Elena Palomo Del Barrio

A Spectral Method for Low-Dimensional Description of Melting/Solidification Within Shape-Stabilized Phase-Change Materials

This paper aims at an accurate description of the thermal behaviour of shape-stabilized phase change material by a low-dimensional set of ordinary differential equations. The proposed method is based on the use of a suitable proper basis allowing identification of some few dominant components, so that a low-dimensional approximate description of the melting/solidification problem is obtained by projection of the initial infinite-dimensional model on the dominant eigenfunctions of the basis. The basis results from proper orthogonal decomposition of a quadratic function whose meaning is close to that of the thermal field covariance and which is calculated by solving a simple Lyapunov equation. The method provides optimal low-dimensional models in the sense of unitary norms of the approximation error.

Thermal characterization of materials using Karhunen–Loève decomposition techniques – Part I. Orthotropic materials

A new method for reliable thermal characterization of orthotropic, homogeneous materials is proposed. It is based on the use of Karhunen–Loève Decomposition (KLD) techniques in association with infrared thermography experiments or any other kind of experimental device providing dense data in the spatial coordinate. Main problem addressed in this paper is how to deal efficiently with large amount of rather noised experimental data. It is proven that orthogonal properties of KLD eigenfunctions and states allow achieving simple estimates of thermal diffusivities which depend only on the first and the second KLD eigenelements. This means that the 2D KLD approximation of the temperature field provides information enough for estimation purposes. As a result, a significant amplification of the signal/noise ratios is reached. Moreover, we prove that spatially uncorrelated noise has no effect on KLD eigenfunctions, the noise being entirely reported on states (time-dependent projection coefficients). This is particularly interesting because thermal diffusivities estimation involves spatial derivatives of the eigenfunctions calculation. Consequently, the proposed method results in an attractive combination of parsimony and robustness to noise. Indeed, because it does not require analytical solutions of the associated heat conduction problem, the method could be extended to application involving heterogeneous materials. The second part of the paper deals with this extension.

Analysis of crystal growth kinetics in undercooled melts by infrared thermography

A new experimental approach based on infrared thermography is proposed in this paper for studying crystal growth kinetics in undercooled melts. The crystallisation of a thin sample of an undercooled melt at constant bulk temperature is induced by a small crystal seed and the growth of the solid phase is observed using infrared camera. The recorded thermal images allow determining the position of crystallisation front at any time, the velocity of advancement of the front at any point and time, and the temperature at the points of the interface at any time. Contrary to experimental techniques based on optical microscopy or video cameras, infrared thermography provides detailed analysis of the interface temperature which is essential when discussing the temperature dependence of experimentally determined growth rates. The appropriateness of infrared thermography for crystal growth kinetics analysis is illustrated through the experimental analysis of erythritol crystallisation.

Thermal characterization of materials using Karhunen–Loève decomposition techniques – Part II. Heterogeneous materials

A new method for thermal characterization of heterogeneous materials has been proposed. As for homogeneous materials in the first part of the paper, the method is based on the use of Karhunen–Loève decomposition (KLD) techniques in association with infrared thermography experiments or any other experimental device providing dense data in the spatial coordinate. Orthogonal properties of KLD eigenfunctions and states are used for achieving simple estimates of thermal diffusivities. It has been proven that diffusivities can be estimated without explicit knowledge of variables and parameters related to heat exchanges at the interfaces (i.e. thermal conductivities, thermal contact resistances). Indeed, the diffusivities estimates only depend on some few KLD eigenelements. As a result, a significant amplification of the signal/noise ratios is reached. Moreover, it is shown that spatially uncorrelated noise has no effect on KLD eigenfunctions, the noise being entirely reported on states (time-dependent projection coefficients). This is particularly interesting because thermal diffusivities estimates involve spatial derivatives of the eigenfunctions. Consequently, the proposed method results in an attractive combination of parsimony and robustness to noise. The effectiveness of the method is illustrated through some simulated experimental applications.

New Method to Characterize Phase Change Materials

A method for thermodynamic characterization of shape-stabilized PCM based on onesingle sample and one-single experiment has been proposed. The simplicity of the experimental device is comparable to that of the T-History method. However, instead of simple energy balances as in T-History method, a numerical heat transfer model is used to retrieve the whole set of parameters/functions characterizing the PCM from temperature measurements at one-single point within the PCM. An efficient inversion technique has been proposed for that. Its most striking feature is that it allows non-parametric identification of the enthalpy-temperature function in an easy way. Such a function is retrieved by solving a problem of moving sources estimation by inversion of a linear heat conduction model.

Experimental analysis of heterogeneous nucleation in undercooled melts by infrared thermography

A new experimental technique for quantitative analysis of heterogeneous nucleation in undercooled melts is proposed in this paper. It is based on the observation by infrared thermography of the thermal behavior on cooling of a large population of small droplets deposited on a substrate. The method allows analyzing the influence of different parameters such as the size of the droplets, the cooling rate and the wettability of the substrate on the nucleation rate. The fundamentals of the method, the associated experimental set-up, and the mathematics required for data processing are described in the paper. The results of the nucleation analyses carried out using erythritol deposited on different substrates are also presented and discussed.