Analysis of building inertia using a modal description
Résumé
The cooling loads of a building and the comfort its induces, depend on the local micro climate, the building, ist occupancy and its shape. The thermophysical and geometrical properties of a building can be described with static and dynamic parameters. These parameters represent the filter effect a building has between the environment and the occupant. The static parameters give an insight of the thermal state of a building in steady state conditions, the climate driving forces being constant. The other parameters are the dynamic ones as they represent the dynamic response of a building to variable driving forces. The modal form of the model for the thermal behaviour enables one to distinguish clearly the intrinsic dynamic parameters which are eigen modes and their corresponding eigenvalue. These parameters are independant of the nature of the outputs and inputs which are applied to the building. the thermal inertia of a building is therefore the physical entity defined as the set of all the eigenmodes and eigenvalues. The number of eigen modes in not a propoerty of the building; this number is related to the precision of the model (it is of the order of the nodes of the grid for finite difference method and is strictly infinite for a model continuous in space). However, simplified assumptions had to be done when elaborating physical and mathematical models. A coherent level of precision with these assumptions will make the best of an important reduction of the eigenmodes describing the interia. As a conslusion, the modal method allows one to strictly define the thermal inertia and it also provides tools for its analysis. Such an analysis will be roughly performed on a particulur example described later.