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.

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 fast, high resolution, second-order central scheme for incompressible flows

A high resolution, second-order central difference method for incompressible flows is presented. The method is based on a recent second-order extension of the classic Lax–Friedrichs scheme introduced for hyperbolic conservation laws (Nessyahu H. & Tadmor E. (1990) J. Comp. Physics. 87, 408-463; Jiang G.-S. & Tadmor E. (1996) UCLA CAM Report 96-36, SIAM J. Sci. Comput., in press) and augmented by a new discrete Hodge projection. The projection is exact, yet the discrete Laplacian operator retains a compact stencil. The scheme is fast, easy to implement, and readily generalizable. Its performance was tested on the standard periodic double shear-layer problem; no spurious vorticity patterns appear when the flow is underresolved. A short discussion of numerical boundary conditions is also given, along with a numerical example.

Generalized flows, intrinsic stochasticity, and turbulent transport

The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows, which are families of probability distributions on the space of solutions to the associated ordinary differential equations which no longer satisfy the uniqueness theorem for ordinary differential equations. Two most natural regularizations of this problem, namely the regularization via adding small molecular diffusion and the regularization via smoothing out the velocity field, are considered. White-in-time random velocity fields are used as an example to examine the variety of phenomena that take place when the velocity field is not spatially regular. Three different regimes, characterized by their degrees of compressibility, are isolated in the parameter space. In the regime of intermediate compressibility, the two different regularizations give rise to two different scaling behaviors for the structure functions of the passive scalar. Physically, this means that the scaling depends on Prandtl number. In the other two regimes, the two different regularizations give rise to the same generalized flows even though the sense of convergence can be very different. The “one force, one solution” principle is established for the scalar field in the weakly compressible regime, and for the difference of the scalar in the strongly compressible regime, which is the regime of inverse cascade. Existence and uniqueness of an invariant measure are also proved in these regimes when the transport equation is suitably forced. Finally incomplete self similarity in the sense of Barenblatt and Chorin is established.

Flows of knowledge from universities and federal laboratories: Modeling the flow of patent citations over time and across institutional and geographic boundaries

The extent to which new technological knowledge flows across institutional and national boundaries is a question of great importance for public policy and the modeling of economic growth. In this paper we develop a model of the process generating subsequent citations to patents as a lens for viewing knowledge diffusion. We find that the probability of patent citation over time after a patent is granted fits well to a double-exponential function that can be interpreted as the mixture of diffusion and obsolescense functions. The results indicate that diffusion is geographically localized. Controlling for other factors, within-country citations are more numerous and come more quickly than those that cross country boundaries.

An evolutionary approach to the delineation of functional areas based on travel-to-work flows

This paper presents a new approach to the delineation of local labor markets based on evolutionary computation. The aim of the exercise is the division of a given territory into functional regions based on travel-to-work flows. Such regions are defined so that a high degree of inter-regional separation and of intra-regional integration in both cases in terms of commuting flows is guaranteed. Additional requirements include the absence of overlap between delineated regions and the exhaustive coverage of the whole territory. The procedure is based on the maximization of a fitness function that measures aggregate intra-region interaction under constraints of inter-region separation and minimum size. In the experimentation stage, two variations of the fitness function are used, and the process is also applied as a final stage for the optimization of the results from one of the most successful existing methods, which are used by the British authorities for the delineation of travel-to-work areas (TTWAs). The empirical exercise is conducted using real data for a sufficiently large territory that is considered to be representative given the density and variety of travel-to-work patterns that it embraces. The paper includes the quantitative comparison with alternative traditional methods, the assessment of the performance of the set of operators which has been specifically designed to handle the regionalization problem and the evaluation of the convergence process. The robustness of the solutions, something crucial in a research and policy-making context, is also discussed in the paper.

International Capital Flows and Monetary Policy Spillovers

This dissertation examines the drivers and implications of international capital flows. The overarching motivation is the observation that countries not at the centre of global financial markets are subject to considerable spillovers from centre countries, notably from their monetary policy. I present new empirical evidence on the determinants of the observed patterns of international capital flows and monetary policy spillovers, and study their effect on both financial markets and the real economy. In Chapter 2 I provide evidence on the determinants of a puzzling negative correlation observed between productivity growth and net capital inflows to developing and emerging market economies (EMEs) since 1980. By disaggregating net capital inflows into their gross components, I show that this negative correlation is explained by capital outflows related to purchases of very liquid assets from the fastest growing countries. My results suggest a desire for international portfolio diversification in liquid assets by fast growing countries is driving much of the original puzzle. In the reminder of my dissertation I pivot to study the foreign characteristics that drive international capital flows and monetary policy spillovers, with a particular focus on the role of unconventional monetary policy in the United States (U.S.). In Chapter 3 I show that a significant portion of the heterogeneity in EMEs' asset price adjustment following the quantitative easing operations by the Federal Reserve (the Fed) during 2008-2014 can be explained by the degree of bilateral capital market frictions between these countries and the U.S. This is true even after accounting for capital controls, exchange rate regimes, and domestic monetary policies. Chapter 4, co-authored with Michal Ksawery Popiel, studies unconventional monetary policy in a small open economy, looking specifically at the case of Canada since the global financial crisis. We quantify the effect Canadian unconventional monetary policy shocks had on the real economy, while carefully controlling for and quantifying spillovers from U.S. unconventional monetary policy. Our results indicate that the Bank of Canada's unconventional monetary policy increased Canadian output significantly from 2009-2010, but that spillovers from the Fed's policy were even more important for increasing Canadian output after 2008.