Mathematical theory of homogenization of partial differential equations is relatively a new area of research (30-40 years or so) though the physical and engineering applications were well known. It has tremendous applications in various branches of engineering and science like : material science ,porous media, study of vibrations of thin structures, composite materials to name a few. There are at present various methods to study homogenization problems (basically asymptotic analysis) and there is a vast amount of literature in various directions. Homogenization arise in problems with oscillatory coefficients, domain with large number of perforations, domain with rough boundary and so on. The latter one has applications in fluid flow which is categorized as oscillating boundaries. In fact ,in this thesis, we consider domains with oscillating boundaries. We plan to study to homogenization of certain optimal control problems with oscillating boundaries. This thesis contains 6 chapters including an introductory Chapter 1 and future proposal Chapter 6. Our main contribution contained in chapters 2-5. The oscillatory domain under consideration is a 3-dimensional cuboid (for simplicity) with a large number of pillars of length O(1) attached on one side, but with a small cross sectional area of order ε2 .As ε0, this gives a geometrical domain with oscillating boundary. We also consider 2-dimensional oscillatory domain which is a cross section of the above 3-dimensional domain. In chapters 2 and 3, we consider the optimal control problem described by the Δ operator with two types of cost functionals, namely L2-cost functional and Dirichlet cost functional. We consider both distributed and boundary controls. The limit analysis was carried by considering the associated optimality system in which the adjoint states are introduced. But the main contribution in all the different cases(L2 and Dirichlet cost functionals, distributed and boundary controls) is the derivation of error estimates what is known as correctors in homogenization literature. Though there is a basic test function, one need to introduce different test functions to obtain correctors. Introducing correctors in homogenization is an important aspect of study which is indeed useful in the analysis, but important in numerical study as well. The setup is the same in Chapter 4 as well. But here we consider Stokes’ Problem and study asymptotic analysis as well as corrector results. We obtain corrector results for velocity and pressure terms and also for its adjoint velocity and adjoint pressure. In Chapter 5, we consider a time dependent Kirchhoff-Love equation with the same domain with oscillating boundaries with a distributed control. The state equation is a fourth order hyperbolic type equation with associated L2-cost functional. We do not have corrector results in this chapter, but the limit cost functional is different and new. In the earlier chapters the limit cost functional were of the same type.

La détermination du champ de pression dans un écoulement et/ou des efforts sur un profil en mouvement à partir de mesures de vitesses effectuées dans le milieu fluide est une problématique actuelle qui intéresse de nombreux domaines de recherche en mécanique des fluides. On pourrait citer en particulier, les systèmes de récupération d'énergie (éolienne, hydrolienne) ou bien les systèmes de contrôle optimal d'aubes de guidage de turbine, etc…Dans ce mémoire, nous apportons notre contribution à ce problème en proposant dans un premier temps, une méthode originale qui permet, à partir de champs de vitesses instationnaires obtenus par mesure optiques PIV, d'approcher ces champs dans l'ensemble du milieu (profil inclus) en utilisant la théorie des polynômes orthogonaux de Legendre. L'équation de Navier-Stokes permet alors d'obtenir des gradients de pression polynomiaux dans l'ensemble du milieu fluide et de pouvoir ainsi calculer le champ de pression dans l'écoulement et ensuite, en utilisant l'équation de bilan de mouvement dans un domaine de référence judicieusement choisi, de déterminer les efforts sur un profil mobile en oscillation. Cette méthode est alors validée sur un profil fixe à partir de données simulées numériquement et de données expérimentales.Dans un deuxième temps, après une série de mesures optiques PIV sur un profil NACA0015 soumis à différents types d'oscillations, nous appliquons la méthode décrite précédemment pour reconstruire les champs de pressions instationnaires et évaluer les efforts instantanées et moyens sur le profil. L'étude d'un certain nombres de plages de fréquences et d'amplitudes permet de comparer nos résultats, pour la recherche d'une meilleure efficacité. / The determination of the pressure field in a flow and/or forces on a moving profile from measurements of velocities carried out in the fluid is a current problem that is of interest to many domains of research in fluid mechanics like the energy recovery systems (wind, hydro) or the speed control of hydraulic turbines, etc…In this PhD thesis, we make a contribution to this problem by initially proposing an original method which allows us to approach unsteady velocity fields in the whole of the flow obtained by PIV optical measurements (including the profile) using Legendre's orthogonal polynomial theory. The Navier-Stokes equations then make it possible to obtain polynomial pressure gradients in the whole of the fluid and thus to be able to calculate the pressure field in the flow by using the momentum balance equation in a judiciously chosen reference range, to determine the forces on an oscillating mobile profile. This method is then validated on a fixed profile using numerically simulated data and experimental data.In a second step, from series of flow PIV measurements on a NACA0015 profile subjected to different types of oscillations, we apply the method described above to reconstruct the unsteady pressure fields and to evaluate the instantaneous and average forces on the profile. The study of a certain number of ranges of frequencies and amplitudes makes it possible to compare our results, in order to seek a better efficiency.

The diploma thesis deals with automatic control of transferring suspended objects. It is a strongly oscillating system for which a physical trial model has been made. An application has been made for this model, which controls this system by means of PLC, frequency inverter and operating panel, everything by Siemens.

Oscillating-foil hydrokinetic turbines have gained interest over the years to extract energy from renewable sources. The influence of the sweep angle on the performance of a fully-passive oscillating-plate hydrokinetic turbine prototype was investigated experimentally in the present work. The sweep angle was introduced to promote spanwise flow along the plate in order to manipulate the leading edge vortex (LEV) and hydrodynamically optimize the performance of the turbine. In the present work, flat plates of two configurations were considered: a plate with a 6° sweep angle and an unswept plate (control), which were undergoing fully-passive pitch and heave motions in uniform inflow at the Reynolds numbers ranging from 15 000 to 30 000. The resulting kinematic parameters and the energy extraction performance were evaluated for both plates. Planar (2D) particle image velocimetry (PIV) was used to obtain patterns of the phase-averaged out-of-plane vorticity during the oscillation cycle. The circulation in the wake was then related to the induced-forces on the plate by calculating the moments of vorticity of the LEV with respect to the pitching axis of the plate. Tomographic (3D) PIV was implemented in evaluating the influence of the spanwise flow on the dynamics of the vortex structure in three-dimensional space. The rate of deformation of the vortex length was quantified by calculating the deformation terms embedded in the vorticity equations, then linked to the stability of the vortex. The results show evidence of delay of the shedding of LEV and increased vortex stability, in the case of the swept plate. The manipulation of the LEV by the spanwise flow was related to the induced kinematics exhibited by the prolonged heave forces experienced by the swept plate, which led to the higher power extraction performance at high inflow velocities. In the presence of spanwise flow, positive vortex stretching along the vortex line increased the stabilization of the vortex core and prevented the onset of helical vortex breakdown, observed in the case of the unswept plate. The use of the sweep profile on the plate has led to the improvement of energy extraction performance of the fully-passive hydrokinetic turbine. / Graduate

Bidirectional air turbines are used in oscillating water column (OWC) power plants for harnessing ocean wave energy. This paper describes the bidirectional aerodynamic and aero-acoustic facility at the University of Siegen for model air turbines performance testing. At least nine test facilities are known worldwide, but their layout, the performance testing procedure and the presentation of performance data are not standardized to this day. The layout of the facility at the University of Siegen follows ideas in ISO 5801 for fan performance testing. The pressurized air supply is bidirectional but steady-state. Achievable values of Reynolds and Mach number of the test turbines are 1,000,000 and 0.5, respectively. In addition, the facility is equipped with acoustic attenuators in the air supply for allowing synchronous determination of aerodynamic and acoustic characteristics of a turbine. A good practice guideline for turbine performance testing and presentation is proposed by showing full sets of non-dimensional aerodynamic and acoustic performance characteristics from two sample model turbines. Eventually, a comparison of in situ data from a full-scale turbine in transient operation with scaled up steady-state model performance measurements underlines the usefulness of steady-state model performance testing.

Several alternative ways of producing energy came up as the world took conscience of the finite availability of fossil fuels and the environmental consequences of its use and processing. Wave and tidal energy are among the so called green energies. Wave energy converters have been under research for the past two decades and yet there hasn’t been one technology that gathered everyone’s acceptance as being the most suitable one. The present work is focused on a self-rectifying turbine for wave energy harnessing. It’s a self-rectifying biplane Wells with an intermediate stator. The main goal is to evaluate the performance of such a turbine. Two different analyses were performed: experimental and computational. The experimental tests were made so that efficiency, velocity profiles and loss coefficients could be calculated. To do so scaled-down prototypes were built from scratch and tested experimentally. The 3D numerical analysis was possible by using a CFD commercial code: Fluent 6.3. Several simulations were performed for different flow coefficients. Three different degrees of mesh refinement were applied and k-ε turbulence model was the one chosen to simulate the viscous behavior of the flow through the turbine. A steady-state analysis is due and two mixing planes were used at the interfaces between the rotors and the stator. In the end comparisons are made between the experimental and numerical results

Indiana University-Purdue University Indianapolis (IUPUI) / In order to conform to pollutant-control regulations and minimize NOx emissions, modern household boilers and central heating systems are moving toward premixed combustors. These combustors have been successful with regards to emissions along with efficiency. However, their implementation has been associated with acoustical instability problems that could be solved through precise optimization in design rather than trial and error experimentation. This thesis introduces an experimental apparatus, which is designed to investigate the acoustic instability problem at the flame level. The goal is an experimental determination of the flame transfer function and comparison of the experimental data with a theoretical model of the flame. An experimental procedure is designed to diagnose the origins of the combustion instabilities by measurement of the flame transfer function. This research is carried out in three steps. The first step is to understand the acoustic instability problem through study of the theoretical models of the flame transfer function and selection of a model, which is most functional in industrial applications. A xiii measurement technique for the flame transfer function is developed according to the required accuracy in measurements, repeatability, and configurability for a wide range of operating conditions. Subsequently, an experimental apparatus is designed to accommodate the flame transfer function measurement technique. The components of the acoustic system are carefully sized to achieve precise measurement of the system parameters such as flows, pressures, and acoustic responses, and the apparatus is built. The apparatus is operated to measure the flame transfer function at several operating conditions. The experimentally measured flame transfer function is compared with a theoretical model for further verification. The experimental apparatus provides an improved assessment of the acoustic instability problem for industrial applications.

The behaviour of particles in pulsating and oscillating flows is of practical interest in devices such as pulsation reactors and ultrasonic elevators. In addition to the resulting flow patterns, the influence of the flow on heat and mass transfer is often important. The state of the art in this area is already quite well developed with many different models, theories, and experiments published. However, only small parameter ranges of the behaviour of particles in pulsating and oscillating flows are considered, while an overarching theoretical framework does not yet exist. Therefore, this work presents a three-stage model for the behaviour of solid single particles in oscillating (pulsating) flows. The relative velocity between particle and fluid as well as the flow patterns around the particle, together with the heat and mass transfer at the particle are considered. The model levels build on top of each other, with the introduced ϵ-Re plain as a common connection between the levels. The number of input parameters could be limited to the five most important ones (fluid velocity amplitude, fluid oscillation frequency, fluid temperature, particle diameter, particle density), but these are considered in very large ranges. The relative velocity is largely calculated analytically using various flow resistance approaches. Direct numerical simulations were carried out to qualitatively estimate the flow patterns around the particle. The quantitative determination of a meta correlation for the entire ϵ-Re plane was carried out using 33 data sets from the literature. Conditions in pulsation reactors are particularly emphasized and their influence investigated.:Chapter 1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Chapter 2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Chapter 3. State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1. Material Treatment in the Pulsation Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2. Particle Motion in an Oscillating Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3. Steady Streaming (Flow Pattern). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.4. Heat and Mass Transfer in Oscillating Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.5. Heat and Mass Transfer in Pulsating Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.6. Non-continuum Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Chapter 4. Basic Assumptions and Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.1. Input Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2. Pulsating Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.3. Forces on the Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.4. Motion of Particles - Stokes Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.5. Harmonic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.6. Dimensionless Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.7. The ϵ-Re Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Chapter 5. Motion of the Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.1. Drag Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.2. Slip Velocity Amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5.3. Particle Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.4. Navigation in the ϵ-Re Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.5. Extension of the Stokes Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.6. Additional Effects at Micro Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.7. Analytical Particle Motion - Summary and Conclusion . . . . . . . . . . . . . . . . . . . . 61 Chapter 6. Flow Patterns in the Vicinity of the Particle . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6.1. Creeping Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6.2. Quasi-steady Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 6.3. Steady Streaming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Chapter 7. Heat and Mass Transfer to Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 7.1. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 7.2. The Quasi-Steady HMT Area of the Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 7.3. Models for Oscillating Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 7.4. Meta Correlation Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 7.5. Deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 7.6. Quasi-Steady Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.7. Heat and Mass Transfer to Small Particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.8. Conclusion of Heat and Mass Transfer to Particles . . . . . . . . . . . . . . . . . . . . . . . . . 83 Chapter 8. Summary & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 8.1. Model Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 8.2. Inŕuence of input parameters on the HMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 8.3. The ϵ-Re Plane in the Special Case of the Pulsation Reactor . . . . . . . . . . . . . . 91 8.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Chapter 9. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Appendix A. Derivation and Solution of Particle Motion in the Stokes Model . . . . . i Appendix B. Derivation and Solution of Particle Motion in the Landau & Lifshitz Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Appendix C. Derivation of Deviation between Stokes and Schiller & Naumann . . . . x Appendix D. Parameters and Algorithm of the Direct Numerical Simulation and Flow Pattern Visualisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Appendix E. Conducted Data Preparation for HMT Models . . . . . . . . . . . . . . . . . . . . . . xv / Das Verhalten von Partikeln in pulsierenden und oszillierenden Strömungen findet praktisches Interesse in Apparaten wie Pulsationsreaktoren und Ultraschalllevitatoren. Dabei ist neben den entstehenden Strömungsmustern oft der Einfluss der Strömung auf den Wärme- und Stoffübergang von Bedeutung. Der Stand der Technik in der Literatur in diesem Bereich ist bereits recht weit entwickelt mit vielen verschiedenen Modellen, Theorien und Experimenten. Dabei werden jedoch stets nur kleine Parameterbereiche des Verhaltens von Partikeln in pulsierenden und oszillierenden Strömungen betrachtet, während ein übergreifender theoretischer Rahmen noch nicht existiert. Deshalb wird in dieser Arbeit ein dreistufiges Modell vorgestellt für das Verhalten von festen Einzelpartikeln in oszillierenden (pulsierenden) Fluidströmungen. Sowohl die Relativgeschwindigkeit zwischen Partikel und Fluid als auch die Strömungsmuster um das Partikel und der Wärme- und Stoffübergang am Partikel werden hierbei betrachtet. Die Modellebenen bauen aufeinander auf, wobei die eingeführte ϵ-Re-Ebene die Modellebenen miteinander verbinden. Die Anzahl der Eingangsparameter konnte auf die wichtigsten fünf (Fluidgeschwindigkeitsamplitude, Fluidoszillationsfrequenz, Fluidtemperatur, Partikeldurchmesser, Partikeldichte) begrenzt werden, diese werden jedoch in sehr großen Bereichen betrachtet. Die Relativgeschwindigkeit wird mittels verschiedener Strömungswiderstandsansätze größtenteils analytisch berechnet. Zur qualitativen Abschätzung der Strömungsmuster um das Partikel wurden direkte numerische Simulationen durchgeführt. Die quantitative Bestimmung einer Metakorrelation für die gesamte ϵ-Re-Ebene wurde mittels 33 Datensätze aus der Literatur durchgeführt. Dabei werden Bedingungen in Pulsationsreaktoren besonders herausgestellt und deren Einfluss untersucht.:Chapter 1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Chapter 2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Chapter 3. State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1. Material Treatment in the Pulsation Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2. Particle Motion in an Oscillating Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3. Steady Streaming (Flow Pattern). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.4. Heat and Mass Transfer in Oscillating Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.5. Heat and Mass Transfer in Pulsating Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.6. Non-continuum Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Chapter 4. Basic Assumptions and Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.1. Input Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2. Pulsating Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.3. Forces on the Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.4. Motion of Particles - Stokes Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.5. Harmonic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.6. Dimensionless Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.7. The ϵ-Re Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Chapter 5. Motion of the Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.1. Drag Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.2. Slip Velocity Amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5.3. Particle Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.4. Navigation in the ϵ-Re Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.5. Extension of the Stokes Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.6. Additional Effects at Micro Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.7. Analytical Particle Motion - Summary and Conclusion . . . . . . . . . . . . . . . . . . . . 61 Chapter 6. Flow Patterns in the Vicinity of the Particle . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6.1. Creeping Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6.2. Quasi-steady Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 6.3. Steady Streaming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Chapter 7. Heat and Mass Transfer to Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 7.1. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 7.2. The Quasi-Steady HMT Area of the Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 7.3. Models for Oscillating Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 7.4. Meta Correlation Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 7.5. Deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 7.6. Quasi-Steady Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.7. Heat and Mass Transfer to Small Particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.8. Conclusion of Heat and Mass Transfer to Particles . . . . . . . . . . . . . . . . . . . . . . . . . 83 Chapter 8. Summary & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 8.1. Model Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 8.2. Inŕuence of input parameters on the HMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 8.3. The ϵ-Re Plane in the Special Case of the Pulsation Reactor . . . . . . . . . . . . . . 91 8.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Chapter 9. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Appendix A. Derivation and Solution of Particle Motion in the Stokes Model . . . . . i Appendix B. Derivation and Solution of Particle Motion in the Landau & Lifshitz Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Appendix C. Derivation of Deviation between Stokes and Schiller & Naumann . . . . x Appendix D. Parameters and Algorithm of the Direct Numerical Simulation and Flow Pattern Visualisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Appendix E. Conducted Data Preparation for HMT Models . . . . . . . . . . . . . . . . . . . . . . xv

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La maîtrise du procédé séchage, étape essentielle dans la transformation du bois, est devenue incontournable pour la filière bois. Cette thèse propose l'utilisation de conduites de séchage oscillantes pour réduire les contraintes de séchage liées au retrait par l'activation du fluage mécanosorptif. A ce jour, la meilleure façon d'appliquer les conduites oscillantes représente un défi pour la communauté scientifique. Dans ce travail, nous avons choisi comme matériel d'étude une essence feuillue fortement utilisée dans la filière et très susceptible aux déformations lors du séchage : le hêtre (Fagus sylvatica). L'effet des conduites oscillantes sur les contraintes de séchage est étudié par une approche expérimentale et par une approche théorique, articulées en trois parties : - Un premier volet expérimental sur un séchoir semi – industriel pour saisir l'effet global des conduites oscillantes à l'échelle d'une pile de planches. L'amélioration de la qualité du bois séché s'est avérée par : une meilleure homogénéité de la teneur en eau finale inter et intra-planche, la diminution des déformations globales et la diminution des contraintes résiduelles exprimées par le gap du « slicing test ». - Ensuite, nous avons développé un volet théorique sur la base de modélisations analytique et numérique pour étudier l'évolution des champs de teneur en eau et de contraintes mécaniques au sein d'une planche lorsque les conditions climatiques oscillent. Une formulation analytique simple, adaptée aux conduites oscillantes, est proposée pour les utilisateurs de séchoirs n'ayant pas accès à un outil numérique sophistiqué. L'approche numérique effectuée avec l'outil de simulation TransPore permet une étude plus réaliste du séchage oscillant. Ainsi, le module mécanique de TransPore a été utilisé pour dégager des configurations pertinentes de séchage permettant d'étudier l'effet des conduites oscillantes sur la relaxation des contraintes. - Enfin, un second volet expérimental a été réalisé sur un séchoir de laboratoire, à l'échelle d'une planche, pour tester les informations issues du volet théorique. Un dispositif de séchage dissymétrique (flying wood) et deux dispositifs de séchage sous charge (poutre cantilever et flexion trois points) ont été utilisés pour étudier l'effet des oscillations. Toutefois, ces essais ne permettent pas de montrer clairement l'effet des oscillations sur la relaxation des contraintes. La confrontation entre les résultats expérimentaux à l'échelle d'une planche et la simulation numérique a mis en évidence l'effet conséquent des oscillations parasites de faibles période et amplitude sur les résultats expérimentaux, provoquées par la régulation du séchoir. Des modifications du modèle de comportement mécanique différé ont été proposées en perspectives de ce travail afin de mieux saisir le comportement observé expérimentalement. / Wood drying is an essential process in the wood industry. A perfect control of wood drying is nowadays very important for the wood industry. In this study, we propose the utilization of oscillating drying conditions to reduce the drying stresses induced by wood shrinkage by activating the mechanosorptive creep. The best way to apply this concept remains an open question in the scientific community. Beech wood (Fagus sylvatica), one of the most commonly used hardwood in France, was chosen for this study owing its elevated risk of drying defaults. The effect of oscillating conditions on drying stresses inside the boards was studied by both an experimental and a theoretical approach, structured in three parts: - A first experimental part realized with a semi – industrial kiln in order to study the global effect of oscillating conditions at the stack scale. Improvement of the quality of dried wood was showed by the best homogeneity of water content inside the board and among the boards and by the decrease of global deformations and residual stresses expressed by the gap measured by the slicing test. - The study was continued with a theoretical part based on analytical and numerical modeling to understand the development of internal heat and mass transfers inside the boards and the evolution of drying stresses during oscillating conditions. A simple analytical model adapted to the oscillating conditions was proposed, particularly for kiln users who don't have access to sophisticated numerical tools. The numerical approach used the simulation tool TransPore, able to simulate oscillating drying in more realistic conditions. Its mechanical module was used to set accurate drying schedules to study the effect of oscillating conditions on stresses relaxation. - Finally, a second experimental part was performed in a laboratory scale kiln, at the board scale, to test the information obtained theoretically. A non-symmetrical drying device (flying wood) and two different loaded drying devices (cantilever beam test and three points bending) were used to study the effect of oscillations. However, it is difficult to see the oscillating conditions effect on the stresses relaxation. The confrontation between experimental results at the board scale and the numerical simulation showed the significant effect produced on experimental results by parasite oscillations of small periods and intensities, originated by the kiln regulation. Further work should consider some modifications of the time dependent mechanical behavior model in order to capture the experimentally observed behavior.