Modelling of Hybrid Building Components with R-c Networks in Macro Elements

This paper presents an effective method for thermal analysis of special building constructions, hybrid systems, and the way in which the resulting mathematical models can be implemented in a commonly used dynamic computer simulation program. The advantage of this method is the fact that only a limited number of nodes are required to obtain reliable results for the simulation. The modelling method is described in detail and the work of two different case studies is presented. Research has been conducted on this method (Jóhannesson 1981, Mao 1997, Akander 2000), and it has been expanded and used on a different class of constructions, hybrid systems. It is essential to estimate the thermal behaviour of the whole building as a system and to open up the research knowledge in this field to a broader audience of building designers, architects and engineers. The presented method could be one step further towards this goal. INTRODUCTION In the past decades, considerable efforts have been made to reduce energy consumption in buildings, for example, by constructing heavily thermally insulated buildings, by improving the quality of window glazing and by using the thermal storage of the construction itself. In order to make the energy use in buildings even more efficient, new low temperature heating and cooling systems are required. A promising solution is the development of hybrid systems. Hybrid systems are building components or a combination of different building components that utilise the heat transfer and heat capacity properties of the whole construction to achieve room conditioning. Sometimes, they are also denoted as thermally activated building components. Embedded pipes in concrete slabs or hollow core slabs, where the entire slab construction is tempered to heat or cool the room, are typical examples. The heat transfer from all of these systems to the rooms takes place mainly via radiation. The room surfaces are kept warm and at a fairly uniform temperature, thereby, a good level of thermal comfort can be provided. Draught from air movements around, e.g. convectors, or burning of dust will not occur. For the dynamic simulation of such a system, several heat transfer mechanisms are involved and have to be treated simultaneously. To carry out the implementation of hybrid building components in buildings, safe, efficient and reliable tools are needed to analyse their thermal performance. The often commonly used one-dimensional or steady state models are not sufficient in estimating the performance of those systems. Existing stand-alonemodels depicting hybrid systems are not satisfactory for design purposes. More dimensional dynamic simulation models, including all possible heat transfer effects, have to be implemented in an effective way into known simulation programs. Efficient models for overall system studies with simulations are needed. Some attention has been paid to the modelling of hybrid systems, especially during the Solar Heating and Cooling Programme and the Energy Conservation in Buildings and Community Service Programme performed by the International Energy Agency (Jørgensen 1984, Scartezzini et al 1987). Also, some generalised design-methods for hybrid systems have been developed (Rittelmann et al 1983, Evans et al 1985, Fort 1989) and a basis for further research has been given. THE MACRO ELEMENT MODELLING METHOD (MEM) A method has been developed for mathematical modelling, for the analysis of thermal conditions of a building component and for the description of multidimensional heat conduction. In this new method, the analysis procedure for wall and ceiling constructions has been extended to include a mass flow inside the construction. Therefore, it is possible to model even hybrid building components with optimised resistorcapacitor (RC) network with a limited number of macro elements. This MEM approach can be divided into the following three basic steps: analysis, transformation and implementation. Analysis of the system The analysis of the solid construction parts is done in the frequency domain and can be conducted in an analytical way. The system responses are directly calculated by analytical methods or, if this is not possible, the construction is implemented in a finite difference program to calculate the system responses. For the analysis, all possible simplifications (e.g. symmetry) are made. The analysis result of the heat transfer balance between two arbitrary isothermals 0 and 1, for example, the surfaces on either side of a multi-layer wall, is in the form of a frequency dependent matrix (Carslaw, Jaeger 1959):