Nonlinear phenomena in thermoacoustic systems with premixed flames

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies, amplitudes and stability of limit cycles. Limit cycles in thermoacoustic systems are reached when the energy input from driving processes and energy losses from damping processes balance each other over a cycle of the oscillation. In this paper an integral relation for the rate of change of energy of a thermoacoustic system is derived. This relation is analogous to the well-known Rayleigh criterion in thermoacoustics, but can be used to calculate the amplitudes of limit cycles, as well as their stability. The relation is applied to a thermoacoustic system of a ducted slot-stabilized 2-D premixed flame. The flame is modelled using a nonlinear kinematic model based on the G-equation, while the acoustics of planar waves in the tube are governed by linearised momentum and energy equations. Using open-loop forced simulations, the flame describing function (FDF) is calculated. The gain and phase information from the FDF is used with the integral relation to construct a cyclic integral rate of change of energy (CIRCE) diagram that indicates the amplitude and stability of limit cycles. This diagram is also used to identify the types of bifurcation the system exhibits and to find the minimum amplitude of excitation needed to reach a stable limit cycle from another linearly stable state, for single- mode thermoacoustic systems. Furthermore, this diagram shows precisely how the choice of velocity model and the amplitudedependence of the gain and the phase of the FDF influence the nonlinear dynamics of the system. Time domain simulations of the coupled thermoacoustic system are performed with a Galerkin discretization for acoustic pressure and velocity. Limit cycle calculations using a single mode, as well as twenty modes, are compared against predictions from the CIRCE diagram. For the single mode system, the time domain calculations agree well with the frequency domain predictions. The heat release rate is highly nonlinear but, because there is only a single acoustic mode, this does not affect the limit cycle amplitude. For the twenty-mode system, however, the higher harmonics of the heat release rate and acoustic velocity interact resulting in a larger limit cycle amplitude. Multimode simulations show that in some situations the contribution from higher harmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Copyright © 2012 by ASME.

Transient response of structures with uncertain properties to nonlinear shock loading

A method is presented to predict the transient response of a structure at the driving point following an impact or a shock loading. The displacement and the contact force are calculated solving the discrete convolution between the impulse response and the contact force itself, expressed in terms of a nonlinear Hertzian contact stiffness. Application of random point process theory allows the calculation of the impulse response function from knowledge of the modal density and the geometric characteristics of the structure only. The theory is applied to a wide range of structures and results are experimentally verified for the case of a rigid object hitting a beam, a plate, a thin and a thick cylinder and for the impact between two cylinders. The modal density of the flexural modes for a thick slender cylinder is derived analytically. Good agreement is found between experimental, simulated and published results, showing the reliability of the method for a wide range of situations including impacts and pyroshock applications. © 2013 Elsevier Ltd. All rights reserved.

Nonlinear thermoacoustics of ducted premixed flames: The influence of perturbation convection speed

When a premixed flame is placed within a duct, acoustic waves induce velocity perturbations at the flame's base. These travel down the flame, distorting its surface and modulating its heat release. This can induce self-sustained thermoacoustic oscillations. Although the phase speed of these perturbations is often assumed to equal the mean flow speed, experiments conducted in other studies and Direct Numerical Simulation (DNS) conducted in this study show that it varies with the acoustic frequency. In this paper, we examine how these variations affect the nonlinear thermoacoustic behaviour. We model the heat release with a nonlinear kinematic G-equation, in which the velocity perturbation is modelled on DNS results. The acoustics are governed by linearised momentum and energy equations. We calculate the flame describing function (FDF) using harmonic forcing at several frequencies and amplitudes. Then we calculate thermoacoustic limit cycles and explain their existence and stability by examining the amplitude-dependence of the gain and phase of the FDF. We find that, when the phase speed equals the mean flow speed, the system has only one stable state. When the phase speed does not equal the mean flow speed, however, the system supports multiple limit cycles because the phase of the FDF changes significantly with oscillation amplitude. This shows that the phase speed of velocity perturbations has a strong influence on the nonlinear thermoacoustic behaviour of ducted premixed flames. © 2013 The Combustion Institute.

Rao-Blackwellized particle smoothers for mixed linear/nonlinear state-space models

We consider the smoothing problem for a class of conditionally linear Gaussian state-space (CLGSS) models, referred to as mixed linear/nonlinear models. In contrast to the better studied hierarchical CLGSS models, these allow for an intricate cross dependence between the linear and the nonlinear parts of the state vector. We derive a Rao-Blackwellized particle smoother (RBPS) for this model class by exploiting its tractable substructure. The smoother is of the forward filtering/backward simulation type. A key feature of the proposed method is that, unlike existing RBPS for this model class, the linear part of the state vector is marginalized out in both the forward direction and in the backward direction. © 2013 IEEE.

Contributions of Pelagic and Benthic Dietary Sources to Freshwater Mussels: Evidence from Stable Carbon Isotope Analysis

In Gonghu Bay of Lake Taihu, tissue of five mussel species showed delta C-13 values similar to or slightly below that of pelagic suspended particulate organic matter (SPOM). This indicated that mussels in this area either fed non-selectively and so reflected available carbon in the pelagic habitat or selected for phytoplankton. The situation was the same for Anodonta woodiana woodiana and Cristaria plicata in Meiliang Bay; however, for the remaining three species, Hyriopsis cumingii, Arconaia lanceolata, and Lamprotula rochechouarti, tissue had intermediate delta C-13 values, falling between those for pelagic SPOM and benthic sediment organic matter (SOM), suggesting a possible preferential selection of phytoplankton from the pelagic SPOM but more likely reflecting local differences in pelagic SPOM and benthic SOM composition and available organic carbon sources. The mixing model showed that pelagic SPOM accounted for over 98% of carbon incorporated by all mussels in Gonghu Bay and two mussels in Meiliang Bay, suggesting the dietary importance of pelagic food sources for mussels. Less than 50% of the assimilation in H. cumingii, A. lanceolata, and L. rochechouarti came from the pelagic carbon sources in Meiliang Bay, which suggested that these species consumed a mix of benthic and pelagic derived carbon sources.

Randomized nonlinear component analysis

Copyright © (2014) by the International Machine Learning Society (IMLS) All rights reserved. Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear re-lationships in data. Although nonlinear variants of PCA and CCA have been proposed, these are computationally prohibitive in the large scale. In a separate strand of recent research, randomized methods have been proposed to construct features that help reveal nonlinear patterns in data. For basic tasks such as regression or classification, random features exhibit little or no loss in performance, while achieving drastic savings in computational requirements. In this paper we leverage randomness to design scalable new variants of nonlinear PCA and CCA; our ideas extend to key multivariate analysis tools such as spectral clustering or LDA. We demonstrate our algorithms through experiments on real- world data, on which we compare against the state-of-the-art. A simple R implementation of the presented algorithms is provided.

Reduction in microcystin concentrations in large and shallow lakes: Water and sediment-interface contributions

Blooms of cyanobacteria, or blue-greens, are known to produce chemicals, such as microcystins, which can be toxic to aquatic and terrestrial organisms. Although previous studies have examined the fate of microcystins in freshwater lakes, primary elimination pathways and factors affecting degradation and loss have not been fully explained. The goal of the present study was to explore sources of algal toxins and investigate the distribution and biodegradation of microcystins in water and sediment through laboratory and field analyses. Water and sediment samples were collected monthly from several locations in Lake Taihu from February 2005 to January 2006. Samples were analyzed for the presence of microcystin. Water and sediment were also used in laboratory studies to determine microcystin degradation rates by spiking environmental samples with known concentrations of the chemical and observing concentration changes over time. Some water samples were found to efficiently degrade microcystins. Microcystin concentrations dropped faster in water collected immediately above lake sediment (overlying water). Degradation in sediments was higher than in water. Based on spatial distribution analyses of microcystin in Lake Taihu, higher concentrations (relative to water concentrations) of the chemical were found in lake sediments. These data suggest that sediments play a critical role in microcystin degradation in aquatic systems. The relatively low levels of microcystins found in the environment are most likely due to bacterial biodegradation. Sediments play a crucial role as a source (to the water column) of bio-degrading bacteria and as a carbon-rich environment for bacteria to proliferate and metabolize microcystin and other biogenic toxins produced by cyanobacteria. These, and other, data provide important information that may be applied to management strategies for improvement of water quality in lakes, reservoirs and other water bodies. (C) 2007 Elsevier Ltd. All rights reserved.

Contributions of phosphatase and microbial activity to internal phosphorus loading and their relation to lake eutrophication

Phosphatase may accelerate the process of lake eutrophication through improving phosphorus bioavailability. This mechanism was studied in three Chinese eutrophic shallow lakes (Lake Taihu, Lake Longyang,and Lake Lianhua). Phosphatase activity was related to the concentration of soluble reactive phosphorus (SRP) and chlorophyll a. Stability of dissolved phosphatase in reverse micelles may be attributed to molecular size, conformation and active residues of the enzyme. At the site with Microcystis bloomed in Lake Taihu, dissolved phosphatase activity was higher and more stable in micelles, SRP concentrations were lower in interstitial water, the contents of different forms of phosphorus and the amounts of aerobic bacteria were lower while respiration efficiency was higher in sediments. Phosphobacteria, both inorganic and organic and other microorganisms were abundant in surface water but rare in sediments. Therefore, internal phosphorus may substantially flux into water column by enzymatic hydrolysis and anaerobic release, together with mobility of bacteria, thereby initiating the bloom. In short, biological mechanism may act in concert with physical and chemical factors to drive the internal phosphorus release and accelerate lake eutrophication.

APSK coded modulation schemes for nonlinear satellite channels with high power and spectral efficiency

A new class of 16-ary Amplitude Phase Shift Keying (APSK) coded modulations deemed double-ring PSK modulations best suited for (satellite) nonlinear channels is proposed. Constellation parameters optimization has been based on geometric and information-theoretic considerations. Furthermore, pre- and post-compensation techniques to reduce the nonlinearity impact have been examined. Digital timing clock and carrier phase have been derived and analyzed for a Turbo coded version of the same new modulation scheme. Finally, the performance of state-of the art Turbo coded modulation for this new 16-ary digital modulation has been investigated and compared to the known TCM schemes. It is shown that for the same coding scheme, double-ring APSK modulation outperforms classical 16-QAM and 16-PSK over a typical satellite nonlinear channel due to its intrinsic robustness against the High Power Amplifier (HPA) nonlinear characteristics. The new modulation is shown to be power- and spectrally-efficient, with interesting applications to satellite communications. © 2002 by the American Institute of Aeronautics and Astronautics, Inc.