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.

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools

We explore the recently developed snapshot-based dynamic mode decomposition (DMD) technique, a matrix-free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L-shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non-linear incompressible discontinuous Galerkin Navier?Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non-linear and linearised Navier?Stokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier?Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three-dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier?Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L-shaped geometry and control the most unstable 3D mode.

Inherently self-calibrating non-Cartesian parallel imaging.

The use of self-calibrating techniques in parallel magnetic resonance imaging eliminates the need for coil sensitivity calibration scans and avoids potential mismatches between calibration scans and subsequent accelerated acquisitions (e.g., as a result of patient motion). Most examples of self-calibrating Cartesian parallel imaging techniques have required the use of modified k-space trajectories that are densely sampled at the center and more sparsely sampled in the periphery. However, spiral and radial trajectories offer inherent self-calibrating characteristics because of their densely sampled center. At no additional cost in acquisition time and with no modification in scanning protocols, in vivo coil sensitivity maps may be extracted from the densely sampled central region of k-space. This work demonstrates the feasibility of self-calibrated spiral and radial parallel imaging using a previously described iterative non-Cartesian sensitivity encoding algorithm.

Metodologia de utilização de dados de sensoriamento remoto em zonas costeiras sob influência da indústria petrolífera

Oil spills in marine environments represent immediate environmental impacts of large magnitude. For that reason the Environmental Sensitivity to Oil Maps constitute a major instrument for planning actions of containment and cleanup. For both the Environmental Sensitivity Maps always need to be updated, to have an appropriate scale and to represent accurately the coastal areas. In this context, this thesis presents a methodology for collecting and processing remote sensing data for the purpose of updating the territorial basis of thematic maps of Environmental Sensitivity to Oil. To ensure greater applicability of the methodology, sensors with complementary characteristics, which provide their data at a low financial cost, were selected and tested. To test the methodology, an area located on the northern coast of the Northeast of Brazil was chosen. The results showed that the products of ASTER data and image hybrid sensor PALSAR + CCD and HRC + CCD, have a great potential to be used as a source of cartographic information on projects that seek to update the Environmental Sensitivity Maps of Oil

Sistemas computacionais espaço-temporais para toma de decisão em questões ambientais relacionadas à indústria de petróleo e gás

The area between São Bento do Norte and Macau cities, located in the northern coast of the Rio Grande do Norte State is submitted to intense and constant processes of littoral and aeolian transport, causing erosion, alterations in the sediments balance and modifications in the shoreline. Beyond these natural factors, the human interference is huge in the surroundings, composed by sensitive places, due to the existence of the Guamaré Petroliferous Pole, RN, the greater terrestrial oil producing in Brazil, besides the activities of the salt companies and shrimp farms. This socioeconomic-environmental context justifies the elaboration of strategies of environmental monitoring of that coastal area. In the environmental monitoring of coastal strips, submitted to human impacts, the use of multi-sources and multitemporal data integrated through a Spatio- Temporal Database that allows the multiuser friendly access. The objective was to use the potential of the computational systems as important tools the managers of environmental monitoring. The stored data in the form of a virtual library aid in making decisions from the related results and presented in different formats. This procedure enlarges the use of the data in the preventive attendance, in the planning of future actions and in the definition of new lines of researches on the area, in a multiscale approach. Another activity of this Thesis consisted on the development of a computational system to automate the process to elaborate Oil-Spill Environmental Sensitivity Maps, based on the temporal variations that some coastal ecosystems present in the sensibility to the oil. The maps generated in this way, based on the methodology proposed by the Ministério do Meio Ambiente, supply more updated information about the behavior of the ecosystem, as a support to the operations in case of oil spill. Some parameters, such as the hydrodynamic data, the declivity of the beach face, types of resources in risk (environmental, economical, human or cultural) and use and occupation of the area are some of the essential basic information in the elaboration of the sensitivity maps, which suffer temporal alterations.In this way, the two computational systems developed are considered support systems to the decision, because they provide operational subsidies to the environmental monitoring of the coastal areas, considering the transformations in the behavior of coastal elements resulting from temporal changes related the human and/or natural interference of the environment

Modelagem e desenvolvimento de um banco de dados geográficos : aplicação à elaboração de mapas de sensibilidade ambiental ao derramamento de óleo na área costeira entre galinhos e São Bento do Norte-RN

The area between Galinhos and São Bento do Norte beaches, located in the northern coast of the Rio Grande do Norte State is submitted to intense and constant processes of littoral and aeolian transport, causing erosion, alterations in the sediments balance and modifications in the shoreline. Beyond these natural factors, the human interference is huge in the surroundings due to the Guamaré Petroliferous Pole nearby, the greater terrestrial oil producing in Brazil. Before all these characteristics had been organized MAMBMARE and MARPETRO projects with the main objective to execute the geo-environmental monitoring of coastal areas on the northern portion of RN. There is a bulky amount of database from the study area such as geologic and geophysical multitemporal data, hydrodynamic measurements, remote sensing multitemporal images, thematic maps, among others; it is of extreme importance to elaborate a Geographic Database (GD), one of the main components of a Geographic Information System (GIS), to store this amount of information, allowing the access to researchers and users. The first part of this work consisted to elaborate a GD to store the data of the area between Galinhos and São Bento do Norte cities. The main goal was to use the potentiality of the GIS as a tool to support decisions in the environmental monitoring of this region, a valuable target for oil exploration, salt companies and shrimp farms. The collected data was stored as a virtual library to assist men decisions from the results presented as digital thematic maps, tables and reports, useful as source of data in the preventive planning and as guidelines to the future research themes both on regional and local context. The second stage of this work consisted on elaborate the Oil-Spill Environmental Sensitivity Maps. These maps based on the Environmental Sensitivity Index Maps to Oil Spill developed by the Ministry of Environment are cartographic products that supply full information to the decision making, contingency planning and assessment in case of an oil spilling incident in any area. They represent the sensitivity of the areas related to oil spilling, through basic data such as geology, geomorphology, oceanographic, social-economic and biology. Some parameters, as hydrodynamic data, sampling data, coastal type, declivity of the beach face, types of resources in risk (biologic, economic, human or cultural) and the land use of the area are some of the essential information used on the environmental sensitivity maps elaboration. Thus using the available data were possible to develop sensitivity maps of the study area on different dates (June/2000 and December/2000) and to perceive that there was a difference on the sensitivity index generated. The area on December presented more sensible to the oil than the June one because hydrodynamic data (wave and tide energy) allowed a faster natural cleaning on June. The use of the GIS on sensitivity maps showed to be a powerful tool, since it was possible to manipulate geographic data with correctness and to elaborate more accurate maps with a higher level of detail to the study area. This presented an medium index (3 to 4) to the long shore and a high index (10) to the mangrove areas highly vulnerable to oil spill

Análise multitemporal dos elementos geoambientais da região da Ponta do Tubarão, área de influência dos campos petrolíferos de Macau e Serra, município de Macau/RN

The study area is inserted in Ponta do Tubarão region, Macau City, setentrional littoral of Rio Grande do Norte State, composed of Tertiary and Quatemary sedimentary rocks and sediments. This region is characterized for the intense action of the coastal processes, causing the morphologic instability in part of the area, beyond the interference of human activities, as the Petroliferous Industrial Polo, salt companies and shrimp farms. This justifies the integration of multidisciplinary and multitemporal detailed scientific studies dealing with the evaluation of the changing behavior of this coastal environment by geoenvironments elements characterization, identifying protected and recuperation areas, mainly those under socioeconomic intervention. The main objective was the coastal monitoring using geoprocessing techniques to prepare thematic maps useful for oil spilling environment risk areas survey. The methodology was based on multitemporal interpretation of remote sensing images and field checking, integrated in a Geographical Information System (GIS). The Geologic, Geomorphologic, Vegetation, Soil and Land Use maps were prepared, and later on they allowed the generation of the Natural Vulnerability and Environmental Vulnerability maps. These maps had been classified in accordance with vulnerability degrees: very low, low, medi um, high and very high. Beyond these maps the GIS allowed the analysis of the shoreline evolution for 10 distinct dates, using Landsat 5 TM and 7 ETM+ and SPOT-HRVIR images. This analysis made possible the attendance of the coastal morphodynamic evolution, where the results had been represented by areasof erosion and accretion (or deposition) of sediments, pointing critical areas under erosive process to the petroliferous industry (Macau and Serra fields). The GIS also provided to prepare the Environmental Sensitivity Maps of Oil Spill (SAO Maps) in operational scale (1: 10.000), according to the norms ofthe Ministério do Meio Ambiente (MMA 2002). The SAO Map in operational scale was based on IKONOS images mosaic where the ESI (Environmental Sensitivity Index) was represented according with two tides phases of theregion. Therewere recognizedfiveESI (3, 4,7,9, 1O) for the low tide; to the high tide the ESI number increased to seven (3, 4, 5, 7, 8, 9, 10). All these information are necessary to the decisions making about oi! spill and its derivatives containment. These techniques application makes possible the optimization and implantation ofnew socioeconomics activities of low environmental impact, indicates areas for better productivity and security exploration, and benefits local communities with fauna and flora preservation. The development of these activities is inserted in the scope of Monitoramento Ambiental de Áreas de Risco a Derrames de Petróleo e Seus Derivados Cooperation Project (Rede 05/01 - PETRORISCO, FINEP/CTPETRO/PETROBRAS) of multidisciplinary and interinstitucional characteristics dealing with subjects involving the environmental monitoring and the petroliferous activity

Estudo da dinâmica costeira da região da foz do rio Piranhas-Açu para geração de mapas de sensibilidade do litoral ao derramamento de óleo

The study area is located in the northern coast of Rio Grande do Norte State comprising the mouth of Açu-Piranhas river including the cities of Porto do Mangue e Areia Branca. The local geological setting comprises Cretaceous, Tertiary and Quaternary geological units of the Potiguar Basin. One is about a region of high morphologic instability due to action of the rigorous dynamic coastal processes, beyond the intense human activities mainly for the performance of the petroliferous industry, salt farms and tanks of shrimp industry.For the accomplishment of this work Landsat 5 TM and Landsat 7 ETM + from four distinct dates were used as cartographic base, in which one applied techniques of digital processing to elaborate thematic maps of the existing natural resources to support the geologic and geomorphologic characterization and the soil and landuse maps. The strategy applied was the interpretation of multitemporal images from aerial and orbital remote sensors alIied to the terrain truth recognition, integrated through a Geographic Information System. These activities had alIowed the production of Sensitivity Maps of the Coast to Oil Spilling for the area, on the basis of the Coastal Sensibility Index. Taking into account the seasons were created maps to distinct datas: July 2003 represents the winter months that presented a sensibility lower when compared with the month of December 2003. For the summer months greater sensitivity is due to the hydrodynamic data that suggest a lesser capacity of natural cleanness of the oil and its derivatives in spilling case.These outcomes are an important and useful database to support an assessment to a risk situation and to taking decision in the face of an environmental disaster with oil spilling in coastal area, alIowing a complete visualization of the area and identifying all portions in the area with thei environmental units and respective Coastal Sensibility Index.

Mapeamento de sensibilidade ambiental a derramentos de petróleo do sistema estuarino de Santos, estado de São Paulo

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

Carta geológico-geotécnica como subsídio a elaboração de cartas de sensibilidade ambiental, a derrames de petróleo e derivados, na região do oleoduto Guararema-São José dos Campos, Vale do Paraíba (SP)

Pós-graduação em Geociências e Meio Ambiente - IGCE

A sensibilidade do lugar: uma proposta metodológica para aplicação da percepção ambiental nos planos de emergência a derrames de óleo

Pós-graduação em Geografia - IGCE

Cartografia temática do atlas de sensibilidade ambiental a derramamentos de óleo do litoral paulista

The objective of this paper is the elaboration and implementation of procedures in a cartographic representation related by fundamental of thematic cartography and graphic semiology for the standardization of the Environmental Oil Spill Sensitivity Maps supported by a Geographic Information Systems (GIS) for handling and modeling of a large number of variables. These make up the Environmental Sensitivity Atlas to Oil Spills in Coastal Paulista, and that represents the phenomena that occur in geographic space accurately so as to highlight the importance of each element in the evaluation and protection of areas of greater sensitivity oil. The composition of the cartographic documents considers the Littoral Sensitivity Index (LSI), biological resources and the resources for human use that could be negatively impacted. Thus, the information contained in each map was carefully evaluated before implementation, so that the cartographic representations of various resources, environments, and other ISLs, the reader should issue an immediate message that could be understood clearly, without requiring prior knowledge of specialized. Another aspect was the distribution harmoniously all the elements contained in the document, so that information could be enough without overwhelming it. It was also taken a certain care, so each symbol could be used properly in order that there is no conflict in the information.

Implementação de um sistema de informação voltado à sensibilidade ambiental ao óleo do litoral sul paulista e avaliação das ações de resposta a derramamentos de óleo

Oil spills cause serious damage to the cost life and environments. Those impacts affect ecologic and socio-economic resources (like fishing and tourism). Within this background, response actions have two main objectives: the contaminant removal, with the less additional impacts, and enhance environment restoration in order to make this process complete in the shortest time possible. The present work proposes to contribute for the emergency environmental management in cases of oil spills by systematization of relevant information for oil spill environmental sensitivity maps. The next stage was to insert all these data on a geographic database, which allows data access by web. Beside that, this work aimed to recommend suitable clean-up techniques for the ecosystems located on the study area, composed by the municipalities: Praia Grande, Mongaguá, Itanhaém and Peruíbe, belonging to Baixada Santista and Iguape, Cananéia and Ilha Comprida, south cost of São Paulo state. This area is situated between two important Brazilian ports: Santos and Paranaguá, and that make it under considerable accident risks. The results were all data inserted on the geodatabase and available to user recover the information by web consulting. With that, this work wishes to contribute to individual emergencial planning of the region.

Metodologia de utilização de dados de sensoriamento remoto em zonas costeiras sob influência da indústria petrolífera

Oil spills in marine environments represent immediate environmental impacts of large magnitude. For that reason the Environmental Sensitivity to Oil Maps constitute a major instrument for planning actions of containment and cleanup. For both the Environmental Sensitivity Maps always need to be updated, to have an appropriate scale and to represent accurately the coastal areas. In this context, this thesis presents a methodology for collecting and processing remote sensing data for the purpose of updating the territorial basis of thematic maps of Environmental Sensitivity to Oil. To ensure greater applicability of the methodology, sensors with complementary characteristics, which provide their data at a low financial cost, were selected and tested. To test the methodology, an area located on the northern coast of the Northeast of Brazil was chosen. The results showed that the products of ASTER data and image hybrid sensor PALSAR + CCD and HRC + CCD, have a great potential to be used as a source of cartographic information on projects that seek to update the Environmental Sensitivity Maps of Oil

Using a Parameterization of a Radiative Transfer Model to Build High-Resolution Maps of Typical Clear-Sky UV Index in Catalonia, Spain

To perform a climatic analysis of the annual UV index (UVI) variations in Catalonia, Spain (northeast of the Iberian Peninsula), a new simple parameterization scheme is presented based on a multilayer radiative transfer model. The parameterization performs fast UVI calculations for a wide range of cloudless and snow-free situations and can be applied anywhere. The following parameters are considered: solar zenith angle, total ozone column, altitude, aerosol optical depth, and single-scattering albedo. A sensitivity analysis is presented to justify this choice with special attention to aerosol information. Comparisons with the base model show good agreement, most of all for the most common cases, giving an absolute error within 0.2 in the UVI for a wide range of cases considered. Two tests are done to show the performance of the parameterization against UVI measurements. One uses data from a high-quality spectroradiometer from Lauder, New Zealand [45.04°S, 169.684°E, 370 m above mean sea level (MSL)], where there is a low presence of aerosols. The other uses data from a Robertson–Berger-type meter from Girona, Spain (41.97°N, 2.82°E, 100 m MSL), where there is more aerosol load and where it has been possible to study the effect of aerosol information on the model versus measurement comparison. The parameterization is applied to a climatic analysis of the annual UVI variation in Catalonia, showing the contributions of solar zenith angle, ozone, and aerosols. High-resolution seasonal maps of typical UV index values in Catalonia are presented