Approximate solution for non-Darcy transient film condensation in a porous medium

The problem of non-darcian transient film condensation adjacent to a vertical flat plate embedded in a porous medium has been considered. The governing equation for the boundary layer thickness was obtained by an integral method and solved approximately by the method of integral relations. It is shown that the results are in good agreement with those obtained exactly by the method of characteristics.

Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms

We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding maps with holes, by ourselves and by Dysman, we show that the Hausdorff dimension and the limit capacity (box dimension) of the repeller are strictly less than the dimension of the ambient manifold.

Simulação numérica da convecção natural no interior de um refrigerador doméstico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Lake sediments as natural seismographs: A compiled record of Late Quaternary earthquakes in Central Switzerland and its implication for Alpine deformation

Central Switzerland lies tectonically in an intraplate area and recurrence rates of strong earthquakes exceed the time span covered by historic chronicles. However, many lakes are present in the area that act as natural seismographs: their continuous, datable and high-resolution sediment succession allows extension of the earthquake catalogue to pre-historic times. This study reviews and compiles available data sets and results from more than 10 years of lacustrine palaeoseismological research in lakes of northern and Central Switzerland. The concept of using lacustrine mass-movement event stratigraphy to identify palaeo-earthquakes is showcased by presenting new data and results from Lake Zurich. The Late Glacial to Holocene mass-movement units in this lake document a complex history of varying tectonic and environmental impacts. Results include sedimentary evidence of three major and three minor, simultaneously triggered basin-wide lateral slope failure events interpreted as the fingerprints of palaeoseismic activity. A refined earthquake catalogue, which includes results from previous lake studies, reveals a non-uniform temporal distribution of earthquakes in northern and Central Switzerland. A higher frequency of earthquakes in the Late Glacial and Late Holocene period documents two different phases of neotectonic activity; they are interpreted to be related to isostatic post-glacial rebound and relatively recent (re-)activation of seismogenic zones, respectively. Magnitudes and epicentre reconstructions for the largest identified earthquakes provide evidence for two possible earthquake sources: (i) a source area in the region of the Alpine or Sub-Alpine Front due to release of accumulated north-west/south-east compressional stress related to an active basal thrust beneath the Aar massif; and (ii) a source area beneath the Alpine foreland due to reactivation of deep-seated strike-slip faults. Such activity has been repeatedly observed instrumentally, for example, during the most recent magnitude 4.2 and 3.5 earthquakes of February 2012, near Zug. The combined lacustrine record from northern and Central Switzerland indicates that at least one of these potential sources has been capable of producing magnitude 6.2 to 6.7 events in the past.

Linear global instability of non-orthogonal incompressible swept attachment-line boundary layer flow

Instability of the orthogonal swept attachment line boundary layer has received attention by local1, 2 and global3–5 analysis methods over several decades, owing to the significance of this model to transition to turbulence on the surface of swept wings. However, substantially less attention has been paid to the problem of laminar flow instability in the non-orthogonal swept attachment-line boundary layer; only a local analysis framework has been employed to-date.6 The present contribution addresses this issue from a linear global (BiGlobal) instability analysis point of view in the incompressible regime. Direct numerical simulations have also been performed in order to verify the analysis results and unravel the limits of validity of the Dorrepaal basic flow7 model analyzed. Cross-validated results document the effect of the angle _ on the critical conditions identified by Hall et al.1 and show linear destabilization of the flow with decreasing AoA, up to a limit at which the assumptions of the Dorrepaal model become questionable. Finally, a simple extension of the extended G¨ortler-H¨ammerlin ODE-based polynomial model proposed by Theofilis et al.4 is presented for the non-orthogonal flow. In this model, the symmetries of the three-dimensional disturbances are broken by the non-orthogonal flow conditions. Temporal and spatial one-dimensional linear eigenvalue codes were developed, obtaining consistent results with BiGlobal stability analysis and DNS. Beyond the computational advantages presented by the ODE-based model, it allows us to understand the functional dependence of the three-dimensional disturbances in the non-orthogonal case as well as their connections with the disturbances of the orthogonal stability problem.

Efficient numerical methods for global linear instability. Analysis and modeling of non-orthogonal swept attachment-line boundary layer flow

The aim of this thesis is to study the mechanisms of instability that occur in swept wings when the angle of attack increases. For this, a simplified model for the a simplified model for the non-orthogonal swept leading edge boundary layer has been used as well as different numerical techniques in order to solve the linear stability problem that describes the behavior of perturbations superposed upon this base flow. Two different approaches, matrix-free and matrix forming methods, have been validated using direct numerical simulations with spectral resolution. In this way, flow instability in the non-orthogonal swept attachment-line boundary layer is addressed in a linear analysis framework via the solution of the pertinent global (Bi-Global) PDE-based eigenvalue problem. Subsequently, a simple extension of the extended G¨ortler-H¨ammerlin ODEbased polynomial model proposed by Theofilis, Fedorov, Obrist & Dallmann (2003) for orthogonal flow, which includes previous models as particular cases and recovers global instability analysis results, is presented for non-orthogonal flow. Direct numerical simulations have been used to verify the stability results and unravel the limits of validity of the basic flow model analyzed. The effect of the angle of attack, AoA, on the critical conditions of the non-orthogonal problem has been documented; an increase of the angle of attack, from AoA = 0 (orthogonal flow) up to values close to _/2 which make the assumptions under which the basic flow is derived questionable, is found to systematically destabilize the flow. The critical conditions of non-orthogonal flows at 0 _ AoA _ _/2 are shown to be recoverable from those of orthogonal flow, via a simple analytical transformation involving AoA. These results can help to understand the mechanisms of destabilization that occurs in the attachment line of wings at finite angles of attack. Studies taking into account variations of the pressure field in the basic flow or the extension to compressible flows are issues that remain open. El objetivo de esta tesis es estudiar los mecanismos de la inestabilidad que se producen en ciertos dispositivos aerodinámicos cuando se aumenta el ángulo de ataque. Para ello se ha utilizado un modelo simplificado del flujo de base, así como diferentes técnicas numéricas, con el fin de resolver el problema de estabilidad lineal asociado que describe el comportamiento de las perturbaciones. Estos métodos; sin y con formación de matriz, se han validado utilizando simulaciones numéricas directas con resolución espectral. De esta manera, la inestabilidad del flujo de capa límite laminar oblicuo entorno a la línea de estancamiento se aborda en un marco de análisis lineal por medio del método Bi-Global de resolución del problema de valores propios en derivadas parciales. Posteriormente se propone una extensión simple para el flujo no-ortogonal del modelo polinomial de ecuaciones diferenciales ordinarias, G¨ortler-H¨ammerlin extendido, propuesto por Theofilis et al. (2003) para el flujo ortogonal, que incluye los modelos previos como casos particulares y recupera los resultados del analisis global de estabilidad lineal. Se han realizado simulaciones directas con el fin de verificar los resultados del análisis de estabilidad así como para investigar los límites de validez del modelo de flujo base utilizado. En este trabajo se ha documentado el efecto del ángulo de ataque AoA en las condiciones críticas del problema no ortogonal obteniendo que el incremento del ángulo de ataque, de AoA = 0 (flujo ortogonal) hasta valores próximos a _/2, en el cual las hipótesis sobre las que se basa el flujo base dejan de ser válidas, tiende sistemáticamente a desestabilizar el flujo. Las condiciones críticas del caso no ortogonal 0 _ AoA _ _/2 pueden recuperarse a partir del caso ortogonal mediante el uso de una transformación analítica simple que implica el ángulo de ataque AoA. Estos resultados pueden ayudar a comprender los mecanismos de desestabilización que se producen en el borde de ataque de las alas de los aviones a ángulos de ataque finitos. Como tareas pendientes quedaría realizar estudios que tengan en cuenta variaciones del campo de presión en el flujo base así como la extensión de éste al caso de flujos compresibles.

An equilibrium statistical model for the spreading phase of open-ocean convection

A “most probable state” equilibrium statistical theory for random distributions of hetons in a closed basin is developed here in the context of two-layer quasigeostrophic models for the spreading phase of open-ocean convection. The theory depends only on bulk conserved quantities such as energy, circulation, and the range of values of potential vorticity in each layer. The simplest theory is formulated for a uniform cooling event over the entire basin that triggers a homogeneous random distribution of convective towers. For a small Rossby deformation radius typical for open-ocean convection sites, the most probable states that arise from this theory strongly resemble the saturated baroclinic states of the spreading phase of convection, with a stabilizing barotropic rim current and localized temperature anomaly.

Theoretical investigation of convective instability in inclined and fluid-saturated three-dimensional fault zones.

The convective instability of pore-fluid flow in inclined and fluid-saturated three-dimensional fault zones has been theoretically investigated in this paper. Due to the consideration of the inclined three-dimensional fault zone with any values of the inclined angle, it is impossible to use the conventional linear stability analysis method for deriving the critical condition (i.e., the critical Rayleigh number) which can be used to investigate the convective instability of the pore-fluid flow in an inclined three-dimensional fault zone system. To overcome this mathematical difficulty, a combination of the variable separation method and the integration elimination method has been used to derive the characteristic equation, which depends on the Rayleigh number and the inclined angle of the inclined three-dimensional fault zone. Using this characteristic equation, the critical Rayleigh number of the system can be numerically found as a function of the inclined angle of the three-dimensional fault zone. For a vertically oriented three-dimensional fault zone system, the critical Rayleigh number of the system can be explicitly derived from the characteristic equation. Comparison of the resulting critical Rayleigh number of the system with that previously derived in a vertically oriented three-dimensional fault zone has demonstrated that the characteristic equation of the Rayleigh number is correct and useful for investigating the convective instability of pore-fluid flow in the inclined three-dimensional fault zone system. The related numerical results from this investigation have indicated that: (1) the convective pore-fluid flow may take place in the inclined three-dimensional fault zone; (2) if the height of the fault zone is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone stabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; (3) if the thickness of the stratum is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone destabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; and that (4) the shape of the inclined three-dimensional fault zone may affect the convective instability of pore-fluid flow in the system. (C) 2004 Published by Elsevier B.V.

On the theory of the modulation instability in optical fiber and laser amplifiers

The modulation instability (MI) in optical fiber amplifiers and lasers with anomalous dispersion leads to CW beam breakup and the growth of multiple pulses. This can be both a detrimental effect, limiting the performance of amplifiers, and also an underlying physical mechanism in the operation of MI-based devices. Here we revisit the analytical theory of MI in fiber optical amplifiers. The results of the exact theory are compared with the previously used adiabatic approximation model, and the range of applicability of the latter is determined. The same technique is applicable to the study of spatial MI in solid state laser amplifiers and MI in non-uniform media. © 2011 SPIE.

Advanced thermal analysis of microelectronics using spreading resistance models

Thermal analysis of electronic devices is one of the most important steps for designing of modern devices. Precise thermal analysis is essential for designing an effective thermal management system of modern electronic devices such as batteries, LEDs, microelectronics, ICs, circuit boards, semiconductors and heat spreaders. For having a precise thermal analysis, the temperature profile and thermal spreading resistance of the device should be calculated by considering the geometry, property and boundary conditions. Thermal spreading resistance occurs when heat enters through a portion of a surface and flows by conduction. It is the primary source of thermal resistance when heat flows from a tiny heat source to a thin and wide heat spreader. In this thesis, analytical models for modeling the temperature behavior and thermal resistance in some common geometries of microelectronic devices such as heat channels and heat tubes are investigated. Different boundary conditions for the system are considered. Along the source plane, a combination of discretely specified heat flux, specified temperatures and adiabatic condition are studied. Along the walls of the system, adiabatic or convective cooling boundary conditions are assumed. Along the sink plane, convective cooling with constant or variable heat transfer coefficient are considered. Also, the effect of orthotropic properties is discussed. This thesis contains nine chapters. Chapter one is the introduction and shows the concepts of thermal spreading resistance besides the originality and importance of the work. Chapter two reviews the literatures on the thermal spreading resistance in the past fifty years with a focus on the recent advances. In chapters three and four, thermal resistance of a twodimensional flux channel with non-uniform convection coefficient in the heat sink plane is studied. The non-uniform convection is modeled by using two functions than can simulate a wide variety of different heat sink configurations. In chapter five, a non-symmetrical flux channel with different heat transfer coefficient along the right and left edges and sink plane is analytically modeled. Due to the edge cooling and non-symmetry, the eigenvalues of the system are defined using the heat transfer coefficient on both edges and for satisfying the orthogonality condition, a normalized function is calculated. In chapter six, thermal behavior of two-dimensional rectangular flux channel with arbitrary boundary conditions on the source plane is presented. The boundary condition along the source plane can be a combination of the first kind boundary condition (Dirichlet or prescribed temperature) and the second kind boundary condition (Neumann or prescribed heat flux). The proposed solution can be used for modeling the flux channels with numerous different source plane boundary conditions without any limitations in the number and position of heat sources. In chapter seven, temperature profile of a circular flux tube with discretely specified boundary conditions along the source plane is presented. Also, the effect of orthotropic properties are discussed. In chapter 8, a three-dimensional rectangular flux channel with a non-uniform heat convection along the heat sink plane is analytically modeled. In chapter nine, a summary of the achievements is presented and some systems are proposed for the future studies. It is worth mentioning that all the models and case studies in the thesis are compared with the Finite Element Method (FEM).

Numerical investigation of the three-dimensional secondary instabilities in the time-developing compressible mixing layer

Mixing layers are present in very different types of physical situations such as atmospheric flows, aerodynamics and combustion. It is, therefore, a well researched subject, but there are aspects that require further studies. Here the instability of two-and three-dimensional perturbations in the compressible mixing layer was investigated by numerical simulations. In the numerical code, the derivatives were discretized using high-order compact finite-difference schemes. A stretching in the normal direction was implemented with both the objective of reducing the sound waves generated by the shear region and improving the resolution near the center. The compact schemes were modified to work with non-uniform grids. Numerical tests started with an analysis of the growth rate in the linear regime to verify the code implementation. Tests were also performed in the non-linear regime and it was possible to reproduce the vortex roll-up and pairing, both in two-and three-dimensional situations. Amplification rate analysis was also performed for the secondary instability of this flow. It was found that, for essentially incompressible flow, maximum growth rates occurred for a spanwise wavelength of approximately 2/3 of the streamwise spacing of the vortices. The result demonstrated the applicability of the theory developed by Pierrehumbet and Widnall. Compressibility effects were then considered and the maximum growth rates obtained for relatively high Mach numbers (typically under 0.8) were also presented.

Vegetable Oil Quenchants: Calculation and Comparison of The Cooling Properties of a Series of Vegetable Oils

The compositions of canola, soybean, corn, cottonseed and sunflower oils suggest that they exhibit substantially different propensity for oxidation following the order of Canola < corn < cottonseed < sunflower approximate to soybean. These data suggest that any of the vegetable oils evaluated could be blended with minimal impact on viscosity although compositional differences would surely affect oxidative stability. Cooling curve analysis showed that similar cooling profiles were obtained for different vegetable oils. Interestingly, no film boiling or transition nucleate boiling was observed with any of the vegetable oils and heat transfer occurs only by pure nucleate boiling and convection. High-temperature cooling properties of vegetable oils are considerable faster than those observed for petroleum oil-based quenchants. (C)2010 Journal of Mechanical Engineering. All rights reserved.

Numerical modelling of double diffusion driven reactive flow transport in deformable fluid-saturated porous media with particular consideration of temperature-dependent chemical reaction rates

Numerical methods ave used to solve double diffusion driven reactive flow transport problems in deformable fluid-saturated porous media. in particular, thp temperature dependent reaction rate in the non-equilibrium chemical reactions is considered. A general numerical solution method, which is a combination of the finite difference method in FLAG and the finite element method in FIDAP, to solve the fully coupled problem involving material deformation, pore-fluid flow, heat transfer and species transport/chemical reactions in deformable fluid-saturated porous media has been developed The coupled problem is divided into two subproblems which are solved interactively until the convergence requirement is met. Owing to the approximate nature of the numerical method, if is essential to justify the numerical solutions through some kind of theoretical analysis. This has been highlighted in this paper The related numerical results, which are justified by the theoretical analysis, have demonstrated that the proposed solution method is useful for and applicable to a wide range of fully coupled problems in the field of science and engineering.