Academic literature on the topic 'PVC Oscillations'

The paper presents the calculation results of the two mathematical models of the variable displacement axial piston pumps PVC 1.85. In the first mathematical model of the pistons averaged force was used, the application point of which corresponds to the offset of the swash plate’s swivel axis. In the second mathematical model the parametric change of the pistons consolidated force magnitude and the coordinates of its application point was taken into account.

Abstract In this experimental study, a passive flow control concept is provided to extend the stable part load operation regime by shifting the rise of the precessing vortex core (PVC), also known as vortex rope, toward lower mass flows respectively deeper part loads. A parametrized runner crown design working as a passive flow control device is derived. This control device aims for shifting the bifurcation point of the PVC to lower flow rates. To determine the most influential design parameters and derive an optimized runner crown design, a design of experiments (DoE) approach is used. This DoE approach is based on data obtained from differential pressure sensors inside the draft tube wall of a generic hydro turbine test rig using air as working fluid. By means of stochastic modeling, the growth rate of the PVC mode is derived from the statistics of the measured pressure signals. The growth rate is used to estimate the bifurcation point of the PVC characterized by a certain normalized flow rate. It is shown that the stable part load operation regime is extended by up to 25% due to the passive impact of the modified runner crown. Moreover, the operational range featuring considerable PVC-induced pressure oscillations is diminished and the pressure recovery of the draft tube is improved compared to the baseline case.

We report on the experimental study of a precessing vortex core (PVC) in an air model of a Francis turbine. The focus is placed on the modal decomposition of the PVC that occurs in the draft tube of the model turbine for a range of operation conditions. The turbulent flow fluctuations in the draft tube are assessed using stereo particle image velocimetry (PIV) measurements. Proper orthogonal decomposition (POD) is applied to the antisymmetric and symmetric components of the velocity fields to distinguish the dynamics of the azimuthal instabilities. The pressure pulsations induced by the PVC are measured by four pressure sensors mounted on the wall of the hydro turbine draft tube. Spatial Fourier decomposition is applied to the signals of the pressure sensors to identify the contributions of azimuthal modes, m=1 and m=2, to the total pressure fluctuations. The analysis based on velocity and pressure data shows similar results regarding the identification of the PVC. The contribution of the m=2 mode to the overall turbulent kinetic energy is significant for the part load regimes, where the flow rates are twice as low as at the best efficiency point (BEP). It is also shown that this mode is not the higher harmonic of the PVC, suggesting that it is driven by a different instability. Finally, we show a linear fit of the saturation amplitudes of the m=1 and m=2 oscillations to determine the critical bifurcation points of these modes. This yields critical swirl numbers of Scr=0.47 and 0.61, respectively. The fact that the PVC dynamics in hydro turbines are driven by two individual instabilities is relevant for the development of tailored active flow control of the PVC.

The hydrodynamic oscillations of a cyclone separator – in particular the precessing vortex core (PVC) phenomena – are investigated by measuring their radiated sound spectra. Strong coherence was observed between internal flow oscillations measured via hot wire anemometry and the external acoustic field measured via microphone. This means that the oscillations can be characterised by using acoustics as a proxy. The oscillations cause narrow-band noise, referred to as cyclone hum. System characterisation by dimensional analysis used velocity and length scales of the vortex core region as scaling parameters. The relevant non-dimensional parameters are a Strouhal number for the cyclone hum centre frequency, a Reynolds number, a geometry based swirl number and numerous geometric scales defining the shape of the device. Cyclones with multiple sizes of inlets and outlets were tested at different flow rates using external microphones to detect the cyclone hum. The results produce an excellent collapse of the data, yielding a simple relationship for Strouhal number as a function of swirl number and the outlet diameter ratio. The non-invasive method of examining oscillations that is presented in this paper could be applied to other swirling systems.

Polymers are used in many applications where they are subjected to cyclic stresses. PVC and HDPE piping are often used in systems that include rotating machinery that cause mechanical vibration. Recent testing of thermoplastics indicates that there may be a large effect on the viscoelastic strains of thermoplastics from oscillating stresses. Cyclic loading on the permanent set of cross-linked elastomers has been studied. Perhaps, as expected, the effect of the oscillating behavior is measurable. Two types of tests have been conducted. First, tensile tests on HDPE standard specimens were conducted where oscillating stresses were superimposed onto an initial static or mean stress. These measurements showed a rapid decrease in the oscillating stresses when compared to measurements when steady nonoscillating stresses are applied to the same type of specimen. In the second test series, pressurized HDPE piping was subject to oscillating bending stresses. Ratcheting of the hoop strains in the pipe occurs. Results show that these strains follow the constitutive relationships of linear viscoelasticity and experimental results imply that viscoelastic changes are accelerated by stress oscillations. These preliminary results seem to indicate that the effects of oscillating stresses on the viscoelastic behavior of thermoplastics may be significant. A systematic study is required to further understand this behavior. [S0094-9930(00)02403-3]

Behavioural studies have consistently found stronger vection responses for oscillating, compared to smooth/constant, patterns of radial flow (the simulated viewpoint oscillation advantage for vection). Traditional accounts predict that simulated viewpoint oscillation should impair vection by increasing visual–vestibular conflicts in stationary observers (as this visual oscillation simulates self-accelerations that should strongly stimulate the vestibular apparatus). However, support for increased vestibular activity during accelerating vection has been mixed in the brain imaging literature. This fMRI study examined BOLD activity in visual (cingulate sulcus visual area — CSv; medial temporal complex — MT+; V6; precuneus motion area — PcM) and vestibular regions (parieto-insular vestibular cortex — PIVC/posterior insular cortex — PIC; ventral intraparietal region — VIP) when stationary observers were exposed to vection-inducing optic flow (i.e., globally coherent oscillating and smooth self-motion displays) as well as two suitable control displays. In line with earlier studies in which no vection occurred, CSv and PIVC/PIC both showed significantly increased BOLD activity during oscillating global motion compared to the other motion conditions (although this effect was found for fewer subjects in PIVC/PIC). The increase in BOLD activity in PIVC/PIC during prolonged exposure to the oscillating (compared to smooth) patterns of global optical flow appears consistent with vestibular facilitation.

A filling operation generates continuous changes over the shape of an air–water interface, which can be captured using a 3D CFD model. This research analyses the influence of different hydro-pneumatic tank pressures and air pocket sizes as initial conditions for studying rapid filling operations in a 7.6 m long PVC pipeline with an irregular profile, using the OpenFOAM software. The analysed scenarios were validated using experimental measurements, where the 3D CFD model was suitable for simulating them. In addition, a mesh sensitivity analysis was performed. Air pocket pressure patterns, water velocity oscillations, and the different shapes of the air–water interface were analysed.

High-speed synchronized stereo particle-imaging velocimetry and OH planar laser-induced fluorescence (PIV/OH-PLIF) measurements are performed on multiple $R{-}\unicode[STIX]{x1D703}$ planes downstream of a high-Reynolds-number swirling jet. Dynamic-mode decomposition (DMD) – a frequency-resolved data-reduction technique – is used to identify and characterize recurrent flow structures. Illustrative results are presented in a swirling flow field for two cases – the nominal flow dynamics and where self-excited combustion driven oscillations provide strong axisymmetric narrowband forcing of the flow. The robust constituent of the nominal reacting swirl flow corresponds to a helical shear-layer disturbance at a Strouhal number ($St$) of ${\sim}0.30$, $St=fD/U_{0}$, where $f$, $D$ and $U_{0}$ denote the precessing vortex core (PVC) frequency (${\sim}800~\text{Hz}$), the swirler exit diameter (19 mm) and the bulk velocity at the swirler exit ($50~\text{m}~\text{s}^{-1}$) respectively. Planar projections of the PVC reveal a pair of oscillating skew-symmetric regions of velocity, vorticity and OH-PLIF intensity that rotate in the same direction as the mean tangential flow. During combustion instabilities, the large-amplitude acoustics-induced axisymmetric forcing of the flow results in a fundamentally different flow response dominated by a nearly axisymmetric disturbance and almost complete suppression of the large-scale helical shear-layer disturbances dominating the nominal flow. In addition, reverse axial flows around the centreline are significantly reduced. Time traces of the robust constituent show reverse axial flows around the centreline and negative axial vorticity along the inner swirling shear layer when the planar velocity is in the same direction as the mean tangential flow. For both stable and unstable combustion, recurrent flow structures decay rapidly downstream of the air swirler, as revealed by the decreasing amplitude of the velocity, axial vorticity and OH-PLIF intensity.

The cognitive deficits of schizophrenia are linked to imbalanced excitatory and inhibitory signalling in the prefrontal cortex (PFC), disrupting gamma oscillations. We previously demonstrated that two mGlu5 receptor-positive allosteric modulators (PAMs), VU0409551 and VU0360172, restore cognitive deficits in the sub-chronic PCP (scPCP) rodent model for schizophrenia via distinct changes in PFC intracellular signalling molecules. Here, we have assessed ex vivo gamma oscillatory activity in PFC slices from scPCP rats and investigated the effects of VU0409551 and VU0360172 upon oscillatory power. mGlu5 receptor, protein kinase C (PKC), and phospholipase C (PLC) inhibition were also used to examine ‘modulation bias’ in PAM activity. The amplitude and area power of gamma oscillations were significantly diminished in the scPCP model. Slice incubation with either VU0409551 or VU0360172 rescued scPCP-induced oscillatory deficits in a concentration-dependent manner. MTEP blocked the PAM-induced restoration of oscillatory power, confirming the requirement of mGlu5 receptor modulation. Whilst PLC inhibition prevented the power increase mediated by both PAMs, PKC inhibition diminished the effects of VU0360172 but not VU0409551. This aligns with previous reports that VU0409551 exhibits preferential activation of the phosphatidylinositol-3-kinase (PI3K) signalling pathway over the PKC cascade. Restoration of the excitatory/inhibitory signalling balance and gamma oscillations may therefore underlie the mGluR5 PAM-mediated correction of scPCP-induced cognitive deficits.

Signals transduced by kinases depend on the extent and duration of substrate phosphorylation. We generated genetically encoded fluorescent reporters for PKC activity that reversibly respond to stimuli activating PKC. Specifically, phosphorylation of the reporter expressed in mammalian cells causes changes in fluorescence resonance energy transfer (FRET), allowing real time imaging of phosphorylation resulting from PKC activation. Targeting of the reporter to the plasma membrane, where PKC is activated, reveals oscillatory phosphorylation in HeLa cells in response to histamine. Each oscillation in substrate phosphorylation follows a calcium oscillation with a lag of ∼10 s. Novel FRET-based reporters for PKC translocation, phosphoinositide bisphosphate conversion to IP3, and diacylglycerol show that in HeLa cells the oscillatory phosphorylations correlate with Ca2+-controlled translocation of conventional PKC to the membrane without oscillations of PLC activity or diacylglycerol. However, in MDCK cells stimulated with ATP, PLC and diacylglycerol fluctuate together with Ca2+ and phosphorylation. Thus, specificity of PKC signaling depends on the local second messenger-controlled equilibrium between kinase and phosphatase activities to result in strict calcium-controlled temporal regulation of substrate phosphorylation.

Information is transmitted from the cell surface to various specific targets in the cell via several cellular signaling pathways. Cytosolic free calcium (Ca2+)is one of the most versatile and ubiquitous intracellular messengers since it is able to regulate diverse number of functions such as proliferation, secretion, fertilization, metabolism, learning and memory. In the last couple of years, evidence has been accumulating that Ca2+ ion is able to integrate information from multiple signaling pathways and convert this information into a code which regulates events ranging from contraction to modification of gene expression (Berridge et al. 1998). It was shown that Ca2+ concentration displays oscillatory behavior in response to agonist stimulation in a variety of cells(Goldbeter 1996) and the frequency of these oscillations increases with the concentration of agonist, a behavior called frequency encoding which has led to the concept that many Ca2+-regulated processes are controlled by these codes(Berridge 1998). Although the presence of Ca2+ oscillations and the sources of Ca2+ pools involved is known in many cell types, it is yet not known how the various frequencies of Ca2+ oscillations are converted into codes that regulate the numerous cellular events. Recently a number of cellular targets that decode Ca2+ signals and are tuned to the frequency of Ca2+ oscillations have been identified. Prominent among them are calcium-calmodulin kinase II (CAM II) and protein kinase C (PKC). The objective of this work is to study and mathematically model the oxytocin and vasopressin-induced Ca2+ oscillations in cells of normal rat liver (Clone 9) and cells of pregnant human myometrium. The proposed model accounts for the receptor-controlled Ca2+ oscillations involving positive feedback leading to activation of phospholipase C (PLC) and negative feedback from PKC onto G-proteins which simulates many of the features of observed intracellular Ca2+. The model also incorporates the concept that coordinated Ca2+ signals in a group of hepatocytes require both effective gap junctions and the presence of agonist at each cell surface. Another objective of this research is to understand the relevance of frequency-encoded signals by performing an analysis of frequencies of Ca2+ oscillations using the Fast Fourier Transform and the Wavelet Transform. The validity of the model was confirmed by using statistical tests to check if the frequencies and amplitudes of the experimental Ca2+ oscillations match with those of the modelled oscillations.

Detta examensarbete är utfört hos Swisslog under våren 2013. De hade problem med den manuella styrningen av deras pallstaplingskran för höglager, som upplevdes ryckig och svår att kontrollera vid låga hastigheter. Huvudsyftet var att undersöka varför detta fenomen uppstod och hur det kunde lösas med både hård- och mjukvarumässiga metoder. Utöver detta undersöktes hur produktionskostnaden, för delarna av kranen som rör den manuella styrningen, kunde reduceras. Det upplevda fenomenet är känt som biodynamic feedthrough. Det innebär att konstruktionens acceleration matas genom operatörens kropp och skapar en återkoppling till styrdonet, i detta fall en joystick. Operatörens hand ger en oavsiktlig störsignal som gör systemet instabilt som i sin tur skapar en oscillation som ökar i amplitud och är svår eller omöjlig att stoppa. Den föreslagna lösningen är att digitalt lågpassfiltrera styrsignalen från joysticken. Det dämpar de skarpaste spikarna i signalen och förhindrar systemet att ta in de snabba handrörelser som kranens acceleration har skapat.
This bachelor thesis was written at Swisslog, who had a problem with the manual control of their high-bay pallet stacker crane. The ride was perceived rough and hard to control at lower speeds.    The main purpose was to examine the source of the phenomenon and how to solve the problem with both software and hardware. It was also requested to investigate ways to lower production costs of the parts of the crane related to the manual control.   The experienced phenomenon is known as biodynamic feedthrough. It refers to the acceleration of the structure affects the body of the operator causing a feedback loop to the input, in this case a joystick. The hand of the operator causes an involuntary control input and making the system unstable and causing an oscillation increasing in amplitude over time. This may be hard or impossible to stop.   The proposed solution is a low-pass filter applied at the output of the joystick. This attenuates the sharpest spikes from the joystick control signal and prevents the system from receiving the fast hand movements caused by the acceleration of the crane.

Cette these est essentiellement consacree a l'etude de limites singulieres oscillantes de systemes issus de la mecanique des fluides ou des plasmas. La premiere partie presente differentes approches des limites quasineutre et gyrocinetique des plasmas, par des techniques formelles, analytiques, pseudodifferentielles ou de mesures de defauts. La deuxieme partie est consacree a l'etude de la limite incompressible et a l'asymptotique des fluides tournants. La troisieme partie presente une justification de la methode w. K. B. Avant les chocs, sur l'equation de schrodinger non lineaire. La derniere partie consiste en l'etude du systeme dit des gaz sans pression

Materials when subjected to deformation exhibit unstable plastic flow beyond the elastic limit. In certain range of temperature and strain rates many solid state solutions, both interstitial as well as substitutional, exhibit the phenomenon of serrated yielding which also goes by the name, the Portevin - Le Chatelier (PLC) effect. The origin of this plastic instability is due to the interaction of dislocations with solute atoms. The objective of the thesis is to provide a dynamical systems approach to the study of this plastic flow instability. The thesis work discusses, within the framework of a model, the connection between microscopic dislocation mechanisms and macroscopic mechanical response of the specimen as stress drops in stress-strain curves. An extension of the model to the associated deformation bands is also considered. The emphasis is on the dynamical aspects of the instability. The methods of nonlinear dynamics like geometrical slow manifold and Poincare map formalism are applied for the first time to study the PLC effect. However, the approach and techniques transcend this particular application as the techniques are equally well applicable for many other physical systems as well, in particular, systems involving multiple time scales. The material covered should be of interest to investigators in the materials science, in particular, those, involved in the dislocation patterning and self organization of dislocations. Many theoretical models for the PLC effect exist in literature. Although the physical phenomenon is inherently dynamic, the conventional theoretical models do not involve any dynamical aspect. A dynamical model for this effect, due to Ananthakrishna, Sahoo and Valsakumar provides an explanation in terms of the dynamic interactions between different dislocation species and evolution of densities of these dislocation species. This model is known to reproduce several of the experimental results. It is within the perspective of this model and its extensions we analyze the PLC effect. The macroscopic manifestation of the PLC effect is the repeated load drops or serration in stress-strain curves (beyond the yield point). Each of the load drop is associated with the formation of a spatial dislocation band and its subsequent propagation. From the perspective of a dynamical system, the changeover from the stress-strain curve with single yield drop to repeated yield drops (the PLC effect) corresponds to a Hopf bifurcation wherein equilibrium state changes over to a periodic steady state. These repeated load drops correspond to auto oscillations of the applied stress (in the absence of any periodic driving force). In particular, as implied by the slow loading and sudden load drops, these oscillations are classified as relaxation oscillations. Relaxation oscillations are a result of disparate time scales of dynamics of the participating modes. Within the context of the model, this refers to very different time scales of evolution of densities of mobile (fast), immobile (slow) dislocations and those with a cloud of solute atoms (not too slow). The focus of attention in the thesis work is on these auto relaxation oscillations. There are several methodologies in nonlinear dynamical systems to study the oscillatory behavior of multidimensional systems with multiple time scales. An effective way is to study the reduced dynamical system in an appropriate space without sacrificing the required dynamical information. To this end, we discuss two techniques which compliment each other. 1.Slow manifold approach: This method utilizes the presence of multiple time scales dynamics. Advantage is that the information on the nature of evolution of the periodic orbit is retained. The limitation is that the transition from one stable state to another as parameter is varied cannot be dealt with. 2.Poincare maps:This approach utilizes the recurrent behavior of the period orbit. This is a convenient methodology to study the nature of stability of periodic orbits. However, in this, the information about the nature of evolution is lost. Both the above techniques provide good description in the presence of high dissipation or larger separation of time scales of the participating modes. For slow manifold analysis, this leads to exact slow manifold structure while in the case of Poincare maps, it leads to simpler, lower dimensional attractors. Specific issues that are dealt with using these approaches and others in this thesis are the following. To start with, we first provide a comprehensive overview of the dynamical behavior as envisaged by the model system in physically relevant two parameter space. The existence of relaxation oscillations bounded by back-to-back Hopf bifurcation is a good representation of the fact that the PLC effect manifests only in a window of strain rates. Within this boundary of Hopf bifurcations relaxation oscillations destabilize to give rise to new states of order, including the chaotic states. The changes in the nature of these oscillations with control parameters is projected through the bifurcation diagrams and analyzed using techniques like Floquet multipliers, Lyapunovs exponents etc. After the identification of the relevant parameter space for the monoperiodic relaxation oscillations, we focus our attention on the time scales involved in these relaxation oscillations and its connection to the time scales apparent in serrations of the stress-strain curve of the PLC effect. This characteristic feature of the PLC effect, the stick-slip nature of stress-strain curves, is believed to result from the negative strain rate dependence of the flow stress. The latter is assumed to arise from a competition of the relevant time scales involved in the phenomenon. However, in the previous works, the identification and the role of the time scales in the dynamical phenomenon is not clear. The motivation of this part of the work is to identify the time scales involved in the stress drops of the time series and their origin. Since the dynamics involves distinct time scales, in the long time limit, the evolution is controlled only by the slow modes. Hence, the adiabatic elimination or quasi-steady state approximation of the fast modes leads to an invariant manifold, the slow manifold which is useful for the analysis of time scales. The geometry of the slow manifold which is atypical with two connected pieces is shown to be at the root of the relaxation oscillations. The analysis of the slow manifold structure helps to understand the time scales of the dynamics operating in different regions of the slow manifold. The analysis also helps us to provide a proper dynamical interpretation for the negative branch of the strain rate sensitivity of the flow stress. The slow-fast dynamical nature manifests itself through multiperiodic oscillations also, in the form of mixed mode oscillations (MMOs), which are oscillations with both large amplitude excursions as well as small amplitude loops. In MMOs, the small amplitude oscillatory loops are confined to one part of the slow manifold (around the fixed point) and the large amplitude excursions arise as jumps from one piece of the slow manifold to the other. More generally, MMOs are a characteristic feature of a family of dynamical systems which also exhibit alternate periodic-chaotic sequences in bifurcation portraits. Usually, the origin of these features is explained in terms of either the approach to a homoclinic bifurcation duo to a saddle fixed point (Shilnikov scenario) or a saddle orbit (Gavrilov-Shilnikov scenario). However, the dynamical model exhibits features from both the above scenarios. The emphasis of this study is on explaining the origin of the incomplete approach to a global bifurcation in the dynamical model. Apart from attempting to understand the complex bifurcation sequences, an additional motivation for this study is the apparent lack of systematic investigation into the incomplete approach to global bifurcation exhibited by a variety of physical systems. The method of the analysis is general and applicable to the family of MMO systems. In the model, using the structure of the bifurcation sequences, and the equilibrium fixed point, a local analysis shows that the approach to homoclinicity is asymptotic at best, and is a result of the ‘softening' of eigenvalues of the saddle equilibrium point. This softening, in turn, is a consequence of back-to-back Hopf bifurcation which reflects the constraint of the physical phenomenon, namely, the occurrence of the multiple stress drops only in an interval of the strain rates. The characteristic features, namely, MMOs, alternate periodic-chaotic sequences, and incomplete approach to homoclinicity are related to each other and arise as a consequence of the atypical slow manifold structure. The slow manifold structure analysis assumes that the evolution of the system is constrained within the neighborhood of the slow manifold which also implies that the dynamical system involves high dissipation. Hence, the dimension of the effective dynamics in the long time limit is reduced. The analysis reveals information regarding the structure of the periodic orbit for a given set of parameter values but does not provide any information regarding the nature of stability of the periodic orbits. However, any insight into the mechanism of the instability of the periodic orbits in the model may lead to a better understanding of the underlying physical phenomenon. Poincare maps and equivalent discrete dynamical systems provide a convenient means to obtain such an insight on the nature of the periodic solutions of the dynamical system. This methodology compliments the invariant slow manifold analysis, since in Poincare maps, the nature of the stability information is preserved at the expense of the structure of the periodic orbit. However, these two methodologies are not exclusive to each other, since the slow manifold structure as well as Poincare maps may be constructed using a common factor, namely, extremal values of the fast variable of the dynamical system. The methodologies adopted for the analysis assumes large dissipation arising out of the multiple time scale behavior such that the next maximal amplitude (NMA) maps can be modeled by one dimensional discrete dynamical systems. The dynamical portrait of the model shows differing nature of dynamics and consequently Poincare maps with different geometrical shapes in the {m,c) plane. Within the framework of one dimensional maps, these shapes can be schematically reconstructed using minimal information regarding the principal periodic orbit embedded in higher dimension and its nature of stability. This suggests that one dimensional maps might be sufficient to represent the higher dimensional dynamical system. For most of the parameter space, the NMA maps of the dynamical model possess characteristic features of a locally smooth maximum and asymptotically long tail. These features have been observed in many other physical systems, both experimental and model systems. Hence, this analysis is focused on a broader issue of Poincare maps in a family of dynamical systems with multiple time scale dynamics and mixed mode oscillations. Here, the dynamical model has been used as a representative dynamical system for this family. The scope of the study is to understand the dynamical features of the MMO systems within the framework of one dimensional systems. Specifically, by using some general constraints on the one dimensional map, we first analyze the basic mechanism that is responsible for the reversal of periodic sequences of RLk type which corresponds to the dominant periodic states of the MMO systems. This in turn allows us to understand the period adding sequences as well. The analysis also helps to demonstrate that the width of the periodic states contained within the chaotic regions bounded by two successive periodic states of the form RLk is smaller than that for RLk .To this end, we first construct a model map which mimics the dominant bifurcation sequences of MMO systems. This map is utilized to verify the analytical results for the parameter width of the periodic windows. This analysis also throws light on the origin of the ordered structure of the isolas of RLk periodic orbits, in MMO systems, which was shown to be the result of a back-to-back Hopf bifurcation. The results indicate the ubiquity in the qualitative dynamical features of physical systems from widely differing origin, exhibiting alternate periodic-chaotic sequences. Although the model for the PLC effect is successful in describing the features of the phenomenon, a shortcoming of the dynamical model has been the absence of the spatial aspect. A dominant process in the PLC effect is the movement of dislocations (mainly through cross glide) which is essentially nonlocal. This feature has been incorporated into the dynamical model through a 'diffusive' term for the mobile dislocations. Preliminary results indicate that various types of band propagation, as seen in experiments, are recovered. It is known that the solute atmosphere aggregation occurs primarily during the waiting time of the mobile dislocations after its arrest. As another extension, the present model has been revised to incorporate these aging effects also. An outline of the thesis is as follows. Focus of this thesis work is on the dynamical aspects of the PLC effect. The phenomenology and few techniques in nonlinear dynamics are introduced in Chapters 1 and 2. Chapter 3 provides a comprehensive tour of dynamical behavior of the model in physically relevant two-parameter space. The rest of the work is presented in three parts (six chapters). In the first part of the thesis, the structure of the relaxation oscillations in the phase space is analyzed using the topology of the slow manifold. A connection between the slow manifold structure and the negative strain rate sensitivity of the flow stress is attempted using this analysis (Chapter 4). As a natural extension, the approach is utilized for the analysis of multiperiodic relaxation oscillations also. The emphasis is on the connection between the dynamical behavior of the model and incomplete approach to a global bifurcation (Chapter 5). In the second part of the thesis, the stability properties of periodic orbits are analyzed in detail using the Poincare map formalism, complimenting the study on the structure of periodic orbits using slow manifold. The structure and gross features of the Poincare map are reproduced utilizing only minimum information regarding the principal periodic orbit in the multidimensional space (Chapter 6). Within the framework of one dimensional systems, we analyze the mechanisms responsible for the structure of bifurcation portraits of MMO systems (Chapter 7). Third and the last part, of work focuses on modeling the spatial aspect of the PLC effect and refinement of the dynamical model (Chapters). The last chapter, Chapter9, is devoted for discussion of the results and scope for future work.

Materials when subjected to deformation exhibit unstable plastic flow beyond the elastic limit. In certain range of temperature and strain rates many solid state solutions, both interstitial as well as substitutional, exhibit the phenomenon of serrated yielding which also goes by the name, the Portevin - Le Chatelier (PLC) effect. The origin of this plastic instability is due to the interaction of dislocations with solute atoms. The objective of the thesis is to provide a dynamical systems approach to the study of this plastic flow instability. The thesis work discusses, within the framework of a model, the connection between microscopic dislocation mechanisms and macroscopic mechanical response of the specimen as stress drops in stress-strain curves. An extension of the model to the associated deformation bands is also considered. The emphasis is on the dynamical aspects of the instability. The methods of nonlinear dynamics like geometrical slow manifold and Poincare map formalism are applied for the first time to study the PLC effect. However, the approach and techniques transcend this particular application as the techniques are equally well applicable for many other physical systems as well, in particular, systems involving multiple time scales. The material covered should be of interest to investigators in the materials science, in particular, those, involved in the dislocation patterning and self organization of dislocations. Many theoretical models for the PLC effect exist in literature. Although the physical phenomenon is inherently dynamic, the conventional theoretical models do not involve any dynamical aspect. A dynamical model for this effect, due to Ananthakrishna, Sahoo and Valsakumar provides an explanation in terms of the dynamic interactions between different dislocation species and evolution of densities of these dislocation species. This model is known to reproduce several of the experimental results. It is within the perspective of this model and its extensions we analyze the PLC effect. The macroscopic manifestation of the PLC effect is the repeated load drops or serration in stress-strain curves (beyond the yield point). Each of the load drop is associated with the formation of a spatial dislocation band and its subsequent propagation. From the perspective of a dynamical system, the changeover from the stress-strain curve with single yield drop to repeated yield drops (the PLC effect) corresponds to a Hopf bifurcation wherein equilibrium state changes over to a periodic steady state. These repeated load drops correspond to auto oscillations of the applied stress (in the absence of any periodic driving force). In particular, as implied by the slow loading and sudden load drops, these oscillations are classified as relaxation oscillations. Relaxation oscillations are a result of disparate time scales of dynamics of the participating modes. Within the context of the model, this refers to very different time scales of evolution of densities of mobile (fast), immobile (slow) dislocations and those with a cloud of solute atoms (not too slow). The focus of attention in the thesis work is on these auto relaxation oscillations. There are several methodologies in nonlinear dynamical systems to study the oscillatory behavior of multidimensional systems with multiple time scales. An effective way is to study the reduced dynamical system in an appropriate space without sacrificing the required dynamical information. To this end, we discuss two techniques which compliment each other. 1.Slow manifold approach: This method utilizes the presence of multiple time scales dynamics. Advantage is that the information on the nature of evolution of the periodic orbit is retained. The limitation is that the transition from one stable state to another as parameter is varied cannot be dealt with. 2.Poincare maps:This approach utilizes the recurrent behavior of the period orbit. This is a convenient methodology to study the nature of stability of periodic orbits. However, in this, the information about the nature of evolution is lost. Both the above techniques provide good description in the presence of high dissipation or larger separation of time scales of the participating modes. For slow manifold analysis, this leads to exact slow manifold structure while in the case of Poincare maps, it leads to simpler, lower dimensional attractors. Specific issues that are dealt with using these approaches and others in this thesis are the following. To start with, we first provide a comprehensive overview of the dynamical behavior as envisaged by the model system in physically relevant two parameter space. The existence of relaxation oscillations bounded by back-to-back Hopf bifurcation is a good representation of the fact that the PLC effect manifests only in a window of strain rates. Within this boundary of Hopf bifurcations relaxation oscillations destabilize to give rise to new states of order, including the chaotic states. The changes in the nature of these oscillations with control parameters is projected through the bifurcation diagrams and analyzed using techniques like Floquet multipliers, Lyapunovs exponents etc. After the identification of the relevant parameter space for the monoperiodic relaxation oscillations, we focus our attention on the time scales involved in these relaxation oscillations and its connection to the time scales apparent in serrations of the stress-strain curve of the PLC effect. This characteristic feature of the PLC effect, the stick-slip nature of stress-strain curves, is believed to result from the negative strain rate dependence of the flow stress. The latter is assumed to arise from a competition of the relevant time scales involved in the phenomenon. However, in the previous works, the identification and the role of the time scales in the dynamical phenomenon is not clear. The motivation of this part of the work is to identify the time scales involved in the stress drops of the time series and their origin. Since the dynamics involves distinct time scales, in the long time limit, the evolution is controlled only by the slow modes. Hence, the adiabatic elimination or quasi-steady state approximation of the fast modes leads to an invariant manifold, the slow manifold which is useful for the analysis of time scales. The geometry of the slow manifold which is atypical with two connected pieces is shown to be at the root of the relaxation oscillations. The analysis of the slow manifold structure helps to understand the time scales of the dynamics operating in different regions of the slow manifold. The analysis also helps us to provide a proper dynamical interpretation for the negative branch of the strain rate sensitivity of the flow stress. The slow-fast dynamical nature manifests itself through multiperiodic oscillations also, in the form of mixed mode oscillations (MMOs), which are oscillations with both large amplitude excursions as well as small amplitude loops. In MMOs, the small amplitude oscillatory loops are confined to one part of the slow manifold (around the fixed point) and the large amplitude excursions arise as jumps from one piece of the slow manifold to the other. More generally, MMOs are a characteristic feature of a family of dynamical systems which also exhibit alternate periodic-chaotic sequences in bifurcation portraits. Usually, the origin of these features is explained in terms of either the approach to a homoclinic bifurcation duo to a saddle fixed point (Shilnikov scenario) or a saddle orbit (Gavrilov-Shilnikov scenario). However, the dynamical model exhibits features from both the above scenarios. The emphasis of this study is on explaining the origin of the incomplete approach to a global bifurcation in the dynamical model. Apart from attempting to understand the complex bifurcation sequences, an additional motivation for this study is the apparent lack of systematic investigation into the incomplete approach to global bifurcation exhibited by a variety of physical systems. The method of the analysis is general and applicable to the family of MMO systems. In the model, using the structure of the bifurcation sequences, and the equilibrium fixed point, a local analysis shows that the approach to homoclinicity is asymptotic at best, and is a result of the ‘softening' of eigenvalues of the saddle equilibrium point. This softening, in turn, is a consequence of back-to-back Hopf bifurcation which reflects the constraint of the physical phenomenon, namely, the occurrence of the multiple stress drops only in an interval of the strain rates. The characteristic features, namely, MMOs, alternate periodic-chaotic sequences, and incomplete approach to homoclinicity are related to each other and arise as a consequence of the atypical slow manifold structure. The slow manifold structure analysis assumes that the evolution of the system is constrained within the neighborhood of the slow manifold which also implies that the dynamical system involves high dissipation. Hence, the dimension of the effective dynamics in the long time limit is reduced. The analysis reveals information regarding the structure of the periodic orbit for a given set of parameter values but does not provide any information regarding the nature of stability of the periodic orbits. However, any insight into the mechanism of the instability of the periodic orbits in the model may lead to a better understanding of the underlying physical phenomenon. Poincare maps and equivalent discrete dynamical systems provide a convenient means to obtain such an insight on the nature of the periodic solutions of the dynamical system. This methodology compliments the invariant slow manifold analysis, since in Poincare maps, the nature of the stability information is preserved at the expense of the structure of the periodic orbit. However, these two methodologies are not exclusive to each other, since the slow manifold structure as well as Poincare maps may be constructed using a common factor, namely, extremal values of the fast variable of the dynamical system. The methodologies adopted for the analysis assumes large dissipation arising out of the multiple time scale behavior such that the next maximal amplitude (NMA) maps can be modeled by one dimensional discrete dynamical systems. The dynamical portrait of the model shows differing nature of dynamics and consequently Poincare maps with different geometrical shapes in the {m,c) plane. Within the framework of one dimensional maps, these shapes can be schematically reconstructed using minimal information regarding the principal periodic orbit embedded in higher dimension and its nature of stability. This suggests that one dimensional maps might be sufficient to represent the higher dimensional dynamical system. For most of the parameter space, the NMA maps of the dynamical model possess characteristic features of a locally smooth maximum and asymptotically long tail. These features have been observed in many other physical systems, both experimental and model systems. Hence, this analysis is focused on a broader issue of Poincare maps in a family of dynamical systems with multiple time scale dynamics and mixed mode oscillations. Here, the dynamical model has been used as a representative dynamical system for this family. The scope of the study is to understand the dynamical features of the MMO systems within the framework of one dimensional systems. Specifically, by using some general constraints on the one dimensional map, we first analyze the basic mechanism that is responsible for the reversal of periodic sequences of RLk type which corresponds to the dominant periodic states of the MMO systems. This in turn allows us to understand the period adding sequences as well. The analysis also helps to demonstrate that the width of the periodic states contained within the chaotic regions bounded by two successive periodic states of the form RLk is smaller than that for RLk .To this end, we first construct a model map which mimics the dominant bifurcation sequences of MMO systems. This map is utilized to verify the analytical results for the parameter width of the periodic windows. This analysis also throws light on the origin of the ordered structure of the isolas of RLk periodic orbits, in MMO systems, which was shown to be the result of a back-to-back Hopf bifurcation. The results indicate the ubiquity in the qualitative dynamical features of physical systems from widely differing origin, exhibiting alternate periodic-chaotic sequences. Although the model for the PLC effect is successful in describing the features of the phenomenon, a shortcoming of the dynamical model has been the absence of the spatial aspect. A dominant process in the PLC effect is the movement of dislocations (mainly through cross glide) which is essentially nonlocal. This feature has been incorporated into the dynamical model through a 'diffusive' term for the mobile dislocations. Preliminary results indicate that various types of band propagation, as seen in experiments, are recovered. It is known that the solute atmosphere aggregation occurs primarily during the waiting time of the mobile dislocations after its arrest. As another extension, the present model has been revised to incorporate these aging effects also. An outline of the thesis is as follows. Focus of this thesis work is on the dynamical aspects of the PLC effect. The phenomenology and few techniques in nonlinear dynamics are introduced in Chapters 1 and 2. Chapter 3 provides a comprehensive tour of dynamical behavior of the model in physically relevant two-parameter space. The rest of the work is presented in three parts (six chapters). In the first part of the thesis, the structure of the relaxation oscillations in the phase space is analyzed using the topology of the slow manifold. A connection between the slow manifold structure and the negative strain rate sensitivity of the flow stress is attempted using this analysis (Chapter 4). As a natural extension, the approach is utilized for the analysis of multiperiodic relaxation oscillations also. The emphasis is on the connection between the dynamical behavior of the model and incomplete approach to a global bifurcation (Chapter 5). In the second part of the thesis, the stability properties of periodic orbits are analyzed in detail using the Poincare map formalism, complimenting the study on the structure of periodic orbits using slow manifold. The structure and gross features of the Poincare map are reproduced utilizing only minimum information regarding the principal periodic orbit in the multidimensional space (Chapter 6). Within the framework of one dimensional systems, we analyze the mechanisms responsible for the structure of bifurcation portraits of MMO systems (Chapter 7). Third and the last part, of work focuses on modeling the spatial aspect of the PLC effect and refinement of the dynamical model (Chapters). The last chapter, Chapter9, is devoted for discussion of the results and scope for future work.

Cyanobakterien sind meist photoautotroph lebende Prokaryoten, welche nahezu alle Biotope der Welt besiedeln. Sie gehören zu den wichtigsten Produzenten der weltweiten Nahrungskette. Um sich auf den täglichen Wechsel von Tag und Nacht einzustellen, besitzen Cyanobakterien eine innere Uhr, bestehend aus den Proteinen KaiA, KaiB und KaiC, deren biochemische Interaktionen zu einem 24-stündigen Rhythmus von Phosphorylierung und Dephosphorylierung führen. Die circadiane Genexpression im Modellorganismus Synechocystis sp. PCC 6803 habe ich mittels drei verschiedener Zeitserienexperimente untersucht, wobei ich einen genauen Zeitplan der Genaktivierung in einer Tag-Nacht-Umgebung, aber keine selbsterhaltenden Rhythmen entdecken konnte. Allerdings beobachtete ich einen überaus starken Anstieg der ribosomalen RNA in der Dunkelheit. Aufgrund ihrer hohen Wachstumsraten und der geringen Anforderungen an die Umwelt bilden Cyanobakterien eine gute Grundlage für die nachhaltige Erzeugung von Biokraftstoffen, für einen industriellen Einsatz sind aber weitere Optimierung und ein verbessertes Verständnis des Metabolismus von Nöten. Hierfür habe ich die Orthologie von verschiedenen Cyanobakterien sowie die Konservierung von Genen und Stoffwechselwegen untersucht. Mit einer neu entwickelten Methode konnte ich gemeinsam vorkommende Gene identifizieren und zeigen, dass diese Gene häufig an einem gemeinsamen biologischen Prozess beteiligt sind, und damit bisher unbekannte Beziehungen aufdecken. Zusätzlich zu den diskutierten Modulen habe ich den SimilarityViewer entwickelt, ein grafisches Computerprogramm für die Identifizierung von gemeinsam vorkommenden Partnern für jedes beliebige Gen. Des Weiteren habe ich für alle Organismen automatische Rekonstruktionen des Stoffwechsels erstellt und konnte zeigen, dass diese die Synthese von gewünschten Stoffen gut vorhersagen, was hilfreich für zukünftige Forschung am Metabolismus von Cyanobakterien sein wird.
Cyanobacteria are photoautotrophic prokaryotes populating virtually all habitats on the surface of the earth. They are one of the prime producers for the global food chain. To cope with the daily alternation of light and darkness, cyanobacteria harbor a circadian clock consisting of the three proteins KaiA, KaiB, and KaiC, whose biochemical interactions result in a phosphorylation cycle with a period of approximately 24 hours. I conducted three time-series experiments in the model organism Synechocystis sp. PCC 6803, which revealed a tight diurnal schedule of gene activation. However, I could not identify any self-sustained oscillations. On the contrary, I observed strong diurnal accumulation of ribosomal RNAs during dark periods, which challenges common assumptions on the amount of ribosomal RNAs. Due to their high growth rates and low demand on their environment, cyanobacteria emerged as a viable option for sustainable production of biofuels. For an industrialized production, however, optimization of growth and comprehensive knowledge of the cyanobacterial metabolism is inevitable. To address this issue, I analyzed the orthology of multiple cyanobacteria and studied the conservation of genes and metabolic pathways. Systematic analysis of genes shared by similar subsets of organisms indicates high rates of functional relationship in such co-occurring genes. I designed a novel approach to identify modules of co-occurring genes, which exhibit a high degree of functional coherence and reveal unknown functional relationships between genes. Complementing the precomputed modules, I developed the SimilarityViewer, a graphical toolbox that facilitates further analysis of co-occurrence with respect to specific cyanobacterial genes of interest. Simulations of automatically generated metabolic reconstructions revealed the biosynthetic capacities of individual cyanobacterial strains, which will assist future research addressing metabolic engineering of cyanobacteria.

L'experience munu a pour but la mesure du moment magnetique du neutrino grace a l'etude de la diffusion antineutrino electronique-electron aupres d'un reacteur nucleaire. Cette these presente le travail de simulation par la methode monte-carlo de l'experience munu. Cette simulation a permis de mettre en evidence les parametres ayant une influence sur les grandeurs observables de l'experience (moment magnetique, angle de weinberg, parametres decrivant les oscillations de neutrinos) ainsi que de preciser la sensibilite a ces grandeurs. En particulier, il apparait que munu permet d'obtenir une limite sur le moment magnetique du neutrino a hauteur de 2 a 3 10#-#1#1 magnetons de bohr. Cette simulation a egalement permis de mettre au point les methodes statistiques les plus performantes pour l'exploitation des donnees de munu.

La propagation des oscillations acoustiques baryoniques a laissé une empreinte dans la répartition de la matière de l’univers, visible sous la forme d’un excès de probabilité pour deux objets d’être séparés par une distance égale à l’échelle acoustique. La mesure de l’échelle acoustique dans la fonction de corrélation à deux points de la matière au redshift z, parallèlement et perpendiculairement à la ligne de visée donne accès, respectivement, aux rapports DH(z)/rd et DM(z)/rd où DH est la distance de Hubble, DM la distance angulaire comobile et rd l’horizon acoustique. On peut suivre la répartition de la matière en utilisant les absorptions Lyman-alpha visibles, sous la forme de forêts, dans les spectres des quasars à haut redshift. Puisque chaque spectre donne accès une centaine d’absorptions, cela permet de mesurer l’échelle acoustique même quand la densité de quasars observés est faible. Dans cette thèse, je décris le processus d’analyse qui, en utilisant environ 200 000 spectres de quasars du relevé eBOSS-SDSS IV, aboutit aux mesures DH(2.34)/rd = 8.86+/-0.29 et DM(2.34)/rd = 37.41+/-1.86. En combinant ces résultats avec les mesures de l’échelle acoustique à d’autres redshifts, j’obtiens la plus forte contrainte actuelle, à bas redshift, sur les paramètres Omega-m et Omega-Lambda dans le cadre du modèle Lambda-CDM
The propagation of the baryonic acoustic oscillations has been unprinted in the matter distribution in the Universe as a probability excess for two objets to be separated by the acoustic scale. Measuring the acoustic scale in the matter 2 point correlation function at redshift z, along and transversally to the line-of-sight, gives access to the DH(z)/rd et DM(z)/rd ratios, with DH the Hubble distance, DM the comoving angular distance and rd the acoustic horizon. We are able to trace the matter in the Universe by using the Lyman-alpha absorptions which shape the spectra of the high redshift quasars. Since each spectrum contain hundreds of absorption, this allow us to measure the acoustic scale even if the observed quasar density is low. In this thesis, I describe the analysis of about 200,000 spectra from the eBOSS-SDSS IV survey which conducts to the measurements DH(2.34)/rd = 8.86 0.29 et DM(2.34)/rd = 37.41 1.86. By combining these results with measurements of the acoustic scale at other redshifts, I obtain the strongest current constraints at low redshift on the Omega-m and Omega-Lambda Lambda-CDM parameters

L'effet d'un champ magnetique alternant a basse frequence sur un metal liquide presentant une surface libre, est etudie a l'aide d'une cuve cylindrique contenant du mercure et placee dans un solenoide alimente par un courant monophase de frequence 1 a 22 hz. Les mouvements internes turbulents, preponderant pour les valeurs de frequence comprises entre 10 et 22 hz, sont, sur de nombreux points, similaires a ceux observes, dans les etudes anterieures, aux plus grandes valeurs de frequence. La principale particularite est la rapide decroissane de la vitesse moyenne typique et du taux de dissipation turbulente. Ce phenomene semble etre correle a la presence de vitesses oscillatoires forcees par la partie pulsatoire des forces de lorentz devient predominante et engendre des mouvements de surface dont la configuration et l'amplitude dependent de l'itensite i et de la frequence f du courant electrique inducteur applique. L'espace des parametres (i, f) peut etre divise en quatre regions correspondant a quatre regimes. Une analyse theorique de la stabilite d'une surface libre soumise a un champ electromagnetique basse frequence montre qu'il apparait un systeme d'ondes concentriques stationnaires forces de frequence 2f et que la croissance des modes azimutaux est gouvernee par un systeme couple d'equations de mathieu. Sous certaines conditions, les ondes azimutales deviennent instables et l'instabilite apparait avec une transition sous-harmonique. La comparaison entre la theorie et l'experience montre que le modele theorique permet une bonne prediction qualitative des phenomenes observes.

This chapter aims to propose an improvement in decision making in the planning sector and production control (PPC) with application of a mathematical model. In the methodology, the qualitative approach was used because the linguistic codifications are interpreted and characterized by a case study applying a questionnaire to the managers of the company of the metal mechanic sector. In this context, six constructs were structured as a proposal for performance improvement, being composed of costs, management, inspection, processes, and capacity. The chapter reports the main results achieved during fuzzy sets application, obtaining a better result compared to FAHP in which there were certain oscillations between the percentage of constructs. The construct prioritized by managers and specialists was the cost construct, reaching 38.60%, being advantageous for the industry when the cost is placed in order of manufacture (subconstruct), followed by the prioritized management construct with 28.50%.

This chapter describes how the magnetosphere is shaped by the tangential shear stress exerted at the magnetopause by collisionless viscosity. In Section 4.2, we discuss the low-latitude boundary layer (LLBL), which contains plasma of solar wind origin that has been transported across the magnetopause current layer. The velocity shear in the LLBL drives field-aligned currents into the ionosphere on the morning side and out of the ionosphere on the evening side (Section 4.3). These currents are of the appropriate sense to drive two-cell convection in the highlatitude ionosphere. The footprint of the LLBL in the ionosphere to which the field aligned currents connect is clearly identifiable by its characteristic particle precipitation (Section 4.4). The shear in the LLBL also generates 1-20 mHz PC 4- 5 micropulsations whose polarizations, tailward propagation, and phase speeds are consistent with the Kelvin-Helmholtz (K-H) instability (Section 4.5). The K-H vortices may couple to “vortex auroras” in the local afternoon sector of the auroral oval (Section 4.6). Vortex auroral dissipation may be responsible for a morningevening asymmetry in the viscous interaction and its manifestations. Organized vortical flows have been observed not only next to the magnetopause, but also near the center of the plasma sheet, accompanied by local quasiperiodic magnetic field oscillations and PC 5 micropulsations on the ground (Section 4.7). In Section 4.8, we discuss observations of a thick boundary layer flow on closed field lines next to the magnetopause 220 RE downstream. This puts us in a position to estimate the rates of particle and energy injection into the magnetosphere due to the viscous interaction (Section 4.9). Spacecraft crossings of the magnetopause last from a few seconds to a few minutes and are characterized by a rapid, distinct rotation of the magnetic field and striking changes in plasma density, pressure, flow velocity, composition, and energetic particle distribution (Williams, 1979a; 1980; Williams et al., 1979). A broader boundary layer lies just inside the magnetopause. The so-called low-latitude boundary layer was first identified at 18 RE radial distance in the magnetotail using Vela 4B (Hones et al., 1972) and Vela 5 and 6 (Akasofu et al., 1973b) low-energy plasma measurements.

Abstract We study the impact of H2 enrichment on the unsteady flow dynamics and thermoacoustic instability in the single nozzle PRECCINSTA swirl combustor. We analyze data from two operating modes, premixed (PM) and technically premixed (TPM). The experiments were performed at atmospheric conditions with H2/CH4 fuel mixtures at a global equivalence ratio of 0.65 while maintaining a constant thermal power of 20 kW. We examine the effect of H2 addition on the flow dynamics by analyzing cases with three fuel compositions: 0% H2, 20% H2 and 50% H2 in both operating modes. A new multi resolution modal decomposition method, using a combination of wavelet transforms and proper orthogonal decomposition (WPOD) of the experimental time resolved high speed flow velocity and OH-PLIF measurements is performed. Thermoacoustic oscillations are observed in the TPM operating mode alone. WPOD results for the 0% H2 TPM operating mode case reveals intermittent helical PVC oscillations along with axi-symmetric hydrodynamic flow oscillations due to the thermoacoustic oscillation. These oscillations cause local flame extinction near the nozzle centrebody resulting in liftoff. A precessing vortex core (PVC) oscillation develops in the flow that enables intermittent flame reattachment and results in intermittent thermoacoustic oscillations in this case. In the 0% H2 PM case, the flame remains lifted off of the centrebody despite the presence of PVC oscillations in this case as well. H2 enrichment results in the suppression of flame lift-off and the PVC in both operating modes. We show from flow strain rate statistics and extinction strain rate calculations that the increase of the latter with H2 addition, allows the flame to stabilize in the region near the centrebody where the pure CH4 cases show lift off. The lack of thermoacoustic oscillations in the PM operating mode shows that the primary heat release driving mechanism is due to fuel-air ratio oscillation that the thermoacoustic oscillation generates. The time averaged flow fields and the emergence of the PVC when the flame is lifted off, together suggest that PVC oscillations are caused by the separation between the vortex breakdown bubble and the wake behind the centrebody, as suggested by prior computational studies.

Abstract The precessing vortex core (PVC) is a self-excited flow oscillation state occurring in swirl nozzles. This is caused by the presence of a marginally unstable hydrodynamic helical mode that induces precession of the vortex breakdown bubble (VBB) around the flow axis. The PVC can impact emissions and thermoacoustic stability characteristics of combustors in various ways, as several prior studies have shown. In this paper, we examine the impact of centrebody diameter (Dc) on the PVC in a non-reacting flow in a single nozzle swirl combustor. Time resolved high speed stereoscopic PIV (sPIV) measurements are performed for combinations of two swirl numbers, S = 0.67 and 1.17 and Dc = 9.5 mm, 4.73 mm and 0 (i.e. no centrebody). The bulk flow velocity at the nozzle exit plane is kept constant as Ub = 8 m/s for all cases (Re ∼ 20,000). The centrebody end face lies in the nozzle exit plane. A new modal decomposition technique based on wavelet filtering and proper orthogonal decomposition (POD) provides insight into flow dynamics in terms of global modes extracted from the data. The results show that without a centrebody, a coherent PVC is present in the flow as expected. The introduction of a centrebody makes the PVC oscillations intermittent. These results suggest two routes to intermittency as follows. For S = 0.67, the vortex breakdown bubble (VBB) and centrebody wake recirculation zone (CWRZ) regions are nominally distinct. Intermittent separation and merger due to turbulence result in PVC oscillations due to the de-stabilization of the hydrodynamic VBB precession mode of the flow. In the S = 1.17 case, the time averaged VBB position causes it to engulf the centrebody. In this case, the emergence of intermittent PVC oscillations is a result of the response of the flow to broadband stochastic forcing imposed on the time averaged vorticity field due to turbulence.

In this study, we apply periodic flow excitation of the PVC at the centerbody of a generic swirl-stabilized combustor to investigate the impact of the precessing vortex core (PVC) on flame shape and flame dynamics. Previous studies revealed considerable influence of the PVC on combustion properties such as flame dynamics and fuel/air mixing. We employ time-resolved OH*-chemiluminescence and pressure measurements to investigate the influence of the PVC on flame dynamics and flame shape transition. The PVC is typically present in flames which are detached from the burner outlet. This lift-off is observed for increasingly lean mixtures in this study. With the help of the PVC actuation, studied in this work, the transition point between attached and detached flame is shifted towards richer mixtures. Moreover, the dynamics of heat release rate fluctuations that are related to PVC and thermoacoustic instabilities are extracted from the OH*-chemiluminescence data. This reveals a considerable damping of the thermoacoustic oscillations due to the PVC actuation under technically premixed conditions and the rise of additional modes due to the interaction of both dynamics.

Combustion instability, or the coupling between flame heat release rate oscillations and combustor acoustics, is a significant issue in the operation of gas turbine combustors. This coupling is often driven by oscillations in the flow field. Shear layer roll-up, in particular, has been shown to drive longitudinal combustion instability in a number of systems, including both laboratory and industrial combustors. One method for suppressing combustion instability would be to suppress the receptivity of the shear layer to acoustic oscillations, severing the coupling mechanism between the acoustics and the flame. Previous work suggested that the existence of a precessing vortex core (PVC) may suppress the receptivity of the shear layer, and the goal of this study is to first, confirm that this suppression is occurring, and second, understand the mechanism by which the PVC suppresses the shear layer receptivity. In this paper, we couple experiment with linear stability analysis to determine whether a PVC can suppress shear layer receptivity to longitudinal acoustic modes in a non-reacting swirling flow at a range of swirl numbers. The shear layer response to the longitudinal acoustic forcing manifests as an m = 0 mode since the acoustic field is axisymmetric. The PVC has been shown both in experiment and linear stability analysis to have m = 1 and m = −1 modal content. By comparing the relative magnitude of the m = 0 and m = −1,1 modes, we quantify the impact that the PVC has on the shear layer response. The mechanism for shear layer response is determined using companion forced response analysis, where the shear layer disturbance growth rates mirror the experimental results. Differences in shear layer thickness and azimuthal velocity profiles drive the suppression of the shear layer receptivity to acoustic forcing.

Abstract The precessing vortex core is a helically-shaped coherent flow structure that occurs in reacting and non-reacting swirling flows undergoing vortex breakdown. In swirl-stabilized combustors, this flow structure affects important phenomena, such as turbulent mixing and thermoacoustic oscillations. In this work, a flow control system is developed to achieve appropriate conditions to systematically investigate the influence of the PVC on turbulent flames. The control consists of a zero-net-mass-flux actuator placed in the mixing section of the combustor, where the PVC is most receptive to periodic forcing. The actuator is driven in a closed loop to achieve phase-opposition control of the PVC. The flow control system is characterized from pressure measurements and particle image velocimetry and the impact on flame dynamics is extracted from OH*-chemiluminescence measurements. The data reveal that the PVC amplitude is considerably suppressed by the phase-opposition control without changing the overall characteristics of flow and flame. This is a very important requirement to study the exclusive effect of the PVC on combustion processes. Moreover, the control allows the PVC amplitude to be adjusted gradually to investigate the PVC impact on turbulent mixing and flame dynamics. It is revealed that the PVC-induced flow fluctuations mainly affect the large-scale mixing, while the small scale mixing remains unchanged. This is because the suppression of the PVC allows other modes to become more dominant and the overall turbulent kinetic energy budget remains unchanged. The destabilization of other modes, such as the axisymmetric mode, may have some implications on thermoacoustic instability.

In a swirl-stabilised liquid fuel burner, the fuel spray response to the Precessing Vortex Core (PVC) and air flow rate modulations is analysed in non-reacting conditions. A siren-like device is used to modulate the air flow rate at a frequency corresponding to longitudinal combustion instability oscillations observed during reacting tests. Time-resolved Mie scattering images of the fuel spray are recorded and treated with multiple post-processing methods based on Dynamic Mode Decomposition. The spray velocity fluctuations induced by the PVC and the siren-generated modulations are extracted from noisy datasets and studied. The evolution of the PVC impact on the spray for different levels of flow rate fluctuations is followed and a nonlinear interaction mode is highlighted for several intensities of flow rate modulations. It is shown that increasing the flow rate modulations tend to weaken the PVC impact on the spray, progressively disturbing its structure, starting from the downstream part and progressing upstream. These observations on the fuel spray can be used to understand and interpret data obtained in reacting conditions, for example when competition between PVC and longitudinal combustion instabilities occurs.

Abstract Precessing vortex cores (PVC), arising from a global instability in swirling flows, can dramatically alter the dynamics of swirl-stabilized flames. Previous study of these instabilities has identified their frequencies and potential for interaction with the shear layer instabilities also present in swirling flows. In this work, we investigate the dynamics of precessing vortex cores at a range of swirl numbers and the impact that turbulence, which tends to increase with swirl number due to the increase in mean shear, has on the dynamics of this instability. This is particularly interesting as stability predictions have previously incorporated turbulence effects using an eddy viscosity model, which only captures the impact of turbulence on the base flow, not on the instantaneous dynamics of the PVC itself. Time-resolved experimental measurements of the three-component velocity field at ten swirl numbers show that at lower swirl numbers, the PVC is affected by turbulence through the presence of vortex jitter. With increasing swirl number, the PVC jitter decreases as the PVC strength increases. There is a critical swirl number below which jitter of the PVC vortex monotonically increases with increasing swirl number, and beyond which the jitter decreases, indicating that the strength of the PVC dominates over turbulent fluctuations at higher swirl numbers, despite the fact that the turbulence intensities continue to rise with increasing swirl number. Further, we use a nonlinear van der Pol oscillator model to explain the competition between the random turbulent fluctuations and coherent oscillations of the PVC. The results of this work indicate that while both the strength of the PVC and magnitude of turbulence intensity increase with increasing swirl number, there are defined regimes where each of them hold a stronger influence on the large-scale, coherent dynamics of the flow field.

Abstract Many industrial combustion systems, especially power generation gas turbines, use fuel-lean combustion to reduce NOx emissions. However, these systems are highly susceptible to combustion instability, the coupling between combustor acoustics and heat release rate oscillations of the flame. It has been shown in previous work by the authors that a precessing vortex core (PVC) can suppress shear layer receptivity to external perturbations, reducing the potential for thermoacoustic coupling. The goal of this study is to understand the effect of combustor exit boundary condition on the flow structure of a swirling jet to increase fundamental understanding of how combustor design impacts PVC dynamics. The swirling jet is generated with a radial-entry, variable-angle swirler, and a quartz cylinder is fixed on the dump plane for confinement. Combustor exit constriction plates of different diameters are used to determine the impact of exit boundary condition on the flow field. Particle image velocimetry (PIV) is used to capture the velocity field inside the combustor. Spectral proper orthogonal decomposition, a frequency-resolved eigenvalue decomposition that can identify energetic structures in the flow, is implemented to identify the PVC at each condition in both energy and frequency space. We find that exit boundary diameter affects both the structure of the flow and the dynamics of the PVC. Higher levels of constriction (smaller diameters) force the downstream stagnation point of the vortex breakdown bubble upstream, resulting in greater divergence of the swirling jet. Further, as the exit diameter decreases, the PVC becomes less energetic and less spatially defined. Despite these changes in the base flow and PVC coherence, the PVC frequency is not altered by the exit boundary constriction. These trends will help inform our understanding of the impact of boundary conditions on both static and dynamic flame stability.

Unsteady helical flow structures, such as the precessing vortex core (PVC), are often observed in swirling flows with vortex breakdown. Although this type of flow is of high relevance for industrial combustors, the role of these flow instabilities in reacting systems, in particular their effect on flame stabilization and combustion instabilities, remains poorly understood. The three-dimensional structure of the interaction between the helical mode and the flame is difficult to assess with common measurement techniques, such as chemiluminescence imaging, due to the non-axisymmetry of the oscillation pattern. In the present work, a novel method is proposed to determine the full field of the heat release rate perturbation associated with the helical mode. This method requires only line-of-sight integrated information from a single camera. Tomographic reconstruction techniques are used, exploiting the fact that the helical mode is a rotating structure. Reconstruction algorithms are presented that are tailored to the specific spatio-temporal structure of the oscillation pattern, and it is shown that these techniques outperform standard methods. The proposed methodology is applied in a turbulent swirl-stabilized model combustor with significant PVC oscillations. Images from an intensified high-speed camera are used for the reconstruction. The analysis shows that the helical mode perturbs the flame in the inner and the outer shear layers of the annular jet and thereby creates helical traveling waves. The perturbation in the outer shear layer grows significantly in downstream direction and causes strong heat release rate fluctuations when impinging on the combustor wall.

It is well known that the process of vortex breakdown plays an important role in establishing the near-field aerodynamic characteristics of fuel injectors, influencing fuel/air mixing and flame stability. The precise nature of the vortex breakdown can take on several forms, which have been shown in previous papers to include both a precessing vortex core (PVC) and the appearance of multiple helical vortices formed in the swirl stream shear layer. The unsteady dynamics of these particular features can play an important role in combustion induced oscillations. The present paper reports an experimental investigation, using PIV and hot-wire-anemometry, to document variations in the relative strength of PVC and helical vortex patterns as the configuration of a generic fuel injector is altered. Examples of geometric changes which have been investigated include: • The combination of an annular swirl stream with and without a central jet; • variation in geometric details of the swirler passage, e.g. alteration in the swirler entry slots to change swirl number, and variations in the area ratio of the swirler passage. The results show that these geometric variations can influence: • the axial location of the origin of the helical vortices (from inside to outside the fuel injector); • the strength of the PVC. For example, in a configuration with no central jet (swirl number S = 0.72) the helical vortex pattern was much less coherent, but the PVC was much stronger than when a central jet was present. These changes modify the magnitude of the turbulence energy in the fuel injector near field dramatically, and hence have an important influence on fuel air mixing patterns.