APPLYING THE MODAL METHOD TO THERMAL MODELLING
The modal method is nowadays an improved method to analyse and solve thermal exchange equations in a system. This method applies to linear systems, offers powerful analysis tools, and allows fast dynamic simulations. We illustrate here the state of the art of this method on three application examples in various fields.
A building is a typical example of a complex thermal system. This complexity leads to a simplification of the modal representation. The order of the model can be reduced by keeping only the dominant modes pointed out by the spectra. This leads to fast and accurate simulations. The modal dominance is one of the basic properties on which the modal analysis relies.
By decoupling spatial and time problem, modal method reduces the complexity linked to multidimensionnal aspect of thermal behaviour. The evolution over long times, for example, is the most significant one of the transient period of a cooling phenomena and is well described by keeping the first eigenmode: in that case, a single temporal scalar function is sufficient to describe this evolution.
When a thermal system includes energy transport, its eigenelements may be complex valued. This case is illustrated on a cooling water loop example. It is found that, for some particular values of the flux variation frequency, the system response is pseudo resonant. These values are given by the imaginary parts of the complex eigenvalues.
With a modal formulation, a thermal analysis doesn't need systematically a temporal simulation because modal tools are able to give directly a pertinent information. Nevertheless, due to its reduction possibilities, the modal method is also an accurate and fast way to make a dynamic simulation.