Olivier Fudym

A Seminumerical Approach for Heat Diffusion in Heterogeneous Media: One Extension of the Analytical Quadrupole Method

The analytical thermal quadrupole method is suitable for the modeling of multidimensional transient heat diffusion in homogeneous media, especially when applied to multilayered media. Here, we propose a new approach in order to extend the quadrupole frame to heterogeneous media. A seminumerical general solution is proposed for transient heat transfer in finite or semi-infinite media in both axial and radial coordinate systems, when the variation of thermal properties is one-dimensional. The presentation of the method is explained with a 2-D two-layer slab case. Some application examples are then presented from this basic case. The analytical expressions allow deep insight about the physical phenomenon.

Autoregressive algorithms and spatially random flash excitation for 2D non destructive evaluation with infrared cameras

Thermal Non Destructive Evaluation methods to detect cracks perpendicular to the plane of a plate needs to implement in-plane thermal gradients. Instead of a flying spot, a spatially random flash excitation on the front face of a thin plate is here proposed. It allows a very simple and quick experiment. Some processing methods of the resulting infrared images are then discussed and experimental results are shown. The main advantage is to allow the simultaneous process of a huge amount of data, sensitive all over the plate to the thermal conductivity mapping.

Thermophysical properties mapping in semi-infinite longitudinally cracked plates by temperature image processing

Thermophysical properties mapping in a solid plate from transient temperature imaging analysis is widely developed, but most usual methods are based on very restrictive assumptions such as the independence of the pixels (local one-dimensional diffusion in the sample). The challenge envisioned in this study is to take into account the three-dimensional spatial correlation between pixels. Moreover, the estimation of the thermophysical properties field from two-dimensional measurements is an ill-posed problem, and the practical implementation of the estimation is affected by the large amount of data to be processed. A semi-numerical analysis with spatially random front face excitation is proposed here in order to overcome such problems. A theoretical new method is proposed for the detection of cracks laid perpendicular to the excitation surface. The estimation method is implemented from a spatial autoregressive method.

Carbon epoxy composites thermal conductivity at 77 K and 300 K

The in-plane and in-depth thermal conductivities of epoxy-carbon fiber composites have been measured at 77u2009K and 300u2009K. The experimental technique rests on the hot disk method. The two thermal conductivities as well as the thermal contact resistance between the probe and the composite materials are estimated from measurement data and an analytical heat transfer model within the experimental configuration. The results obtained at 77u2009K explained well the ignition test results performed on the composites at 77u2009K with regards to liquid oxygen storage.

Mathematical modelling of temperature profile of volcanic soils affected by an external thermal impact

In this work, the soil temperature at depth was measured in the laboratory, and a mathematical model to fit the temperature profile in volcanic soils classified as Ultisols and Andisols was used. The mathematical model considered the transient heat diffusion equation, and a numerical discrete method was used to solve the equations system. The soil surface was heated for 2500 s and the temperature rose close to 700°C; the soil temperature decreased with depth; the temperature v. time curves showed a constant value when the temperature reached around 100°C, associated with water phase change and related to the water content of soils. The model was corrected by including the heat volumetric formulation. The observed relative errors are close to 10% in all fitted curves with respect to experimental data, showing the quality of the parametrisation chosen in the mathematical model. The fitting curve deviations were reduced when the actual position of thermocouples was considered, showing the sensitivity of the mathematical model. The simplified mathematical transient diffusion model proposed, which considers 2 ranges of thermal conductivity of soils and the surface temperature, was able to describe the experimental temperature profile in volcanic soils with wide differences in mineralogy, organic matter, and moisture contents.

Measurement of thermophysical properties in semi-infinite media by random heating and fractional model identification

Transient hot probe methods are widely used for the measurement of thermal properties in semi-infinite media. In this article, the three-dimensional temperature impulse response of a rectangular probe is analyzed using an analytical solution based on the Green’s functions, such that two characteristic times relative to the asymptotic behaviors of the probe can be calculated. A strategy for the estimation of two uncorrelated properties is deduced from this approach. The identification technique, based on a fractional model approach, is optimized by applying a random input heat flux to the probe. This kind of random heating is shown to provide a frequency content in the range where both the thermal conductivity and thermal effusivity are uncorrelated. Some experimental results obtained with samples with well-known thermal properties are used to validate the proposed method.

APPLICATION OF THE HOT DISK METHOD TO THE THERMOPHYSICAL CHARACTERIZATION OF SOILS

The thermal properties of soils, as thermal conductivity, have been usually determined by different designs of the quasi-permanent hot wire method. In the present paper the hot disk method was used to determine the effective thermal diffusivity (ETD) and thermal conductivity (TC) of soils derived from volcanic materials (one Ultisol and two Andisols) as a function of temperature from 25C to 280C. The volumetric heat capacity was also calculated from ETD and TC estimations. The TC values at 25C ranges from 0.84-0.94 for Andisols to 1.27 Wm-1K-1 for the Ultisol, and are similar to those reported by the hot-wire method. Values decrease down to 0.28-0.32 for Andisols and 0.67 Wm-1K-1 for Ultisol when heating temperature increases from 25C to 280C. The TC increases when soil density or water content increases, and decreases when soil organic matter content increases. The values of the thermal properties depend on water and organic carbon content, and mineralogy of samples

CHARACTERIZATION OF THE POROUS STRUCTURE OF CHILEAN VOLCANIC SOILS BY NITROGEN ADSORPTION AND MERCURY POROSIMETRY

Pore volume, specific surface area (SSA), and total intragranular porosity (TIP) of Chilean soils derived from volcanic materials were studied. Soil samples involving the 0-15 and 15-30 cm depth of virgin and cultivated Collipulli (Ultisol) and Diguillin (Andisol) soils at two particle size fractions (<1 mm and <2 µm) were considered. From mercury porosimetry and N2 adsorption, mainly mesopores (pore diameter, dpore, about 10 nm) were determined for <1 mm Collipulli samples. Diguillin <1 mm soil shows macroporosity with dpore from 70 nm to 7000 nm. The clay fraction of Collipulli has macropores (dpore from 2000 nm to 40000 nm) and mesopores (dpore from 3 nm to 23 nm), while for Diguillin clay-size fraction most of the porosity comes from macropores (dpore from 50 nm to 800 nm). For all samples the SSA linearly correlates with the mesopore volume (r2=0.781; n=16) determined by N2 adsorption, and with the mesopore + macropore volume (r2= 0.771; n=12) when Collipulli <1mm samples are excluded; an inverse relationship between SSA and organic carbon content was found (r2=0.854; n=14). Thus, the SSA defined mainly by mesopores and macropores is probably related to the soil organic matter content. Mesopores and macropores mainly give the TIP, which increases as particle size decreases. No important changes in micropore and macropore volume, and in TIP were seen as result of cultivation. Mesopore volume is more important in samples dominated by kaolinite than in samples dominated by allophane (4 to 20 times). In general the soil pore distribution, its SSA and TIP are related to its mineralogy and organic matter content

Extension of the hot wire method to the characterization of stratified soils with multiple temperature analysis

The aim of this article is to develop a practical device able to estimate a thermal conductivity profile in stratified media such as burned soils in Chile. The classical hot wire method consists of measuring the temperature response of a heat step imposed on a thin cylindrical probe by Joule effect. The main characteristic of the extension of the method consists of analyzing the two-dimensional temperature response of multiple thermocouples equally spaced along the heating cylinder. A semianalytical method (quadrupole method) is then implemented in order to obtain a transfer matrix between the heat flux excitation and the temperature response vectors. Such method is suitable to obtain asymptotic expansions in order to investigate the sensitivity analysis and the estimation strategy. A complete two-dimensional model is used in order to define a time window in which the one-dimensional radial heat transfer assumption is valid. Some experiments and estimation results are presented in a case where the characteristic diffusion times in the radial direction are small compared to the inter-layers diffusion time.