On the role of global flow instability analysis in closed loop flow control

Control of linear flow instabilities has been demonstrated to be an effective theoretical flow control methodology, capable of modifying transitional flow on canonical geometries such as the plane channel and the flat-plate boundary layer.

Global instability analysis and control of three-dimensional long open cavity flow

The three-dimensional wall-bounded open cavity may be considered as a simplified geometry found in industrial applications such as leading gear or slotted flats on the airplane. Understanding the three-dimensional complex flow structure that surrounds this particular geometry is therefore of major industrial interest. At the light of the remarkable former investigations in this kind of flows, enough evidences suggest that the lateral walls have a great influence on the flow features and hence on their instability modes. Nevertheless, even though there is a large body of literature on cavity flows, most of them are based on the assumption that the flow is two-dimensional and spanwise-periodic. The flow over realistic open cavity should be considered. This thesis presents an investigation of three-dimensional wall-bounded open cavity with geometric ratio 6:2:1. To this aim, three-dimensional Direct Numerical Simulation (DNS) and global linear instability have been performed. Linear instability analysis reveals that the onset of the first instability in this open cavity is around Recr 1080. The three-dimensional shear layer mode with a complex structure is shown to be the most unstable mode. I t is noteworthy that the flow pattern of this high-frequency shear layer mode is similar to the observed unstable oscillations in supercritical unstable case. DNS of the cavity flow carried out at different Reynolds number from steady state until a nonlinear saturated state is obtained. The comparison of time histories of kinetic energy presents a clearly dominant energetic mode which shifts between low-frequency and highfrequency oscillation. A complete flow patterns from subcritical cases to supercritical case has been put in evidence. The flow structure at the supercritical case Re=1100 resembles typical wake-shedding instability oscillations with a lateral motion existed in the subcritical cases. Also, This flow pattern is similar to the observations in experiments. In order to validate the linear instability analysis results, the topology of the composite flow fields reconstructed by linear superposition of a three-dimensional base flow and its leading three-dimensional global eigenmodes has been studied. The instantaneous wall streamlines of those composited flows display distinguish influence region of each eigenmode. Attention has been focused on the leading high-frequency shear layer mode; the composite flow fields have been fully recognized with respect to the downstream wave shedding. The three-dimensional shear layer mode is shown to give rise to a typical wake-shedding instability with a lateral motions occurring downstream which is in good agreement with the experiment results. Moreover, the spanwise-periodic, open cavity with the same length to depth ratio has been also studied. The most unstable linear mode is different from the real three-dimensional cavity flow, because of the existence of the side walls. Structure sensitivity of the unstable global mode is analyzed in the flow control context. The adjoint-based sensitivity analysis has been employed to localized the receptivity region, where the flow is more sensible to momentum forcing and mass injection. Because of the non-normality of the linearized Navier-Stokes equations, the direct and adjoint field has a large spatial separation. The strongest sensitivity region is locate in the upstream lip of the three-dimensional cavity. This numerical finding is in agreement with experimental observations. Finally, a prototype of passive flow control strategy is applied.

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.

DNA-protein binding assays from a single sea urchin egg: a high-sensitivity capillary electrophoresis method.

A capillary electrophoresis method has been developed to study DNA-protein complexes by mobility-shift assay. This method is at least 100 times more sensitive than conventional gel mobility-shift procedures. Key features of the technique include the use of a neutral coated capillary, a small amount of linear polymer in the separation medium, and use of covalently dye-labeled DNA probes that can be detected with a commercially available laser-induced fluorescence monitor. The capillary method provides quantitative data in runs requiring < 20 min, from which dissociation constants are readily determined. As a test case we studied interactions of a developmentally important sea urchin embryo transcription factor, SpP3A2. As little as 2-10 x 10(6) molecules of specific SpP3A2-oligonucleotide complex were reproducibly detected, using recombinant SpP3A2, crude nuclear extract, egg lysates, and even a single sea urchin egg lysed within the capillary column.

Avaliação de métodos numéricos de análise linear de estabilidade para perfis de aço formados a frio.

Para o projeto de estruturas com perfis de aço formados a frio, é fundamental a compreensão dos fenômenos da instabilidade local e global, uma vez que estes apresentam alta esbeltez e baixa rigidez à torção. A determinação do carregamento crítico e a identificação do modo de instabilidade contribuem para o entendimento do comportamento dessas estruturas. Este trabalho avalia três metodologias para a análise linear de estabilidade de perfis de aço formados a frio isolados, com o objetivo de determinar os carregamentos críticos elásticos de bifurcação e os modos de instabilidade associados. Estritamente, analisa-se perfis de seção U enrijecido e Z enrijecido isolados, de diversos comprimentos e diferentes condições de vinculação e carregamento. Determinam-se os carregamentos críticos elásticos de bifurcação e os modos de instabilidade globais e locais por meio de: (i) análise com o Método das Faixas Finitas (MFF), através do uso do programa computacional CUFSM; (ii) análise com elementos finitos de barra baseados na Teoria Generalizada de Vigas (MEF-GBT), via uso do programa GBTUL; e (iii) análise com elementos finitos de casca (MEF-cascas) por meio do uso do programa ABAQUS. Algumas restrições e ressalvas com relação ao uso do MFF são apresentadas, assim como limitações da Teoria Generalizada de Viga e precauções a serem tomadas nos modelos de cascas. Analisa-se também a influência do grau de discretização da seção transversal. No entanto, não é feita avaliação em relação aos procedimentos normativos e tampouco análises não lineares, considerando as imperfeições geométricas iniciais, tensões residuais e o comportamento elastoplástico do material.

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.

Lateral instability of slender reinforced concrete columns in a fire environment

The research concerns the development and application of an analytical computer program, SAFE-ROC, that models material behaviour and structural behaviour of a slender reinforced concrete column that is part of an overall structure and is subjected to elevated temperatures as a result of exposure to fire. The analysis approach used in SAFE-RCC is non-linear. Computer calculations are used that take account of restraint and continuity, and the interaction of the column with the surrounding structure during the fire. Within a given time step an iterative approach is used to find a deformed shape for the column which results in equilibrium between the forces associated with the external loads and internal stresses and degradation. Non-linear geometric effects are taken into account by updating the geometry of the structure during deformation. The structural response program SAFE-ROC includes a total strain model which takes account of the compatibility of strain due to temperature and loading. The total strain model represents a constitutive law that governs the material behaviour for concrete and steel. The material behaviour models employed for concrete and steel take account of the dimensional changes caused by the temperature differentials and changes in the material mechanical properties with changes in temperature. Non-linear stress-strain laws are used that take account of loading to a strain greater than that corresponding to the peak stress of the concrete stress-strain relation, and model the inelastic deformation associated with unloading of the steel stress-strain relation. The cross section temperatures caused by the fire environment are obtained by a preceding non-linear thermal analysis, a computer program FIRES-T.

Purchasing power parity and structural instability in the US/UK exchange rate

The aim of this study is to determine if nonlinearities have affected purchasing power parity (PPP) since 1885. Also using recent advances in the econometrics of structural change we segment the sample space according to the identified breaks and look at whether the PPP condition holds in each sub-sample and whether this involves linear or non-linear adjustment. Our results suggest that during some sub-periods, PPP holds, although whether it holds or not and whether the adjustment is linear or non-linear, depends primarily on the type of exchange rate regime in operation at any point in time.

Stochastically driven instability in rotating shear flows

Origin of hydrodynamic turbulence in rotating shear flows is investigated. The particular emphasis is on flows whose angular velocities decrease but specific angular momenta increase with increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain observed data. Such a mismatch between the linear theory and observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and the corresponding turbulence therein is ruled out. The present work explores the effect of stochastic noise on such hydrodynamic flows. We focus on a small section of such a flow which is essentially a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disk. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities, and hence large energy dissipations, that presumably generate instability. A range of angular velocity profiles (for the steady flow), starting with the constant angular momentum to that of the constant circular velocity are explored. It is shown that the growth and roughness exponents calculated from the contour (envelope) of the perturbed flows are all identical, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand origin of instability and turbulence in the three-dimensional Rayleigh stable rotating shear flows by introducing additive stochastic noise to the underlying linearized governing equations. This has important implications in resolving the turbulence problem in astrophysical hydrodynamic flows such as accretion disks.

Stochastically driven instability in rotating shear flows

Origin of hydrodynamic turbulence in rotating shear flows is investigated. The particular emphasis is on flows whose angular velocities decrease but specific angular momenta increase with increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain observed data. Such a mismatch between the linear theory and observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and the corresponding turbulence therein is ruled out. The present work explores the effect of stochastic noise on such hydrodynamic flows. We focus on a small section of such a flow which is essentially a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disk. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities, and hence large energy dissipations, that presumably generate instability. A range of angular velocity profiles (for the steady flow), starting with the constant angular momentum to that of the constant circular velocity are explored. It is shown that the growth and roughness exponents calculated from the contour (envelope) of the perturbed flows are all identical, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand origin of instability and turbulence in the three-dimensional Rayleigh stable rotating shear flows by introducing additive stochastic noise to the underlying linearized governing equations. This has important implications in resolving the turbulence problem in astrophysical hydrodynamic flows such as accretion disks.

Generation of 1.7-μJ pulses at 1.55μm by a self-modelocked all-fiber laser with a kilometers-long linear-ring cavity

We report on the record-high pulse energy of nearly 1.7 μJ obtained directly from a self-mode-locked all-fiber erbium laser with a linear-ring cavity owing its extreme elongation up to several kilometers. Specially selected telecommunication fibers, providing large normal net cavity dispersion in the vicinity of 1.55 μm, have been used for this purpose. Along with compensation for polarization instability in the longer linear arm of the cavity, such approach has ensured stable wavebreaking- free mode-locked lasing with an ultra-low pulse repetition rate of 35.1 kHz. © 2010 by Astro Ltd.

Applications of capillary electrophoresis and mass spectrometry for the analysis of thiosalts

Thiosalt species are unstable, partially oxidized sulfur oxyanions formed in sulfur-rich environments but also during the flotation and milling of sulfidic minerals especially those containing pyrite (FeS₂) and pyrrhotite (Fe₍₁₋ₓ₎S, x = 0 to 0.2). Detecting and quantifying the major thiosalt species such as sulfate (SO₄²⁻), thiosulfate (S₂O₃²⁻), trithionate (S₃O₆²⁻), tetrathionate (S₄O₆²⁻) and higher polythionates (SₓO₆²⁻, where 3 ≤ x ≤ 10) in the milling process and in the treated tailings is important to understand how thiosalts are generated and provides insight into potential treatment. As these species are unstable, a fast and reliable analytical technique is required for their analysis. Three capillary zone electrophoresis (CZE) methods using indirect UV-vis detection were developed for the simultaneous separation and determination of five thiosalt anions: SO₄²⁻, S₂O₃²⁻, S₃O₆²⁻, S₄O₆²⁻ and S₅O₆²⁻. Both univariate and multivariate experimental design approaches were used to optimize the most critical factors (background electrolyte (BGE) and instrumental conditions) to achieve fast separation and quantitative analysis of the thiosalt species. The mathematically predicted responses for the multivariate experiments were in good agreement with the experimental results. Limits of detection (LODs) (S/N = 3) for the methods were between 0.09 and 0.34 μg/mL without a sample stacking technique and nearly four-fold increase in LODs with the application of field-amplified sample stacking. As direct analysis of thiosalts by mass spectrometry (MS) is limited by their low m/z values and detection in negative mode electrospray ionization (ESI), which is typically less sensitive than positive ESI, imidazolium-based (IP-L-Imid and IP-T-Imid) and phosphonium-based (IP-T-Phos) tricationic ion-pairing reagents were used to form stable high mass ions non-covalent +1 ion-pairs with these species for ESI-MS analysis and the association constants (Kassoc) determined for these ion-pairs. Kassoc values were between 6.85 × 10² M⁻¹ and 3.56 × 10⁵ M⁻¹ with the linear IP-L-Imid; 1.89 ×10³ M⁻¹ and 1.05 × 10⁵ M⁻¹ with the trigonal IP-T-Imid ion-pairs; and 7.51×10² M⁻¹ and 4.91× 10⁴ M⁻¹ with the trigonal IP-T-Phos ion-pairs. The highest formation constants were obtained for S₃O₆²⁻ and the imidazolium-based linear ion-pairing reagent (IP-L-Imid), whereas the lowest were for IP-L-Imid: SO₄²⁻ ion-pair.

Kelvin-Helmholtz instability in solar chromospheric jets: theory and observation

Using data obtained by the high-resolution CRisp Imaging SpectroPolarimeter instrument on the Swedish 1 m Solar Telescope, we investigate the dynamics and stability of quiet-Sun chromospheric jets observed at the disk center. Small-scale features, such as rapid redshifted and blueshifted excursions, appearing as high-peed jets in the wings of the Hα line, are characterized by short lifetimes and rapid fading without any descending behavior. To study the theoretical aspects of their stability without considering their formation mechanism, we model chromospheric jets as twisted magnetic flux tubes moving along their axis, and use the ideal linear incompressible magnetohydrodynamic approximation to derive the governing dispersion equation. Analytical solutions of the dispersion equation indicate that this type of jet is unstable to Kelvin–Helmholtz instability (KHI), with a very short (few seconds) instability growth time at high upflow speeds. The generated vortices and unresolved turbulent flows associated with the KHI could be observed as a broadening of chromospheric spectral lines. Analysis of the Hα line profiles shows that the detected structures have enhanced line widths with respect to the background. We also investigate the stability of a larger-scale Hα jet that was ejected along the line of sight. Vortex-like features, rapidly developing around the jet’s boundary, are considered as evidence of the KHI. The analysis of the energy equation in the partially ionized plasma shows that ion–neutral collisions may lead to fast heating of the KH vortices over timescales comparable to the lifetime of chromospheric jets.

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.

Predicting water permeability in sedimentary rocks from capillary imbibition and pore structure

In this paper, absolute water permeability is estimated from capillary imbibition and pore structure for 15 sedimentary rock types. They present a wide range of petrographic characteristics that provide degrees of connectivity, porosities, pore size distributions, water absorption coefficients by capillarity and water permeabilities. A statistical analysis shows strong correlations among the petrophysical parameters of the studied rocks. Several fundamental properties are fitted into different linear and multiple expressions where water permeability is expressed as a generalized function of the properties. Some practical aspects of these correlations are highlighted in order to use capillary imbibition tests to estimate permeability. The permeability–porosity relation is discussed in the context of the influence of pore connectivity and wettability. As a consequence, we propose a generalized model for permeability that includes information about water fluid rate (water absorption coefficient by capillarity), water properties (density and viscosity), wetting (interfacial tension and contact angle) and pore structure (pore radius and porosity). Its application is examined in terms of the type of pores that contribute to water transport and wettability. The results indicate that the threshold pore radius, in which water percolates through rock, achieves the best description of the pore system. The proposed equation is compared against Carman–Kozeny's and Katz–Thompson's equations. The proposed equation achieves very accurate predictions of the water permeability in the range of 0.01 to 1000 mD.