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P. Le Quéré
In the spectrum of themes present in the Department, the Transfer Dynamics group finds itself between the Fluid dynamics Group with which it shares the same methodology and tools and the Energetics Group with which it shares the same objectives, that is investigation of heat and mass transfer. The specificity of the studies lies in the detailed investigation of heat and mass transfer phenomena, in general under dominant convection. In this case, the equations which describe the configuration (Navier-Stokes equations for the fluid motion, transport-diffusion equations for temperature or concentration) are highly non-linear and generally exhibit complex time and space behaviours. One of our goals is to investigate these motions and, since our investigation tools are mostly numerical, to provide accurate numerical solutions. Another characteristics is that the flows which are studied are often driven by body forces such as thermal or mass buoyancy forces or wall viscous shear. These studies involve two different aspects, one fundamental concerning general behaviors and the other more applied directed towards practical configurations of interest in the industrial world
On the fundamental side our objectives are to understand the elementary mechanisms involved in heat and mass transfer processes. In particular, we want to understand the conditions under which some classes of flows become unstable, the mechanisms which are responsible of these instabilities and the sequences of bifurcations through which they become chaotic and turbulent. The arrival of L. Tuckerman will strenghten this research theme. We have also undertaken simulations of the same classes of flows (natural convection in differentially heated cavities, flows between rotating discs) for values of the parameters that correspond to turbulent flows in reality in order to compute directly the second order moments which are used in classical turbulent modelling approach of these flows. We have also started investigating flows through porous media, both dynamically to investigate the non-linear corrections to Darcy's law, and also with thermal coupling to understand the adsorption of sound as a function of the characteristic parameters. We are also working on a model of bubble growth in pool boiling, and E. Gadoin, hired as associate professor at Paris VI, will work on this theme.
On the more applied side, our objectives are to provide some answers to the complex questions which are generally raised in the industrial world. This complexity stems from the fact that several elementary mechanisms have to be taken into account simultaneously and also by the fact that complex geometries have to be dealt with. Modelling and simulation of a car head light is one such typical example as well as the ventilation of a car indoors. We have also worked on a numerical simulation software for testing the possibility of two-phase cooling on internal combustion engines. This could help increase the compactness of these engines.
Most of these studies are performed with the help of numerical tools and the group has a great variety of numerical algorithms for the resolution of the Navier-Stokes, both by the formulation (velocity-pressure, vorticity-stream function, vorticity-velocity) and the numerical approximation (finite differences, finite volume, finite element and spectral methods). In particular all the studies on transition and routes to chaos require very accurate algorithms both in time and space. This accuracy limits the approach to relatively simple geometries. This allows us to develop efficient and accurate numerical algorithms based on finite differences and spectral methods tailored to the configuration at hand. Simulations in more complex geometries are generally performed using either finite volume or finite elements algorithms. Improving these numerical tools is obviously part of our permanent objectives, in collaboration of the Fluid Dynamics Group.
The research activity in the group is presently focused around 5 main themes which are:
TOPIC 1: THERMO-CAPILLARY AND THERMO SOLUTAL CONVECTION
(G. Labrosse)
Many crystal growth processes are based on the growth from the melt, the supply of material to the growing crystal being due to a convective transport. The dynamics of the growing process largely depends on the dynamics of the flow, and it is well known that unsteady fluid flow resulting from flow instabilities can result in undesirable effects such as inhomogeneities or striations that alter the quality of the growing crystal. Various devices have been foreseen to control this fluid transport, essentially through micro or macro gravity. Macrogravity can be realised on the earth surface in centrifugators, with the drawback of a more complex hydrodynamics configuration resulting from the additional Coriolis effect, additional control parameters and intrinsically three dimensional configurations. In floating zone processes which involve free surfaces, it is also necessary to take into account Marangoni effects. We have thus developed a three dimensional spectral algorithm for the integration of the Navier-Stokes equations with free surfaces. In particular an original projection diffusion technique was developed in order to maintain the incompressibility. This study has been performed with the support of a BRITE-EURAM contract. This work was part of the thesis of A. Batoul, which he defended successfully last January. E. Chenier, a new thesis student, is carrying on this work by starting to compute directly, with the methods proposed by L. Tuckerman, the spectrum of the jacobian of the flow in the vicinity of the transition curve and the associated eigenfunctions. E. Delouche is extending the method by investigating the stability of Rayleigh Benard type motion in a rotating cylindrical tank under thermal and solutal buoyancy forces, including Soret effect. The aim is to relate the flow structure and its instabilities to the earth magnetic field.
TOPIC 2 - ROTATING DISC FLOWS AND HEAT TRANSFER (O .Daube)
Rotating disc flows are found in many practical configurations of industrial interest such as turbomachines, fluid couplings, etc... In turbomachines for example increasing the thermodynamics efficiency requires an increase of the temperature differences and hence a better knowledge of the heat transfer coefficients along the walls of these rotating cavities, and consequently of the flow structures in such rotating cavities. Due to the strong inhomogeneity and anisotropy; an accurate prediction of these flows in the turbulent regime represents a formidable challenge. Our goal is to perform ultimately direct numerical simulations of these flows for parameter values of interest, which correspond in general to weakly turbulent flows. In a first study, which is the subject thesis of N. Cousin-Rittemard, we have focused on the loss of stability of rotor stator flows in cavities of moderately large aspect ratio. Our aim was to qualify the numerical algorithms and to gain some insight into some of the instability mechanisms responsible of the transition to turbulence. We have encountered some difficulties, due to the fact that two thin boundary layers develop along the rotor and stator. These boundary layers soon become convectively unstable and although the global solution is still absolutely stable, the asymptotic numerical solution can remain unsteady due to the fact that numerical inaccuracies can play the same role as external noise in open boundary layers. As a consequence the numerical solution is extremely sensitive to the numerical resolution which is used and it is very difficult to find "a" critical value of the Reynolds number. Let us also say that the same behaviors were observed with different numerical codes (spectral finte difference, finite volume). Despite these difficulties, we have started a new thesis, with R. Jacques, on the computation of these flows at very large values of the Reynolds numbers. Both studies are part of the ARTICA program. We have also started working on parallel versions of these codes (spectral and finite difference).
TOPIC 3 - NATURAL CONVECTION : INSTABILITIES, TURBULENCE (P. Le Quéré)
Flows driven by temperature differences occur in many engineering configurations such as cooling and ventilation, insulation.,,, In many cases the temperature diffrences and characteristic sizes are such that the corresponding flows are tubulent, in fact weakly turbulent. Predicting the corresponding flow structures and related heat transfer properties is thus of major interest, but a difficult task. It is also of interest to understand the physical mechanisms responsible for turning the flow from laminar to turbulent. These are two main objectives of the studies performed in this theme. On the instability side, we have performed a linear stability analysis of a class of parallel solutions found in the gap between two concentric differentialy heated vertical cylinders and performed some simulations of these solutions in the non-linear regime. We have also studied the stability of some typical 2D solutions found in differentially heated cavities with respect to three dimensional disturbances (see further). We are also investigating the transition to unsteadiness of the full 3D solution in a cubical box with adiabatic top and bottom and lateral faces. On the turbulent side, we have recently performed direct numerical simulations of some solutions for values of the Rayleigh number that correspond to turbulent flows in actual configurations. The aim of these simulations is to investigate the dynamics of these chaotic solutions but also to compute the statistical quantities such as the time averaged temperature and velocity fields and the second order Reynolds stress tensor which are modelled in classical approaches of turbulence based on Reynolds decomposition. We have thus simultaneously undertaken to solve the Reynolds averaged equations to allow for a direct comparison between the direct simulations and the solution of the averaged equations. Comparisons which have been performed in a cavity of aspect ratio 4 for values of the Rayleigh number up to 1010, confirm, if needed that standard k-epsilon models largely overestimate the turbulent intensities. Other comparisons with laboratory experiments done in Poitiers have led us to question the validity of the boundary conditions imposed on the top and bottom horizontal walls and we have recently performed simulations with modified boundary conditions that result in a much better agreement with experimental observations. These studies have been supported through a DRET contract. We are also performing, in collaboration with EDF, direct simulations of natural convection in vertical channels of intinite extension, to study the behavior of turbulent stresses and heat flux stresses close to walls. This is the subject of the thesis of R. Boudjemadi.
TOPIC 4 - THERMAL ENGINEERING (J. Pakleza)
In this research theme, the objective is to deal with problems which are closer to the industrial needs, by dealing with complex configurations both by the geometry or by the fact that different coupled modes of heat transfer have to be taken into account.. One such example is the car head light, since their increasing compacity makes thermal problems more and more acute and result in deformation of the shell. Since all three modes of heat transfer intervene in comparable proportions, a complete treatment is necessary. A software dedicated to this configuration has been developed in contract with VALEO, with a twofold objective: to develop a design and optimisation tool on one hand and to acquire the capability to deal with these complex configurations on the other hand. This was the subject of the thesis of M. Said that he defended last December. We have also developed, in contract with RENAULT, a software for the simulation of the fluid and thermal behaviour of the circuitry of a car engine, with whom it is possible to test the possibility of two-phase cooling.
TOPIC 5 - FLUID-POROUS MEDIUM COUPLING (M. Firdaouss)
We have started a detailed study of the fluid flow and heat and mass transfer in porous media. The initial aim was to examine the validity of Darcy's law in adsorption processes and to determine the macroscopic coefficients that appear in global models of adsorption columns. We have started in parallel a detailed investigation of the non-linear correction to Darcy's law, both numerically and theoretically. New general conditions under which the non-inear correction is cubical ave been given. Simultaneously, an investigation of adsorption of sound in porous media has been started in coaboration with the Laboratoire d'Acoustique de l'Université du Mans.
Some typical examples of these research themes are found in the next pages.
Most of Professors and Associate Professors who work in the group do their teaching in two Universities, either University Paris Sud in Orsay or University Pierre et Marie Curie in Paris. In addition most of the researchers teach at the graduate level in 3rd cycle courses. These courses comprise either fluid mechanics, coupled heat and fluid flow or numerical methods for the solution of the Navier Stokes equations. A few courses on numerical methods are also given in various places.
The group is part of some of the co-operative programs within CNRS. We have organised several workshops on numerical software for thermal problems, on the use of characteristic methods, projection methods and domain decomposition methods for the Navier-Stokes equations. We have also organised a one week spring school on numerical methods with the help and support of the CNRS Groupement de Recherche Mécanique des Fluides Numérique.
The group has many international relationships with researchers working on similar problems, both on methodological developments and on the applications. In particular, we work with Professor M. Deville for the development of spectral methods. Ruud Henkes from Delft University came to spend one year with us in 1993. A co-operation agreement has been signed with Professor Hyun from KAIST (Korea). L. Tuckerman, who was previously working at the Center for Non-linear Dynamics in Austin (Texas), has many relationships with US researchers.