1 THERMAL RESPONSE OF THERMALLY ACTIVATED BUILDING SYSTEMS (TABS) IN OFFICE BUILDINGS M. Sourbron, M. Baelmans, L. Helsen K.U.Leuven, Mechanical Engineering Department, Division Applied Mechanics and Energy Conversion Phone: +32 (0)16 32 25 11 ABSTRACT The thermal resistance and capacity of Thermally Activated Building Systems (TABS) influence the HVAC control strategy. To correctly determine this strategy and its parameter settings, it is important to know the dynamic behaviour of the TABS being a thermal energy storage in an office building zone and their response to input signals.

In this paper the dominant periods of the input signals to the office building are determined to be in the range of 2.2 h to 168 h and the reaction of the TABS floors and ceilings to these inputs is examined. It is concluded that the thermal properties highly influence the response of the TABS and therefore the controllability. Moreover, relative errors in the estimation of particular model parameters, such as the natural convection heat transfer coefficient at the TABS surfaces, result in relative errors of the same order for the calculated heat flows. 1. INTRODUCTION In thermally activated building systems (TABS) water tubes are integrated in the concrete floors or ceilings of a building, to provide heating and cooling to the different building zones.

Thus, the large thermal capacity of the building mass is actively used and integrated in the HVAC system. The large activated area results in required water temperatures which are relatively low for heating (< 30 °C) and relatively high for cooling (> 15 °C). This increases HVAC system efficiencies and enables the use of low exergy systems such as ground coupled heat pump systems. The buffering capacity of the TABS also spreads out load peaks, resulting in a lower installed power needed for heat and cold production systems. Though this large thermal capacity is advantageous, it inherently hampers an adequate control when excessive and unexpected heating or cooling loads take place.

After all, heat exchange between the TABS and the building zone is determined by a combined heat transfer coefficient h (h = f(hconvective,hradiative)) and the temperature difference ∆T between TABS surface and air. Since h.∆T is small compared to load peaks in the building zone, these peaks will result in a rise of the zone air temperature, before they are absorbed by the TABS. The TABS surface temperature can be controlled by changing the water temperature in the tubes, but with a large time delay, caused by the high thermal capacity in between. Therefore, in order to elaborate an optimal control of the heat and cold storage, it is necessary to assess all time constants present in the system.

Furthermore, as time scales of heat loads might be well below the ones of TABS, model based predictive control (MPC) seems to be indispensable. Therefore, it is crucial to know to which extent available simulation models are capable to predict the thermal behaviour.

Although no analytical solution in the time domain exists for the two dimensional heat flow in TABS [1, 2], in the frequency domain it is possible to analytically solve Fourier’s heat conduction equation. Therefore, in this paper, resistance-capacitance (RC) models are used in the frequency domain as an approach to model the dynamic thermal behaviour of the building


2 zone equipped with TABS. Hereby, thermal performance is characterised by using the definition of admittance A and transmittance σ, which are frequency based transfer functions for heat flow Qi versus temperature Ti: i i i Q A T = and i ij j Q T σ = .

A sinusoidal input (Ti) results in a sinusoidal output (Qi) with the same frequency but with different amplitude and phase. The thermal capacity of the TABS will at least partially block the heat flow from the zone to the water tubes for high frequency input. The difference between admittance at the TABS surface and transmittance from surface to water tubes is a measure for the buffering function of the TABS.

In this paper, the dynamic behaviour of the TABS is investigated by means of a typical office building zone with a TABS ceiling and a floor consisting of TABS with raised floor. RC- models, validated with frequency response techniques, for both building zone [4-6] and TABS [2, 3, 7] are combined to model the building zone with TABS. Input signals are the outdoor temperature Tout, the solar radiation Qsol and the internal gains Qint. By means of the Fourier transform, the dominant frequencies in these signals are determined. The output signal is the building zone temperature Tzone. The control parameter is the water temperature Tw in the TABS.

The validity range of the RC-models, as defined by other researchers [1, 2, 4, 5], is compared to the frequency range of input signals influencing the zone temperature. The time constants and the frequency response of the TABS determine the usefulness of TABS as a controlled thermal storage in the building zone. The building zone temperature is affected when input signals have a higher frequency than the one related to the time constant of the TABS. As a consequence, cooling and heating installations characterized by smaller time constants (such as air-based systems) may be needed in combination with TABS to guarantee thermal comfort in the building zone at all times.

In this paper, TABS are studied without the presence of complementary systems. A sensitivity analysis of the TABS thickness and the natural convection heat transfer coefficient will reveal the influence of both parameters on the dynamic thermal behaviour of the TABS.

Finally, in the conclusion, a link is made between the frequency response of the TABS model and the behaviour of the TABS as a controller of the zone temperature. 2. INVESTIGATED OFFICE BUILDING ZONE An internal office zone is investigated with a TABS-ceiling and a raised floor combined with TABS (Figure 1). It is assumed that the TABS primarily works from the ceiling. The thermal resistance of the raised floor is such that the upward heat flow from the TABS to the zone is strongly reduced. Figure 1 also shows the corresponding RC model.

The outside wall consists of a brick layer (10 cm), a cavity, an insulation layer (10 cm) and heavyweight concrete (10 cm).

TABS have a thickness of 20 cm with the pipes in the centre. The raised floor is 20 cm high and tiles are made of gypsum related material. The thermal conditions in a building zone are mainly influenced by three signals: outdoor temperature Tout, solar radiation Qsol through the windows and internal gains Qint. Internal gains are composed of heat transmitted by people, appliances and lighting. The windows are assumed to have no thermal capacity and consequently don’t introduce additional time constants in the model.


3 Figure 1 : View inside the building with TABS and schematic presentation of the corresponding RC-model The RC representation of the TABS as validated by Weber et al. [3] and Kochenz and Lehmann [7] is used here to model the TABS with raised floor. Weber [2] has optimized the star RC-network for an asymmetrical TABS floor. Admittance at the water tube in the TABS yields very good results down to periods of 40 min. Transmittance from the water tube to the TABS surface can show a deviation up to 4% in steady state and shows a deviation of more than 10% at periods smaller than 3.5 h [3]. As demonstrated by Weber et al.

[3], adding an extra RC-link for the raised floor, provides a good representation to obtain accurate temperatures inside the concrete floor.

For walls Fraisse [5] reports domains of validity for different RC representations. Modelling the wall with a 3R4C network is a good compromise for both external and internal inputs to the wall. The model is not valid for periods smaller than 3.1 h. The latter will only cause problems for the response to internal gains, where periods as small as 2.2 h appear. However, the amplitude of this part of the input signal is low. In this case, as in many buildings, thermal capacities are located at the inner and outer layer of the wall (concrete and brick) separated by insulation with a high thermal resistance and low thermal capacity.

3. FREQUENCY RANGE OF INPUT SIGNALS Because the response of the building zone is dependent on the frequency of the input signal, it is important to know which frequencies are dominant in the input signals. In this section, the dominant frequencies occurring in the three input signals to the building zone are identified. For the analysis of the weather data the typical meteorological file for Uccle, Belgium, as provided by TRNSYS [10], is used. This analysis based on a typical meteorological year yields results comparable to the analysis of one recorded year by Keller [11]. Outdoor temperature For the analysis of the outdoor temperature it is assumed that hourly values are available, which is the case for most meteorological data.

This monitoring frequency (1/Ts with Ts the sample period) determines the maximum frequency 1 1 max 1 1 0.5 12 2. 2 f h day Ts h − − = for which the Fourier analysis will give a solution. Smaller frequencies can not be detected.


4 Analysing these data by the fast Fourier transformation (Matlab tool fft) provides the dominant periods as shown in Figure 2. Periods with amplitude smaller than 0.1°C are considered as noise and are filtered out for the sake of clarity. The average outdoor temperature is 9.73°C and important periods are at 365 days, at 1 day and ½ day. Figure 2 : Outdoor temperature profile and frequency spectrum for Uccle (Belgium) Solar radiation on a vertical plane Without the influence of atmospheric phenomena, such as clouds, mist or turbid air, solar radiation is no more than a cut-off cosine curve [11].

The height of the cut-off is determined by the geographical location and the time of the year. In reality, solar radiation is evidently highly influenced by these atmospheric conditions. Particularly in winter cloudiness will cause larger frequencies to be apparent in the frequency spectrum of solar radiation. Figure 3 : Solar radiation on a south facing vertical plane for Uccle (Belgium) For solar radiation on a vertical plane, the peaks in the frequency spectrum are at periods of 24 h, 12 h, 8 h, 6 h and 4.8 h.

Internal gains Internal gains are caused by heat emitted by people working in the zone, by appliances such as computers, printers or other office equipment and by lighting in the zone. In building energy calculations, default values are often used, as for example provided by ASHRAE [12]. People emit 120 W/person, lighting 15 W/m² and for appliances 150 W/person during occupation hours and 10 W/person during non-occupation hours is used. Combined with office hours from 8 h-12 h and 13 h-18 h, this yields a profile as shown in Figure 4. The largest period occurring in the signal is at 7 days (168h), the second dominant period is at 3.5 days (84 h).

In the range below 24 h there are a lot of periods occurring in the signal : 24 h, 8 h and 6 h. The smallest occurring period is around 2 h.


5 Figure 4 : Time and frequency plot of typical internal gains in an office environment 4. FREQUENCY RESPONSE OF THE BUILDING ELEMENT RC-MODELS The building zone with TABS has two important thermal capacities, namely the TABS ceiling and the outer wall. Heat exchange between the zone and the TABS floor is blocked by the raised floor. Through frequency analysis, this section presents the interaction between the occurring input signals and these thermal capacities. In section 2, the errors determined for specific frequency ranges for the star-network RC-model to simulate TABS and for the wall RC model, are reported.

These errors should be taken into account when interpreting the response of the building elements to inputs with frequencies in that range. Frequency response of the TABS The frequency analysis of the TABS investigates the admittance and the transmittance of a sinusoidal input at the TABS surface. Input signals directly influencing the TABS are the internal gains (Qint) and the solar radiation (Qsol). Therefore, the periods range of interest is, as defined in section 4: 2.2 h – 168 h.

Figure 5 shows the admittance ( surf surf q T ) and the transmittance ( pipes surf q T ) for a case with 10 cm of concrete between pipes and lower TABS surface (TABS total thickness is 20 cm). The trends presented in Figure 5 are similar to the ones presented by Weber et al. [2] . Both internal gains and solar radiation will induce heat transfer to the water tubes in the TABS, but at small periods thermal energy is buffered to a large extent. 0.1 0.2 0.3 0.4 0.5 0.6 1 10 100 1000 Period (Hour) Admittance; Transmittance (W/m²K) Qint Qsol Transmit to w Admit Heat storage Transmit_tot Figure 5 : Heat flow at the TABS lower surface (Admit), at the water tubes (Transmit to w) and the total heat flow at the water tubes + at the upper surface (Transmit_tot) in response to a temperature variation at the lower surface


6 The difference between the transmittance curve and the admittance curve is proportional to the amount of energy that is stored in the TABS but not transmitted to the water tubes and thus not ‘seen’ by the HVAC system. This difference (‘Heat storage’ arrow) is the amplitude of the heat storage and heat release caused by the sinusoidal temperature change characterized by a certain period at the TABS surface. In time domain, the integral of this heat storage sine is the thermal energy storage/release as a function of time per unit area and per degree temperature difference.

Conversely, the ‘Heat storage’ arrow also quantifies the controllability of the TABS.

Varying the water temperature in the tubes with frequencies at which the transmittance tends towards zero is futile. Changing between heating and cooling with frequencies at which the difference between admittance and transmittance is large, means that energy is exchanged between the heating and the cooling system without a useful effect on the zone temperature. Frequency response of the outer wall Figure 6 shows the transmittance of the outer wall with a temperature variation at the outer wall surface. The insulation layer causes a low transmittance for all periods considered. The range of small periods associated with Qsol is completely blocked by the wall.

The influence of Qsol and Tout through the wall to the zone temperature is thus relatively small. 0.05 0.1 0.15 0.2 0.25 0.3 1 10 100 1000 Period (Hour) Transmittance (W/m²K) Tout Qsol Transmit Figure 6 : Heat flow at the inner wall surface in response to a temperature variation at the outer surface 5. INFLUENCE OF MODEL PARAMETERS ON THE FREQUENCY RESPONSE TO INPUT SIGNALS The frequency response of the TABS model is influenced by physical parameters, such as the TABS thermal capacity and the combined heat transfer coefficient h at the TABS surface. The introduction of this paper already identified h as the driving force in the heat transfer mechanism between TABS and the building zone.

Thermal capacity First, the influence of the thermal capacity of TABS on the frequency response of the model is investigated. To this end, the TABS thickness is varied from 20 cm to 30 cm and 40 cm (Figure 7). While the admittance is hardly affected by the change in thickness (which lies within the expectations), the transmittance is largely influenced. For the smallest periods of the input signals, the transmittance for the 40 cm TABS is reduced with 89% compared to the 20 cm TABS. For the large periods, the influence of the thermal capacity on the frequency response disappears gradually and only a 6% reduction is observed.


7 0.1 0.2 0.3 0.4 0.5 0.6 1 10 100 1000 Period (Hour) Admittance; Transmittance (W/m²K) Qint Qsol Admit Transmit -89% -78% -50% -6% Figure 7 : Heat flow at the TABS lower surface (Admit) and at the water tubes (Transmit) in response to a temperature variation at the surface for 3 concrete layer thicknesses (triangle : 40 cm, square : 30 cm and circle : 20 cm thickness) Natural convection heat transfer coefficient hc The combined heat transfer coefficient h consists of a convective part hc and a radiative part hr. Correct determination of hc has been the subject of many scientific contributions.

Khalifa [9] presented a review on this subject and concluded that values vary widely. Figure 8 shows the frequency response for two extreme values. For hc = 0.5 W/m²K (heated surface facing downwards) and hc = 4.4 W/m²K (cooled surface facing downwards) [8], the magnitude of the transmittance changes from 0.43 W/m²K to 3.22 W/m²K or a factor 7.5. A 10% relative change of hc = 0.5 W/m²K results in a 9.7% change in amplitude, while a relative change of 10% to hc = 4.4 W/m²K results in a 7.5% change in amplitude.

On the other hand, the two frequency responses plotted as the magnitude relative to the value at large periods show the same trend : for every period an 87 to 88 % difference for the two values of hc is observed. This means that, if the value of hc is wrongly estimated in the building zone model, the trend of the model response will not indicate any fault occurring, but the amplitude and thus the calculated energy flows in the time domain will show a significant deviation with reality. It should be concluded that the RC-model used to describe the dynamic behaviour of the TABS thermal storage is very sensitive to the choice of the natural convection heat transfer coefficient.

0.5 1 1.5 2 2.5 3 3.5 1 10 100 1000 Period (Hour) Transmittance (W/m²K) Qint Qsol Transmit (h c =0.5W/m²K) Transmit (h c =4.4W/m²K) -88% -88% -87% -87% Figure 8 : Heat flow at the water tubes (Transmit) in response to a temperature variation at the surface for two values of the natural convection heat transfer coefficient.


8 6. CONCLUSIONS Applying TABS in an office building, introduces a large thermal capacity in the control scheme of an HVAC installation. Since TABS behave differently from a standard water storage tank regarding the injection and extraction of heat or cold, it is important to characterize its dynamic behaviour, with respect to realistic input signals.

The frequency response plot of a validated RC model for TABS shows that due to the high thermal capacity, heat loads characterized by small periods (periods < 5 h to 10 h) will not result in a significant heat flow to the HVAC system. The difference between admittance and transmittance in the frequency response plot is a measure for the buffering function of the TABS and is high for small periods. As such, it is concluded that TABS control in time intervals similar to the fastest varying input signals is of no use. However, altering the TABS thermal capacity shifts the frequency response and thus the controllability.

On the other hand, the choice of model parameters has a large impact on the amplitude of the model output. Especially, the natural convection heat transfer coefficient hc at the surface of the TABS, which is a parameter that is hard to identify in reality, highly influences the absolute value of the model output. An error in the estimation of hc results in an error of the same order for the calculated heat flows. This sensitivity might hamper the introduction of robust, model based control strategies for TABS.

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