Intermittent Instabilities Research Articles

Intermittent subharmonic and chaos in parallel Buck converters with coupled interference signal

This paper studies intermittent instabilities in parallel power system. Taking parallel buck converters with coupled interference signals as an example, model and actual system are established. By numerical simulation, the nonlinear behaviours are captured under some conditions. Characteristics and mechanism of intermittency are depicted by nonlinear theory. In this paper, mappings time to parameter are established and discrete iterative mappings for nonlinear systems are derived. All the simulation results are consistent with the theoretical analysis results. The research method adopted in the paper is applicable for the other parallel powersystems. The conclusion can provide a reference for the parallel converters to maintain stable operation and serves as a theoretical basis for further optimization design and system control.

Formula omitted] enrichment of [formula omitted] blends in lean premixed gas turbine combustion: An experimental study on effects on flame shape and thermoacoustic oscillation dynamics

Thermoacoustic instabilities under lean operation in gas turbine burners hinder the development of lean premixed combustion mode of operation, thus limiting the potential to decrease NOx emissions. A method to improve stability of lean combustion while maintaining low thermal NOx formation is to add hydrogen in typical gas turbine fuels such as natural gas. The present work examines the thermoacoustic dynamic characteristics of hydrogen-enriched methane blends in a swirl stabilized model gas turbine combustor. We blend CH4 with increasing H2 molar content (from 0% to 40%) at a global equivalence ratio of ϕ=0.55 on a constant Reynolds number Re = 19000. The reference case of pure methane is susceptible to blow off at the same equivalence ratio. On increasing the hydrogen content at 10% H2, the flammability limits are extended. However, further increase of the H2 content leads to manifestation of random short bursts of dynamic pressure and heat release. Thermoacoustic dynamics are intermittently injected between a quiescent state and a regime of high amplitude oscillations. On further increasing H2 content, the dynamics are attracted towards a limit cycle; a fully established high amplitude regime, where no requiescence is observed. In this regime, heat release rate and dynamic pressure oscillate in phase and at the same frequency. Based on the observed dynamics, we seek a mixture property to characterize the dynamic state, the combustor operates in. We show that the extinction strain rate associated with each mixture can collapse the dynamic transitions from quiescent to intermittent instabilities and finally to fully established thermoacoustic oscillations. In each dynamic state, we examine the mechanism that affiliates coherent structures of the underlying thermodynamic flow field with the flame through the relation of the spatial distribution of the flow imposed strain rate over the extinction strain rate of each mixture. It is shown that the flame anchoring locations for a given mixture are dictated by the flow imposed strain rate and then that increased extinction resistance couples the flame with naturally excited to swirling flows helical instabilities, that may instigate mechanisms responsible for intermittent heat release rate bursts. Finally, the combustor demonstrates a limit cycle behaviour where the flow-imposed strain rate oscillates about the extinction strain rate along the inner shear layers causing local extinction of the flame at the root close to the centerbody.

Analysis of intermittent instabilities in switching power converters using Filippov’s method

PurposeIn the design and development stage of the power converter systems, an abnormal intermittency is naturally experienced in nonautonomous system because of coupling of the interference signals. The study of identifying the possible conditions at which such an undesirable operation emerges is vital. Hence, the purpose of this paper is to explore the intermittent instabilities that evolve in the voltage-mode controlled quadratic buck converter when the sinusoidal interference signal coupled in reference voltage.Design/methodology/approachVoltage-mode controlled quadratic buck converter with the sinusoidal interference signal coupled in reference voltage manifests a symmetrical period-doubling bifurcation in intermittent periods for significant interference signal strength with the frequency near to the switching frequency or its rational multiples. The complete dynamics of the system is investigated for the various inference signal frequencies by numerical simulations.FindingsHere, the intermittent instabilities are verified using a simple Filippov’s method with supporting evidence of Floquet multipliers (eigenvalues) movement. The analytical result obtained is found to agree well with the simulation results.Practical implicationsPower supplies are liable to an ambiguous complex behavior when it is seldom protected against the interference signal. The experimental study has made an attempt to explicit a detailed behavior observed in voltage-mode controlled quadratic buck converter when a sinusoidal intruding signal of different amplitude and frequency are coupled with the reference voltage. Such an analysis gives considerable focus for the power electronics engineers to meet the design requirements.Originality/valueTo the authors’ knowledge, all the research works on intermittent instabilities in power converters are analyzed only using conventional method of Poincare map technique which emerges to be complicated when the order of the system is higher. Alternatively, in this paper, Filippov’s technique is used for stability analysis of periodic orbit. The evolution of bifurcation point is predicted by the calculating the Floquet multipliers of monodromy matrix, and it is known to achieve the same objective as the Poincare map technique in much more straightforward way.

Intermittent heat instabilities in an air plume

Abstract. We report the results of heating experiments carried out in an abandoned limestone quarry close to Paris, in an isolated room of a volume of about 400 m3. A heat source made of a metallic resistor of power 100 W was installed on the floor of the room, at distance from the walls. High-quality temperature sensors, with a response time of 20 s, were fixed on a 2 m long bar. In a series of 24 h heating experiments the bar had been set up horizontally at different heights or vertically along the axis of the plume to record changes in temperature distribution with a sampling time varying from 20 to 120 s. When taken in averages over 24 h, the temperatures present the classical shape of steady-state plumes, as described by classical models. On the contrary, the temperature time series show a rich dynamic plume flow with intermittent trains of oscillations, spatially coherent, of large amplitude and a period around 400 s, separated by intervals of relative quiescence whose duration can reach several hours. To our knowledge, no specific theory is available to explain this behavior, which appears to be a chaotic interaction between a turbulent plume and a stratified environment. The observed behavior, with first-order factorization of a smooth spatial function with a global temporal intermittent function, could be a universal feature of some turbulent plumes in geophysical environments.

Probabilistic Description of Extreme Events in Intermittently Unstable Dynamical Systems Excited by Correlated Stochastic Processes

In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and give rise to heavy-tailed probability distributions. By making appropriate assumptions on the form of these instabilities, which are valid for a broad range of systems, we formulate a method for the analytical approximation of the probability distribution function (pdf) of the system response (both the main probability mass and the heavy-tail structure). In particular, this method relies on conditioning the probability density of the response on the occurrence of an instability and the separate analysis of the two states of the system, the unstable and stable state. In the stable regime we employ steady state assumptions, which lead to the derivation of the conditional response pdf using standard methods for random dynamical systems. The unstable regime is inherently transient and in order to analyze this regime we characterize the statistics under the assumption of an exponential growth phase and a subsequent decay phase until the system is brought back to the stable attractor. The method we present allows us to capture the statistics associated with the dynamics that give rise to heavy-tails in the system response and the analytical approximations compare favorably with direct Monte Carlo simulations, which we illustrate for two prototype intermittent systems: an intermittently unstable mechanical oscillator excited by correlated multiplicative noise and a complex mode in a turbulent signal with fixed frequency, where multiplicative stochastic damping and additive noise model interactions between various modes.

The Fluid Dynamics of Solid Mechanical Shear Zones

Shear zones in outcrops and core drillings on active faults commonly reveal two scales of localization, with centimeter to tens of meters thick deformation zones embedding much narrower zones of mm-scale to cm-scale. The narrow zones are often attributed to some form of fast instability such as earthquakes or slow slip events. Surprisingly, the double localisation phenomenon seem to be independent of the mode of failure, as it is observed in brittle cataclastic fault zones as well as ductile mylonitic shear zones. In both, a very thin layer of chemically altered, ultra fine grained ultracataclasite or ultramylonite is noted. We present an extension to the classical solid mechanical theory where both length scales emerge as part of the same evolutionary process of shearing the host rock. We highlight the important role of any type of solid-fluid phase transitions that govern the second degree localisation process in the core of the shear zone. In both brittle and ductile shear zones, chemistry stops the localisation process caused by a multiphysics feedback loop leading to an unstable slip. The microstructural evolutionary processes govern the time-scale of the transition between slow background shear and fast, intermittent instabilities in the fault zone core. The fast cataclastic fragmentation processes are limiting the rates of forming the ultracataclasites in the brittle domain, while the slow dynamic recrystallisation prolongs the transition to ultramylonites into a slow slip instability in the ductile realm.

Non‐linear intermittent instabilities and their control in an interleaved DC/DC converter

The undesirable intermittent instabilities in periodically driven parallel power converter are caused due to periodic interferences in input voltage. This is a more common problem in power electronic circuit design and such operations are usually avoided by controlling the circuit parameters. In this study, the mechanism and conditions for the emergence of intermittent instabilities and remerging chaotic band attractors (or Feigenbaum sequences) in a master-slave controlled parallel buck converter are investigated. It is found that sinusoidal-type interference in input voltage at frequencies near the switching frequency or its rational multiples of this circuit results typically in period-bubbling, chaos and intermittency. It is also shown that an optimal, phase-shifted sinusoidal interference added to the reference voltage controls the period-bubbling behaviour and significantly extends the parameter range of desirable period-1 operation. The dynamics of this converter has been first investigated with suitable numerical simulations. The ordered and the chaotic dynamics of this system have been further mathematically described and analysed with a simple discrete map and experimental means. Experimental observations are found to be in good agreement with the analytical and simulation results.

Fundamental limitations of polynomial chaos for uncertainty quantification in systems with intermittent instabilities

Here, we examine the suitability of truncated Polynomial Chaos Expansions (PCE) and truncated GramCharlier Expansions (GrChE) as possible methods for uncertainty quantification (UQ) in nonlinear systems with intermittency and positive Lyapunov exponents. These two methods rely on truncated Galerkin projections of either the system variables in a fixed polynomial basis spanning the ‘uncertain’ subspace (PCE) or a suitable eigenfunction expansion of the joint probability distribution associated with the uncertain evolution of the system (GrChE). Based on a simple, statistically exactly solvable non-linear and non-Gaussian test model, we show in detail that methods exploiting truncated spectral expansions, be it PCE or GrChE, have significant limitations for uncertainty quantification in systems with intermittent instabilities or parametric uncertainties in the damping. Intermittency and fat-tailed probability densities are hallmark features of the inertial and dissipation ranges of turbulence and we show that in such important dynamical regimes PCE performs, at best, similarly to the vastly simpler Gaussian moment closure technique utilized earlier by the authors in a different context for UQ within a framework of Empirical Information Theory. Moreover, we show that the non-realizability of the GrChE approximations is linked to the onset of intermittency in the dynamics and it is frequently accompanied by an erroneous blow-up of the second-order statistics at short times. These limitations of the two types of truncated spectral expansions arise from the following: (i) Non-uniform convergence in time of PCE and GrChE resulting in a rapidly increasing number of terms necessary for a good approximation of the random process as time evolves, (ii) Fundamental problems with capturing the constant flux of randomness due to white Gaussian noise forcing via finite truncations of the spectral representation of the associated Wiener process, (iii) Slow decay of PCE and GrChE coefficients in the presence of intermittency, hampering implementation of sparse truncation methods which have been widely used in nearly elliptic problems or in low Reynolds number flows. Rigorous justification of these limitations is richly illustrated by straightforward tests exploiting a simple nonlinear and non-Gaussian but statistically exactly solvable test model which is proposed here as a challenging benchmark for algorithms for UQ in systems with intermittency.

Pore fluid chemistry, stress–strain behaviour, and yielding in reconstituted highly plastic clay

Extensive deposits of proglacial Lake Agassiz clay in the Red River valley in southern Manitoba, Canada are smectite-rich, expansive, strain-softening, and cemented by gypsum (CaSO 4.2H 2O). Mechanical properties of the clay are affected by pore fluid chemistry. They control the engineering behaviour of projects such as shallow foundations, riverbank instabilities, landfill liners and other engineered barriers. Reconstituted Lake Agassiz clay is being considered as a component of the sealing system for a Canadian repository for used nuclear fuel. The project that stimulated this study involved intermittent instabilities of retention dykes for the reservoir (forebay) of a hydroelectric generating station. Testing for cation concentrations suggested that natural seepage beneath the dykes removed gypsum cementation and reduced the strength of the foundation soils. To examine this, blocks of reconstituted clay were prepared using different pore fluids. Specimens that were saturated with gypsum displayed similar yield stresses and peak strengths, even though there were other differences in their pore fluid chemistry. Specimens that were under-saturated with gypsum yielded at lower stresses. The results suggest that early straining up to 1 to 2% axial strain was controlled by the presence of gypsum at near-saturation concentrations.

Localized Instability and Attraction along Invariant Manifolds

We derive a simple criterion for transverse instabilities along a general invariant manifold of a multidimensional dynamical system. The criterion requires an appropriately defined normal infinitesimal Lyapunov exponent (NILE) to be positive over regions of transverse instability on the manifold. Unlike classic Lyapunov-type numbers in the theory of normally hyperbolic invariant manifolds, the NILE can be computed analytically in applications. This enables us to locate, for example, regions of transient jumping along an invariant manifold that is otherwise globally attracting. To illustrate our results, we determine the locations of intermittent instabilities in bubble motion past a cylinder, in predator-prey interactions, and in soft-stiff structural systems.

Transverse effects in photorefractive ring resonators

Transverse effects in unidirectional and bidirectional photorefractive ring resonators with high Fresnel numbers are investigated numerically. The onset of transverse-mode competition, as well as symmetry-breaking intermittent instabilities, is observed as the cavity detuning is varied. Phase relations and frequency shifts in the intracavity field, in particular, antisymmetric response with respect to the frequency shift and cavity detuning, are considered. The buildup of ordered transverse patterns whose temporal dynamics are either periodic or chaotic is followed. The temporal evolution of chaotic mode oscillation is identified as a crisis-induced intermittency at a heteroclinic tangency.