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Microclimatic quality analysis. Application of the Transfer Function Method to a single thermal zone of an Italian museum. Virginia Gori1, Carla Balocco1*, Luca Citi2, Roberto Boddi3

1 Dipartimento di Energetica, Università degli Studi di Firenze, via Santa Marta 3, Firenze. Italy. * Corresponding Author: carla.balocco@unifi.it

2 Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139. USA. 3 Servizio di Climatologia e Conservazione Preventiva, Opificio delle Pietre Dure, Fortezza Da Basso, Firenze. Italy. The measurement of indoor climate in heritage buildings can provide valuable sources of data needed for an optimal use and management of the works of art exhibited inside. It is a fundamental technique to evaluate environmental damage and degradation processes, to support the protection, conservation and preservation of works of art, improving the quality of museum environments. This is particularly important when the old buildings have special architectural and historical value. In most cases, the buildings themselves are works of art and at the same time preserve various precious objects. The stability requirements of microclimatic conditions play a key role in the deterioration processes of the various materials of building and works of art. It is necessary to reduce variations in thermo-physical parameters because they are as damaging as their absolute values, ensuring a sufficient comfort level for users. In the present paper results from experimental measurements performed inside a historical building used as a museum, located in Fucecchio (near Florence, Italy), are discussed. A method based on the implementation of the current standard UNI EN ISO 13786, was used to study the heat transfer to and from a single thermal zone (one of the exhibition rooms) of the museum. Making some basic assumptions, the time-varying thermodynamic measures could be decomposed, by means of the Discrete Fourier Transform (DFT), into a sinusoidal frequency component. These components could be independently analysed by means of the norm above and the results combined to estimate the total heat transfer wave through the room envelope. These results can provide a useful support in decision making about the choice of the most suitable environmental control strategies such as passive control, controlled ventilation, shading and added insulation of building, modular and movable heating plant systems (e.g. radiant platform) and, if possible, Heating Ventilation Air Conditioning (HVAC) system. In addition, this method allowed an estimate of the time-course of the temperature on the internal surface of the walls, which is an important factor for optimally arranging the paintings inside the exposition rooms. Keywords: monitoring campaigns, cultural heritage, transfer function method

Introduction Comparing the situation in the rest of Europe and in the United States, in Italy about the 80% of the museums are located in buildings that were not designed for this purpose. Nowadays, the museum is not only an exhibition place of collected works of art, but it must provide various services as an answer to the collection of different kinds of visitor [5]. A museum is not only a general collection of objects but also a set of managerial services that has to be provided. In this perspective, the building itself becomes part of the collection. The building where the museum is located can have itself a historical and artistic value that has to be preserved and maintained. The conversion of an existing, historical building into a museum requires an initial analysis of the building meant as a complex system, that has to satisfy numerous safety requirements [1,2]. Among other things, control of the indoor climatic conditions and thermo-dynamic behaviour of the whole building-plant system is fundamental [3,4,6]. Monitoring campaigns connected to computational thermo-fluidynamic modelling and transient simulations are fundamental in order to assess if the building can be used as a museum and if it is possible to reactivate passive systems (lighting, cooling, natural ventilation). Most existing literature refers to non invasive techniques (e.g. optical coherence tomography [12], laser and optical systems for cleaning applications, analysis and diagnostics (laser-induced fluorescence (LIF), laser-induced-breakdown spectroscopy (LIBS), Raman and IR spectroscopies, [11]) applied to

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artefacts with cultural importance. Several studies are based on experimental monitoring campaigns consisting of non-invasive in situ placement of instruments, whose results provide a characterisation of works of art and the environment where they are exhibited. Monitoring campaigns need lengthy processing and high realization costs. Furthermore, non invasive techniques that use sophisticated instruments are very expensive. In this paper we provide a methodological approach based on the combined use of some basic data (building, materials and external climate) and transient simulations using thermo-fluid modelling of the building museum system. The efficacy of the proposed method is due to the fact that, when experimental data are not available, results can be carried out just using data provided by literature, historical references and standards. We think that this method can also be an useful tool for exhibition planning and management solutions. It can help in defining preservation – maintenance and plants intervention. In particular, the knowledge of indoor climate conditions concerning the different zones of the buildings connected to the dynamic thermal performance of the walls, is a non-invasive technique which permit identification of the best solution for the arrangement of the various works of art. The Museum The Museum of Religious Art in Fucecchio (near Florence, Italy) is set in the Corsini Farmhouse, opposite the Collegiate Church in the upper part of the town. After its purchase during 1981 by the Municipality it was converted into a cultural centre for the public library and archives, making it the ideal seat for the town museum. The main building was constructed on the city walls and subdivided into two floors culminating in a loggia. Preserved inside the building structure there are traces of medieval constructions that probably date back to the 13th century. Recently two wings were connected to the main building. At present the two wings house the public library and historical archive, while the main building houses the museum. The ground floor houses the Archaeological Museum with its fossils and finds from various periods, but also with medieval archaeological finds that allow reconstruction of the ancient houses in the urban centre. The “Piano Nobile”, a true picture gallery, is intended for the Museum of Religious Art where the works are divided into different sectors (paintings, silver works, vestments) and displayed in chronological order (Fig.1). Among the paintings, “Nativity” by Larciani, a lunette portraying the “Trinity and the Evangelists” and “Madonna and Child” by Giovanni di Ser Giovanni are particularly important (Fig.2). From the staircase visitors can enter the “Salone del Cinquecento”, which is connected to three more rooms: the one with the oldest works, the room of the 17th century paintings and the frescoed room.

Fig.1 The first Floor of the museum and the investigated rooms

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Fig.2 Room8, The “Nativity” by Larciani. Fig.3 Room7, Room of Paintings and Minor Arts 13th - 15th

centuries The experimental measurements and apparatus The experimental measurements were carried out in six of the nine rooms of the first floor of the museum. In particular, following the reference numeration of the museum, rooms 7, 8, 10, 12, 13 and 15 were monitored (Fig.1). Among them, Room7 is the one that had the worst performance. Room7 holds Paintings and fine arts from the 13th to 15th centuries (Fig.3). In this room there are one fan-coil, four 100 watt halogen spotlights and one pedestal lamp with two 36 watt incandescence lamps. It is important to notice that all the windows of the museum are always kept closed and shielded by external and internal shuttering. In addition, due to the low and sporadic presence of visitors, the fan-coil system is mainly turned on during the summer season. This is because of the heat and moisture realised by people. Measurements were performed using a multiple data acquisition device (Babuc-ABC,LSI-Lastem instrument) with a multi-data logger by cordless data acquisition. The acquisition process was carried out every 5 minutes with hourly data and daily data processing. The sensors system is composed of: platinum resistance thermometers PT100, under standards for ambient temperature measurement (range (-20 ÷ +60)°C; accuracy 0.1%; resolution 0.001%); capacitance humidity sensors for Relative Humidity (RH) measurement (range (0 ÷ 100)%; accuracy 2%); one black globe thermometer (located in the Room15, Fig.4) with a 150 mm diameter and an internal temperature sensor PT100 and a probe BST131 (range (-40 ÷ +80)°C; accuracy (0.15 ÷ 0.35)%; 20 minutes response time). The sensors were located so as not to interfere with visitors and museum technicians (Fig.5).

Fig.4 Room 15 - The black globe thermometer location. Fig.5 Room 7 - The sensor that was hung on the wooden beam.

Experimental measurement results Data from June 2009 until May 2010 were collected and processed. The damage caused by incorrect control of the air temperature and RH falls into three broad categories: biological, chemical and mechanical [7,8,13,15,16].The general accepted classes concerning the RH fluctuations and connected risks for preventive conservation of wooden artefacts are deducted by [8]. Fig.6 and 7 provide the air and due-point temperature and relative humidity daily trend during the whole monitoring campaign of Room7. Comparing experimental data of all the rooms, it can be deduced that the mean air temperature values inside all of them

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are higher than the limit suggested by [5,13,15] and the rules provided by Italian Law [8,15,16]; even if the limit value suggested for the RH is always respected (compare Tab.1).

Room 7, experimental data: june09-may2010

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Tmean RH mean Tdue-point mean

Room 7, experimental data: june09-may2010

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Tmin Tmax URmin URmax

Fig.6 Room7, air and due-point temperature, RH – daily values Fig.7 Room7, air temperature, RH – mean and max daily values

Results obtained for the most important room of the museum (Room7) were analysed in detail. From the end of July to about mid September the air temperature was higher than the limit suggested by law. At the end of September 2009 some serious cracks and internal tensions were observed on the wooden panel of the “Madonna and Child” by Giovanni di Ser Giovanni. Consequently, timely interventions for conservation and safety solutions were applied on the surface of the oil painting (Fig.3). This room is the one that presented higher cycles in temperature and RH, responsible for dimensional changes and internal tensions in the wooden panels. Daily cycles in temperature and RH were checked processing the experimental data collected. For wooden artworks the Italian Standard [15] suggests the interval (0-4)% for RH and (0-1.5)°C for air temperature. To study changes of the indoor climatic conditions of Room7, cumulative frequency distribution of temperature and relative humidity were carried out using daily experimental data. Concerning the air temperature, 40% of the experimental data respect the upper limit of 24°C suggested by law, and about 38% respect the lower limit of 19°C; for the RH all experimental data are lower than the upper limit suggested of 65%, and about 43% of data respect the lower limit of 45%. The cumulative frequency distribution of the air temperature and RH cycles were obtained using daily data. The [15] suggests (0-1.5)°C / day of temperature, and (0-4)% / day of RH in daily cycles. The standard [16] suggests different limit range of these parameters in daily cycles: (0-3.2)°C / day for the air temperature and (0-7)% / day for the RH. Taking into account the limit values suggested by [14], for temperature differences about 75% of the data respect the upper limit and for the RH about 38% of data respect the upper limit. Considering the limits suggested by the [16], about 98% of the temperature differences data respect the upper limit and about the 80% of data respect the upper limit suggested for RH. The data exceeding the limits suggested explain the many cracks found in the most important wooden panel of the room. On the other hand, the specific air humidity calculated using experimental daily data provides the minimum value of 4.83 gvapour / kgdry-air at the 16 December, when the mean air temperature is 15.59°C and the mean RH is 42.20%. Similarly the maximum value of specific air humidity is 13.50 gvapour / kgdry-air on 9 September, when the mean air temperature is 30.68°C and the mean RH is 43.8%. The mean value of the specific humidity from all the daily data is 9.86 gvapour / kgdry-air. Temperature and RH ranges suggested as upper and lower values, imply that for the upper limit of 24°C temperature and 65% RH the corresponding specific air humidity must be 9.47 gvapour / kgdry-air. Similarly, for the lower limit of 19°C temperature and 45% RH the corresponding specific humidity must be 6.13 gvapour / kgdry-air. Then, the evaluation of the cumulative frequency of the specific humidity from daily experimental data shows that 42% respect the upper limit and less than 10% respect the lower limit. This trend highlights particular climatic conditions for Room7, that is an average dry indoor climate.

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Tab. 1 The higher hourly experimental values Room

7 8 10 12 13 15 Tmean [°C] 32.70 30.93 31.19 32.20 32.90 32.89 Tmax [°C] 32.40 31.30 31.21 32.26 33.03 32.92 RHmean [%] 64.30 58.10 59.30 69.80 67.60 52.70 RHmax [%] 64.60 58.80 60.20 71.30 71.00 55.10

The method Transient heat transfer through the building envelope is one of the principal components of space cooling/heating loads and energy requirements. Models for transient heat transfer through buildings are important parts of building energy and HVAC system simulation programs. In current building simulation programs such as DOE-2, TRNSYS and ENERGY-PLUS, as well as space cooling load calculations, provided by ASHRAE, the dynamic thermal behaviour data of buildings including thermal response factors, Conduction Transfer Function (CTF) coefficients or periodic response factors are usually calculated by various algorithms, and then utilized in conjunction with weather data to calculate the heat flow through the buildings. The accuracy of the dynamic thermal behaviour of the building envelope directly affects the accuracy of the building load and/or energy calculations. In this study, a method based on the implementation of the current standard UNI EN ISO 13786 [19] concerning the TFM based on the approach of the steady-cyclic thermal transmittances evaluation, was used to estimate the heat transfer to and from a single thermal zone (one of the exhibition rooms) of the museum. This standard concerns the thermal properties of a building component (e.g. a wall) subjected to variable boundary conditions, i.e., variable temperature and/or heat flux on one or both sides, when these time-varying measures are sinusoids at the same frequency. The thermal properties considered are the admittance and transmittance. The thermal admittance relates the sinusoidal heat flow variation with the sinusoidal temperature variations on the same side of the component. The transmittance links the values of the thermal quantities on one side of the component with those at the other side. The standard allows finding these properties for single- and multi-layer components starting, from the thickness, mass density, thermal conductivity, and specific thermal capacity of each layer. In this work this approach was taken one step further and the constraint of a sinusoidal regime was relaxed. Under specific assumptions, that will be discussed in detail later, the generically time-varying known thermodynamic measures (temperature or heat flux) could be decomposed, by means of the Discrete Fourier Transform (DFT), into sinusoidal frequency components. For each frequency component, the standard above could be applied to evaluate the corresponding frequency component of the unknown thermodynamic measures. As the standard assumes the linearity of the model, the superposition principle could be used to find the generic waveform of the unknown thermodynamic measures as the sum of its sinusoidal frequency components. The main assumption in order to perform the DFT is a steady-cyclic condition, i.e. an exactly repeating pattern of excitation lasting for several cycles (ideally an infinite number of cycles, i.e., periodic). If, in a steady-cyclic condition, the thermodynamic variables are sampled at a regular interval (every hour) for one period (a day), then the DFT can be used to decompose the time-course of each thermodynamic variables into a finite sum of sinusoidal components. This means that the proposed method can be used to model a hot summer day, preceded and followed by similarly hot days, or a cold winter day, surrounded by similarly cold days, but it cannot take into account severe, sudden climatic stress. Application Room7 was the case study because of its worst indoor thermal condition. We estimated the heat flow through the envelope of this room considering an HVAC system working to maintain a set-point air temperature of 24°C. The air temperature of the surrounding rooms was assumed as coincident with the experimental value of the hourly air temperature measured in Room7 during the central day of the hottest week of summer 2009. This assumption is physically correct because the cooling plant (fan-coils) was switched off during the period

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considered and it is assumed that only Room7 will be conditioned. The external sun-air temperatures [9] during the same day were taken into account as boundary condition for the external walls. These thermal boundary conditions were considered as vectors of 24 (hourly) measurements representing one period (one day) of a cyclic-stationary regime. Therefore it was possible to apply the DFT decomposition above and study each of the sinusoidal frequency components separately: period infinity, i.e., constant regime, period 24 hours, period 12 hours, and so on, down to period 2 hours, i.e., the shortest allowed for an hourly sampling. For each period (frequency), the values of admittance and transmittance of each wall were found according to the UNI EN ISO 13786 [19] starting from the thermal properties of building materials of the different walls. This allowed the calculation of the heat flow through the building envelope and the temperatures of internal wall surfaces, for each period. Summing the sinusoids corresponding to the different periods, the full 24 hour waveform of the thermodynamic variables of interest could be determined. The proposed method was implemented using free software [10]. Results and discussion The aim of the proposed method is to investigate if the climatic cyclic stress of the external (and consequently indoor) air temperature over time (Fig.8) produces cyclic heat flow variation through the building envelope (Fig.10) that stresses both building and works of art materials, causing their deterioration. In addition, the surface temperature of walls, ceiling and floor was computed (Fig.11). Fig.8 provides the experimentally measured temperature profiles for the southern and western orientation compared to the temperature trend of the internal air temperature of the other rooms. From this figure it can be inferred that external temperature fluctuations are smoothed by the thermal inertia of building. Furthermore, the low and slow cyclic temperature stress certainly enter the ambient even if smoothed, while the incidence of the fast cyclic temperature stress does not affect indoor air temperature variation. Fig.10 presents the heat flow of the different walls of the room.

0 5 10 15 2022

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38Temperature of the regions exchanging heat with the room [C]

Sol-air tem perature Sud

Sol-air tem perature West

Tem perature other room s

Fig.8 Sun-air temperature of the external walls and indoor air temperature – hourly values, central day of the hottest summer week. Results concerning heat transfer through the external walls show the low amplitude of load fluctuations and summer heat loads for all the orientations of the thin external building walls compared to the heavy and massive ones. The heat peak is present at 11 pm, showing that the thermal wave phase shift of 8-10 hours imposed by Italian Standards [14,19] is satisfied. The total heat load of Room7 that corresponds to the plant design thermal peak load to assure a constant internal temperature of 24°C, can be computed by the sum of each heat load component of all the walls at the same time instant, adding also the internal thermal gains due to visitors and lighting equipment. As a matter of fact the heating and cooling loads of the rooms studied were calculated using the method based on the Cooling Load Temperature Differential/Cooling Load Factors (TFM-ASHRAE, [9]). The space air temperature Transfer Functions (heat extraction equations) were used to analyse the effects of the changing room air temperature on convective heat flow from mass walls to room air, taking into account internal gains from occupants (sensible and latent heat; [9]) and internal gains from the present artificial lighting system. Results show that due to the high thermal inertia of the building, the real

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need for the museum rooms is right air change and then correct ventilation and humidity control (the peak thermal load for the all rooms, is 39 kW for winter and 14 kW for summer; Fig.9). This agrees with transient thermal behaviour of Room7 obtained by CTF-DTF method proposed.

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Fig.9 Winter and summer thermal peak loads for all the rooms.

In Fig.11, the surface temperature trend of the internal walls is shown. The analysis of this result is particularly important to decide the correct location of different kind of works of art. As a matter of fact, temperature variations for all the walls except the ceiling are in the range (24.49-25.29)°C. This result agrees with temperature limits suggested [8,15,16] for the preservation and preventive maintenance of works of art like those in Room7. In particular, analysing Fig.11, it can be deduced that the internal surface temperature of the ceiling has the worst fluctuations and higher values over time. This fact is due to the lower thermal capacity and inertia of the ceilings compared to the walls and floors.

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Fig.10 Thermal loads (a) and internal surface temperature (b) of the envelope of Room7 – hourly values of the central day of the hottest summer week. Conclusion The method proposed in this paper is a fundamental tool for defining different scenarios concerning exhibition, works of art and historical building materials maintenance and preservation, museum management, lighting and cooling/heating plant design or refurbishment and also important energy saving solutions. Moreover, the methodological approach proposed is a basic tool for monitoring campaign and non-invasive techniques application planning, oriented both to works of art and the historical building where they are contained. The efficacy and robustness of the proposed method is provided by the possibility of its application without long and expensive experimental data measurements. Moreover, its reliability is due to the fact that it uses algorithms provided by Standards, that take into account computation error evaluation. In addition, it can be implemented using free and open sources software,

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without requiring any particular knowledge of CFD and FEM methods. It can be easily used by museum technicians and not only by engineers and experts. Moreover, the proposed method is both comprehensive and reasonably easy to implement. References

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