Reduced order modeling of three dimensional external aerodynamic flows

A method is presented to construct computationally efficient reduced-order models (ROMs) of three-dimensional aerodynamic flows around commercial aircraft components. The method is based on the proper orthogonal decomposition (POD) of a set of steady snapshots, which are calculated using an industrial solver based on some Reynolds averaged Navier-Stokes (RANS) equations. The POD-mode amplitudes are calculated by minimizing a residual defined from the Euler equations, even though the snapshots themselves are calculated from viscous equations. This makes the ROM independent of the peculiarities of the solver used to calculate the snapshots. Also, both the POD modes and the residual are calculated using points in the computational mesh that are concentrated in a close vicinity of the aircraft, which constitute a much smaller number than the total number of mesh points. Despite these simplifications, the method provides quite good approximations of the flow variables distributions in the whole computational domain, including the boundary layer attached to the aircraft surface and the wake. Thus, the method is both robust and computationally efficient, which is checked considering the aerodynamic flow around a horizontal tail plane, in the transonic range 0.4?Mach number?0.8, ?3°?angle of attack?3°.

Far wake structure in rarefied plasma flows past charged bodies

The asymptotic structure of the far-wake behind a charged body in a rarefied plasma flow is investigated under the assumption of small ion-to-electron temperature ratio and of flow speed hypersonic with respect to the ions but not with respect to the electrons. It is found that waves are excited even if the flow is subacoustic (flow velocity less than the ion-acoustic speed). For both superacoustic and subacoustic velocities a steep wave front develops separating the weakly perturbed, quasineutral plasma ahead, from the region behind where ion waves appear. Near the axis a trailing front develops;the region between this and the axis is quasineutral for superacoustic speeds. The decay laws in all of these regions, the self-similar structure of the fronts and the general character of the waves are determined.The damping of the waves and special flow detail for bodies large and small compared with the Debye length are discussed. A nonlinear analysis of the leading wave front in superacoustic flow is carried out. A hyperacoustic equivalence principle is presented.

Flujos de gases de efecto invernadero en suelos forestales y agroforestales del centro de la Península Ibérica=Greenhouse gas flows in forest and agroforestry soils in the center of the Iberian Peninsula

Debido a la complejidad de los procesos que controlan el intercambio de gases de carbono (C) y nitrógeno (N) entre el suelo y la atmósfera, en los sistemas forestales y agroforestales, son comprensibles las incógnitas existentes respecto a la estimación de los flujos de los gases de efecto invernadero (GEI) y la capacidad como reservorios de carbono de los suelos, bajo diferentes formas de uso y regímenes de alteración a escala regional y global. Esta escasez de información justifica la necesidad de caracterizar la dinámica de intercambio de GEI en los ecosistemas Mediterráneos, en especial en el contexto actual de cambio climático, y el incremento asociado de temperatura y periodos de sequía, alteración de los patrones de precipitación, y el riesgo de incendios forestales; cuyas consecuencias afectarán tanto a los compartimentos de C y de N del suelo como a la capacidad de secuestro de C de estos ecosistemas. Dentro de este contexto se enmarca la presente tesis doctoral cuyo objetivo ha sido cuantificar y caracterizar los flujos de dióxido de carbono (CO2), de oxido nitroso (N2O) y de metano (CH4), junto con los stocks de C y N, en suelos forestales de Quercus ilex, Quercus pyrenaica y Pinus sylvestris afectados por incendios forestales; así como el estudiar el efecto de la gestión y la cubierta arbórea en la respiración del suelo y los stocks de C y N en una dehesa situada en el centro de la Península Ibérica. De manera que los flujos de CO2, N2O y CH4; y los parámetros físico-químicos y biológicos del suelo fueron estudiados en los diferentes tratamientos y ecosistemas a lo largo del trabajo que se presenta. Los resultados obtenidos muestran la existencia de variaciones temporales y espaciales de la respiración del suelo dentro de una escala geográfica pequeña, controladas principalmente por la temperatura y la humedad del suelo; y por los contenidos de C y N del suelo en un bosque de Pinus sylvestris en la vertiente norte de la Sierra de Guadarrama , en España. El análisis de los efectos de los incendios forestales a largo plazo (6-8 años) revela que las pérdidas anuales de C a través de la respiración del suelo en las zonas quemadas de Quercus ilex, Quercus pyrenaica y Pinus sylvestris fueron 450 gCm-2yr-1, 790 gCm-2yr-1 y 1220 gCm-2yr-1, respectivamente; lo que representa una reducción del 43%, 22% y 11% en comparación con las zonas no quemadas de dichas especies, debido a la destrucción de la masa arbórea. El efecto del fuego también alteró los flujos N2O y CH4 del suelo, de una forma diferente en los distintos ecosistemas y estacionalidades estudiadas. De tal modo, que los suelos quemados mostraron una mayor oxidación del CH4 en las masas de Q. ilex, y una menor oxidación en las de P. sylvestris; además de una disminución de los flujos de N2O en Q. pyrenaica. Los incendios también afectaron los parámetros microclimáticos de los suelos forestales, observándose un incremento de la temperatura del suelo y una disminución de la humedad en los emplazamientos quemados que en los no quemados. Los cationes intercambiables, el pH, el cociente C/N, el contenido en raicillas y la biomasa microbiana también disminuyeron en las zonas quemadas. Aunque el C orgánico del suelo no se alteró de manera significativa, si lo hizo la calidad de la materia orgánica, disminuyendo el carbono lábil y aumentando las formas recalcitrantes lo que se tradujo en menor sensibilidad de la respiración del suelo a la temperatura (valores de Q10) en las zonas quemadas. Los resultados del estudio realizado en la Dehesa muestran que las actividades silvopastorales estudiadas afectaron levemente y de forma no constante a la respiración del suelo y las condiciones microclimáticas del suelo. Se observó una reducción 12% de la respiración del suelo por efecto del pastoreo no intensivo. Sin embargo, se observaron incrementos de 3Mg/ha en los stocks de C y de 0.3 Mg/ha en los stocks de N en los suelos pastoreados en comparación con los no pastoreados. Aunque, no se observó un claro efecto de la labranza sobre la respiración del suelo en nuestro experimento, sin embargo si se observó una disminución de 3.5 Mg/ha en las reservas de C y de 0.3 Mg/ ha en las de N en los suelos labrados comparados con los no labrados. La copa del arbolado influyó de forma positiva tanto en la respiración del suelo, como en los stocks de C y N de los suelos. La humedad del suelo jugó un papel relevante en la sensibilidad de la respiración a la temperatura del suelo. Nuestros resultados ponen de manifiesto la sensibilidad de la respiración del suelo a cambios en la humedad y los parámetros edáficos, y sugieren que la aplicación de modelos estándar para estimar la respiración del suelo en áreas geográficas pequeñas puede no ser adecuada a menos que otros factores sean considerados en combinación con la temperatura del suelo. Además, las diferentes respuestas de los flujos de gases de efecto invernadero a los cambios, años después de la ocurrencia de incendios forestales, destaca la necesidad de incluir estos cambios en las futuras investigaciones de la dinámica del carbono en los ecosistemas mediterráneos. Por otra parte, las respuestas divergentes en los valores de respiración del suelo y en los contenidos de C y N del suelo observados en la dehesa, además de la contribución de la copa de los árboles en los nutrientes del suelo ilustran la importancia de mantener la gestión tradicional aplicada en beneficio de la capacidad de almacenar C en la dehesa estudiada. La información obtenida en este trabajo pretende contribuir a la mejora del conocimiento de la dinámica y el balance de C en los sistemas mediterráneos, además de ayudar a predecir el impacto del cambio climático en el intercambio de C entre los ecosistemas forestales y agroforestales y la atmósfera. ABSTRACT Due to the complexity of the processes that control the exchange of carbon (C) and nitrogen (N) gasses between soils and the atmosphere in forest and agroforestry ecosystems, understandable uncertainties exist as regards the estimation of greenhouse gas (GHG) fluxes and the soil sink capacity at regional and global scale under different forms of land use and disturbance regimes. These uncertainties justify the need to characterize the exchange dynamics of GHG between the atmosphere and soils in Mediterranean terrestrial ecosystems, particularly in the current context of climate change and the associated increase in temperature, drought periods, heavy rainfall events, and increased risk of wildfires, which affect not only the C and N pools but also the soil C sink capacity of these ecosystems. Within this context, the aims of the present thesis were, firstly, to quantify and characterize the fluxes of carbon dioxide (CO2), nitrous oxide (N2O) and methane (CH4) as well as the C and N stocks in Quercus ilex, Quercus pyrenaica and Pinus sylvestris stands affected by wildfires, and secondly, to study the effects of Quercus ilex canopy and management on both soil respiration and C and N pools in dehesa systems in the center of Iberian Peninsula. Soil CO2, N2O and CH4 fluxes, and soil physical-chemical and biological parameters were studied under the different treatments and ecosystems considered in this study. The results showed seasonal and spatial variations in soil respiration within small geographic areas, mainly controlled by soil temperature and moisture in addition to soil carbon and nitrogen stocks in mixed pine–oak forest ecosystems on the north facing slopes of the Sierra de Guadarrama in Spain. The analysis of long term effects of wildfires (6–8 years) revealed that annual carbon losses through soil respiration from burned sites in Quercus ilex, Quercus pyrenaica and Pinus sylvestris stands were 450 gCm-2yr-1, 790 gCm-2yr-1 and 1220 gCm-2yr-1, respectively; with burned sites emitting 43%, 22% and 11% less in burned as opposed to non-burned sites due the loss of trees. Fire may alter both N2O and CH4 fluxes although the magnitude of such variation depends on the site, soil characteristics and seasonal climatic conditions. The burned sites showed higher CH4 oxidation in Q.ilex stands, and lower oxidation rates in P. sylvestris stands. A reduction in N2O fluxes in Q. pyrenaica stands was detected at burned sites along with changes in soil microclimate; higher soil temperature and lower soil moisture content. Exchangeable cations, the C/N ratio, pH, fine root and microbial biomass were also found to decrease at burned sites. Although the soil organic carbon was not significantly altered, the quality of the organic matter changed, displaying a decrease in labile carbon and a relative increase in refractory forms, leading to lower sensitivity of soil respiration to temperature (Q10 values) at burned sites. The results from the dehesa study show that light grazing and superficial tilling practices used in the studied dehesa system in Spain had a slight but non-consistent impact on soil respiration and soil microclimate over the study period. The reduction in soil respiration in the dehesa system due to the effects of grazing was around 12 %. However, increments of 3Mg/ha in C stocks and 0.3 Mg/ha in N stocks in grazed soils were observed. Although no clear effect of tilling on soil respiration was found, a decrease of 3.5 Mg/ha in C stocks and 0.3 Mg/ha in N stocks was detected for tilled soils. The presence of a tree canopy induced increases in soil respiration, soil C and N stocks, while soil moisture was found to play an important role in soil respiration temperature response. Our results suggest that the use of standard models to estimate soil respiration in small geographical areas may not be adequate unless other factors are considered in addition to soil temperature. Furthermore, the different responses of GHG flux to climatic shifts, many years after the occurrence of wildfire, highlight the need to include these shifts in C dynamics in future research undertaken in Mediterranean ecosystems. Furthermore, divergent responses in soil respiration and soil C and N stocks to grazing or tilling practices in Dehesa systems, and the influence of tree canopy on soil respiration and soil nutrient content, illustrate the importance of maintaining beneficial management practices. Moreover, the carbon sequestration capacity of the Dehesa system studied may be enhanced through improvements in the management applied. It is hoped that the information obtained through this research will contribute towards improving our understanding of the dynamics and balance of C in Mediterranean systems, and help predict the impact of climate change on the exchange of C between forest and agroforestry ecosystems and the atmosphere.

The Lagrangian description of aperiodic flows: a case study of the Kuroshio Current

This article reviews several recently developed Lagrangian tools and shows how their com- bined use succeeds in obtaining a detailed description of purely advective transport events in general aperiodic flows. In particular, because of the climate impact of ocean transport processes, we illustrate a 2D application on altimeter data sets over the area of the Kuroshio Current, although the proposed techniques are general and applicable to arbitrary time depen- dent aperiodic flows. The first challenge for describing transport in aperiodical time dependent flows is obtaining a representation of the phase portrait where the most relevant dynamical features may be identified. This representation is accomplished by using global Lagrangian descriptors that when applied for instance to the altimeter data sets retrieve over the ocean surface a phase portrait where the geometry of interconnected dynamical systems is visible. The phase portrait picture is essential because it evinces which transport routes are acting on the whole flow. Once these routes are roughly recognised it is possible to complete a detailed description by the direct computation of the finite time stable and unstable manifolds of special hyperbolic trajectories that act as organising centres of the flow.

Numerical characterization of particle dispersion in the turbulent recirculation zones of sudden expansion pipe flows

The dispersion of solid particles in the turbulent recirculation zones of sudden expansion pipes can be characterized by different Stokes numbers and mean drift parameter and its study is important because this kind of flows appears in many technological applications.

Experimental measurements of the scattered-light polarization from different liquid flows

An experimental system designed to measure very low optical powers, of the order of a few picowatts, is presented. Its main aid is to detect the polarisation state of scattered light from a fluid flow, in different angular directions with respect to the longitudinal axis of the flow. A laser beam incident linearly polarized crosses the fluid flow orthogonally. The scattered light is detected by means of a photodetector situated behind a lineal polarizer whose orientation can be rotated. The outgoing electrical signal is amplified by means of a Mode-lockin amplifier and is digitally processed.

Instability Analysis of Incompressible Open Cavity Flows

El problema del flujo sobre una cavidad abierta ha sido estudiado en profundidad en la literatura, tanto por el interés académico del problema como por sus aplicaciones prácticas en gran variedad de problemas ingenieriles, como puede ser el alojamiento del tren de aterrizaje de aeronaves, o el depósito de agua de aviones contraincendios. Desde hace muchos a˜nos se estudian los distintos tipos de inestabilidades asociadas a este problema: los modos bidimensionales en la capa de cortadura, y los modos tridimensionales en el torbellino de recirculación principal dentro de la cavidad. En esta tesis se presenta un estudio paramétrico completo del límite incompresible del problema, empleando la herramienta de estabilidad lineal conocida como BiGlobal. Esta aproximación permite contemplar la estabilidad global del flujo, y obtener tanto la forma como las características de los modos propios del problema físico, sean estables o inestables. El estudio realizado permite caracterizar con gran detalle todos los modos relevantes, así como la envolvente de estabilidad en el espacio paramétrico del problema incompresible (Mach nulo, variación de Reynolds, espesor de capa límite incidente, relación altura/profundidad de la cavidad, y longitud característica de la perturbación en la dirección transversal). A la luz de los resultados obtenidos se proponen una serie de relaciones entre los parámetros y características de los modos principales, como por ejemplo entre el Reynolds crítico de un modo, y la longitud característica del mismo. Los resultados numéricos se contrastan con una campaña experimental, siendo la principal conclusión de dicha comparación que los modos lineales están presentes en el flujo real saturado, pero que existen diferencias notables en frecuencia entre las predicciones teóricas y los experimentos. Para intentar determinar la naturaleza de dichas diferencias se realiza una simulación numérica directa tridimensional, y se utiliza un algoritmo de DMD (descomposición dinámica de modos) para describir el proceso de saturación. ABSTRACT The problem of the flow over an open cavity has been studied in depth in the literature, both for being an interesting academical problem and due to the multitude of industrial applications, like the landing gear of aircraft, or the water deposit of firefighter airplanes. The different types of instabilities appearing in this flow studied in the literature are two: the two-dimensional shear layer modes, and the three-dimensional modes that appear in the main recirculating vortex inside the cavity. In this thesis a parametric study in the incompressible limit of the problem is presented, using the linear stability analysis known as BiGlobal. This approximation allows to obtain the global stability behaviour of the flow, and to capture both the morphological features and the characteristics of the eigenmodes of the physical problem, whether they are stable or unstable. The study presented here characterizes with great detail all the relevant eigenmodes, as well as the hypersurface of instability on the parameter space of the incompressible problem (Mach equal to zero, and variation of the Reynolds number, the incoming boundary layer thickness, the length to depth aspect ratio of the cavity and the spanwise length of the perturbation). The results allow to construct parametric relations between the characteristics of the leading eigenmodes and the parameters of the problem, like for example the one existing between the critical Reynolds number and its characteristic length. The numerical results presented here are compared with those of an experimental campaign, with the main conclusion of said comparison being that the linear eigenmode are present in the real saturated flow, albeit with some significant differences in the frequencies of the experiments and those predicted by the theory. To try to determine the nature of those differences a three-dimensional direct numerical simulation, analyzed with Dynamic Mode Decomposition algorithm, was used to describe the process of saturation.

Modelling of short runout propagation landslides and debris flows

This paper proposes an extension of methods used to predict the propagation of landslides having a long runout to smaller landslides with much shorter propagation distances. The method is based on: (1) a depth-integrated mathematical model including the coupling between the soil skeleton and the pore fluids, (2) suitable rheological models describing the relation between the stress and the rate of deformation tensors for fluidised soils and (3) a meshless numerical method, Smooth Particle Hydrodynamics, which separates the computational mesh (or set of computational nodes) from the mesh describing the terrain topography, which is of structured type – thus accelerating search operations. The proposed model is validated using two examples for which there are analytical solutions, and then it is applied to two short runout landslides which happened in Hong Kong in 1995, for which there is available information.

Variable-density jet flows induced by concentrated sources of momentum and energy

The planar and axisymmetric variable-density flows induced in a quiescent gas by a concentrated source of momentum that is simultaneously either a source or a sink of energy are investigated for application to the description of the velocity and temperature far fields in laminar gaseous jets with either large or small values of the initial jet-to-ambient temperature ratio. The source fluxes of momentum and heat are used to construct the characteristic scales of velocity and length in the region where the density differences are of the order of the ambient density, which is slender for the large values of the Reynolds number considered herein. The problem reduces to the integration of the dimensionless boundary-layer conservation equations, giving a solution that depends on the gas transport properties but is otherwise free of parameters. The boundary conditions at the jet exit for integration are obtained by analysing the self-similar flow that appears near the heat source in planar and axisymmetric configurations and also near the heat sink in the planar case. Numerical integrations of the boundary-layer equations with these conditions give solutions that describe accurately the velocity and temperature fields of very hot planar and round jets and also of very cold plane jets in the far field region where the density and temperature differences are comparable to the ambient values. Simple scaling arguments indicate that the point source description does not apply, however, to cold round jets, whose far field region is not large compared with the jet development region, as verified by numerical integrations

Enhanced radon emission in natural CO2 flows in Campo de Calatrava region (central Spain)

Activity of radon gas in natural soils is commonly low (in the order of few thousands of Bq·m-3) due to the fast decay (half-life= 3.8 days in the case of 222Rn) that prevents accumulation in soil pores. Exceptionally, high Rn soil activity (up to 430 KBq·m-3) is found around point sources of deep CO2 fluxes. These fluxes allow the transport of trace gases (including Rn) to long distances in the geosphere leading to a potential hazard as Rn accumulation in buildings. CO2 degassing is common in active or ancient volcanic fields and occurs as free gas fluxes or dissolved in groundwater. In this work, the occurrence of Rnbearing, CO2 fluxes from the Campo de Calatrava region in Central Spain has been studied in order to determine their (1) magnitude, (2) migration paths and (3) potential impact on the environment, and (4) methodologies to best detection and measurement.

Numerical issues in Lagrangian tracking and topological evolution of fluid particles in wallbounded turbulent flows

The determination of the local Lagrangian evolution of the flow topology in wall-bounded turbulence, and of the Lagrangian evolution associated with entrainment across the turbulent / non-turbulent interface into a turbulent boundary layer, require accurate tracking of a fluid particle and its local velocity gradients. This paper addresses the implementation of fluid-particle tracking in both a turbulent boundary layer direct numerical simulation and in a fully developed channel flow simulation. Determination of the sub-grid particle velocity is performed using both cubic B-spline, four-point Hermite spline and higher-order Hermite spline interpolation. Both wall-bounded flows show similar oscillations in the Lagrangian tracers of both velocity and velocity gradients, corresponding to the movement of particles across the boundaries of computational cells. While these oscillation in the particle velocity are relatively small and have negligible effect on the particle trajectories for time-steps of the order of CFL = 0.1, they appear to be the cause of significant oscillations in the evolution of the invariants of the velocity gradient tensor.

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.

Global Stability Analysis of Turbulent Transonic Flows on Airfoil geometries

La aparición de inestabilidades en un flujo es un problema importante que puede afectar a algunas aplicaciones aerodinámicas. De hecho existen diferentes tipos de fenómenos no-estacionarios que actualmente son tema de investigación; casos como la separación a altos ángulos de ataque o el buffet transónico son dos ejemplos de cierta relevancia. El análisis de estabilidad global permite identificar la aparición de dichas condiciones inestables, proporcionando información importante sobre la región donde la inestabilidad es dominante y sobre la frecuencia del fenómeno inestable. La metodología empleada es capaz de calcular un flujo base promediado mediante una discretización con volúmenes finitos y posteriormente la solución de un problema de autovalores asociado a la linealización que aparece al perturbar el flujo base. El cálculo numérico se puede dividir en tres pasos: primero se calcula una solución estacionaria para las ecuaciones RANS, luego se extrae la matriz del Jacobiano que representa el problema linealizado y finalmente se deriva y se resuelve el problema de autovalores generalizado mediante el método iterativo de Arnoldi. Como primer caso de validación, la técnica descrita ha sido aplicada a un cilindro circular en condiciones laminares para detectar el principio de las oscilaciones de los vórtices de von Karman, y se han comparado los resultados con experimentos y cálculos anteriores. La parte más importante del estudio se centra en el análisis de flujos compresibles en régimen turbulento. La predicción de la aparición y la progresión de flujo separado a altos ángulos de ataque se han estudiado en el perfil NACA0012 en condiciones tanto subsónicas como supersónicas y en una sección del ala del A310 en condiciones de despegue. Para todas las geometrías analizadas, se ha podido observar que la separación gradual genera la aparición de un modo inestable específico para altos ángulos de ataque siempre mayores que el ángulo asociado al máximo coeficiente de sustentación. Además, se ha estudiado el problema adjunto para obtener información sobre la zona donde una fuerza externa provoca el máximo cambio en el campo fluido. El estudio se ha completado calculando el mapa de sensibilidad estructural y localizando el centro de la inestabilidad. En el presente trabajo de tesis se ha analizado otro importante fenómeno: el buffet transónico. En condiciones transónicas, la interacción entre la onda de choque y la capa límite genera una oscilación de la posición de la onda de choque y, por consiguiente, de las fuerzas aerodinámicas. El conocimiento de las condiciones críticas y su origen puede ayudar a evitar la oscilación causada por estas fuerzas. Las condiciones para las cuales comienza la inestabilidad han sido calculadas y comparadas con trabajos anteriores. Por otra parte, los resultados del correspondiente problema adjunto y el mapa de sensibilidad se han obtenido por primera vez para el buffet, indicando la región del dominio que sera necesario modificar para crear el mayor cambio en las propiedades del campo fluido. Dado el gran consumo de memoria requerido para los casos 3D, se ha realizado un estudio sobre la reducción del domino con la finalidad de reducirlo a la región donde está localizada la inestabilidad. La eficacia de dicha reducción de dominio ha sido evaluada investigando el cambio en la dimensión de la matriz del Jacobiano, no resultando muy eficiente en términos del consumo de memoria. Dado que el buffet es un problema en general tridimensional, el análisis TriGlobal de una geometría 3D podría considerarse el auténtico reto futuro. Como aproximación al problema, un primer estudio se ha realizado empleando una geometría tridimensional extruida del NACA00f2. El cálculo del flujo 3D y, por primera vez en casos tridimensionales compresibles y turbulentos, el análisis de estabilidad TriGlobal, se han llevado a cabo. La comparación de los resultados obtenidos con los resultados del anterior modelo 2D, ha permitido, primero, verificar la exactitud del cálculo 2D realizado anteriormente y también ha proporcionado una estimación del consumo de memoria requerido para el caso 3D. ABSTRACT Flow unsteadiness is an important problem in aerodynamic applications. In fact, there are several types of unsteady phenomena that are still at the cutting edge of research in the field; separation at high angles of attack and transonic buffet are two important examples. Global Stability Analysis can identify the unstable onset conditions, providing important information about the instability location in the domain and the frequency of the unstable phenomenon. The methodology computes a base flow averaged state based on a finite volume discretization and a solution for a generalized eigenvalue problem corresponding to the perturbed linearized equations. The numerical computation is then performed in three steps: first, a steady solution for the RANS equation is computed; second, the Jacobian matrix that represents the linearized problem is obtained; and finally, the generalized eigenvalue problem is derived and solved with an Arnoldi iterative method. As a first validation test, the technique has been applied on a laminar circular cylinder in order to detect the von Karman vortex shedding onset, comparing the results with experiments and with previous calculations. The main part of the study focusses on turbulent and compressible cases. The prediction of the origin and progression of separated flows at high angles of attack has been studied on the NACA0012 airfoil at subsonic and transonic conditions and for the A310 airfoil in take-off configuration. For all the analyzed geometries, it has been found that gradual separation generates the appearance of one specific unstable mode for angles of attack always greater than the ones related to the maximum lift coefficient. In addition, the adjoint problem has been studied to suggest the location of an external force that results in the largest change to the flow field. From the direct and the adjoint analysis the structural sensitivity map has been computed and the core of the instability has been located. The other important phenomenon analyzed in this work is the transonic buffet. In transonic conditions, the interaction between the shock wave and the boundary layer leads to an oscillation of the shock location and, consequently, of the aerodynamic forces. Knowing the critical operational conditions and its origin can be helpful in preventing such fluctuating forces. The instability onset has then been computed and compared with the literature. Moreover, results of the corresponding adjoint problem and a sensitivity map have been provided for the first time for the buffet problem, indicating the region that must be modified to create the biggest change in flow field properties. Because of the large memory consumption required when a 3D case is approached, a domain reduction study has been carried out with the aim of limiting the domain size to the region where the instability is located. The effectiveness of the domain reduction has been evaluated by investigating the change in the Jacobian matrix size, not being very efficient in terms of memory consumption. Since buffet is a three-dimensional problem, TriGlobal stability analysis can be seen as a future challenge. To approximate the problem, a first study has been carried out on an extruded three-dimensional geometry of the NACA0012 airfoil. The 3D flow computation and the TriGlobal stability analysis have been performed for the first time on a compressible and turbulent 3D case. The results have been compared with a 2D model, confirming that the buffet onset evaluated in the 2D case is well detected. Moreover, the computation has given an indication about the memory consumption for a 3D case.

Ricci flows on surfaces related to the Einstein weyl and Abelian vortex equations

There are described equations for a pair comprising a Riemannian metric and a Killing field on a surface that contain as special cases the Einstein Weyl equations (in the sense of D. Calderbank) and a real version of a special case of the Abelian vortex equations, and it is shown that the property that a metric solve these equations is preserved by the Ricci flow. The equations are solved explicitly, and among the metrics obtained are all steady gradient Ricci solitons (e.g. the cigar soliton) and the sausage metric; there are found other examples of eternal, ancient, and immortal Ricci flows, as well as some Ricci flows with conical singularities.

Measurement of velocity in rotational flows using ultrasonic anemometry: the flowmeter

In this paper a previously developed theoretical model of the measurement process performed by a transit-time ultrasonic anemometer is applied to a fluid flowing through a circular section pipe. This model considers the influence of the shift of the acoustic pulse trajectory from straight propagation due to the flow on the measured speed. The aim of this work is to estimate the errors induced in the measured velocity by the shift of the acoustic pulse trajectory. Using different duct’s flow models, laminar and turbulent regimes have been analyzed. The results show that neglecting the effect of shift of the acoustic pulse trajectory leads to flow rate measurement underestimation.