Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile

In this work, various turbulent solutions of the two-dimensional (2D) and three-dimensional compressible Reynolds averaged Navier?Stokes equations are analyzed using global stability theory. This analysis is motivated by the onset of flow unsteadiness (Hopf bifurcation) for transonic buffet conditions where moderately high Reynolds numbers and compressible effects must be considered. The buffet phenomenon involves a complex interaction between the separated flow and a shock wave. The efficient numerical methodology presented in this paper predicts the critical parameters, namely, the angle of attack and Mach and Reynolds numbers beyond which the onset of flow unsteadiness appears. The geometry, a NACA0012 profile, and flow parameters selected reproduce situations of practical interest for aeronautical applications. The numerical computation is performed in three steps. First, a steady baseflow solution is obtained; second, the Jacobian matrix for the RANS equations based on a finite volume discretization is computed; and finally, the generalized eigenvalue problem is derived when the baseflow is linearly perturbed. The methodology is validated predicting the 2D Hopf bifurcation for a circular cylinder under laminar flow condition. This benchmark shows good agreement with the previous published computations and experimental data. In the transonic buffet case, the baseflow is computed using the Spalart?Allmaras turbulence model and represents a mean flow where the high frequency content and length scales of the order of the shear-layer thickness have been averaged. The lower frequency content is assumed to be decoupled from the high frequencies, thus allowing a stability analysis to be performed on the low frequency range. In addition, results of the corresponding adjoint problem and the sensitivity map are provided for the first time for the buffet problem. Finally, an extruded three-dimensional geometry of the NACA0012 airfoil, where all velocity components are considered, was also analyzed as a Triglobal stability case, and the outcoming results were compared to the previous 2D limited model, confirming that the buffet onset is well detected.

Stability analysis of a free falling pararotor

The pararotor is a decelerator device based on the autorotation of a rotating wing. When it is dropped, it generates an aerodynamic force parallel to the main motion direction, acting as a decelerating force. In this paper, the rotational motion equations are shown for the vertical flight without any lateral wind component and some simplifying assumptions are introduced to obtain analytic solutions of the motion. First, the equilibrium state is obtained as a function of the main parameters. Then the equilibrium stability is analyzed. The motion stability depends on two nondimensional parameters, which contain geometric, inertia, and aerodynamic characteristics of the device. Based on these two parameters a stability diagram can be defined. Some stability regions with different types of stability trajectories (nodes, spirals, focuses) can be identified for spinning motion around axes close to the major, minor, and intermediate principal axes. It is found that the blades contribute to stability in a case of spin around the intermediate principal inertia axis, which is otherwise unstable. Subsequently, the equations for determining the angles of nutation and spin of the body are obtained, thus defining the orientation of the body for a stationary motion and the parameters on which that position depends.

Methodology for Dynamic Stability and Robustness Analysis of Commercial-Power-Module-Based DC-Distributed Systems

El propósito de esta tesis es presentar una metodología para realizar análisis de la dinámica en pequeña señal y el comportamiento de sistemas de alimentación distribuidos de corriente continua (CC), formados por módulos comerciales. Para ello se hace uso de un método sencillo que indica los márgenes de estabilidad menos conservadores posibles mediante un solo número. Este índice es calculado en cada una de las interfaces que componen el sistema y puede usarse para obtener un índice global que indica la estabilidad del sistema global. De esta manera se posibilita la comparación de sistemas de alimentación distribuidos en términos de robustez. La interconexión de convertidores CC-CC entre ellos y con los filtros EMI necesarios puede originar interacciones no deseadas que dan lugar a la degradación del comportamiento de los convertidores, haciendo el sistema más propenso a inestabilidades. Esta diferencia en el comportamiento se debe a interacciones entre las impedancias de los diversos elementos del sistema. En la mayoría de los casos, los sistemas de alimentación distribuida están formados por módulos comerciales cuya estructura interna es desconocida. Por ello los análisis presentados en esta tesis se basan en medidas de la respuesta en frecuencia del convertidor que pueden realizarse desde los terminales de entrada y salida del mismo. Utilizando las medidas de las impedancias de entrada y salida de los elementos del sistema, se puede construir una función de sensibilidad que proporciona los márgenes de estabilidad de las diferentes interfaces. En esta tesis se utiliza el concepto del valor máximo de la función de sensibilidad (MPC por sus siglas en inglés) para indicar los márgenes de estabilidad como un único número. Una vez que la estabilidad de todas las interfaces del sistema se han evaluado individualmente, los índices obtenidos pueden combinarse para obtener un único número con el que comparar la estabilidad de diferentes sistemas. Igualmente se han analizado las posibles interacciones en la entrada y la salida de los convertidores CC-CC, obteniéndose expresiones analíticas con las que describir en detalle los acoplamientos generados en el sistema. Los estudios analíticos realizados se han validado experimentalmente a lo largo de la tesis. El análisis presentado en esta tesis se culmina con la obtención de un índice que condensa los márgenes de estabilidad menos conservativos. También se demuestra que la robustez del sistema está asegurada si las impedancias utilizadas en la función de sensibilidad se obtienen justamente en la entrada o la salida del subsistema que está siendo analizado. Por otra parte, la tesis presenta un conjunto de parámetros internos asimilados a impedancias, junto con sus expresiones analíticas, que permiten una explicación detallada de las interacciones en el sistema. Dichas expresiones analíticas pueden obtenerse bien mediante las funciones de transferencia analíticas si se conoce la estructura interna, o utilizando medidas en frecuencia o identificación de las mismas a través de la respuesta temporal del convertidor. De acuerdo a las metodologías presentadas en esta tesis se puede predecir la estabilidad y el comportamiento de sistemas compuestos básicamente por convertidores CC-CC y filtros, cuya estructura interna es desconocida. La predicción se basa en un índice que condensa la información de los márgenes de estabilidad y que permite la obtención de un indicador de la estabilidad global de todo el sistema, permitiendo la comparación de la estabilidad de diferentes arquitecturas de sistemas de alimentación distribuidos. ABSTRACT The purpose of this thesis is to present dynamic small-signal stability and performance analysis methodology for dc-distributed systems consisting of commercial power modules. Furthermore, the objective is to introduce simple method to state the least conservative margins for robust stability as a single number. In addition, an index characterizing the overall system stability is obtained, based on which different dc-distributed systems can be compared in terms of robustness. The interconnected systems are prone to impedance-based interactions which might lead to transient-performance degradation or even instability. These systems typically are constructed using commercial converters with unknown internal structure. Therefore, the analysis presented throughout this thesis is based on frequency responses measurable from the input and output terminals. The stability margins are stated utilizing a concept of maximum peak criteria, derived from the behavior of impedance-based sensitivity function that provides a single number to state robust stability. Using this concept, the stability information at every system interface is combined to a meaningful number to state the average robustness of the system. In addition, theoretical formulas are extracted to assess source and load side interactions in order to describe detailed couplings within the system. The presented theoretical analysis methodologies are experimentally validated throughout the thesis. In this thesis, according to the presented analysis, the least conservative stability margins are provided as a single number guaranteeing robustness. It is also shown that within the interconnected system the robust stability is ensured only if the impedance-based minor-loop gain is determined at the very input or output of each subsystem. Moreover, a complete set of impedance-type internal parameters as well as the formulas according to which the interaction sensitivity can be fully explained and analyzed, is provided. The given formulation can be utilized equally either based on measured frequency responses, time-domain identified internal parameters or extracted analytic transfer functions. Based on the analysis methodologies presented in this thesis, the stability and performance of interconnected systems consisting of converters with unknown internal structure, can be predicted. Moreover, the provided concept to assess the least conservative stability margins enables to obtain an index to state the overall robust stability of distributed power architecture and thus to compare different systems in terms of stability.

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.

A Toolbox for Quantitative Gene Expression in Varroa destructor : RNA Degradation in Field Samples and Systematic Analysis of Reference Gene Stability

Funding: This project has received funding from the European Union’s Seventh Framework Programme for research, technological development and demonstration under grant agreement no. 613960 (SMARTBEES) (http://www.smartbees-fp7.eu/) and Veterinary Medicines Directorate, Department for Environment Food & Rural Affairs (Project # VM0517) (https://www.gov.uk/government/organisations/veterinary-medicines-directorate). CHM was supported by a Biosciences Knowledge Transfer Network Biotechnology and Biological Sciences Research Council (KTN-BBSRC CASE) Studentship (BB/L502467/1) (http://www.bbsrc.ac.uk/). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Acknowledgments We gratefully acknowledge Mr Sebastian Bacz’s expert help and advice with beekeeping.

“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

Procedures for preliminary analysis of tidal inlet hydraulics and stability /

"December 1977."

Analysis of salinity structure and stability for Texax estuaries /

"July 1991."

Expression and biochemical analysis of the entire HIV-2 gp41 ectodomain: determinants of stability map to N- and C-terminal sequences outside the 6-helix bundle core

The folding of HIV gp41 into a 6-helix bundle drives virus-cell membrane fusion. To examine the structural relationship between the 6-helix bundle core domain and other regions of gp41, we expressed in Escherichia coli, the entire ectodomain of HIV-2(ST) gp41 as a soluble, trimeric maltose-binding protein (MBP)/gp41 chimera. Limiting proteolysis indicated that the Cys-591-Cys-597 disulfide-bonded region is outside a core domain comprising two peptides, Thr-529-Trp-589 and Val-604-Ser-666. A biochemical examination of MBP/gp41 chimeras encompassing these core peptides; indicated that the N-terminal polar segment, 521-528, and C-terminal membrane-proximal segment, 658-666, cooperate in stabilizing the ectodomain. A functional interaction between sequences outside the gp41 core may contribute energy to membrane fusion. (C) 2004 Published by Elsevier B.V. on behalf of the Federation of European Biochemical Societies.

Liposome formulation of poorly water soluble drugs:optimisation of drug loading and ESEM analysis of stability

Liposomes due to their biphasic characteristic and diversity in design, composition and construction, offer a dynamic and adaptable technology for enhancing drug solubility. Starting with equimolar egg-phosphatidylcholine (PC)/cholesterol liposomes, the influence of the liposomal composition and surface charge on the incorporation and retention of a model poorly water soluble drug, ibuprofen was investigated. Both the incorporation and the release of ibuprofen were influenced by the lipid composition of the multi-lamellar vesicles (MLV) with inclusion of the long alkyl chain lipid (dilignoceroyl phosphatidylcholine (C 24PC)) resulting in enhanced ibuprofen incorporation efficiency and retention. The cholesterol content of the liposome bilayer was also shown to influence ibuprofen incorporation with maximum ibuprofen incorporation efficiency achieved when 4 μmol of cholesterol was present in the MLV formulation. Addition of anionic lipid dicetylphosphate (DCP) reduced ibuprofen drug loading presumably due to electrostatic repulsive forces between the carboxyl group of ibuprofen and the anionic head-group of DCP. In contrast, the addition of 2 μmol of the cationic lipid stearylamine (SA) to the liposome formulation (PC:Chol - 16 μmol:4 μmol) increased ibuprofen incorporation efficiency by approximately 8%. However further increases of the SA content to 4 μmol and above reduced incorporation by almost 50% compared to liposome formulations excluding the cationic lipid. Environmental scanning electron microscopy (ESEM) was used to dynamically follow the changes in liposome morphology during dehydration to provide an alternative assay of liposome stability. ESEM analysis clearly demonstrated that ibuprofen incorporation improved the stability of PC:Chol liposomes as evidenced by an increased resistance to coalescence during dehydration. These finding suggest a positive interaction between amphiphilic ibuprofen molecules and the bilayer structure of the liposome. © 2004 Elsevier B.V. All rights reserved.

Multiscale Schemes for the BGK--Vlasov--Poisson System in the Quasi-Neutral and Fluid Limits. Stability Analysis and First Order Schemes

This paper deals with the development and the analysis of asymptotically stable and consistent schemes in the joint quasi-neutral and fluid limits for the collisional Vlasov-Poisson system. In these limits, the classical explicit schemes suffer from time step restrictions due to the small plasma period and Knudsen number. To solve this problem, we propose a new scheme stable for choices of time steps independent from the small scales dynamics and with comparable computational cost with respect to standard explicit schemes. In addition, this scheme reduces automatically to consistent discretizations of the underlying asymptotic systems. In this first work on this subject, we propose a first order in time scheme and we perform a relative linear stability analysis to deal with such problems. The framework we propose permits to extend this approach to high order schemes in the next future. We finally show the capability of the method in dealing with small scales through numerical experiments.

STABILITY ANALYSIS OF THE SLOPE ALONG US-2 BETWEEN EPOUFETTE BAY AND THE CUT RIVER BRIDGE

Recently, water was observed flowing from a section of steep slope along US-2 near St. Ignace, Michigan in addition to soil sloughing in the area where the water is flowing from the slope. An inspection of the area also showed the presence of sinkholes. The original construction drawing for US-2 also indicated that sinkholes were present in this area prior to road construction in 1948. An investigation was conducted to determine the overall stability of the slope. The slope consists primarily of aeolian sand deposits. Laboratory testing determined the shear strength of the slope material to have a friction angle around 30°, which is also the slope angle. Thus, the slope is at its maximum angle for stability—however, the slope is also heavily wooded which provides additional support to the slope. Although the area surrounding the water flow has been sloughing, the remaining slope remains intact.

STABILITY ANALYSIS AND HAZARD ASSESSMENT OF THE NORTHERN SLOPES OF SAN VICENTE VOLCANO IN CENTRAL EL SALVADOR

Geologic hazards affect the lives of millions of people worldwide every year. El Salvador is a country that is regularly affected by natural disasters, including earthquakes, volcanic eruptions and tropical storms. Additionally, rainfall-induced landslides and debris flows are a major threat to the livelihood of thousands. The San Vicente Volcano in central El Salvador has a recurring and destructive pattern of landslides and debris flows occurring on the northern slopes of the volcano. In recent memory there have been at least seven major destructive debris flows on San Vicente volcano. Despite this problem, there has been no known attempt to study the inherent stability of these volcanic slopes and to determine the thresholds of rainfall that might lead to slope instability. This thesis explores this issue and outlines a suggested method for predicting the likelihood of slope instability during intense rainfall events. The material properties obtained from a field campaign and laboratory testing were used for a 2-D slope stability analysis on a recent landslide on San Vicente volcano. This analysis confirmed that the surface materials of the volcano are highly permeable and have very low shear strength and provided insight into the groundwater table behavior during a rainstorm. The biggest factors on the stability of the slopes were found to be slope geometry, rainfall totals and initial groundwater table location. Using the results from this analysis a stability chart was created that took into account these main factors and provided an estimate of the stability of a slope in various rainfall scenarios. This chart could be used by local authorities in the event of a known extreme rainfall event to help make decisions regarding possible evacuation. Recommendations are given to improve the methodology for future application in other areas as well as in central El Salvador.