Validation of a lumped RC model for thermal simulation of a double skin natural and mechanical ventilated test cell
Introduction
The last two decades have seen an increased public awareness of the environmental and operational costs of building energy consumption. As a result, most current building thermal codes impose upper limits to the predicted annual energy demand for heating, ventilation and air conditioning systems (HVAC). In the building design phase these predictions are obtained using thermal simulation models with variable levels of detail and approximations. The most complex buildings require models with several thermal zones and, in some cases, tri-dimensional computational fluid dynamics simulations (CFD). For small buildings with simple indoor climate control systems, such as single-family homes and apartments, there is an increase in use of single thermal zone simulation models. In response to this increased use, the research community is continuously working on improved models with all levels of complexity.
The main challenges of building thermal simulation are in modelling of room airflow and heat transfer in building elements with high thermal mass (floor, walls, etc.). In the majority of simple thermal models room air is considered perfectly mixed and represented as a single thermal node that is connected to all room internal surfaces via thermal resistances [1]. Heat transfer in building elements with high thermal mass can be modelled using variable levels of detail, ranging from detailed finite difference methods to conduction transfer functions (CTF) [2] or, in the simplest approach thermal resistances connected to a thermal capacitance. The thermal resistance and capacitance used in the models have physical meaning and can be calculated approximately from the thermal properties of the building elements. Fig. 1 shows the combination of a perfectly mixed room air approach with a resistance capacitance model for the high thermal mass elements, this approach is known as an RC model. These models are typically labeled according to the number of resistances and thermal capacities used. EN ISO 13790 standard [3], adopted by many European countries as the reference methodology to assess overheating in buildings during summer and calculate building energy demand, uses a single capacitance that represents all high thermal mass elements and five thermal resistances (making it a 5R1C model).
The widespread use of the 5R1C model makes it a preferred target for further development. This paper presents an extension of this model for application to double skin façade (DSF) buildings. The proposed model is validated using a set of detailed thermal measurements obtained in a free-running double skin test cell [4]. The next section presents a review of existing RC models and model validation studies. The following section presents the model methodology followed by the presentation of free-running test cell measurements. The final section presents the results of the model validation.
Section snippets
Literature review
One category of RC models – the lumped parameter construction element models – approximates each building element with high thermal mass (e.g. walls, roofs, floors) by one or more capacitances (Fig. 2). A first-order representation refers to a single capacitance by each building element, a second-order refers to two capacitances. Therefore, the whole room model can have several capacitances and their number increases for higher order representations. It is noteworthy that thermal capacitances
The single thermal zone model
The RC model for a single thermal zone described in EN ISO 13790 standard has five resistances and one capacitance (5R1C). The resistances (or the inverse, the conductances) connect the following temperature nodes: supply air, external air, internal air, ‘star’ and mass. The ‘star’ temperature node results from the delta-star simplification, taking values in the range of internal air, light and heavy elements surface temperatures, although it does not have a specific physical meaning. The
Room and sunspaces thermal envelope
The heavy elements of DSF test cell, with a total area of 58.04 m2, are the external walls, the external roof and the ground floor (Table 2, Table 3). The light elements are the two double glazed windows and vents, that in this experiment are kept closed (Tables 2 and 3). The internal wall partition is also assumed as a light thermal mass element (negligible mass) due to its small area compared to the total heavy elements area. The ratio between total surface area and floor area (At/Af) is
Error parameters
Assuming yi as the measured air temperature at time-step i and , the corresponding model calculated value, for a total of n time-steps, the following error parameters expressed in temperature units or percentage, by normalisation, considering as normalised factor the measured absolute temperature difference defined by ymax − ymin, with:
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Mean absolute error (MAE) [°C] and normalised mean absolute error (NMAE) [%]
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Mean bias (MB) [°C]
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Conclusions
This paper presented a successful extension of the 5R1C model used in EN ISO 13790 standard that allows for its application to the prediction of the internal air temperature of free-running buildings with double skin facades. The extension consists in an increased number of thermal resistances used to model the double skin façade zone. The predicted room and façade sunspace air temperatures were compared with Energy Plus simulations and detailed measurements performed in a test cell located in
Acknowledgments
The authors acknowledge the support from Fundação Calouste Gulbenkian, through Ph.D. Grant no. 126724.
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