AN ABSTRACT OF THE DISSERTATION OF PAYAM SHARIFI, for the Doctor of Philosophy degree in ENGINEERING SCIENCE, presented on April 2011, at Southern Illinois University Carbondale. TITLE: FUNDAMENTAL STUDIES ON THE EFFECT OF ELECTRIC FIELD ON INTERFACE INSTABILITY, FILM BOILING, AND FILM CONDENSATION MAJOR PROFESSOR: Dr. A. Esmaeeli This research focuses on investigation of uniform electric field on three inter-related interfacial phenomena including interface under electric field, film boiling under applied electric field, and film condensation under applied electric field. The idea of applying electric field to enhancement boiling and condensation heat transfer has been considered one of the active enhancement methods. However, understanding the details of interaction of electric field and phase change demands a strong tool to go beyond the limitations of experimental and theoretical approaches. We perform Direct Numerical Simulations (DNS) using front-tracking/finite-difference techniques to fully resolve the electric, flow, and heat transfer fields in continuum scales. In terms of electric field-induced interface instability problem, we studied the dynamics of interface under AC/DC uniform electric fields for a wide range of fluid physical properties and investigated the individual effect of their corresponding nondimensional numbers. We observed that application of DC electric field destabilizes the interface in such a way that it goes over several cycles of oscillations and then settles to its steady-state form and remains quiescent. However, for AC electric field, the interface oscillations follows the frequency of applied electric potential source. For the film boiling under applied electric field, we studied the effect of individual governing nondimensional numbers on the behavior of film boiling under DC/AC electric fields. Electric field makes the interface more unstable by elongating the bubbles, decreasing the most dangerous wavelength, and expediting the formation of bubbles. The impact of these effects on heat transfer can be observed from the evolution of Nu number in the course of film boiling. We realized that for the same conditions AC field alters the transient spatially averaged Nu number in a way that it follows the oscillations of applied electric potential source. However, the heat transfer enhancement does not get affected by applying either AC or DC electric fields. We extended our research to multimode film boiling to observe the interaction of bubbles growing next to each other. Also, we carried out a study on the effect of electric field on downward-facing film condensation over a horizontal flat plate. This problem is similar to film boiling over a horizontal flat plate which we already studied although the phase change occurs in opposite direction. Like the effect of electric field on film boiling, electric field made the interface of condensate more unstable by decreasing its most dangerous wave length. However, in this case, the enhancement becomes more effective due to cooperation of gravitational and electrical forces. Our studies show that phase change heat transfer coefficient can be enhanced in the presence of electric field by more that 70%. Condensation of vapors over the bank of horizontal tubes has always been the host of many engineering applications in power plants, chemical and petrochemical plants, etc. To take the first step toward the study of enhancement effect of electric field on complex geometries, we also carried out a study on the condensation over tube banks in the absence of electric field. This study mainly concentrates on the effect of tube distance on heat transfer coefficient in a vertically in-lined tube bank. Our study reveals that heat transfer coefficient can be highly dependent on tube diameter and spacing such that choosing an appropriate spacing can lead to a more than 50% enhancement.

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Dans ce travail, nous étudions l'écoulement au sein d'un canal symétrique avec une expansion et une contraction soudaines. Cette configuration peut être considérée comme constituée de deux cavités face à face, deux cavités en miroir, que nous dénommons "double cavité". Le sujet est traité expérimentalement, numériquement et analytiquement, en faisant varier la vitesse d'entrée et de la distance entre cavités, mais en restant à des nombres de Reynolds modérés. L'accent est mis sur l'interaction entre les deux couches de cisaillement et sur le mécanisme de rétroaction intracavitaire dans la limite des écoulements incompressibles. Expérimentalement, on mesure la vitesse par Vélocimétrie par Images de Particules non résolue en temps (PIV 2D2C) dans un plan longitudinal permettent de quanti er le champ de vitesse en moyenne temporelle. Par ailleurs, des mesures par Vélocimétrie Laser à effet Doppler (LDV) et des mesures résolues en temps par PIV 2D2C permettent d'accéder à la composition spectrale des fluctuations de vitesse dans la direction de l'écoulement. L'écoulement est caractérisé à partir des séries temporelles, enregistrées dans les couches de cisaillement d'une des deux cavités, pour une large gamme de vitesses d'entrée et des distances entre cavités. Des simulations numériques directes 2D et 3D, permettent d'étudier le mécanisme hydrodynamique de rétroaction intracavitaire, à partir des champs de vitesse complet. Le champ de vorticité issu des simulations numériques 2D montre l'importance de la rotation d'ensemble au sein de la cavité qui transporte les injections de vorticité induites par les oscillations de la couche de mélange conduisant à une structure de type "carrousel" elle-même à l'origine du mécanisme de rétroaction responsable des oscillations auto-entretenues de la couche de cisaillement. La quanti cation des temps caractéristiques de cette rotation permet d'identifier le régime dans lequel se trouve l'écoulement. Une analyse de stabilité en temps seul, ainsi qu'en temps et espace est réalisée pour des écoulements non visqueux, en prenant un écoulement de base unidimensionnel pour chacun des cas: cavité simple ou double. Pour prendre en compte l'extension finie du système, dans le cas de l'analyse de stabilité linéaire spatio-temporel, on ajoute la condition dite de Kulikowskii, qui permet de prendre en compte la réflexion des ondes d'instabilité hydrodynamique aux bornes du domaine de la cavité. Ce mécanisme de rétroaction produit un ensemble discret de fréquences non-harmoniques, dont certaines correspondent effectivement aux données expérimentales. / This work investigates the flow in a symmetric channel with a sudden expansion and contraction, creating two facing cavities, a so called double cavity. Double cavity flow at moderate Reynolds numbers is studied experimentally, numerically and analytically, as the inflow velocity and the distance between the cavities are varied. The focus is put on the interaction of the two shear layers and the intracavitary hydrodynamic feedback in the incompressible limit.Experimentally, standard 2D2C particle image velocimetry (PIV) measurements in a given spanwise plane provide information on the instantaneous and mean velocity flow fields. Laser Doppler velocimetry and time resolved 2D2C PIV measurements reveal the richness of the streamwise fluctuating velocity spectra. The flow is characterized based on times series, recorded in one of the cavity's shear layers, for a wide range of inflow velocities and cavity distances.Two dimensional and three dimensional direct numerical simulations, which give easy access to the entire flow field, are used to study the intracavitary hydrodynamic feedback mechanism. Vorticity fields, obtained from 2D numerical simulations, show the importance of the recirculating intracavitary back flow. Vorticity packages, injected by the oscillating and impinging shear layer at the downstream cavity edge, are advected upstream in the recirculation region, creating a ``carousel-like'' pattern. The interaction of this vortex carousel with the oscillating shear layer is found to be responsible for the self-sustained oscillations observed experimentally in single and double cavity flow. The quantification of three characteristic time scales of the rotation allows to identify in which regime the flow resides.Temporal and spatio-temporal inviscid linear stability analyses are applied to a one dimensional base flow of single and double cavity flows. To account for the finite extent of the system, the spatio-temporal linear stability analysis is conditioned by a so called Kulikowskii condition, which allows the reflection of hydrodynamic instability waves within the cavity domain. This feedback mechanism yields a set of discrete, non-harmonic frequencies, some of which compare well with experimental results.

The linear instability of laterally diverging/converging flows is an important aspect towards understanding the laminar-transition process in many viscous flows. In this work the linear instability of constant pressure laterally diverging/converging flow has been investigated. The laminar velocity field for laterally diverging/converging flows, under the source/sink approximation, has been reduced to two-dimensional flows. This reduction is alternative to the Mangier transformation used earlier. For a constant pressure laterally strained flow, the laminar velocity is found to be governed by the Blasius equation for flow over a flat plate. The non-parallel linear instability of constant pressure laterally strained flows has been examined. The instability equation is found to be same as that for the Blasius flow. This implies that the stability is same as that for the Blasius flow. A lateral divergence/convergence is shown to alter the Reynolds number from that in a two-dimensional flow. The instability of a laterally converging/diverging flow thus can be obtained from the available results for the Blasius flow by scaling the Reynolds numbers. This leads to the result that while a diverging flow is more unstable than the Blasius flow, a converging flow is more stable. Some additional relevant results are also presented.

Cette thèse présente quelques contributions à l'étude qualitative de solutions d'équations aux dérivées partielles non linéaires dans des modèles issus de l'optique et de la mécanique des fluides. Nous nous intéressons plus précisément à l'existence de solutions et à leur stabilité temporelle. Le Chapitre 1 est consacré à l'équation de Lugiato-Lefever, qui est une variante de l'équation de Schrödinger non linéaire et qui a été dérivée dans plusieurs contextes en optique. En utilisant des outils de la théorie des bifurcations et des formes normales, nous procédons à une étude systématique des solutions stationnaires de cette équation, et prouvons l'existence de solutions périodiques et localisées. Dans le Chapitre 2, nous présentons un critère simple d'instabilité linéaire pour des ondes non linéaires. Nous appliquons ce résultat aux équations de Lugiato-Lefever, de Kadomtsev-Petviashvili-I et de Davey-Stewartson. Ces deux dernières équations sont des équations modèles dérivées en mécanique des fluides. Dans le Chapitre 3, nous montrons un critère d'instabilité linéaire pour des solutions périodiques de petite amplitude, par rapport à certaines perturbations quasipériodiques. Ce résultat est ensuite appliqué à l'équation de Lugiato-Lefever. / In this thesis we present several contributions to qualitative study of solutions of nonlinear partial differential equations in optics and fluid mechanics models. More precisely, we focus on the existence of solutions and their stability properties. In Chapter 1, we study the Lugiato-lefever equation, which is a variant of the nonlinear Schrödinger equation arising in sereval contexts in nonlinear optics. Using tools from bifurcation and normal forms theory, we perfom a systematic analysis of stationary solutions of this equation and prove the existence of periodic and localized solutions. In Chapter 2, we present a simple criterion for linear instability of nonlinear waves. We then apply this result to the Lugiato-Lefever equation, to the Kadomtsev-Petviashvili-I equation and the Davey-Stewartson equations. These last two equations are model equations arising in fluid mechanics. In Chapter 3, we prove a criterion for linear instability of periodic solutions with small amplitude, with respect to certain quasiperiodic perturbations. This result is then applied to the Lugiato-Lefever equation.