Development of a simplified and accurate building model based on electrical analogy

doi:10.1016/S0378-7788(02)00019-1

Energy and Buildings

Volume 34, Issue 10, November 2002, Pages 1017-1031

https://doi.org/10.1016/S0378-7788(02)00019-1 Get rights and content

Abstract

The modeling of the thermal behavior of buildings requires using relatively heavy data processing when it comes to reproducing reality accurately. Electrical analogy makes it possible to develop directly accurate and simplified models insofar as the temperatures within the walls are not required.

We present the various stages, which led us to propose the global analogical model of the building. Initially, we have studied how to transform a multi-layer wall into a three resistances and four capacities model (3R4C). We will compare this model with other electrical models thanks to a time and frequency analysis. Then, we will deal with the principle of aggregation of several walls. In order to facilitate the iterative resolutions related to numerical simulations, the lumped model integrates a heating floor.

Introduction

The interest of the thermal behavior modeling of buildings need not be demonstrated. The fact that summer thermal comfort is now taken into account in the new French thermal regulation [1] through a transient calculation is the best evidence. Building model is in this case very simplified.

The simplified models reproducing reality accurately are generally obtained after reduction of detailed models. Insofar as temperatures within the walls are not necessary, it is possible to obtain an accurate and simplified model directly. The advantage of this approach is to limit both calculations and the number of parameters to be defined by the user. We applied this approach to the development of an analogical building model including a heating floor.

We are interested, at first, in one of the most delicate problems: conduction in walls. We represent the walls with a three resistances and four capacities model (3R4C) which we compare with a reference model and two other simplified models (3R2C and 1R2C). The convective exchanges (the zone is supposed to be thermally homogeneous) and long wave (LW) exchanges are dealt with a linear way (model 1R).

The heating floor is modeled with the will to simplify. The water loop is represented by means of model 2R1C. Finally, taking into account all the whole of heat exchanges within the building leads us to present the global analogical model of the building. This model was integrated in the simulation software TRNSYS.

Section snippets

Analogical modeling of heat transfers

Electrical analogy [2], [3] draws a parallel between heat transfers and electrical currents. The thermal balance is equivalent to the electrical current conservation equation at the corresponding node.

Development of a building model based on electrical analogy

Here are the various stages which led us to define the global model. A great part of this study relates to the simplified and accurate modeling of the conductive exchanges. A multi-layer wall is modeled with a 3R4C model. We show how to aggregate several models. The global model integrates a heating floor in order to limit numerical problems during simulations.

Conclusion

We highlighted the interest of electrical analogy in developing directly accurate simplified models. The 3R4C model is able to reproduce the conductive transfers if the temperature distribution within the wall is not necessary. The domain of validity of this model, in the case studied, corresponds to periods of internal inputs higher than 3 h.

We also approached the principle of aggregation of several walls in only one 3R4C model. The validity of this approach obviously depends on the similarity

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View full text

Development of a simplified and accurate building model based on electrical analogy

Abstract

Introduction

Section snippets

Analogical modeling of heat transfers

Development of a building model based on electrical analogy

Conclusion

Building and Environment

Franklin Institute Journal

International Journal of Thermal Sciences

La modélisation thermique par la méthode nodale: ses principes, ses succès et ses limites

Revue Générale de Thermique

Review of correlations for convective heat transfer from flat surfaces in air

Chaleur et Climats

Radiation analysis by the network method

ASME Transactions

Etude comparative de différentes méthodes de modélisation des échanges radiatifs de courtes et grandes longueurs d’onde dans une cellule d’habitation

Annales de l’Institut Technique du Bâtiment et des travaux publics