Utilisation de modèles d'identification non entiers pour la résolution de problèmes inverses en conduction

Heat flux estimation through inverted non-integer identification models. A model of non-integer order that reproduced the transient thermal behaviour of a system is identified. This model is expressed as a linear relationship between the fractionnal derivates of the temperature at a point of the medium and those of the solicitation applied on the system. Using recursive form of the derivates lead to identify the unknows of the model applying the linear least square method from experimental data. The application concerned a semi-infinite medium submited to a single heat flux on its surface. Among the applications of this approach, the identified model is used in an inverse technique to estimate the heat flux applied on the medium.     

Un modèle simple de la pénétration couplée de chaleur et de matière dans l'absorption gaz-liquide en film ruisselant laminaire

In this paper we present a simple model based on the coupled penetration of heat and mass fronts for the study of the absorption kinetics of vapor in a concentrated salt solution falling in laminar flow down an adiabatic wall. Though this model is very simple, it permits a concrete and intuitive comprehension of the numerical integration of differential equations. The forecasts of this model, in the case of the absorption of water vapor in the lithium bromide solution, are presented and compared to the results of the numerical solution.     

Modèles de transferts thermiques lors de la fusion d'une solution binaire dispersée

Heat transfer models during the melting of a dispersed binary solution. In this paper, we present a model for heat transfers occurring during the melting of crystallized droplets of a binary solution dispersed within an oil. This model takes into account the heat conduction within the emulsion associated with a heat source (sink) due to the eutectic melting of droplets followed by the progressive melting. The model has been applied to the differential scanning calorimetry in the case of aqueous solutions of ammonium chloride dispersed in a motor oil. The investigated cell containing the emulsion is a cylinder a few mm ³ in volume. By simulation, we could replicate the shape of the experimental thermogramms. The validation of the model permits determining some parameters which are experimentally inaccessible due to the small size of the cell, like the space–time evolution of the temperature inside the DSC sample or the concentration of every droplet as well as the melted proportion.     

Estimation des propriétés thermiques à l'échelle millimétrique par méthodes périodiques: Résolution du problème direct et du problème inverse

Estimation of thermal properties by periodic methods: direct problem and inverse problem solving. This article presents two processes of thermal diffusivity measurement for homogeneous material. The experimental bench uses a periodic method dedicated to millimeter scale study. Simulation of this experimental method is studied in detail. The case of a homogeneous material of unknown diffusivity to be measured is studied. Sensitivity coefficient and calculus of Cramer–Rao bounds (BCR) prove the good conditioning of diffusivity estimation and illustrate the action of thermal losses. Simulations of Monte Carlo compare performances of least squares estimator to optimal performances defined by the BCR. Two experimental processes are validated by a study of the iron ARMCO chosen as material of reference.     

Représentation non locale d'un milieu hétérogène en diffusion pure

For a one-dimensional diffusive transfer through a spatially periodic heterogeneous medium, the quadrupoles method allows to obtain the exact non-local (in time) equation describing the transfer. The case of reversible (that is to say when input and output can be permuted) and non-reversible media is examined separately. Some examples are treated for illustration: degenerated media (made of pure resistances or capacitances) or real media. The obtained equation cannot be reduced to the hyperbolic Cattaneo–Vernotte equation, which is unable to describe diffusive transfer through heterogeneous media.     

Simulation numérique des jets turbulents subsoniques à masse volumique variable par le modèle k–ε

A numerical investigation is reported for round free turbulent non-isothermal binary mixing incompressible jets discharging into a quiescent atmosphere. The standard k–ε model is used. The standard closure schemes in Favre averaged variables are first introduced. The parabolic numerical simulation method of Patankar and Spalding [Heat and Mass Transfer in Boundary Layer, Intertext Books, London, 1970] is followed. The numerical simulations show a satisfactory agreement with the experimental results of Chassaing [Mélange turbulent de gaz inertes dans un jet de tube libre, Thèse d'état, INPT, 1979], Birch et al. [J. Fluid Mech. 88 (3) (1978) 431–449] and Panchapakesan et Lumley [J. Fluid Mech. 246 (1993) 197–223, 225–247]. The developed numerical code is used to study the sensitivity of turbulent characteristics to the density ratio between the jet and the ambient air. The decay rate of the mean axial velocity, temperature and mass fraction are shown to increase with decreasing density ratio. This confirms a higher mixing efficiency (parameter which determines the quantity of mass or heat injected at the jet exit and found further from the axis) when the density ratio between the jet and the quiescent air decreases. Finally, it is shown that the density effects are affected by the buoyancy terms in the similarity region of the jet.     

Version étendue du filtre de Kalman discret appliquée à un problème inverse de conduction de chaleur non linéaire

An extended version of the discrete Kalman filter applied to a nonlinear inverse heat conduction problem. A nonlinear inverse heat conduction problem is resolved by using a formulation of the Kalman filter based on a statistical approach and extended to nonlinear systems. The time evolution of a surface heat flux density is reconstructed from a numerical simulation which allowed us to analyse the influence of some parameters, that condition the running of the filter, on the estimation result. A suitable choice of these parameters, guided by the filter behaviour observations, leads to a solution that remains stable when using noisy data, but that is slightly time-lagged compared to the exact function. This time-lag depends on the location of the interior temperature measurement needed for the inversion and on the model error caused by the approximation of the heat flux with a piece-wise constant function. The application of the extended Kalman filter with real measurements recorded from an experimental set-up, shows that this technique fits the stochastic structure of experimental measurements. The provided results are validated by using the Raynaud's and Bransier's inverse method and are in good agreement with the heat flux density estimated with this method.     

Etude des structures convectives et du transfert thermique autour d'un cylindre en deuxième nappe dans une configuration en quinconce,en écoulement d'air chargé de gouttelettes d'eau

We describe an experimental study of the influence of longitudinal and transversal pitch on the convective transfer around a cylinder on the second row of a three cylinder staggered bank, operating in an airstream charged with sprayed water at moderate Reynolds number. The analysis of the wall velocity gradient and its fluctuation shows the effects of geometrical parameters on various characteristic zones of the flow: laminar boundary layer, separation and vortices. The modifications of local Nusselt number evolution compared with the single cylinder are explained. For the disposition which gives the highest heat transfer, a correlation of local Nusselt number is proposed.