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.     

Les aspects théoriques régissant l'instrumentation d'un capteur thermique pariétal à faible inertie

The theoretical aspects of the instrumentation of a weak inertia parietal thermal sensor. From a simple semi-infinite model, we present theoretical developments allowing the optimisation of the instrumentation of parietal thermal sensors. Generally equipped with two thin thermocouples, these sensors must present a weak thermal inertia in order to characterise thermal boundary conditions in fast unsteady regime. Performances of such sensors are described by three characteristics: response time, measurement sensitivity and accuracy. For a given material, the constraint on the response time determines diameter and position of the second thermocouple. In a second time, the position of the first thermocouple results from a good compromise between measurement sensitivity and accuracy. This compromise depends itself on the sensor response time, particularly at the beginning of the studied thermal phenomena.     

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.     

Convection mixte autour d'un cylindre horizontal. Influence des variations des propriétés physiques avec la température

The effects of variable properties with temperature are considered on a transverse mixed convection problem about an horizontal and isothermal circular cylinder. The problem is supposed laminar and stationary. The Navier-Stokes equations, coupled with the transport energy equation are written in the (Ψ, ω, θ) formulation and solved by a finite difference technique. The results, presented for air and water are compared with those obtained by using the Boussinesq approximation.     

Convection thermique pour l'écoulement de couette avec débit axial; cas d'un fluide pseudo-plastique

The different patterns of psuedo-plastic fluid flow between two coaxial cylinders, with an axial component of velocity, have been determined. A new mode on stability was set obviousness. The incidence of the flow's structure and heat flux on the Nusselt number has been examined. The variation of rheological properties has been accounted for in the correlation between the mean Nusselt number and the usual dimensionless parameters.     

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.     

Modélisation d'un panache d'émetteur de chaleur pour le logiciel de simulation énergétique des bâtiments SPARK

Plume's convector modeling for object-oriented thermal building simulation software SPARK. In this paper, a zonal model used to predict air movement and temperature distribution in a room is presented. This model is based on a rough partitioning of the room: it is an intermediate approach between one-node models (that consider a homogeneous temperature in each room) and CFD models. Flow rates are calculated in respect to the pressure distribution in low velocity domains and specific laws describe plumes and jets. The airflow model is coupled with a building envelope model. They are implemented in an object-oriented environment called SPARK. The modularity of SPARK allows the creation of very flexible tools, and its strict syntax permits having the simulations automatically generated.     

Étude numérique de l'évaporation dans un courant d'air humide laminaire d'un film d'eau ruisselant sur une plaque inclinée

Numerical study of the evaporation in laminar humid air flow of a liquid film flowing over an inclined plate. By using an implicit centered finite differences method with a non-uniform grid, the authors study numerically the evaporation of a thin liquid film flowing over an inclined plate in a forced humid-air flow. They consider the existence of two-dimensional laminar boundary-layers with variable physical properties and show that the term of enthalpy diffusion is always negligible, whether the plate is adiabatic, isothermal or heated by a constant heat flux density. By using in the liquid film transfer equations which are one-dimensional, partially two-dimensional and two-dimensional, the authors additionally show the following features. If the plate is adiabatic, the liquid mass flow rate is without influence on the transfers and the gas–liquid interface behaves like an isotherm surface at rest. In this case, one may use a one-dimensional model in the film whatever liquid mass flow rate is. If the wall is isotherm or heated by a constant heat flux and when the liquid mass flow rate is less than 10⁻³ kg·m⁻¹·s⁻¹, the one-dimensional model is sufficient; if it is included in the interval [10⁻³ kg·m⁻¹·s⁻¹, 10⁻² kg·m⁻¹·s⁻¹[, the partially two-dimensional model is useful; if it is superior to 10⁻² kg·m⁻¹·s⁻¹, it is necessary to use the two-dimensional model. Generally, whatever the thermal conditions on the plate are, heat transfer is dominated by the liquid-vapor transition.     

Étude numérique d'une surface plane uniformément accessible dans un écoulement permanent et laminaire d'un fluide newtonien

The authors show numerically that a plane surface situated in the middle of a conduct, whose walls are equilateral hyperbolic surfaces, is uniformly accessible from a small distance of the entrance when a Newtonian fluid runs in steady laminar flow inside the conduct. They specify this distance according to the values of Reynolds and Prandtl numbers and to the ratio factor of the conduct. Calculations concern the heat transfer but are available for mass transfer by replacing the Prandtl and Nusselt numbers and the temperature respectively by the Schmidt and Sherwood numbers and the concentration of the diffusing substance.     

Évaporation en convection forcée d'un film liquide mince ostwaldien ruisselant en régime laminaire permanent sur une surface plane isotherme et inclinée

The authors study, in forced convection, the evaporation of an Ostwaldian film flowing over an isothermal inclined plane surface to determine the influence of the behaviour index of the liquid on the dynamic and thermal characteristics of liquid-air system. The liquid flow is considered partially two-dimensional whereas for the air it is two-dimensional. The coupled equations with the interfacial conditions are solved using a fully implicit finite differences method. From the study, it appears that the behaviour index influences considerably the transfers which are more important for pseudoplastic liquids than for dilatant ones.     

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.     

Séchage superficiel d'un matériau poreux humide par convection forcée d'air chaud: couplage entre les équations de transfert dans le matériau et celles de la couche limite

The authors considered drying of a thick slab of humid porous material immersed in a laminar steady flow of hot air parallel to its surface. They wrote the boundary layer equations in air (continuity, momentum, energy and mass), those describing humidity and heat transfer in the porous medium deduced from Luikov's theory. Then, they coupled them at the air-product interface by expressing the continuity of the thermal and mass fluxes taking into account the evaporation. They solved numerically the resulting system of differential equations using an implicit finite-difference method. They determined the instantaneous evaluation of the spatial distributions of heat and humidity, the local values of the Nusselt and Sherwood numbers. They also studied the influences of principal parameters of the system.     

Session A: Les matières premières alcooligènes

Various commercially available natural ventilation devices supply fresh air without mechanical assistance. These devices offer a low-energy alternative to mechanical air handling units. However, they often cannot satisfy recommended ventilation rates due to their dependence on both macro- and microclimate wind speeds. This work examines the feasibility of achieving the recommended fresh air delivery rates without impacting on the device energy requirements. A numerical investigation is carried out using a standard passive stack device geometry combined with a simulated low-powered axial fan. The investigation shows that a low-induced pressure of 20 Pa is enough to satisfy the legislative requirements. Depending on the macroclimate conditions, this induced pressure could be generated from a commercially available solar-powered system. As the fan system is only used in periods of low external wind velocities (1 m/s), it is termed a passive-assisted stack.     

Réponse a un signal thermique sinusoïdal dans le cas d'un écoulement laminaire a plan directeur

A theoretical and numerical study of laminar forced convection in both parallel-plate channels, subjected to a sinusoidally varying inlet temperature, is presented. The plate's thermal response is coupled to the fluid via the congugation conditions at the interface (boundary condition of the fourth kind). A thermal diffusion in the plate and a boundary condition that accounts for external convection are considered. The temperature amplitude and phase lag are determined as a function of four parameters. The results are compared at the classical hypothesis of isothermal plates used by several authors. Exactness of the numerical scheme solutions are established by comparison with exact solutions for slug flows.     

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.     

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.     

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.     

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.     

Prevision numérique de la convection forcée turbulente dans une cavité bidimensionnelle entrainée

Turbulent flow and associated heat transfer in confined geometry (driven closed cavity flow in two dimensions) has been studied using a finite-difference numerical method in primitive variables. Turbulence modelling is based on one point closures derived from the classicalk-ε model. Calculated mean velocity and turbulent kinetic energy are compared with available experimental data. In spite of its limitations, the k-ε model proved to be a useful tool for prediction of global quantities. The case of forced heat convection with fixed wall temperature is considered. Mean temperature field and overall thermal properties of the cavity flow are studied. Correlations giving Nusselt numbers at each face of the cavity versus Reynolds number are deduced from numerical results, they sum up mean transfer properties of such a flow configuration.