In this thesis direct numerical simulations are used to investigate two phenomenain shear flows: laminar-turbulent transition over a flat plate and periodicvortex shedding induced by a jet in cross flow. The emphasis is on understanding and controlling the flow dynamics using tools from dynamical systems and control theory. In particular, the global behavior of complex flows is describedand low-dimensional models suitable for control design are developed; this isdone by decomposing the flow into global modes determined from spectral analysisof various linear operators associated with the Navier–Stokes equations.Two distinct self-sustained global oscillations, associated with the sheddingof vortices, are identified from direct numerical simulations of the jet incrossflow. The investigation is split into a linear stability analysis of the steadyflow and a nonlinear analysis of the unsteady flow. The eigenmodes of theNavier–Stokes equations, linearized about an unstable steady solution revealthe presence of elliptic, Kelvin-Helmholtz and von K´arm´an type instabilities.The unsteady nonlinear dynamics is decomposed into a sequence of Koopmanmodes, determined from the spectral analysis of the Koopman operator. Thesemodes represent spatial structures with periodic behavior in time. A shearlayermode and a wall mode are identified, corresponding to high-frequency andlow-frequency self-sustained oscillations in the jet in crossflow, respectively.The knowledge of global modes is also useful for transition control, wherethe objective is to reduce the growth of small-amplitude disturbances to delaythe transition to turbulence. Using a particular basis of global modes, knownas balanced modes, low-dimensional models that capture the behavior betweenactuator and sensor signals in a flat-plate boundary layer are constructed andused to design optimal feedback controllers. It is shown that by using controltheory in combination with sensing/actuation in small, localized, regionsnear the rigid wall, the energy of disturbances may be reduced by an order of magnitude.

Rsum : La mesure des profils transitoires et de la vitesse de solidification sont deux donnes importantes pour le contrle de procds industriels impliquant un changement de phase. Dans le cas de llectrolyse de laluminium, ce processus de solidification assure la protection du systme et influe sur la performance nergtique du procd de fabrication. Malheureusement, ces donnes se rvlent, dans la plupart des cas, difficilement accessibles. Ce travail de thse porte sur le dveloppement de nouveaux outils permettant ltude et la caractrisation de la solidification de matriaux changement de phase et haute temprature. Lobjectif est de dvelopper un systme de mesure du front de solidification de matriaux changement de phase non destructif et ne perturbant pas le milieu de mesure, tout en assurant une prcision et une rponse suffisamment rapide pour exploiter de nouvelles stratgies de contrle dans les cuves dlectrolyse. Ce travail couple une tude exprimentale fondamentale de la solidification de la cryolithe avec une modlisation numrique de phnomne de changement de phase solide-liquide dans des conditions proches du fonctionnement de cuves dlectrolyse. // Abstract : Measurement of transient solidification fronts and of solidification rate are two important data for controlling industrial processes involving a solid-liquid phase change. In the case of aluminium electrolysis, this solidification process protects the system and affects the energy performance of the manufacturing process. Unfortunately, these data are not easy to obtain in most cases. This thesis focuses on the development of new tools for the study and on the solidification characterization of phase change materials at high temperature. The goal is to develop a nondestructive solidification front measurement system for phase change materials without disturbing the measurement medium, while ensuring accuracy and a fast enough response time to exploit new control strategies in electrolysis cells. This work couples a fundamental experimental study of the cryolite solidification with numerical modeling of solid-liquid phase change phenomenon under conditions close to those during normal operation of electrolytic cells.

Recently, a new kind of turbulence has been discovered in the flow of concentrated polymer melts and solutions. These flows, known as purely elastic flows, become unstable when the elastic forces are stronger than the viscous forces. This contrasts with Newtonian turbulence, a more familiar regime where the fluid inertia dominates. While there is little understanding of purely elastic turbulence, there is a well-established dynamical systems approach to the transition from laminar flow to Newtonian turbulence. In this project, I apply this approach to purely elastic flows. Laminar flows are characterised by ordered, locally-parallel streamlines of fluid, with only diffusive mixing perpendicular to the flow direction. In contrast, turbulent flows are in a state of continuous instability: tiny differences in the location of fluid elements upstream make a large difference to their later locations downstream. The emerging understanding of the transition from a laminar to turbulent flow is in terms of exact coherent structures (ECS) — patterns of the flow that occur near to the transition to turbulence. The problem I address in this thesis is how to predict when a purely elastic flow will become unstable and when it will transition to turbulence. I consider a variety of flows and examine the purely elastic instabilities that arise. This prepares the ground for the identification of a three-dimensional steady state solution to the equations, corresponding to an exact coherent structure. I have organised my research primarily around obtaining a purely elastic exact coherent structure, however, solving this problem requires a very accurate prediction of the exact solution to the equations of motion. In Chapter 2 I start from a Newtonian ECS (travelling wave solutions in two-dimensional flow) and attempt to connect it to the purely elastic regime. Although I found no such connection, the results corroborate other evidence on the effect of elasticity on travelling waves in Poiseuille flow. The Newtonian plane Couette ECS is sustained by the Kelvin-Helmholtz instability. I discover a purely elastic counterpart of this mechanism in Chapter 3, and explore the non-linear evolution of this instability in Chapter 4. In Chapter 5 I turn to a slightly different problem, a (previously unexplained) instability in a purely elastic oscillatory shear flow. My numerical analysis supports the experimental evidence for instability of this flow, and relates it to the instability described in Chapter 3. In Chapter 6 I discover a self-sustaining flow, and discuss how it may lead to a purely elastic 3D exact coherent structure.

This thesis considers the hydrodynamic instability and optimal forcing of a number of incompressible flow cases. In the first part, the instabilities of three problems that are of great interest in energy and aerospace applications are studied, namely a Blasius boundary layer subject to localized wall-suction, a Falkner–Skan–Cooke boundary layer with a localized surface roughness, and a pair of helical vortices. The two boundary layer flows are studied through spectral element simulations and eigenvalue computations, which enable their long-term behavior as well as the mechanisms causing transition to be determined. The emergence of transition in these cases is found to originate from a linear flow instability, but whereas the onset of this instability in the Blasius flow can be associated with a localized region in the vicinity of the suction orifice, the instability in the Falkner–Skan–Cooke flow involves the entire flow field. Due to this difference, the results of the eigenvalue analysis in the former case are found to be robust with respect to numerical parameters and domain size, whereas the results in the latter case exhibit an extreme sensitivity that prevents domain independent critical parameters from being determined. The instability of the two helices is primarily addressed through experiments and analytic theory. It is shown that the well known pairing instability of neighboring vortex filaments is responsible for transition, and careful measurements enable growth rates of the instabilities to be obtained that are in close agreement with theoretical predictions. Using the experimental baseflow data, a successful attempt is subsequently also made to reproduce this experiment numerically. In the second part of the thesis, a novel method for computing the optimal forcing of a dynamical system is developed. The method is based on an application of the inverse power method preconditioned by the Laplace preconditioner to the direct and adjoint resolvent operators. The method is analyzed for the Ginzburg–Landau equation and afterwards the Navier–Stokes equations, where it is implemented in the spectral element method and validated on the two-dimensional lid-driven cavity flow and the flow around a cylinder. / <p>QC 20171124</p>

[ES] El proyecto ESTiMatE nace con el objetivo de mejorar la precisión de las predicciones de hollín para la reducción de emisiones y una mayor sostenibilidad ambiental en la aviación. Para ello es crucial comprender a fondo fenómenos que influyen en la formación de hollín, incluyendo atomización del combustible, mezcla, combustión y formación de emisiones. La presente tesis, como parte del proyecto, se centra en el primer paso para caracterizar las spray flames, el proceso de atomización del líquido. Existen modelos empíricos para ello, pero el objetivo de este trabajo es desarrollar un nuevo modelo fenomenológico a través de simulaciones de alta fidelidad. Se propone acoplar este modelo a los códigos PRECISE-UNS y Alya para inyectar gotas en simulaciones Lagrangianas, reproduciendo de forma efectiva las características clave de atomización primaria en la formación del spray. Realizar estudios sobre la configuración anular de atomizadores prefilming airblast es un gran desafío, por lo que los esfuerzos se han enfocado en la configuración plana como alternativa que proporciona información valiosa. El KIT ha hecho contribuciones notables en este sentido al desarrollar un banco de pruebas de configuración plana, generando una base de datos extensa con resultados que abarcan diversos fluidos de trabajo y condiciones de operación para validar los cálculos. Esta tesis investiga la atomización primaria en estos dispositivos con un enfoque computacional a través de simulaciones eDNS con el código PARIS Simulator. Se utilizan simulaciones VOF-DNS del borde del atomizador para obtener información, y simulaciones LES monofásicas precursoras que permiten tener en cuenta la turbulencia del gas en la entrada. No obstante, se han propuesto dos metodologías derivadas a partir de eDNS, extendiéndola con simulaciones LES bifásicas adicionales. La primera de ellas impone un espesor y velocidad constantes para la película líquida en la entrada, pero sus valores medios se obtienen procesando las nuevas simulaciones LES bifásicas. Esta metodología ha sido validada para una condición de operación de referencia, representativa del reencendido en altitud. La segunda, introduce un espesor y velocidad variables de la película líquida, constituyendo una condición de contorno más realista. Se han realizado dos estudios diferentes. Por un lado, utilizando la primera metodología, se realizó un estudio paramétrico para investigar el impacto de la velocidad media del gas y las propiedades del fluido en la formación de estructuras líquidas. Al variar estos parámetros se observan diferencias en los mecanismos de ruptura basadas en M como en la literatura. La base para un modelo fenomenológico se ha establecido utilizando estos resultados y puede extenderse con más condiciones de operación siguiendo la metodología descrita. Por otra parte, se ha realizado una comparación entre ambas metodologías para considerar la influencia de la historia de la película de combustible en la atomización primaria. En este estudio, al mejorar las condiciones de contorno a la entrada, se ha reproducido con éxito la fenomenología presente en los experimentos, al contrario que con la eDNS estándar. Se ha propuesto una nueva técnica de postprocesado para caracterizar las estructuras líquidas. Los métodos habituales detectan gotas en un dominio 3D, pero solamente detectan ligamentos en una proyección 2D utilizando optimización de funciones algebraicas. Sin embargo, este nuevo método es capaz de encontrar gotas y ligamentos en 3D mediante OpenCV. También ha sido validado con resultados de la literatura. Con todo, la tesis ha sentado las bases para el desarrollo de modelos específicos de atomización airblast mediante simulaciones de alta fidelidad, contribuyendo a una mejor predicción de los fenómenos de inyección, atomización, evaporación, mezcla y combustión de aeromotores que permita realizar un diseño más eficiente de éstos hacia una movilidad aérea sostenible. / [CA] El projecte ESTiMatE naix amb l'objectiu de millorar la precisió de les prediccions de sutge per a la reducció d'emissions i una major sostenibilitat ambiental en l'aviació. Per això, és crucial comprendre a fons fenòmens que influeixen en la formació de sutge, incloent atomització del combustible, mescla, combustió i formació d'emissions. La present tesi, com a part del projecte, se centra en el primer pas per caracteritzar les spray flames, el procés d'atomització del líquid. Existeixen alguns models empírics per això, però l'objectiu d'aquest treball és desenvolupar un nou model fenomenològic a través de simulacions d'alta fildelitat. Es proposa acoblar aquest model als codis PRECISE-UNS i Alya per injectar gotes en simulacions Lagrangianes, reproduint de manera efectiva les característiques clau d'atomització primària en la formació de l'spray. Realitzar estudis sobre la configuració anul·lar d'atomitzadors prefilming airblast és un gran desafiament, per la qual cosa els investigadors han enfocat els seus esforços en la configuració plana com alternativa que proporciona informació valuosa. El KIT ha fet contribucions notables en aquest sentit en desenvolupar un banc de proves de configuració plana, generant una base de dades extensa amb resultats que abasten diversos fluids de treball i condicions d'operació per a validar els càlculs. Esta tesi investiga l'atomització primària en aquests dispositius amb un enfocament computacional a través de simulacions eDNS emprant el codi PARIS Simulator. S'utilitzen simulacions VOF-DNS de la vora de l'atomitzador per a obtindre informació, i simulacions LES monofàsiques precursores que permeten tindre en compte la turbulència del gas a l'entrada. No obstant això, s'han proposat dues noves metodologies derivades a partir de eDNS, estenent-la amb simulacions LES bifàsiques addicionals. La primera d'elles imposa una grossària i velocitat constants per a la pel·lícula líquida en l'entrada, però els seus valors mitjans s'obtenen processant les noves simulacions LES bifàsiques. Aquesta metodologia ha sigut validada per a una condició d'operació de referència, representativa de la reencesa en altitud. La segona, introduïx una grossària i velocitat variables de la pel·lícula líquida, constituint una condició de contorn més realista. S'han realitzat dos estudis diferents. D'una banda, utilitzant la primera metodologia, es va realitzar un estudi paramètric per a investigar l'impacte de la velocitat mitjana del gas i les propietats del fluid en la formació d'estructures líquides. En variar estos paràmetres s'observen diferènciesen els mecanismes de ruptura basades en M com a la literatura. La base per a un model fenomenològic s'ha establit utilitzant aquests resultats i pot estendre's amb més condicions d'operació seguint la metodologia descrita. D'altra banda, s'ha realitzat en paral·lel una comparació entre totes dues metodologies per a considerar la influència de la història de la pel·lícula de combustible en l'atomització primària. En aquest estudi, en millorar les condicionsde contorn a l'entrada, s'ha reproduït amb èxit la fenomenologia present en els experiments, al contrari que amb la eDNS estàndard. S'ha proposat una nova tècnica de postprocessament per a caracteritzar les estructures líquides. Els mètodes habituals detecten gotes en un domini 3D, però solament detecten lligaments en una projecció 2D utilitzant optimització de funcions algebraiques. No obstant això, aquest nou mètode és capaç de trobar gotes i lligaments en 3D mitjançant la llibrería OpenCV. També ha sigut validat amb resultats de la literatura. Amb tot, la tesi ha establit les bases per al desenvolupament de models específics d'atomització airblast mitjançant simulacions d'alta fidelitat, contribuïnt a una millor predicció dels fenòmens d'injecció, atomització, evaporació, mescla i combustió dels aeromotors que permeta realitzar un disseny més eficient dels mateixos cap a una mobilitat aèria sostenible. / [EN] The project ESTiMatE emerges aiming to enhance the precision of soot predictions leading to reduced emissions and improved environmental sustainability in aviation. To achieve this, it is crucial to thoroughly understand various phenomena that influence soot formation, including fuel atomization, mixing, combustion, and subsequent emissions formation. The present thesis, as part of the project, focuses in the first step to characterize spray flames, the liquid atomization process. There exist some empirical models to characterize atomization, but the objective of this specific work package is to develop a new phenomenological model through high-fidelity simulations instead of empirical results. This model is proposed to be coupled to the PRECISE-UNS and Alya codes to inject droplets in Lagrangian simulations, effectively reproducing the key features of the primary atomization process on the spray formation. Conducting fundamental studies on the annular configuration of prefilming airblast atomizers is challenging, so researchers have directed their attention towards planar configurations as an alternative that can provide valuable insights. The KIT has made notable contributions in this regard by developing a dedicated planar test rig, generating a substantial database of results encompassing various working fluids and operating conditions for validation. This thesis investigates primary atomization in these devices with a computational approach using eDNS within the PARIS Simulator code. VOF-DNS simulations of the atomizing Edge are performed to obtain useful data, and precursor one-phase LES simulations in order to account for gas inflow turbulence at the DNS inlet. Nevertheless, two methodologies have been derived from eDNS, extending it with additional precursor two-phase LES simulations. The first one, imposes constant liquid film thickness and velocity at the DNS inlet, but their mean values are obtained processing the new two-phase LES simulations. It has been validated for a reference operating condition, representative of altitude relight. The second one, introduces variable liquid film thickness and velocity instead, constituting a more realistic boundary condition for the DNS. Two different studies have been conducted in this regard. On the one hand, using the former methodology, a parametric study was performed to investigate the impact of mean gas velocity and fluid properties on the formation of liquid structures. By varying these parameters differences on the breakup mechanisms are observed based on M as found in the literature. The basis for a phenomenological model has been established using these results, and it can be extended with more operating conditions following the described methodology. On the other hand, a comparison between both methodologies has been carried out in parallel, in order to account for the influence of film history on the primary atomization process. In this study, by improving the inlet boundary conditions, the phenomenology observed in the experiments has been succesfully reproduced, unlike with the standard eDNS. A novel post-processing technique for characterizing liquid structures has been proposed. Usual post-processing methods detect droplets in a 3D domain, but only detect ligaments in a top view 2D projection of it using algebraic functions optimization. However, this new method is able to find both droplets and ligaments as well as its 3D properties using the Open Computer Vision Library (OpenCV) instead. It has been also validated with the results in the literature. Overall, the thesis has laid the foundations for the development of specific airblast atomization models through the use of high-fidelity simulations,contributing to a better prediction of the injection, atomization, evaporation, mixing and combustion phenomena in aero engines, enabling a more efficient design towards sustainable air mobility. / Moreno Montagud, C. (2024). Computational Modelling of the Primary Atomization in Aero Engine Airblast Atomizers through a DNS Approach [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/211359