‘Daylighting Design of European Building’ and secondly its proximity permitted the extension of monitoring to room acoustics. In the present paper, only the atrium is analysed to check the conformity between the simulation and monitored results.
Figure 3 South facade (left) and atrium (right) of the EOS building
The overall dimensions of the atrium are 7 m by 8 m and 17 m high. Its roof and its East façade are fully glazed. The ground floor of the atrium is finished with marble tiles and the partitions between the atrium and the offices are made of two 12.5 mm plasterboards with 50 mm mineral fibre insulation in between. The ceiling of the circulation is in concrete covered by a roughcast plaster. Finally, the raised floors are made of 40 mm chipboard, covered with a fitted carpet.
The materials used in the atrium space and the existence of the hard wooden stairs may provide the characteristics for a diffuse sound field that is required for the use of the calculation methods presented here.
The monitored reverberation time in Figure 4 corresponds to the mean profile obtained by measurement at three different locations in the atrium according to the procedure recommended by the ISO 3382 . Among the three calculation methods, the Sabine approach predicted the best results. This is not surprising as this equation is the most suited for an average surface-absorption coefficient which is the case in the atrium is equal to 0.14 [-]. The simulation results show good agreement with the monitored data. The calculated reverberation time in Figure 4 is representative for an air temperature of 28°C and a relative humidity of 60%, which corresponds to the conditions observed during monitoring (summer day).
Figure 4 also indicates that reverberation times are greatest at intermediate frequencies. This is due to the large area of atrium glass, which absorbs low frequency sound, while the carpet absorbs high frequencies. In order to improve the acoustic absorption at medium frequencies it is necessary to add an element that acts like a membrane. This can be achieved, for instance, using suspended plasterboard on the ceiling. The benefit of this solution on the room acoustics performance will be counterbalanced by the reduction of thermal inertia that occurs if the massive ceiling is no longer in direct contact with the atrium air. This could be unfavorable for the thermal comfort of the occupants.
Figure 4 Monitored and calculated (Sabine) reverberation time (RT) for the atrium of the EOS building
(The error of the measurements was has been estimated as 8%).
The previous section was used to check the agreement between simulation results and monitored data. This good agreement allows further investigation to determine the effect of improving room acoustics on the thermal comfort of the occupants. These performances were simulated for the following three ceiling compositions:
1. High thermal inertia: The roughcast concrete ceiling is fully exposed. This corresponds to the existing building.
2. Medium thermal inertia: Half of the ceiling is covered with suspended perforated plasterboard with mineral insulation, in order to increase the sound absorption at mid-frequencies.
3. Low thermal inertia: The whole ceiling is covered with the suspended ceiling.
Thermal comfort was simulated with ESP-r and is defined by the percentage of person dissatisfied (PPD) with the thermal condition (Clo: 0.7 and Met: 1.2). Figure 5 and 6 summarise respectively the room acoustics and thermal comfort performance of these three variants. As can be seen in these two figures, the room acoustics is improved by the false ceiling, but to the detriment of occupants’ thermal comfort. Increased ceiling coverage with the suspended ceiling, lowers the reverberation time, but at the expense of increased thermal discomfort.
The two peaks observed in the thermal comfort figure, correspond to the two period of the day, when the sun strikes the glazed surfaces of the atrium. The peak in the morning corresponds to the solar gains entering trough the East façade. These gains are partly reduced to the obstruction of the adjoining building. During a clear day, the natural ventilation and thermal inertia of the existing atrium (variant 1.) could not remove sufficient solar gains to maintain thermal comfort conditions. This leads to the occupants to experience overheating. A post-occupancy evaluation of the EOS building (i.e. with high thermal inertia), confirmed that one third experience overheating often and one third sometimes during the summer period. This agrees with the simulated performance.
Figure 5 Reverberation time for three ceiling compositions.
Figure 6 Thermal comfort for three ceiling compositions.
The existing atrium is used as a circulation space only. Therefore acoustical performance was of less importance than thermal. As is demonstrated, the use ox exposed thermal mass in the ceiling provides the best thermal and worst acoustical performance of analysed cases. The increase in thermal comfort due to the exposed ceiling (variant 1) is approximately 20% compared with the suspended acoustical ceiling (variant 3). If the space was on a more permanent use, then the acoustical performance would have to be improved. This could be achieved by partially covering the ceiling (variant 2). This would have a determinant effect on the occupants’ thermal comfort. This latter could be improved by using solar control glazing or external shading elements without affecting the acoustical performance.
 J. A. Clarke, "Building Performance Simulation Using the ESP-r System," presented at The fifth international IBPSA conference, Building simulation '97, Prague, Czech Republic, 1997.
 W. C. Sabine, Collected Papers on Acoustics (Originally 1921). Los Altos, CA: Peninsula Publishing, 1993.
 Millington, "A Modified formula for reverberation," Journal of the Acoustical Society of America, vol. 69, pp, 1932.
 C. F. Eyring, "Reverberation time in "dead" rooms," Journal of the Acoustical Society of America, pp. 217-241, 1930.
 E. McCue and R. H. Talaske, "Acoustical Design of Musical Education Facilities," Syracuse, Ed. New York, USA, 1990.
 V. O. Knudsen and C. M. Harris, Acoustical Designing in Architecture: The Acoustical Society of America, 1970.
 European Committee for Standardisation (CEN), "PrEN 12354/6 - Building acoustics - Estimation of acoustic performance of building from the performance of elements - Part 6 - Sound absorption in enclosed spaces." Brussels, 2000.
 International Organisation for Standardisation (ISO), "ISO 9613/1 - Acoustics - Attenuation of sound during propagation outdoors - Part 1- Calculation of the absorption by the atmosphere," 1993.
 P. Lienard and P. François, Acoustique industrielle et environnement, vol. 46. Paris: Eyrolles, 1983.
 International Organisation for Standardisation (ISO), "ISO 3382 - Measurements of reverberation time in auditoria," 1975.