Certain metals (Mg, V, Pd, etc.) or intermetallic compounds are known for their ability to reversibly absorb large quantities of hydrogen. The compounds thus formed are called metal hydrides. Physicists and chemists have never stopped giving increased interest to metal hydrides as a rather interesting class of materials. This interest arose well and truly after the discovery of their application as a moderator in nuclear reactors or also after the discovery of the astonishing sorption properties of hydrogen by intermetallic compounds (namely heat of reaction, storage capacity, rapidity of the absorption - desorption cycle, etc.). Thanks to these thermodynamic properties, hydrides have been used to develop a large number of clean and quiet industrial applications such as fuel cells, thermal and electrical energy storage units, hydrogen storage, heat pumps, Even though the benefits of these various industrial applications are undeniable, they are still predicated on two bets: one on competitiveness, and one on safety, which is made even more compelling by the fact that the majority of us consumers will be impacted by these applications, whether it be through the production of high or low temperatures or the power supply of homes, computers, and mobile phones. Indeed, while hydrogen is a clean fuel that generates far fewer chemical pollutants than a conventional internal combustion engine, for example, it is also a potentially dangerous gas that can ignite or explode in the presence of air if certain conditions are met. Metal-hydrogen reactors are important components of several types of industrial facilities. The main qualities of these reactors are first of all to ensure the conditions for applying the temperature and the pressure to the mass of occluded powder, by optimizing the heat transfers therein in a homogeneous and rapid manner. As the formation of hydrides is exothermic (discharge = endothermic), it is necessary to know how to control these transfers for the best dynamics of the system. Therefore, a strong activity of numerical simulation and calculations is essential, on the one hand, to guide the definition of the geometric characteristics and the choice of packaging and exchange materials, on the other hand, for the optimized control of the reactor ( calorie/cold intake, kinetics of extraction/insertion of H2 under pressure, pressure control, control of endothermicity/exothermicity, etc.). Therefore, several experimental and numerical investigations, describing these complex transfer mechanisms, have been carried out. At the national level, there are essentially two teams (at the Laboratory for the Study of Thermal and Energetic Systems at the National School of Engineers of Monastir and at the Laboratory of Materials and Processes at the Higher School of Science and Technology of Tunis ) who work on metal hydrides. The first focuses on heat and mass transfers in metal-hydrogen reactors, the characterization of hydrides and their applications in the energy field. The second deals with the physico-chemical phenomenon of hydrides. On an international scale, given the great interest given to metal hydrides and their applications, several international congresses which have a relationship with metal hydrides are organized. Mention may be made of: the International Symposium on Metal Hydride Systems, Grove Fuel Cell Symposium, European Hydrogen Energy Conferences. According to a bibliographic study, it turned out that the existing works are approached and are based on the following simplifying assumptions:

According to a bibliographic study, it turned out that the existing works are approached and are based on the following simplifying assumptions:

• * Transfers are one-dimensional.
• * The temperatures of the solid (metal) and of the gas (hydrogen) are equal (ETL).
• * The gas pressure is constant.
• * Flow is governed by Darcy's law.
• * The flow and transfers in the expansion zone of the reactor are negligible.
• * Radiative transfers are negligible.
• * The simulated reactors are of simple geometric shapes.

These assumptions lead to very restrictive numerical models and codes. Hence the need for a rigorous study which will make it possible, on the one hand, to better understand the phenomena and to qualify the implications of these hypotheses and, on the other hand, to establish fairly general models, and flexible and efficient numerical tools. Up to the present time, the work carried out within LESTE has enabled the development of a model which takes into account the two-dimensional effects, the resistance to flow, the difference between the temperature of the solid and fluid, radiative transfers and the flow and transfers in the expansion zone of the reactor. A computer tool is set up to simulate the operation of the reactor using this model. Thus, these investigations made it possible to extend the numerical study to more realistic configurations of metal-hydrogen reactors. The theoretical model involves parameters, the most influential of which (following a sensitivity study that we carried out) are: the equilibrium pressure, the kinetics of extraction/insertion of H2 under pressure and the thermal conductivity. Then a measuring bench (metal-hydrogen reactor, hydrogen tank, measuring instruments, etc.) was created in order to determine these properties. The experimental measurements allowed us to propose analytical models for the equilibrium pressure and the kinetics of the hydriding/dehydriding reaction.

Objectives of the research program:

We propose in this program to develop fairly general numerical simulation software for metal-hydrogen systems and to set up experimental tools allowing the validation of the software and the characterization of a wide variety of metals and intermetallic compounds. These digital and experimental tools will allow us to:

• * Better understand the complex phenomena of coupled heat and mass transfer in metal-hydrogen reactors.
• * Assess the degree of safety of storage systems for hydrogen and energy in the form of hydride.
• * Make the right choice of materials when carrying out a hydride-based application (cost, weight, kinetics, storage capacity, etc.).

In this research program, we also propose to design a hydride heat pump and storage systems for solar energy and hydrogen.

Expected results of the research program:

• * Implementation of tools for theoretical and experimental studies of Stirling engines.
• * Production of Stirling engine prototypes.

Methodology and approach envisaged for carrying out the research program:

The methodology envisaged for carrying out the proposed research program is as follows: For

For the theoretical part:

• * Discretization of the system of equations using the MVCEF with an unstructured mesh.
• * Resolution of the algebraic system governing the operation of the reactor in an axisymmetric configuration.
• * Validation of the calculation code.
• * Extension of the unstructured mesh computer code to reactors operating at high temperature by integrating radiative transfers.
• * Extension of the software to three-dimensional configurations.
• * Numerical simulation of the operation of metal-hydrogen reactors.
• * Numerical simulation of the operation of heat pumps and hydride energy accumulators

For the practical part:

In order to improve and computerize the existing measurement bench, we adopt the following approach:

• * Design and production of instrumented prototypes of hydrogen reactors and tanks.
• * Use of these measurement benches for the validation of models, to experimentally study heat and mass transfers and determine the kinetics, the equilibrium pressure and possibly other characteristics.

Opportunities for promoting research results:

The tools put in place and the knowledge acquired can be used to design and manufacture hydrogen and energy accumulators and hydride heat pumps.

Drying is an operation frequently encountered in several industrial sectors (construction materials, agro-food, textiles, pharmaceutical products, etc.). This is an operation which consumes a lot of energy and which, when carried out incorrectly, can lead to an alteration in the quality of the dried product (deformation, cracking, oxidation, etc.). For several years, many researchers have been interested in the heat and mass transfer phenomena that take place during drying, with the aim of reducing the cost without affecting the quality of the finished product. Despite the abundance of publications on drying, it emerges from the bibliographical study that:

• * Studies on drying in the presence of a solute in the liquid are rare and incomplete.
• * There are very few studies on drying that rigorously take into account the coupling between transfers in the fluid medium and in porous media. In general, transfers in the fluid medium are approximated by constant exchange coefficients during drying.
• * The drying of materials with double porosity (granular media, fibrous media, textiles, papers, etc.) has not been the subject of sufficient studies.

In the laboratory, we have developed models that govern transfers in porous media and in the drying fluid. Calculation codes have been implemented. These codes allowed us to conduct the following studies:

1. A first study in which we analyzed in detail the phenomenon of water evaporation in a two-dimensional flow of dry air, moist air and superheated steam. The study was carried out mainly on the domain of validity of the analogy between heat and mass transfer and on the inversion temperature. This contribution led to the following main conclusions:
   • ° At high temperature and in the presence of radiation, the interfacial velocity affects the different profiles.
   • ° The inversion temperature increases with speed and ambient pressure and decreases with heating.
   • ° Heat transfer by radiation causes the inversion temperature to decrease.
   • ° The analogy between heat transfer and mass transfer is valid only for low concentrations and low ambient temperatures; in the presence of radiant heat transfer, the analogy does not hold.
2. A second study during which we analyzed, at the macroscopic scale, the two-dimensional heat and mass transfers during the convective drying of an unsaturated porous plate, composed of an inert and non-deformable solid matrix, a liquid phase (pure water) and a gaseous phase (air + water vapor). Transfers in fluid media are represented by exchange coefficients obtained from the previous study. The simulations take into account the gas pressure and show the effect of the external and initial conditions on the state variables (environment temperature, gas pressure and water saturation). They also show the effect of variations in the local coefficients of heat and mass transfer, obtained under several conditions, on the drying operation.
3. A third study, also on a macroscopic scale, where we were interested in the drying of granular media by natural, forced and mixed convection. The grains are porous media and the granular medium is a double porosity medium. We assumed that the grains are indeformable and that there is no liquid phase in the macro pores. The effects of internal and external parameters on heat and mass transfer by natural and forced convection are presented and analyzed. The study in the case of natural convection takes into account the radiative transfer. In the study of heat and mass transfer during drying, we mainly encountered the problem of strong gradients of liquid content during the appearance of the drying front. This problem is more noticeable at high ambient temperatures and concentrations, significantly increases calculation time, prevents consideration of treating the coupling of transfers within the porous medium and in the external fluid rigorously, and prevents the development of simulations for configurations with complex geometries.

Objectives of the research program:

• * Improved implementation of numerical codes making them faster, more robust and easily usable for more complex geometries. The codes currently available to us are based on the methods of finite volumes in structured mesh and therefore are difficult to apply for complex geometries.
• * Improvement of the models by more thorough consideration of the coupling between the transfers in the porous medium and the surrounding fluid as well as the various transfer modes (conductive, convective, and radiative).
• * Improvement of experimental tools (drying loop, characterization benches, etc.).
• * Study of water and solute transfers during the drying of a porous medium.
• * Study of the drying of media with double porosity (granular media, fibrous media, etc.).

Expected results of the research program:

• * Implementation of high-performance and non-restrictive theoretical study tools for the study of heat and mass transfer during drying.
• * Improvement of experimental tools (drying loop, characterization benches, etc.).
• * Understanding and mastering the phenomena of heat and mass transfer during the drying of porous media with double porosity.
• * Understanding and mastering the phenomena of crystallization and heat and mass transfer during drying when the liquid phase contains a solute.

Methodology and approach envisaged for carrying out the research program:

We carry out comparisons of the performances of the solvers (ORTHOMIN, GMRES, BIGRADIENT, …) and the strategies of numerical resolution (coupled, not coupled). This allows us to choose the most suitable solvers and strategies for the considered problems. On the other hand we count, in order to have computer codes which can adapt easily to complex geometries, to carry out the discretization by the methods of control volume based on finite elements using an unstructured mesh. In order to further generalize the models, we introduce the effect of radiation and we deal more rigorously with the coupling between transfers in the porous medium and those in the surrounding fluid medium. It is a question of simultaneously solving the transport equations in the two media. The drying loop will be improved by eliminating vibration and more accurately regulating temperature and humidity. Thus, this loop makes it possible to carry out drying tests which is used to determine the kinetics of drying and to refine and validate the theoretical models. Drying when the water is loaded with salts is studied mainly at the pore scale. This study is based on experiments on capillaries and on etched networks (micro-model), numerical simulations on pore networks and with regard to certain theoretical aspects on the theory of percolation (invasion percolation, percolation gradient invasion). For a capillary of different geometries, we try to answer the following two questions: what is the impact of salt on the evaporation fluxes? In which region of the capillary or network will crystallization appear? Answers to these questions will be obtained by combining order of magnitude studies, numerical and/or analytical solutions and experimental visualizations. Concerning the drying of materials presenting a double porosity, we generalize our theoretical tools by taking into account the presence of a liquid phase in the macro pores.

Opportunities for promoting research results:

The tools put in place can be used to:

• * Optimize and control the energy expenditure of industrial dryers.
• * Improve storage conditions in grain silos by limiting condensation areas to avoid the possibility of germination, mold and the appearance of insects.
• * Construct new, more efficient dryers.
• * Produce desiccators.

The formation of a gaseous phase, within a porous medium, by expansion of a liquid solution supersaturated with gas or by boiling, constitutes a first-order transition, in which two events play a decisive role: the appearance of gas bubbles by nucleation, then the development of these bubbles whose volume increases by expansion and diffusion to bring the system back to a new state of equilibrium. From a practical point of view, this phenomenon plays an important role in many industrial processes (drying, heat pipe, bubble pump, oil, etc.). In petroleum engineering when some oil fields are being produced, it is occasionally acceptable to first open the wells and allow the fields to decompress. In these conditions, the gas initially dissolved in the oil is desorbed and the gaseous phase thus created moves the oil towards the production wells. This practice of harnessing the potential energy of the deposit is called natural drainage or primary recovery. The study of heat and mass transfers during the formation of the gas phase has been the subject of numerous theoretical and experimental works. Two approaches are used. The macroscopic approach is where the phenomena are described as averages over a representative elementary volume, containing several tens of pores. In general, for real porous media, the geometric distributions of the phases are unknown and therefore only this approach is applicable. The microscopic approach where the phenomena are described on the scale of the pore allows a detailed analysis but is only applicable in the case of porous media for which the geometric distributions of the phases are known (etched networks, periodic geometry, etc. .). During boiling or gas formation, the porous medium will possibly be formed of saturated zones (gas or liquid) and unsaturated zones (gas+liquid) separated by mobile interfaces. As a result, a difficulty appears, during the numerical resolution of the macroscopic equations, at the level of the adaptation of the mesh and its modification over time. Some solving methods fix the interface by performing a transformation of the spatial and temporal coordinates. Other methods consider that the porous medium contains everywhere a liquid phase and a gaseous phase. The porous medium is then everywhere unsaturated. Transfers are governed by three equations relating to temperature, gas phase pressure and saturation. The enthalpy formulation of the problem is also used. The porous medium is considered to be a single phase and the same transfer equations govern the problem throughout the porous medium. In the Laboratory, we have studied, at the macroscopic scale, boiling in porous media using the enthalpy formulation (or mixing method). The finite volume method was used for the discretization of the system of equations. The cavity model, subjected to a flow of heat from below and cooled from above, was chosen to validate the obtained results (stability, convection, etc.) using the computer code developed. Results concerning the study of boiling in a heated porous layer are obtained. It emerges from the bibliographical study that: the existing theoretical tools for studying, at the macroscopic scale, the boiling or the formation of gases in porous media are restrictive (negligible three-dimensional effects; negligible inertia, etc.) and difficult to use for complex geometric configurations. The boiling or the formation of gases in porous media, when fluids are in motion, have not been treated at the microscopic scale. The simulations, at the existing microscopic scale, do not take into account the three-dimensional effects.

Objectives of the research program:

• Description and understanding of phenomena related to boiling and the formation of gases in porous media.
• Implementation of numerical resolution codes for fast, robust macroscopic equations, which take into account most of the effects (three-dimensional effects, effect of inertia, effect of hygroscopicity, etc.) and are easily usable for complex geometric configurations.
• Implementation of experimental tools for the study of the formation of bubbles in a transparent artificial porous medium (etched network), at the microscopic scale.
• Implementation of a simulator, at the microscopic scale, of the growth of the gaseous phase in a network of capillaries.

Expected results of the research program

• Control of heat and mass transfers during the formation of gases in porous media.
• Implementation of theoretical and experimental tools to quantify heat and mass transfers during the formation of gases in porous media.

Methodology and approach envisaged for carrying out the research program

In a first approach, we analyze the phenomena from a macroscopic description. In this context, we establish a model that takes into account most of the effects. The established equations are then solved numerically by finite element-based control volume methods using an unstructured mesh. We compare the different solvers and the different resolution strategies and we try to determine the advantages and disadvantages of the enthalpy and temperature – pressure – saturation formulations. Subsequently, a study of certain boiling or gas formation problems (bubble pumps, cooling by boiling, etc.) are carried out. In a second approach, we study the phenomena at the pore scale. This study is based on experiments on etched networks (micro-model), and numerical simulations on pore networks and with regard to certain theoretical aspects on the theory of percolation (invasion percolation, invasion percolation under gradient).

Opportunities for promoting research results:

• * Control and reduction of the energy cost of certain drying processes.
• * Design and construction of bubble pumps using porous media.
• * Design and manufacture of heat pipes and cooling systems for electronic components.
• * Planning oil field exploitation with more accuracy and efficiency.

Melting and solidification are two phenomena frequently encountered both in nature and in industry (metallurgy, energy storage, production and storage of ice, food preservation, freezing, etc.).
The study of heat and mass transfer during melting or solidification is an essential prerequisite for reducing the energy cost and improving the quality of the finished product for certain applications.
Indeed, badly conducted solidification can lead to the formation of voids, heterogeneities, deformations and cracks. Even though there is a lot of published work, the majority of it is concerned with simple configurations, pure materials, and neglects three-dimensional effects. Work on the melting and solidification of multi-component materials is rarer and often incomplete. At the laboratory level, we have modeled and numerically simulated two-dimensional heat and mass transfers during the melting and solidification of pure and multi-component materials.
The equations are discretized using control volume methods based on mesh-structured finite elements. Results concerning the effects of inclination, aspect ratio and Grashof numbers are presented and analysed.

Objectives of the research program

• * Describing and understanding phenomena related to solid/liquid phase change.
• * Implementing a fast numerical resolution code that takes into account three-dimensional effects and which is easily usable for complex geometric configurations.

Methodology and approach envisaged for carrying out the research program

For the problems of fusion and solidification the analytical solutions exist only for simple and limited cases (semi-infinite unidirectional geometry) without much practical interest. For real configurations of more complex geometry, numerical approaches are the only way to solve these problems. The main difficulty associated with melting and solidification problems lies in the determination of the interface. Three techniques are commonly used in solving phase change problems: Interface-tracking methods, interface-fixing methods, and enthalpy methods. Enthalpy methods are based on the use of a fixed mesh. The energy conservation equation is written in the whole study domain without taking into account in a direct way the jump condition at the interface. The momentum conservation equations contain a source term which cancels the velocity fields in the solid and which makes it possible to find the equations of the flow in the fluid phase and in the zone of change of state considered to be a porous medium. We plan to improve this code by making it faster (by using more powerful solvers) and applicable to complex geometries (by using an unstructured mesh), then we plan to extend it to take into account three-dimensional effects. This code will be used to study some practical cases.

Opportunities for promoting research results:

The tools put in place and the obtained results will be used to:

• * Control and reduce the energy cost of certain industrial processes involving solid/liquid phase changes.
• * Design and build energy accumulators by latent heat.

Wetting and impregnation of porous media play an important role in a large number of energy and thermal systems and processes (heat pipe, drying, oil recovery, boiling and gas phase formation, etc.). Thus a large number of works relating to these subjects are published. This work concerns:

• * The effect of surface treatments (mechanical and chemical) on wetting.
• * Flow in capillaries of different sections and in capillary networks.
• * Impregnation of porous media.

At the laboratory level, we are interested in the wetting of fibers treated by chemical grafting. Measurements of contact angle and surface energy as a function of roughness and grafting rate were performed.

Objectives of the research program:

• * Modeling and numerical simulation of flow in capillaries and in capillary networks.
• * Modeling and numerical simulation of the impregnation of porous media.
• * Creation of experimental devices for studying wetting and impregnation.

Methodology and approach envisaged for carrying out the research program:

In order to deepen our knowledge, we carry out a bibliographic study on the theory of wetting and on the experimental techniques used. We then formulate the equations that govern wetting and flow in capillaries. We also perform contact angle and surface energy measurements of materials. We currently have experimental devices for measuring these quantities (Kahn balance and Digidrope). In parallel, we experimentally study the impregnation of porous media depending on the nature and structure of the solid (for example, in the case of textiles, the weave and the nature of the fiber). The contact angle and surface energy measurements are used to interpret the results obtained during the impregnation experiments. Finally we verify the validity of the models used for the impregnation and possibly propose a new model. Currently most of the modelings used are based on the Washburn equation which consists in supposing that the flow in a porous medium is governed by an equation of the same form as that which governs the flow in a capillary.

Opportunities for promoting research results:

The obtained results can be improved by producing hydrophobic or hydrophilic materials as well as various drying and textile finishing technics

The thermal control and the cooling of the various gears, machines and devices constitute a very important stake within the framework of the optimization of their operations, since their performances, cost and reliability, depend directly on it. Heat pipes are a suitable solution to this kind of problem. Indeed, they make it possible to evacuate high densities of heat flow without having recourse to any mechanical contribution of external origin. In this regard, they have been used in several fields of application. One of the most promising is the use of micro heat pipes for cooling electronic components, the subject of several recent research studies. Indeed, they are reliable, compact and act within the heat source itself.
The current challenges consist in their integration within the systems to be cooled in order to limit thermal contact resistances as much as possible. The driving mechanism for the operation of a heat pipe is the liquid-vapor phase change since the heat transfer takes place by transformation of sensible heat into latent heat, which explains the remarkable thermal conductivity of heat pipe systems.
Several parameters, such as the operating temperature, the imposed heat flux, the geometry, the nature of the capillary structure, the type and the load of the heat transfer fluid, are of great importance in the optimization of the operation of the heat pipes.
Although it has thermal properties that allow it to reach exceptional levels of performance, the heat pipe is subject to limitations that affect its proper functioning. They are essentially generated by the flow of vapor or by the flow of liquid inside the enclosure. Several research teams around the world are interested in theoretical and experimental studies of heat pipes.
The majority of the theoretical work published relates either to the determination of the operating limits, or to the establishment of the thermal conductances at the evaporator and at the condenser and are based on more or less important simplifying hypotheses. As for the experimental studies, they are few in number and present the difficulty of measuring the operating parameters.