Coalescence of particles by differential sedimentation

We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a size-dependent terminal velocity. They are either allowed to merge whenever they cross or there is a size ratio criterion enforced to account for collision efficiency. Such a system may be described, in mean field approximation, by the Smoluchowski kinetic equation with a differential sedimentation kernel. We obtain self-similar steady-state and time-dependent solutions to the kinetic equation, using methods borrowed from weak turbulence theory. Analytical results are compared with direct numerical simulations (DNS) of moving and merging particles, and a good agreement is found.

Spatially-antisymmetric localization of matter wave in a bichromatic optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Symmetry breaking in a localized interacting binary Bose-Einstein condensate in a bichromatic optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Localization of collisionally inhomogeneous condensates in a bichromatic optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length

A study was conducted on the dynamics of 2D and 3D Bose-Einstein condensates in the case when the scattering length in the Gross-Pitaevskii (GP) equation which contains constant (dc) and time-variable (ac) parts. Using the variational approximation (VA), simulating the GP equation directly, and applying the averaging procedure to the GP equation without the use of the VA, it was demonstrated that the ac component of the nonlinearity makes it possible to maintain the condensate in a stable self-confined state without external traps.

Localization of a Bose-Einstein condensate in a bichromatic optical lattice

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation, we study different aspects of the localization of a noninteracting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential. Such a quasiperiodic potential, used in a recent experiment on the localization of a BEC, can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a noninteracting BEC. We also simulate the nonlinear dynamics when a harmonically trapped BEC is suddenly released into a quasiperiodic potential, as done experimentally in a laser speckle potential. We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms. © 2009 The American Physical Society.

Mitigação de riscos e catástrofes naturais: análise numérico-experimental de roll waves evoluindo em canais inclinados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Reynolds stress model for turbulent flows of viscoelastic fluids

A second-order closure is developed for predicting turbulent flows of viscoelastic fluids described by a modified generalised Newtonian fluid model incorporating a nonlinear viscosity that depends on a strain-hardening Trouton ratio as a means to handle some of the effects of viscoelasticity upon turbulent flows. Its performance is assessed by comparing its predictions for fully developed turbulent pipe flow with experimental data for four different dilute polymeric solutions and also with two sets of direct numerical simulation data for fluids theoretically described by the finitely extensible nonlinear elastic - Peterlin model. The model is based on a Newtonian Reynolds stress closure to predict Newtonian fluid flows, which incorporates low Reynolds number damping functions to properly deal with wall effects and to provide the capability to handle fluid viscoelasticity more effectively. This new turbulence model was able to capture well the drag reduction of various viscoelastic fluids over a wide range of Reynolds numbers and performed better than previously developed models for the same type of constitutive equation, even if the streamwise and wall-normal turbulence intensities were underpredicted.

Compressible modes in a square lid-driven cavity

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Influence of Goertler vortices spanwise wavelength on heat transfer rates

The boundary layer over concave surfaces can be unstable due to centrifugal forces, giving rise to Goertler vortices. These vortices create two regions in the spanwise direction—the upwash and downwash regions. The downwash region is responsible for compressing the boundary layer toward the wall, increasing the heat transfer rate. The upwash region does the opposite. In the nonlinear development of the Goertler vortices, it can be observed that the upwash region becomes narrow and the spanwise–average heat transfer rate is higher than that for a Blasius boundary layer. This paper analyzes the influence of the spanwise wavelength of the Goertler the heat transfer. The equation is written in vorticity-velocity formulation. The time integration is done via a classical fourth-order Runge-Kutta method. The spatial derivatives are calculated using high-order compact finite difference and spectral methods. Three different wavelengths are analyzed. The results show that steady Goertler flow can increase the heat transfer rates to values close to the values of turbulence, without the existence of a secondary instability. The geometry (and computation domain) are presented

Flugzeuggetragene in-situ Messungen zur Eis- und Flüssigphase troposphärischer Wolken

Die Mikrophysik in Wolken bestimmt deren Strahlungseigenschaften und beeinflusst somit auch den Strahlungshaushalt des Planeten Erde. Aus diesem Grund werden im Rahmen der vorliegenden Arbeit die mikrophysikalischen Charakteristika von Cirrus-Wolken sowie von arktischen Grenzschicht-Wolken behandelt. Die Untersuchung dieser Wolken wurde mithilfe verschiedener Instrumente verwirklicht, welche Partikel in einem Durchmesserbereich von 250nm bis zu 6.4mm vermessen und an Forschungsflugzeugen montiert werden. Ein Instrumentenvergleich bestätigt, dass innerhalb der Bereiche in denen sich die Messungen dieser Instrumente überlappen, die auftretenden Diskrepanzen als sehr gering einzustufen sind. Das vorrangig verwendete Instrument trägt die Bezeichnung CCP (Cloud Combination Probe) und ist eine Kombination aus einem Instrument, das Wolkenpartikel anhand von vorwärts-gerichtetem Streulicht detektiert und einem weiteren, das zweidimensionale Schattenbilder einzelner Wolkenpartikel aufzeichnet. Die Untersuchung von Cirrus-Wolken erfolgt mittels Daten der AIRTOSS-ICE (AIRcraft TOwed Sensor Shuttle - Inhomogeneous Cirrus Experiment) Kampagne, welche im Jahr 2013 über der deutschen Nord- und Ostsee stattfand. Parameter wie Partikeldurchmesser, Partikelanzahlkonzentration, Partikelform, Eiswassergehalt, Wolkenhöhe und Wolkendicke der detektierten Cirrus-Wolken werden bestimmt und im Kontext des aktuellen Wissenstandes diskutiert. Des Weiteren wird eine beprobte Cirrus-Wolke im Detail analysiert, welche den typischen Entwicklungsprozess und die vertikale Struktur dieser Wolkengattung widerspiegelt. Arktische Grenzschicht-Wolken werden anhand von Daten untersucht, die während der VERDI (VERtical Distribution of Ice in Arctic Clouds) Kampagne im Jahr 2012 über der kanadischen Beaufortsee aufgezeichnet wurden. Diese Messkampagne fand im Frühling statt, um die Entwicklung von Eis-Wolken über Mischphasen-Wolken bis hin zu Flüssigwasser-Wolken zu beobachten. Unter bestimmten atmosphärischen Bedingungen tritt innerhalb von Mischphasen-Wolken der sogenannte Wegener-Bergeron-Findeisen Prozess auf, bei dem Flüssigwassertropfen zugunsten von Eispartikeln verdampfen. Es wird bestätigt, dass dieser Prozess anhand von mikrophysikalischen Messungen, insbesondere den daraus resultierenden Größenverteilungen, nachweisbar ist. Darüber hinaus wird eine arktische Flüssigwasser-Wolke im Detail untersucht, welche im Inneren das Auftreten von monomodalen Tröpfchen-Größenverteilungen zeigt. Mit zunehmender Höhe wachsen die Tropfen an und die Maxima der Größenverteilungen verschieben sich hin zu größeren Durchmessern. Dahingegen findet im oberen Übergangsbereich dieser Flüssigwasser-Wolke, zwischen Wolke und freier Atmosphäre, ein Wechsel von monomodalen zu bimodalen Tröpfchen-Größenverteilungen statt. Diese weisen eine Mode 1 mit einem Tropfendurchmesser von 20μm und eine Mode 2 mit einem Tropfendurchmesser von 10μm auf. Das dieses Phänomen eventuell typisch für arktische Flüssigwasser-Wolken ist, zeigen an dem Datensatz durchgeführte Analysen. Mögliche Entstehungsprozesse der zweiten Mode können durch Kondensation von Wasserdampf auf eingetragenen Aerosolpartikeln, die aus einer Luftschicht oberhalb der Wolke stammen oder durch Wirbel, welche trockene Luftmassen in die Wolke induzieren und Verdampfungsprozesse von Wolkentröpfchen hervorrufen, erklärt werden. Unter Verwendung einer direkten numerischen Simulation wird gezeigt, dass die Einmischung von trockenen Luftmassen in den Übergangsbereich der Wolke am wahrscheinlichsten die Ausbildung von Mode 2 verursacht.

Stabilization of subcritical bypass transition in the leading-edge boundary layer by suction

This work investigates the subcritical spatial transition in the swept Hiemenz boundary layer by means of direct numerical simulations (DNS). A pair of steady co-rotating vortices located at the attachment line is enforced as a primary disturbance leading to streaks which are stable. A small secondary, time-dependent disturbance interacts with these streaks such that instability and breakdown to turbulence may occur. The instability only occurs for a certain band of secondary disturbance frequencies. Positive secondary instability growth rates could be observed for Reynolds numbers as low as , whereas the linear critical Reynolds number is. Uniform wall suction is shown to stabilise this transition mechanism, analogously to results from linear stability theory. The effects of suction on the formation of primary streaks and on the secondary growth rate are decoupled. For streaks of different suction whose amplitude is held constant by adjusting the Reynolds number, the suction is shown to increase the growth rate of the secondary instability. The stabilising influence of wall suction consists in decreasing the streak amplitude only. Depending on the Reynolds number and the suction strength, breakdown may either occur locally and may be convected along the far-field streamlines, or occur globally and cover broad regions in the downstream direction.

Instability and topology bifurcations on a hemisphere-cylinder at high angle of attack

La configuración de un cilindro acoplado a una semi-esfera, conocida como ’hemispherecylinder’, se considera como un modelo simplificado para numerosas aplicaciones industriales tales como fuselaje de aviones o submarinos. Por tanto, el estudio y entendimiento de los fenómenos fluidos que ocurren alrededor de dicha geometría presenta gran interés. En esta tesis se muestra la investigación del origen y evolución de los, ya conocidos, patrones de flujo (burbuja de separación, vórtices ’horn’ y vórtices ’leeward’) que se dan en esta geometría bajo condiciones de flujo separado. Para ello se han llevado a cabo simulaciones numéricas (DNS) y ensayos experimentales usando la técnica de Particle Image Velocimetry (PIV), para una variedad de números de Reynolds (Re) y ángulos de ataque (AoA). Se ha aplicado sobre los resultados numéricos la teoría de puntos críticos obteniendo, por primera vez para esta geometría, un diagrama de bifurcaciones que clasifica los diferentes regímenes topológicos en función del número de Reynolds y del ángulo de ataque. Se ha llevado a cabo una caracterización completa sobre el origen y la evolución de los patrones estructurales característicos del cuerpo estudiado. Puntos críticos de superficie y líneas de corriente tridimensionales han ayudado a describir el origen y la evolución de las principales estructuras presentes en el flujo hasta alcanzar un estado de estabilidad desde el punto de vista topológico. Este estado se asocia con el patrón de los vórtices ’horn’, definido por una topología característica que se encuentra en un rango de números de Reynolds muy amplio y en regímenes compresibles e incompresibles. Por otro lado, con el objeto de determinar las estructuras presentes en el flujo y sus frecuencias asociadas, se han usado distintas técnicas de análisis: Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD) y análisis de Fourier. Dichas técnicas se han aplicado sobre los datos experimentales y numéricos, demostrándose la buena concordancia entre ambos resultados. Finalmente, se ha encontrado en ambos casos, una frecuencia dominante asociada con una inestabilidad de los vórtices ’leeward’. ABSTRACT The hemisphere-cylinder may be considered as a simplified model for several geometries found in industrial applications such as aircrafts’ fuselages or submarines. Understanding the complex flow phenomena that surrounds this particular geometry is therefore of major industrial interest. This thesis presents an investigation of the origin and evolution of the complex flow pattern; i.e. separation bubbles, horn vortices and leeward vortices, around the hemisphere-cylinder under separated flow conditions. To this aim, threedimensional Direct Numerical Simulations (DNS) and experimental tests, using Particle Image Velocimetry (PIV) techniques, have been performed for a variety of Reynolds numbers (Re) and angles of attack (AoA). Critical point theory has been applied to the numerical simulations to provide, for the first time for this geometry, a bifurcation diagram that classifies the different flow topology regimes as a function of the Reynolds number and the angle of attack. A complete characterization about the origin and evolution of the complex structural patterns of this geometry has been put in evidence. Surface critical points and surface and volume streamlines were able to describe the main flow structures and their strong dependence with the flow conditions up to reach the structurally stable state. This state was associated with the pattern of the horn vortices, found on ranges from low to high Reynolds numbers and from incompressible to compressible regimes. In addition, different structural analysis techniques have been employed: Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD) and Fourier analysis. These techniques have been applied to the experimental and numerical data to extract flow structure information (i.e. modes and frequencies). Experimental and numerical modes are shown to be in good agreement. A dominant frequency associated with an instability of the leeward vortices has been identified in both, experimental and numerical results.

Advances in global instability computations: from incompressible to hypersonic flow

Esta tesis constituye un gran avance en el conocimiento del estudio y análisis de inestabilidades hidrodinámicas desde un punto de vista físico y teórico, como consecuencia de haber desarrollado innovadoras técnicas para la resolución computacional eficiente y precisa de la parte principal del espectro correspondiente a los problemas de autovalores (EVP) multidimensionales que gobiernan la inestabilidad de flujos con dos o tres direcciones espaciales inhomogéneas, denominados problemas de estabilidad global lineal. En el contexto del trabajo de desarrollo de herramientas computacionales presentado en la tesis, la discretización mediante métodos de diferencias finitas estables de alto orden de los EVP bidimensionales y tridimensionales que se derivan de las ecuaciones de Navier-Stokes linealizadas sobre flujos con dos o tres direcciones espaciales inhomogéneas, ha permitido una aceleración de cuatro órdenes de magnitud en su resolución. Esta mejora de eficiencia numérica se ha conseguido gracias al hecho de que usando estos esquemas de diferencias finitas, técnicas eficientes de resolución de problemas lineales son utilizables, explotando el alto nivel de dispersión o alto número de elementos nulos en las matrices involucradas en los problemas tratados. Como más notable consecuencia cabe destacar que la resolución de EVPs multidimensionales de inestabilidad global, que hasta la fecha necesitaban de superordenadores, se ha podido realizar en ordenadores de sobremesa. Además de la solución de problemas de estabilidad global lineal, el mencionado desarrollo numérico facilitó la extensión de las ecuaciones de estabilidad parabolizadas (PSE) lineales y no lineales para analizar la inestabilidad de flujos que dependen fuertemente en dos direcciones espaciales y suavemente en la tercera con las ecuaciones de estabilidad parabolizadas tridimensionales (PSE-3D). Precisamente la capacidad de extensión del novedoso algoritmo PSE-3D para el estudio de interacciones no lineales de los modos de estabilidad, desarrollado íntegramente en esta tesis, permite la predicción de transición en flujos complejos de gran interés industrial y por lo tanto extiende el concepto clásico de PSE, el cuál ha sido empleado exitosamente durante las pasadas tres décadas en el mismo contexto para problemas de capa límite bidimensional. Típicos ejemplos de flujos incompresibles se han analizado en este trabajo sin la necesidad de recurrir a restrictivas presuposiciones usadas en el pasado. Se han estudiado problemas vorticales como es el caso de un vórtice aislado o sistemas de vórtices simulando la estela de alas, en los que la homogeneidad axial no se impone y así se puede considerar la difusión viscosa del flujo. Además, se ha estudiado el chorro giratorio turbulento, cuya inestabilidad se utiliza para mejorar las características de funcionamiento de combustores. En la tesis se abarcan adicionalmente problemas de flujos compresibles. Se presenta el estudio de inestabilidad de flujos de borde de ataque a diferentes velocidades de vuelo. También se analiza la estela formada por un elemento rugoso aislado en capa límite supersónica e hipersónica, mostrando excelentes comparaciones con resultados obtenidos mediante simulación numérica directa. Finalmente, nuevas inestabilidades se han identificado en el flujo hipersónico a Mach 7 alrededor de un cono elíptico que modela el vehículo de pruebas en vuelo HIFiRE-5. Los resultados comparan favorablemente con experimentos en vuelo, lo que subraya aún más el potencial de las metodologías de análisis de estabilidad desarrolladas en esta tesis. ABSTRACT The present thesis constitutes a step forward in advancing the frontiers of knowledge of fluid flow instability from a physical point of view, as a consequence of having been successful in developing groundbreaking methodologies for the efficient and accurate computation of the leading part of the spectrum pertinent to multi-dimensional eigenvalue problems (EVP) governing instability of flows with two or three inhomogeneous spatial directions. In the context of the numerical work presented in this thesis, the discretization of the spatial operator resulting from linearization of the Navier-Stokes equations around flows with two or three inhomogeneous spatial directions by variable-high-order stable finite-difference methods has permitted a speedup of four orders of magnitude in the solution of the corresponding two- and three-dimensional EVPs. This improvement of numerical performance has been achieved thanks to the high-sparsity level offered by the high-order finite-difference schemes employed for the discretization of the operators. This permitted use of efficient sparse linear algebra techniques without sacrificing accuracy and, consequently, solutions being obtained on typical workstations, as opposed to the previously employed supercomputers. Besides solution of the two- and three-dimensional EVPs of global linear instability, this development paved the way for the extension of the (linear and nonlinear) Parabolized Stability Equations (PSE) to analyze instability of flows which depend in a strongly-coupled inhomogeneous manner on two spatial directions and weakly on the third. Precisely the extensibility of the novel PSE-3D algorithm developed in the framework of the present thesis to study nonlinear flow instability permits transition prediction in flows of industrial interest, thus extending the classic PSE concept which has been successfully employed in the same context to boundary-layer type of flows over the last three decades. Typical examples of incompressible flows, the instability of which was analyzed in the present thesis without the need to resort to the restrictive assumptions used in the past, range from isolated vortices, and systems thereof, in which axial homogeneity is relaxed to consider viscous diffusion, as well as turbulent swirling jets, the instability of which is exploited in order to improve flame-holding properties of combustors. The instability of compressible subsonic and supersonic leading edge flows has been solved, and the wake of an isolated roughness element in a supersonic and hypersonic boundary-layer has also been analyzed with respect to its instability: excellent agreement with direct numerical simulation results has been obtained in all cases. Finally, instability analysis of Mach number 7 ow around an elliptic cone modeling the HIFiRE-5 flight test vehicle has unraveled flow instabilities near the minor-axis centerline, results comparing favorably with flight test predictions.

Accurate Parabolic Navier-Stokes solutions of the supersonic flow around and elliptic cone

Flows of relevance to new generation aerospace vehicles exist, which are weakly dependent on the streamwise direction and strongly dependent on the other two spatial directions, such as the flow around the (flattened) nose of the vehicle and the associated elliptic cone model. Exploiting these characteristics, a parabolic integration of the Navier-Stokes equations is more appropriate than solution of the full equations, resulting in the so-called Parabolic Navier-Stokes (PNS). This approach not only is the best candidate, in terms of computational efficiency and accuracy, for the computation of steady base flows with the appointed properties, but also permits performing instability analysis and laminar-turbulent transition studies a-posteriori to the base flow computation. This is to be contrasted with the alternative approach of using order-of-magnitude more expensive spatial Direct Numerical Simulations (DNS) for the description of the transition process. The PNS equations used here have been formulated for an arbitrary coordinate transformation and the spatial discretization is performed using a novel stable high-order finite-difference-based numerical scheme, ensuring the recovery of highly accurate solutions using modest computing resources. For verification purposes, the boundary layer solution around a circular cone at zero angle of attack is compared in the incompressible limit with theoretical profiles. Also, the recovered shock wave angle at supersonic conditions is compared with theoretical predictions in the same circular-base cone geometry. Finally, the entire flow field, including shock position and compressible boundary layer around a 2:1 elliptic cone is recovered at Mach numbers 3 and 4