W. Maréchal. PhD Thesis, École Doctorale Sciences Exactes et leurs Applications (Pau, Pyrénées Atlantiques), April 24th 2014.
Absract: With the development of intermittent sources of energy and the depletion of fossil fuels, the subject of energy storage is becoming an important topic. One of the studied options is tthe latent hermal storage using of phase change materials (PCM). One application for this type of energy storage is to improve the thermal insulation in buildings. To make the best use of these materials it is necessary to be able to predict their energy behavior. This requires a precise knowledge of their thermophysical properties, first of all of the specific enthalpy function of the material . Currently, it is often suggested to approximate the enthalpy by the direct integration of the thermograms obtained through calorimetry experiments (notion of "equivalent" calorific capacity). This approach is false because thermograms are only a time related representation of complex phenomena where thermal transfers arise in the cell of the calorimeter acting with the thermophysical properties. As a result, for example, the shape of thermograms depends on the heating rate and on the mass of the sample, which is not the case for the enthalpy of the PCM, which depends, at constant pressure, only on the temperature or on the concentration (for the solutions). We propose to compare the results given by a of a numerical direct model with experimental thermograms. The main objective in this thesis is then to use this direct model in an inverse method in order to identify the parameters of the equation of state, which enables us to calculate the specific enthalpy . First of all, the detail of an enthalpy model is presented, and then validated by comparison with experiments, allowing us to reconstruct the thermograms of pure substances or of salt solutions, of which the enthalpies are known. A study of the influence of the various parameters ( , , , .,..) on the shape of thermograms is also undertaken in order to deduce their sensibilities. A reduced model is then developed in order to reduce the calculating time of the direct model. This optimized model allows the use of inverse methods with acceptable durations. Several inverses algorithms are then presented: Levenberg-Marquardt, evolutionary and Simplex which has proved to be the fastest). We shall then apply this algorithm to identify, from calorimetric experiments, the enthalpy function of pure substances or of salt solutions. The results that we obtain show that it is possible to identify a function independent of the heating rate and of the mass, which validates the method. An analysis of the various sources of errors in the identification process and of their influences on the result allows us to estimate the quality of the enthalpy function that we identify.