For repeated transient solutions of geometrically nonlinear structures the numerical effort often poses a major obstacle. Thus, the introduction of a reduced order model, which takes the nonlinear effects into account and accelerates the calculations considerably, is often necessary.This work yields a method that allows for rapid, accurate and parameterisable solutions by means of a reduced model of the original structure. The structure is discretised and its dynamic equilibrium described by a matrix equation. The projection on a reduced basis is introduced to obtain the reduced model. A comprehensive numerical study on several common reduced bases shows that the simple introduction of a constant basis is not sufficient to account for the nonlinear behaviour. Three requirements for an rapid, accurate and parameterisable solution are derived. The solution algorithm has to take into account the nonlinear evolution of the solution, the solution has to be independent of the nonlinear finite element terms and the basis has to be adapted to external parameters.Three approaches are provided, each responding to one requirement. These approaches are assembled to the integrated method. The approaches are the update and augmentation of the basis, the polynomial formulation of the nonlinear terms and the interpolation of the basis. A Newmark-type time-marching algorithm provides the frame of the integrated method. The application of the integrated method on test-cases with geometrically nonlinear finite elements confirms that this method leads to the initial aim of a rapid, accurate and parameterisable transient solution.

An experimental study was designed to investigate the effect of different parameters on the development and structure of turbulent 3D offset jets. The present investigation considered the effects of offset height ratio, expansion ratio, surface roughness and rib placement on the flow dynamics of a turbulent 3D offset jet. The velocity measurements were performed using an acoustic Doppler velocimetry (ADV) and particle image velocimetry (PIV). Measurements were conducted within the symmetry and lateral planes. For the PIV technique, the measurements in the symmetry and lateral planes were conducted over a streamwise range of 0 ≤ x/bo ≤ 80 and 12 ≤ x/bo ≤ 60, respectively (where bo is the nozzle height). Likewise, velocity measurements using the ADV technique were conducted over a range of 4 ≤ x/bo ≤ 45 in both the symmetry and lateral planes. The velocity measurements were analyzed using both one-point and multi-point statistics. The one-point statistics included profiles of the mean velocities, Reynolds stresses and some of the budget terms in the turbulent kinetic energy transport equation. The quadrant analysis technique was used to investigate the dominant events that contribute towards the Reynolds shear stress. The two-point correlation analysis was used to investigate how the turbulence quantities are correlated. Information obtained from the two-point correlation analysis was also used to investigate the inclination of vortical structures within the inner and outer shear layers of the 3D offset jet. The direction of the positive mean shear gradient played an active role in the inclination of these vortical structures within the inner and outer shear layers. The reattachment process resulted in the breakdown of these structures within the developing region. Similarly, various length scales were estimated from these structures. The proper orthogonal decomposition was used to examine the distribution of the turbulent kinetic energy within the offset jet flow. Also, the dynamic role of the large scale structures towards the turbulent intensities, turbulent kinetic energy and Reynolds shear stress was investigated. / October 2016

Dans les centrales nucléaires et thermiques, certaines installations sont sujettes à des couplages acousto-mécaniques pouvant nuire fortement à leur bon fonctionnement. La compréhension et la prédiction de ces couplages multi-physiques nécessitent le développement de modèles numériques de très grande précision. Ces modèles sont si coûteux à résoudre qu’il n’est pas envisageable de les utiliser dans des boucles de contrôle ou encore d’optimisation paramétrique. Dans ce manuscrit de thèse, le but est d’exploiter un nombre limité de calculs coûteux pour construire un modèle numérique qui soit de très faible dimension. Ces modèles numériques réduits doivent être capables, en temps réel, de reproduire ces calculs haute-fidélité mais aussi d’extrapoler ces résultats à d’autres points de fonctionnement plus ou moins proches. L’évolution dé petites perturbations compressibles au sein d’un écoulement complexe moyenné est modélisée à partir des équations d’Euler linéarisées dont la nature hyperbolique complique l’application des méthodes de réduction classiques. Les principales problématiques théoriques et numériques qui émergent lors de la construction du système réduit par méthode de projection sont alors exposées. En particulier, les problèmes fondamentaux de la préservation de la stabilité et du contrôle de l’énergie des systèmes réduits sont largement développés et une nouvelle méthode de stabilisation est proposée. Leur sensibilité paramétrique est aussi discutée. Les modèles réduits stables sont ensuite intégrées dans un code de calcul industriel pour prendre en compte des géométries complexes. De plus, la présence de solides dont les parois peuvent être fixes ou mobiles est abordée. En particulier, les petits déplacements de paroi sont modélisés avec une loi de transpiration. Cette condition aux limites est intégrée dans le formalisme du contrôle de façon à lever la difficulté induite par sa non homogénéité. Finalement, les modèles réduits sont exploités pour prédire en temps réel la réponse des systèmes à une loi de contrôle arbitraire. Par exemple, la fréquence et l’amplitude du chargement peuvent varier. Le code de calcul réduit ainsi développé a pour principale vocation de rendre possible des expertises aéroélastiques à faible coût. / In nuclear and thermal power stations, some installations produce acoustics/mechanics coupling which may cause important damage and bad operating performances. Prediction and understanding of these physical phenomena need the development of high-fidelity numerical models which are prohibitive to solve. Therefore, these models cannot be used for control or even parametric optimization applications. In this work, the goal is to use some high-fidelity solutions for building reduced-order models which are able to calculate again these solutions but in real-time, and also to predict solutions for other close configurations. Modelling of compressible disturbances in a complex mean flow is given by hyperbolic linearized Euler equations which create some difficulties to perform classical reduction methods. Theoretical and numerical problems are then introduced when a projection method is applied. In particular, the conservation of stability and the control of energy of reduced-order models are studied and a new stabilization procedure is proposed. Parametric sensitivity is also discussed. Afterwards, stable reduced-order models are developed in an industrial code to consider complex geometries. Furthermore, modelling of solids with fixed or vibrating walls are taken into account. Particularly, small vibrations are modelled thanks to a transpiration law. This boundary condition is implemented in the framework of linear control theory to apply reduction methods. Finally, reduced-order models are tested to predict solutions in real time. For instance, frequency and amplitude of the loading can change. The developed reduced order model should be used for aeroelastic industrial problems with more realistic costs.

Model reduction is a powerful and ubiquitous tool used to reduce the complexity of a dynamical system while preserving the input-output behavior. It has been applied throughout many different disciplines, including controls, fluid and structural dynamics. Model reduction via proper orthogonal decomposition (POD) is utilized for of control of partial differential equations. In this thesis, the analytical expressions of POD modes are derived for the heat equation. The autocorrelation function of the latter is viewed as the kernel of a self adjoint compact operator, and the POD modes and corresponding eigenvalues are computed by solving homogeneous integral equations of the second kind. The computed POD modes are compared to the modes obtained from snapshots for both the one-dimensional and two-dimensional heat equation. Boundary feedback control is obtained through reduced-order POD models of the heat equation and the effectiveness of reduced-order control is compared to the full-order control. Moreover, the explicit computation of the POD modes and eigenvalues are shown to allow the computation of different n-widths approximations for the heat equation, including the linear, Kolmogorov, Gelfand, and Bernstein n-widths.

The validation of UV reactors is currently accomplished by biodosimetry, in which the reactor is treated as a "black-box" and hence cannot account for the dependence of the dose delivery on the complex hydrodynamics and the spatial variation in UV intensity. Alternative methods, such as fluorescent microspheres as non-biological surrogates and computational fluid dynamics (CFD) simulations, have been developed; however, each method has its shortcomings. In this study, a novel technique for the spatial and temporal assessment of the hydrodynamics and the UV dose delivered and the link between these two factors in a lab-scale UV reactor using three dimensional laser induced fluorescence (3DLIF) is developed. This tool can also be utilized for the optimization of UV reactors and to provide data for validation of CFD-based simulation techniques. Regions of optimization include areas around the UV lamp where short-circuiting occurred, a longer inlet approach section that enhances the performance of the reactor by reducing short circuiting paths and a longer outlet region to provide greater mixing. 3DLIF allows real time characterization of mixing and dose delivery in a single lamp UV reactor placed perpendicular to flow by capturing fluorescence images emitted from a laser dye, Rhodamine 6G, using a high speed CCD camera. In addition to three-dimensional mixing, the technique successfully visualized the two-dimensional, transient mixing behaviors such as the recirculation zone and the von Karman vortices and the fluence delivery within the reactor, which has not been possible with traditional tracer test techniques. Finally, a decomposition technique was applied to the flow and fluence delivery based concentration data to reveal similar structures that affect these phenomena. Based on this analysis, changing the flow in the reactor, i.e. the Reynolds number, will directly affect the fluence delivery.

Future generation of all-electric ships will be highly dependent on electric power, since every single system aboard such as the drive propulsion, the weapon system, the communication and navigation systems will be electrically powered. Power conversion modules (PCM) will be used to transform and distribute the power as desired in various zone within the ships. As power densities increase at both components and systems-levels, high-fidelity thermal models of those PCMs are indispensable to reach high performance and energy efficient designs. Efficient systems-level thermal management requires modeling and analysis of complex turbulent fluid flow and heat transfer processes across several decades of length scales. In this thesis, a methodology for thermal modeling of complex PCM cabinets used in naval applications is offered. High fidelity computational fluid dynamics and heat transfer (CFD/HT) models are created in order to analyze the heat dissipation from the chip to the multi-cabinet level and optimize turbulent convection cooling inside the cabinet enclosure. Conventional CFD/HT modeling techniques for such complex and multi-scale systems are severely limited as a design or optimization tool. The large size of such models and the complex physics involved result in extremely slow processing time. A multi-scale approach has been developed to predict accurately the overall airflow conditions at the cabinet level as well as the airflow around components which dictates the chip temperature in details. Various models of different length scales are linked together by matching the boundary conditions. The advantage is that it allows high fidelity models at each length scale and more detailed simulations are obtained than what could have been accomplished with a single model methodology. It was found that the power cabinets under the prescribed design parameters, experience operating point airflow rates that are much lower than the design requirements. The flow is unevenly distributed through the various bays. Approximately 90 % of the cold plenum inlet flow rate goes exclusively through Bay 1 and Bay 2. Re-circulation and reverse flow are observed in regions experiencing a lack of flow motion. As a result high temperature of the air flow and consequently high component temperatures are also experienced in the upper bays of the cabinet. A proper orthogonal decomposition (POD) methodology has been performed to develop reduced-order compact models of the PCM cabinets. The reduced-order modeling approach based on POD reduces the numerical models containing 35 x 109 DOF down to less than 20 DOF, while still retaining a great accuracy. The reduced-order models developed yields prediction of the full-field 3-D cabinet within 30 seconds as opposed to the CFD/HT simulations that take more than 3 hours using a high power computer cluster. The reduced-order modeling methodology developed could be a useful tool to quickly and accurately characterize the thermal behavior of any electronics system and provides a good basis for thermal design and optimization purposes.

In this study the dynamical modeling of the unsteady flow over a flapping wing is considered. The technique is based on collecting instantaneous velocity field data of the flow using Particle Image Velocimetry (PIV), applying image processing to these snapshots to locate the airfoil, filling the airfoil and its surface with proper velocity data, applying Proper Orthogonal Decomposition (POD) to these post-processed images to compute the POD modes and time coefficients, and finally fitting a discrete time state space dynamical model to the trajectories of the time coefficients using subspace system identification (N4SID). The procedure is applied using MATLAB for the data obtained from NACA 0012, SD 7003, elliptic airfoil and flat plate, and the results show that the dynamical model obtained can represent the flow dynamics with acceptable accuracy.

Data centers are computing infrastructure facilities that house arrays of electronic racks containing high power dissipation data processing and storage equipment whose temperature must be maintained within allowable limits. In this research, the sustainable and reliable operations of the electronic equipment in data centers are shown to be possible through the Open Engineering Systems paradigm. A design approach is developed to bring adaptability and robustness, two main features of open systems, in multi-scale convective systems such as data centers. The presented approach is centered on the integration of three constructs: a) Proper Orthogonal Decomposition (POD) based multi-scale modeling, b) compromise Decision Support Problem (cDSP), and c) robust design to overcome the challenges in thermal-fluid modeling, having multiple objectives, and inherent variability management, respectively. Two new POD based reduced order thermal modeling methods are presented to simulate multi-parameter dependent temperature field in multi-scale thermal/fluid systems such as data centers. The methods are verified to achieve an adaptable, robust, and energy efficient thermal design of an air-cooled data center cell with an annual increase in the power consumption for the next ten years. Also, a simpler reduced order modeling approach centered on POD technique with modal coefficient interpolation is validated against experimental measurements in an operational data center facility.

Variable Valve Timing (VVT) presents a powerful tool in the relentless pursuit of efficiency improvements in the internal combustion engine. As the valves have such ultimate control over the gas exchange processes, extensive research effort in this area has shown how valve event timing can be manipulated to reduce engine pumping losses, fuel consumption and engine out emissions. Pumping losses may be significantly reduced by use of throttleless strategies, making use of intake valve duration for load control, while alternative cycles such as the Miller cycle allow modification of the effective compression ratio. More recently, the value of single valve operation in part load conditions is exploited, bringing with it the concept of asymmetric valve lifts. Work in this area found the side effect of asymmetric valve operation is a significant change in the behaviour of the in-cylinder flow structures, velocities and turbulence intensity. Work presented in this thesis exploits asymmetric valve strategies to modify the in-cylinder flow conditions. The Proper Orthogonal Decomposition (POD) is a method employed in the fluids dynamics field to facilitate the separation of coherent motion structures from the turbulence. In the presented work, the application of POD to in-cylinder flow analysis is further developed by the introduction of a novel method for identifying the POD modes representative of coherent motion and those representative of the turbulence. A POD mode correlation based technique is introduced and developed, with the resulting fields showing evidence of coherence and turbulence respectively. Experimental tests are carried out using a full length optically accessible, single cylinder research engine equipped with a fully variable valve train (FVVT) to allow full control of both valve timing and lift. In-cylinder flow is measured through the use of Particle Image Velocimetry (PIV) at several crank angle timings during the intake stroke whilst the engine is operated under a range of asymmetric valve strategies. The exhaust valves and one intake valve have their respective schedules fixed, while the second intake valve schedule is adjusted to 80\%, 60\%, 40\%, 20\%, 0\% lift. The resulting PIV fields are separated into coherent motion and turbulence using the developed technique, allowing for analysis of each constituent independently. The coherent element gives insight to large scale flows, often of the order of magnitude of the cylinder. These structures not only give a clear indication of the overall motion and allow assessment of flow characteristics such as swirl and tumble ratio, but the variation in the spatial location of these structures provides additional insight to the cyclic to cycle variation (CCV) of the flow, which would not otherwise be possible due to the inclusion of the turbulent data. Similarly, with the cyclic variation removed from the turbulent velocity field, a true account of the fluctuating velocity, u' and derived values such as the Turbulent Kinetic Energy (TKE) may be gained. Results show how manipulation of a one intake valve timing can influence both the large scale motions and the turbulence intensity. By the reduction of lift, the swirl ratio is increased almost linearly as the typical counter-rotating vortex pair becomes asymmetric, before a single vortex structure is observed in the lowest lift cases. A switching mechanism between the two is identified and found to be responsible for increased levels of CCV. With the reduction in lift, TKE is observed not only to increase, but change the spatial distribution of turbulence. Of course, the reduction in valve lift comes with the penalty of a reduced valve curtain area. However, it was identified both in literature and throughout this study that the reduction in lift did not negatively influence the engine breathing as the same trapped mass was achieved under all cases with no adjustment of manifold pressure. While literature shows both bulk motion and turbulence are key in liquid fuel break-up during the intake stroke, the mixing effects under port-injected natural gas were investigated experimentally using Laser Induced Fluorescence (LIF). The valve strategy was found to have no significant effect on the mixture distribution at the time of spark.

This work is concerned with the fluid dynamic processes and the associated loss of acoustic energy produced by circular apertures within noise absorbing perforated walls. Although applicable to a wide range of engineering applications particular emphasis in this work is placed on the use of such features within a gas turbine combustion system. The primary aim for noise absorbers in gas turbine combustion systems is the elimination of thermo-acoustic instabilities, which are characterised by rapidly rising pressure amplitudes which are potentially damaging to the combustion system components. By increasing the amount of acoustic energy being absorbed the occurrence of thermo-acoustic instabilities can be avoided. The fundamental acoustic characteristics relating to linear acoustic absorption are presented. It is shown that changes in orifice geometry, in terms of gas turbine combustion system representative length-to-diameter ratios, result in changes in the measured Rayleigh Conductivity. Furthermore in the linear regime the maximum possible acoustic energy absorption for a given cooling mass flow budget of a conventional combustor wall will be identified. An investigation into current Rayleigh Conductivity and aperture impedance (1D) modelling techniques are assessed and the ranges of validity for these modelling techniques will be identified. Moreover possible improvements to the modelling techniques are discussed. Within a gas turbine system absorption can also occur in the non-linear operating regime. Hence the influence of the orifice geometry upon the optimum non-linear acoustic absorption is also investigated. Furthermore the performance of non-linear acoustic absorption modelling techniques is evaluated against the conducted measurements. As the amplitudes within the combustion system increase the acoustic absorption will transition from the linear to the non-linear regime. This is important for the design of absorbers or cooling geometries for gas turbine combustion systems as the propensity for hot gas ingestion increases. Hence the relevant parameters and phenomena are investigated during the transition process from linear to non-linear acoustic absorption. The unsteady velocity field during linear and non-linear acoustic absorption is captured using particle image velocimetry. A novel analysis technique is developed which enables the identification of the unsteady flow field associated with the acoustic absorption. In this way an investigation into the relevant mechanisms within the unsteady flow fields to describe the acoustic absorption behaviour of the investigated orifice plates is conducted. This methodology will also help in the development and optimisation of future damping systems and provide validation for more sophisticated 3D numerical modelling methods. Finally a set of design tools developed during this work will be discussed which enable a comprehensive preliminary design of non-resonant and resonant acoustic absorbers with multiple perforated liners within a gas turbine combustion system. The tool set is applied to assess the impact of the gas turbine combustion system space envelope, complex swirling flow fields and the propensity to hot gas ingestion in the preliminary design stages.