Three-dimensional flow instability in a lid-driven isosceles triangular cavity

Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isosceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular corner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular corner, a stationary three-dimensional instability is found. If the motion is directed towards the corner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed.

Mixing Snapshots and Fast Time Integration of PDEs

A local proper orthogonal decomposition (POD) plus Galerkin projection method was recently developed to accelerate time dependent numerical solvers of PDEs. This method is based on the combined use of a numerical code (NC) and a Galerkin sys- tem (GS) in a sequence of interspersed time intervals, INC and IGS, respectively. POD is performed on some sets of snapshots calculated by the numerical solver in the INC inter- vals. The governing equations are Galerkin projected onto the most energetic POD modes and the resulting GS is time integrated in the next IGS interval. The major computa- tional e®ort is associated with the snapshots calculation in the ¯rst INC interval, where the POD manifold needs to be completely constructed (it is only updated in subsequent INC intervals, which can thus be quite small). As the POD manifold depends only weakly on the particular values of the parameters of the problem, a suitable library can be con- structed adapting the snapshots calculated in other runs to drastically reduce the size of the ¯rst INC interval and thus the involved computational cost. The strategy is success- fully tested in (i) the one-dimensional complex Ginzburg-Landau equation, including the case in which it exhibits transient chaos, and (ii) the two-dimensional unsteady lid-driven cavity problem

Reduced order modeling of some fluid flows of industrial interest

Some basic ideas are presented for the construction of robust, computationally efficient reduced order models amenable to be used in industrial environments, combined with somewhat rough computational fluid dynamics solvers. These ideas result from a critical review of the basic principles of proper orthogonal decomposition-based reduced order modeling of both steady and unsteady fluid flows. In particular, the extent to which some artifacts of the computational fluid dynamics solvers can be ignored is addressed, which opens up the possibility of obtaining quite flexible reduced order models. The methods are illustrated with the steady aerodynamic flow around a horizontal tail plane of a commercial aircraft in transonic conditions, and the unsteady lid-driven cavity problem. In both cases, the approximations are fairly good, thus reducing the computational cost by a significant factor.

Language identification based on a discriminative text categorization technique

In this paper, we describe new results and improvements to a lan-guage identification (LID) system based on PPRLM previously introduced in [1] and [2]. In this case, we use as parallel phone recognizers the ones provided by the Brno University of Technology for Czech, Hungarian, and Russian lan-guages, and instead of using traditional n-gram language models we use a lan-guage model that is created using a ranking with the most frequent and discrim-inative n-grams. In this language model approach, the distance between the ranking for the input sentence and the ranking for each language is computed, based on the difference in relative positions for each n-gram. This approach is able to model reliably longer span information than in traditional language models obtaining more reliable estimations. We also describe the modifications that we have being introducing along the time to the original ranking technique, e.g., different discriminative formulas to establish the ranking, variations of the template size, the suppression of repeated consecutive phones, and a new clus-tering technique for the ranking scores. Results show that this technique pro-vides a 12.9% relative improvement over PPRLM. Finally, we also describe re-sults where the traditional PPRLM and our ranking technique are combined.

Patrol team language identification system for DARPA RATS P1 evaluation

This paper describes the language identification (LID) system developed by the Patrol team for the first phase of the DARPA RATS (Robust Automatic Transcription of Speech) program, which seeks to advance state of the art detection capabilities on audio from highly degraded communication channels. We show that techniques originally developed for LID on telephone speech (e.g., for the NIST language recognition evaluations) remain effective on the noisy RATS data, provided that careful consideration is applied when designing the training and development sets. In addition, we show significant improvements from the use of Wiener filtering, neural network based and language dependent i-vector modeling, and fusion.

Phonotactic language recognition using i-vectors and phoneme posteriogram counts

This paper describes a novel approach to phonotactic LID, where instead of using soft-counts based on phoneme lattices, we use posteriogram to obtain n-gram counts. The high-dimensional vectors of counts are reduced to low-dimensional units for which we adapted the commonly used term i-vectors. The reduction is based on multinomial subspace modeling and is designed to work in the total-variability space. The proposed technique was tested on the NIST 2009 LRE set with better results to a system based on using soft-counts (Cavg on 30s: 3.15% vs 3.43%), and with very good results when fused with an acoustic i-vector LID system (Cavg on 30s acoustic 2.4% vs 1.25%). The proposed technique is also compared with another low dimensional projection system based on PCA. In comparison with the original soft-counts, the proposed technique provides better results, reduces the problems due to sparse counts, and avoids the process of using pruning techniques when creating the lattices.

Matrix-free time-stepping methods for the solution of TriGlobal instability problems

La inmensa mayoría de los flujos de relevancia ingenieril permanecen sin estudiar en el marco de la teoría de estabilidad global. Esto es debido a dos razones fundamentalmente, las dificultades asociadas con el análisis de los flujos turbulentos y los inmensos recursos computacionales requeridos para obtener la solución del problema de autovalores asociado al análisis de inestabilidad de flujos tridimensionales, también conocido como problema TriGlobal. En esta tesis se aborda el problema asociado con la tridimensionalidad. Se ha desarrollado una metodología general para obtener soluciones de problemas de análisis modal de las inestabilidades lineales globales mediante el acoplamiento de métodos de evolución temporal, desarrollados en este trabajo, con códigos de mecánica de fluidos computacional de segundo orden, utilizados de forma general en la industria. Esta metodología consiste en la resolución del problema de autovalores asociado al análisis de inestabilidad mediante métodos de proyección en subespacios de Krylov, con la particularidad de que dichos subespacios son generados por medio de la integración temporal de un vector inicial usando cualquier código de mecánica de fluidos computacional. Se han elegido tres problemas desafiantes en función de la exigencia de recursos computacionales necesarios y de la complejidad física para la demostración de la presente metodología: (i) el flujo en el interior de una cavidad tridimensional impulsada por una de sus tapas, (ii) el flujo alrededor de un cilindro equipado con aletas helicoidales a lo largo su envergadura y (iii) el flujo a través de una cavidad abierta tridimensinal en ausencia de homogeneidades espaciales. Para la validación de la tecnología se ha obtenido la solución del problema TriGlobal asociado al flujo en la cavidad tridimensional, utilizando el método de evolución temporal desarrollado acoplado con los operadores numéricos de flujo incompresible del código CFD OpenFOAM (código libre). Los resultados obtenidos coinciden plentamente con la literatura. La aplicación de esta metodología al estudio de inestabilidades globales de flujos abiertos tridimensionales ha proporcionado por primera vez, información sobre la transición tridimensional de estos flujos. Además, la metodología ha sido adaptada para resolver problemas adjuntos TriGlobales, permitiendo el control de flujo basado en modificaciones de las inestabilidades globales. Finalmente, se ha demostrado que la cantidad moderada de los recursos computacionales requeridos para la solución del problema de valor propio TriGlobal usando este método numérico, junto a su versatilidad al poder acoplarse a cualquier código aerodinámico, permite la realización de análisis de inestabilidad global y control de flujos complejos de relevancia industrial. Abstract Most flows of engineering relevance still remain unexplored in a global instability theory context for two reasons. First, because of the difficulties associated with the analysis of turbulent flows and, second, for the formidable computational resources required for the solution of the eigenvalue problem associated with the instability analysis of three-dimensional base flows, also known as TriGlobal problem. In this thesis, the problem associated with the three-dimensionality is addressed by means of the development of a general approach to the solution of large-scale global linear instability analysis by coupling a time-stepping approach with second order aerodynamic codes employed in industry. Three challenging flows in the terms of required computational resources and physical complexity have been chosen for demonstration of the present methodology; (i) the flow inside a wall-bounded three-dimensional lid-driven cavity, (ii) the flow past a cylinder fitted with helical strakes and (iii) the flow over a inhomogeneous three-dimensional open cavity. Results in excellent agreement with the literature have been obtained for the three-dimensional lid-driven cavity by using this methodology coupled with the incompressible solver of the open-source toolbox OpenFOAM®, which has served as validation. Moreover, significant physical insight of the instability of three-dimensional open flows has been gained through the application of the present time-stepping methodology to the other two cases. In addition, modifications to the present approach have been proposed in order to perform adjoint instability analysis of three-dimensional base flows and flow control; validation and TriGlobal examples are presented. Finally, it has been demonstrated that the moderate amount of computational resources required for the solution of the TriGlobal eigenvalue problem using this method enables the performance of instability analysis and control of flows of industrial relevance.

On the Use of Matrix-Free Shift-Invert Strategies For Global Flow Instability Analysis

A novel time-stepping shift-invert algorithm for linear stability analysis of laminar flows in complex geometries is presented. This method, based on a Krylov subspace iteration, enables the solution of complex non-symmetric eigenvalue problems in a matrix-free framework. Validations and comparisons to the classical exponential method have been performed in three different cases: (i) stenotic flow, (ii) backward-facing step and (iii) lid-driven swirling flow. Results show that this new approach speeds up the required Krylov subspace iterations and has the capability of converging to specific parts of the global spectrum. It is shown that, although the exponential method remains the method of choice if leading eigenvalues are sought, the performance of the present method could be dramatically improved with the use of a preconditioner. In addition, as opposed to other methods, this strategy can be directly applied to any time-stepper, regardless of the temporal or spatial discretization of the latter.

On the role of global flow instability analysis in closed loop flow control

Control of linear flow instabilities has been demonstrated to be an effective theoretical flow control methodology, capable of modifying transitional flows on canonical geometries such as the plane channel and the flat-plate boundary layer. Extending the well-developed theoretical flow control techniques to flows over or through complex geometries requires addressing the issue of efficient capturing of the leading members of the global eigenspectrum pertinent to such flows. The present contribution describes state-of-the-art modal global instability analysis methodologies recently developed in our group, based on matrix formation and time-stepping, respectively. The relative performance of these algorithms is assessed on the recovery of BiGlobal and TriGlobal eigenspectra in the spanwise periodic and the cubic lid-driven cavity, respectively; the adjoint eigenspectrum in the latter flow is recovered for the first time. For three-dimensional flows without any homogeneous spatial direction, the time-stepping methodology was found to outperform the matrix-forming approach and permit recovering the leading TriGlobal eigenmodes in an three-dimensional open cavity of aspect ratio L : D : W = 5 : 1 : 1; theoretical flow control of this configuration is underway.

Evaluación y optimización de parámetros PLLR en sistemas de reconocimiento de idioma fonotácticos

Este trabajo tiene como objetivo por un lado describir el estado de la cuestión relacionado con el reconocimiento de idioma (LID), haciendo especial énfasis en aquellos temas que están más relacionados con el desarrollo de este trabajo. Por otra parte se presentan los resultados y conclusiones obtenidos tras el estudio y análisis de diferentes técnicas basadas en los parámetros “Phone Log-Likelihood Ratios” (PLLR) para mejorar el rendimiento de un sistema de reconocimiento de idioma basado en iVectores. En concreto, se presentarán los estudios realizados sobre dos familias de reconocedores de idioma PLLR: los basados en las probabilidades de los fonemas y los basados en las probabilidades de los estados de cada fonema. Estos últimos serán objeto de un estudio más profundo.

Evolución de la vegetación en el sector biogeográfico Castellano Cantábrico durante el Cuaternario Final, a través del registro tobáceo

En esta memoria de Tesis Doctoral se aborda el estudio paleobotánico de seis yacimientos tobáceos situados en las localidades burgalesas de Tubilla del Agua, Sedano, Herrán, Tobera y Frías, y en la alavesa de Ocio. El registro fósil encontrado en estos afloramientos se analiza de forma conjunta con el objetivo de conocer la evolución de la vegetación en el sector biogeográfico Castellano Cantábrico. Este sector se considera el territorio para el cual los hallazgos paleobotánicos son representativos y extrapolables, en tanto que constituye una región homogénea desde el punto de vista florístico, que abarca todos los yacimientos prospectados. El contexto temporal en el que se enmarca este estudio es el final del Cuaternario, desde el Pleistoceno Medio hasta la actualidad. Este intervalo se ha establecido a partir de la edad de los depósitos estudiados, la cual ha sido determinada —para los yacimientos de los que no se disponía de edades fiables— mediante la datación de muestras extraídas de las diferentes unidades litológicas identificadas. Para ello han sido empleadas las técnicas de carbono-14, desequilibrio de las series del uranio y racemización de aminoácidos. Los resultados geocronológicos obtenidos junto con el análisis geomorfológico de los yacimientos han permitido vincular la génesis de las 13 unidades litológicas identificadas con diferentes estadíos climáticos. Estos abarcan un amplio rango de condiciones ambientales, desde las más extremas del Último Máximo Glacial, hasta las más benignas de los Estadíos Isotópicos Marinos interglaciares 1 y 5. Como resultado de la prospección de los depósitos de toba fueron recuperados 1.820 fósiles, la mayoría impresiones foliares, pero también moldes de estróbilos femeninos, ramas y corteza, así como 42 carbones y restos subfósiles de Pinus sp. La identificación taxonómica de estos restos se ha realizado fundamentalmente a partir del análisis de caracteres diagnósticos morfológicos. Como resultado de ello, han sido descritos 28 taxones pertenecientes a las subclases Bryidae, Polypodiidae, Pinidae y Magnoliidae. La flora de los yacimientos estudiados se puede clasificar en tres grupos en función de sus requerimientos ecológicos: (i) uno formado por dos especies de alta tolerancia a la continentalidad —Pinus nigra y Quercus faginea—, las cuales aparecen bien representadas en la mayoría de los depósitos; (ii) otro constituido fundamentalmente por un conjunto de árboles y arbustos que habitualmente tienen el papel de especies acompañantes en los bosques ibéricos submediterráneos y eurosiberianos; y (iii) un tercer grupo compuesto por taxones hidrófitos o edafohigrófilos asociados al ecosistema del fitohermo activo y la vegetación de ribera. En el capítulo de Discusión se propone y analiza la hipótesis de que P. nigra y Q. faginea habrían sido las especies protagonistas de la vegetación zonal del sector Castellano Cantábrico durante el Cuaternario Final. Estas podrían haber persistido como tal incluso durante las épocas más frías, debido a su amplia valencia ecológica y a la capacidad de reproducirse vegetativamente en el caso del quejigo. Por el contrario, los taxones mesofíticos y eurosiberianos pudieron haber sufrido la expansión y retracción de sus poblaciones al ritmo de las oscilaciones climáticas. Sin embargo, la orografía diversa del sector Castellano Cantábrico proporciona emplazamientos en los que se combinan las diversas variables fisiográficas, de tal forma que pudieron haber existido microrrefugios en los que encontraron cobijo algunos taxones mesotérmicos y eurosiberianos durante los periodos glaciales. Por último, la historia evolutiva reciente de la vegetación de este territorio ha estado marcada por la acción antrópica, la cual empezó a ser manifiesta a partir del Neolítico. Esta se tradujo en la degradación y reducción de la cubierta forestal, así como en la extinción del pino laricio del Sector Castellano Cantábrico en los dos últimos milenios. ABSTRACT This PhD Dissertation focuses in the study of six tufa formations located nearby the villages of Tubilla del Agua, Sedano, Herrán, Tobera y Frías, all of them in the province of Burgos, and Ocio, which belongs to the province of Álava. We analyze the palaeobotanical archives of these sites with the purpose of unveiling and understanding the evolution of the vegetation of the Castilian Cantabrian biogeographical sector. This area is considered to be the territory that is represented in the palaeobotanical sample of the studied tufa archives. It is the homogeneous phitogeographical area with the lowest rank that include all the sites. The time frame of this study is the last part of the Quaternary, since the Middle Pleistocene to the present time. This interval is defined by the age of the tufa deposits, which were dated —for the ones that there were not available datings— throughout the analysis of 20 tufa samples taken from the 13 identified lithostratigraphic units. The age of the samples has been determined by using the methods of radiocarbon, U-Th dating and amino acid racemization. Chronological results, along with the chronostratigraphic study of the sites has allowed us to relate the build-up of the 13 identified lithostratigraphic units with different climatic stages. These structures were deposited in a wide range of climatic conditions, from the most extreme ones of the Last Glacial Maximum, to the warmer ones of the Marine Isotopic Stages 1 and 5. A total of 1,820 fossils were recovered from the tufa deposits, most of them were leaf impressions, but also pine cones, branches and bark moulds, along with charcoal and Pinus nigra macro remains. The taxonomical identification of these remains has been done mainly through the analysis of morphological traits. As a result of this process, 28 taxa belonging to the subclass of Bryidae, Polypodiidae, Pinidae and Magnoliidae were identified. The persistency of some taxa can be traced along different climatic stages in this fossil record. This fossil flora can be classified in three different groups: (i) the first one would be composed of two species with high continental climate tolerance —Pinus nigra y Quercus faginea—, which can be found in most of the deposits, (ii) the second group would be mostly formed by trees and shrubs that usually grow in the Iberian forests as an accessory species and (iii) the third one is composed of hydrophytes or hydrophilic taxa associate to the streams, riparian zones or the active tufa ecosystem. In the Discussion chapter we propose and analyse the hypothesis that P.nigra and Q. faginea were the main species of the zonal vegetation of the Castilian Cantabrian biogeographical sector during the last part of the Quaternary. This species could have persisted due to their wide ecological amplitude and also due to the capacity of asexual reproduction in the cases of the oak. On the other hand, mesophitic taxa could have suffered the retraction and expansion of their population following the climate oscillations. However, the diverse orography of the Castilian Cantabrian biogeographical sector provides a variety of combinations of physiographic variables, which could have been suitable refuges for some of the mesophitic taxa. The recent evolutionary history of the vegetation in this territory has been affected by human activities, which started to be relevant since the Neolithic. This led to a reduction of the forests and eventually, to the extinction of P. nigra in the Castilian Cantabrian biogeographical sector in the last two thousands of years.

Discrete linear stability and sensitivity analysis of fluid flows

Este trabajo presenta un método discreto para el cálculo de estabilidad hidrodinámica y análisis de sensibilidad a perturbaciones externas para ecuaciones diferenciales y en particular para las ecuaciones de Navier-Stokes compressible. Se utiliza una aproximación con variable compleja para obtener una precisión analítica en la evaluación de la matriz Jacobiana. Además, mapas de sensibilidad para la sensibilidad a las modificaciones del flujo de base y a una fuerza constante permiten identificar las regiones del campo fluido donde una modificacin (ej. fuerza puntual) tiene un efecto estabilizador del flujo. Se presentan cuatro casos de prueba: (1) un caso analítico para comprobar la derivación discreta, (2) una cavidad cerrada a bajo Reynolds para mostrar la mayor precisión en el cálculo de los valores propios con la aproximación de paso complejo, (3) flujo 2D en un cilindro circular para validar la metodología, y (4) flujo en un cavidad abierta, presentado para validar el método en casos de inestabilidades convectivamente inestables. Los tres últimos casos mencionados (2-4) se resolvieron con las ecuaciones de Navier-Stokes compresibles, utilizando un método Discontinuous Galerkin Spectral Element Method. Se obtuvo una buena concordancia para el caso de validación (3), cuando se comparó el nuevo método con resultados de la literatura. Además, este trabajo muestra que para el cálculo de los modos propios directos y adjuntos, así como para los mapas de sensibilidad, el uso de variables complejas es de suprema importancia para obtener una predicción precisa. El método descrito es aplicado al análisis para la estabilización de la estela generada por un disco actuador, que representa un modelo sencillo para hélices, rotores de helicópteros o turbinas eólicas. Se explora la primera bifurcación del flujo para un disco actuador, y se sugiere que está asociada a una inestabilidad de tipo Kelvin-Helmholtz, cuya estabilidad se controla con en el número de Reynolds y en la resistencia del disco actuador (o fuerza resistente). En primer lugar, se verifica que la disminución de la resistencia del disco tiene un efecto estabilizador parecido a una disminución del Reynolds. En segundo lugar, el análisis hidrodinmico discreto identifica dos regiones para la colocación de una fuerza puntual que controle las inestabilidades, una cerca del disco y otra en una zona aguas abajo. En tercer lugar, se muestra que la inclusión de un forzamiento localizado cerca del actuador produce una estabilización más eficiente que al forzar aguas abajo. El análisis de los campos de flujo controlados confirma que modificando el gradiente de velocidad cerca del actuador es más eficiente para estabilizar la estela. Estos resultados podrían proporcionar nuevas directrices para la estabilización de la estela de turbinas de viento o de marea cuando estén instaladas en un parque eólico y minimizar las interacciones no estacionarias entre turbinas. ABSTRACT A discrete framework for computing the global stability and sensitivity analysis to external perturbations for any set of partial differential equations is presented. In particular, a complex-step approximation is used to achieve near analytical accuracy for the evaluation of the Jacobian matrix. Sensitivity maps for the sensitivity to base flow modifications and to a steady force are computed to identify regions of the flow field where an input could have a stabilising effect. Four test cases are presented: (1) an analytical test case to prove the theory of the discrete framework, (2) a lid-driven cavity at low Reynolds case to show the improved accuracy in the calculation of the eigenvalues when using the complex-step approximation, (3) the 2D flow past a circular cylinder at just below the critical Reynolds number is used to validate the methodology, and finally, (4) the flow past an open cavity is presented to give an example of the discrete method applied to a convectively unstable case. The latter three (2–4) of the aforementioned cases were solved with the 2D compressible Navier–Stokes equations using a Discontinuous Galerkin Spectral Element Method. Good agreement was obtained for the validation test case, (3), with appropriate results in the literature. Furthermore, it is shown that for the calculation of the direct and adjoint eigenmodes and their sensitivity maps to external perturbations, the use of complex variables is paramount for obtaining an accurate prediction. An analysis for stabilising the wake past an actuator disc, which represents a simple model for propellers, helicopter rotors or wind turbines is also presented. We explore the first flow bifurcation for an actuator disc and it suggests that it is associated to a Kelvin- Helmholtz type instability whose stability relies on the Reynolds number and the flow resistance applied through the disc (or actuator forcing). First, we report that decreasing the disc resistance has a similar stabilising effect to an decrease in the Reynolds number. Second, a discrete sensitivity analysis identifies two regions for suitable placement of flow control forcing, one close to the disc and one far downstream where the instability originates. Third, we show that adding a localised forcing close to the actuator provides more stabilisation that forcing far downstream. The analysis of the controlled flow fields, confirms that modifying the velocity gradient close to the actuator is more efficient to stabilise the wake than controlling the sheared flow far downstream. An interesting application of these results is to provide guidelines for stabilising the wake of wind or tidal turbines when placed in an energy farm to minimise unsteady interactions.