Flame Double Input Describing Function analysis

The Flame Describing Function (FDF) is a useful and relatively cheap approximation of a flame’s nonlinearity with respect to harmonic velocity fluctuations. When embedded into a linear acoustic network, it is able to predict the amplitude and stability of harmonic thermoacoustic oscillations through the harmonic balance procedure. However, situations exist in which these oscillations are not periodic, but their spectrum contains peaks at several incommensurate frequencies. If one assumes that two frequencies dominate the spectrum, these oscillations are quasiperiodic, and the FDF concept can be extended by forcing the flame with two amplitudes and two frequencies. The nonlinearity is then approximated by a Flame Double Input Describing Function (FDIDF), which is a more expensive object to calculate than the FDF, but contains more information about the nonlinear response. In this study, we present the calculation of a non-static flame’s FDIDF. We use a G-equation-based laminar conical flame. We embed the FDIDF into a thermoacoustic network and we predict the nature and amplitude of thermoacoustic oscillations through the harmonic balance method. A criterion for the stability of these oscillations is outlined. We compare our results with a classical FDF analysis and self-excited time domain simulations of the same system. We show how the FDIDF improves the stability prediction provided by the FDF. At a numerical cost roughly equivalent to that of two FDFs, the FDIDF is capable to predict the onset of Neimark-Sacker bifurcations and to identify the frequency of oscillations around unstable limit cycles. At a higher cost, it can also saturate in amplitude these oscillations and predict the amplitude and stability of quasiperiodic oscillations.This project was funded by the European Research Council through Project ALORS 2590620.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Elsevier

Frequency domain and time domain analysis of thermoacoustic oscillations with wave-based acoustics

Many thermoacoustic systems exhibit rich nonlinear behaviour. Recent studies show that this nonlinear dynamics can be well captured by low-order time domain models that couple a level set kinematic model for a laminar flame, the $G$-equation, with a state-space realization of the linearized acoustic equations. However, so far the $G$-equation has been coupled only with straight ducts with uniform mean acoustic properties, which is a simplistic configuration. In this study, we incorporate a wave-based model of the acoustic network, containing area and temperature variations and frequency-dependent boundary conditions. We cast the linear acoustics into state-space form using a different approach from that in the existing literature. We then use this state-space form to investigate the stability of the thermoacoustic system, both in the frequency and time domains, using the flame position as a control parameter. We observe frequency-locked, quasiperiodic and chaotic oscillations. We identify the location of Neimark–Sacker bifurcations with Floquet theory. We also find the Ruelle–Takens–Newhouse route to chaos with nonlinear time series analysis techniques. We highlight important differences between the nonlinear response predicted by the frequency domain and the time domain methods. This reveals deficiencies with the frequency domain technique, which is commonly used in academic and industrial studies of thermoacoustic systems. We then demonstrate a more accurate approach based on continuation analysis applied to time domain techniques.This project was funded by the European Research Council through Project ALORS 2590620.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2015.13

Weakly nonlinear analysis of thermoacoustic bifurcations in the Rijke tube

In this study we present a theoretical weakly nonlinear framework for the prediction of thermoacoustic oscillations close to Hopf bifurcations. We demonstrate the method for a thermoacoustic network that describes the dynamics of an electrically heated Rijke tube. We solve the weakly nonlinear equations order by order, discuss their contribution on the overall dynamics and show how solvability conditions at odd orders give rise to Stuart-Landau equations. These equations, combined together, describe the nonlinear dynamical evolution of the oscillations' amplitude and their frequency. Because we retain the contribution of several acoustic modes in the thermoacoustic system, the use of adjoint methods is required to derive the Landau coefficients. The analysis is performed up to fifth order and compared with time domain simulations, showing good agreement. The theoretical framework presented here can be used to reduce the cost of investigating oscillations and subcritical phenomena close to Hopf bifurcations in numerical simulations and experiments and can be readily extended to consider, e.g. the weakly nonlinear interaction of two unstable thermoacoustic modes

Rough on Rats

1Squalling children, scolding wife,Were not the pest of my poor lifeWherever I lived in house or flats,My plague has been those horrid Rats;They ate our meat, our bread and shoes,We could not have qui-et snooze;One day my wife did chance to dozethey pinned my baby by the nose ChorusR-r-rats! Rats! Rats! Rough on Rats!Hang your dogs and drown your cats;We give a plan for every manTo clear his house with Rough on Rats 2I got a cat, I set a trap,And thought to have a quiet nap,But scare in bed we snug were laidWhen round the room the villains playedMy wife jumped out up-on the floor,To strike a light, but soon did roarAs well she might, for you must know,The steel-trap had her by the toe 3But Rats were not the only pest,To spoil our food, and spoil the rest,Fresh troubles di each day a-rise,Mice, Roaches, Bugs, Mosquitoes, FliesBut now I\u27ve got the tip at last.And soundly sleep and eat quite fast;For we have banished all the crew,And you shall learn the secret too

G-equation modelling of thermo-acoustic oscillations of partially-premixed flames

Numerical simulations aid combustor design to avoid and reduce thermo-acoustic oscillations. Non-linear heat release rate estimation and its modelling are essential for the prediction of saturation amplitudes of limit cycles. The heat release dynamics of flames can be approximated by a Flame Describing Function (FDF). To calculate an FDF, a wide range of forcing amplitudes and frequencies needs to be considered. For this reason, we present a computationally inexpensive level-set approach, which accounts for equivalence ratio perturbations on flames with arbitrarily-complex shapes. The influence of flame parameters and modelling approaches on flame describing functions and time delay coefficient distributions are discussed in detail. The numerically-obtained flame describing functions are compared with experimental data and used in an acoustic network model for limit cycle prediction. A reasonable agreement of the heat release gain and limit cycle frequency is achieved even with a simplistic, analytical velocity fluctuation model. However, the phase decay is over-predicted. For sophisticated flame shapes, only the realistic modelling of large-scale flow structures allows the correct phase decay predictions of the heat release rate response.This work was conducted within the EU 7th Framework Project Joint Technology Initiatives - Clean Sky (AMEL- Advanced Methods for the Prediction of Lean-burn Combustor Unsteady Phenomena), project number: JTI-CS-2013-3-SAGE- 06-009 / 641453. This work was performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/), provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and funding from the Science and Technology Facilities Council

G-equation modelling of thermo-acoustic oscillations of partially-premixed flames

Numerical simulations aid combustor design to avoid and reduce thermo-acoustic oscillations. Non-linear heat release rate estimation and its modelling are essential for the prediction of saturation amplitudes of limit cycles. The heat release dynamics of flames can be approximated by a Flame Describing Function (FDF). To calculate an FDF, a wide range of forcing amplitudes and frequencies needs to be considered. For this reason, we present a computationally inexpensive level-set approach, which accounts for equivalence ratio perturbations on flames with arbitrarily-complex shapes. The influence of flame parameters and modelling approaches on flame describing functions and time delay coefficient distributions are discussed in detail. The numerically-obtained flame describing functions are compared with experimental data and used in an acoustic network model for limit cycle prediction. A reasonable agreement of the heat release gain and limit cycle frequency is achieved even with a simplistic, analytical velocity fluctuation model. However, the phase decay is over-predicted. For sophisticated flame shapes, only the realistic modelling of large-scale flow structures allows the correct phase decay predictions of the heat release rate response.This work was conducted within the EU 7th Framework Project Joint Technology Initiatives - Clean Sky (AMEL- Advanced Methods for the Prediction of Lean-burn Combustor Unsteady Phenomena), project number: JTI-CS-2013-3-SAGE- 06-009 / 641453. This work was performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/), provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and funding from the Science and Technology Facilities Council

Four-Hundred-and-Ninety-Million-Year Record of Bacteriogenic Iron Oxide Precipitation at Sea-Floor Hydrothermal Vents

Fe oxide deposits are commonly found at hydrothermal vent sites at mid-ocean ridge and back-arc sea floor spreading centers, seamounts associated with these spreading centers, and intra-plate seamounts, and can cover extensive areas of the seafloor. These deposits can be attributed to several abiogenic processes and commonly contain micron-scale filamentous textures. Some filaments are cylindrical casts of Fe oxyhydroxides formed around bacterial cells and are thus unquestionably biogenic. The filaments have distinctive morphologies very like structures formed by neutrophilic Fe oxidizing bacteria. It is becoming increasingly apparent that Fe oxidizing bacteria have a significant role in the formation of Fe oxide deposits at marine hydrothermal vents. The presence of Fe oxide filaments in Fe oxides is thus of great potential as a biomarker for Fe oxidizing bacteria in modern and ancient marine hydrothermal vent deposits. The ancient analogues of modern deep-sea hydrothermal Fe oxide deposits are jaspers. A number of jaspers, ranging in age from the early Ordovician to late Eocene, contain abundant Fe oxide filamentous textures with a wide variety of morphologies. Some of these filaments are like structures formed by modern Fe oxidizing bacteria. Together with new data from the modern TAG site, we show that there is direct evidence for bacteriogenic Fe oxide precipitation at marine hydrothermal vent sites for at least the last 490 Ma of the Phanerozoic

Effects of short-term treatment with atorvastatin in smokers with asthma - a randomized controlled trial

<b>Background</b> The immune modulating properties of statins may benefit smokers with asthma. We tested the hypothesis that short-term treatment with atorvastatin improves lung function or indices of asthma control in smokers with asthma.<p></p> <b>Methods</b> Seventy one smokers with mild to moderate asthma were recruited to a randomized double-blind parallel group trial comparing treatment with atorvastatin (40 mg per day) versus placebo for 4 weeks. After 4 weeks treatment inhaled beclometasone (400 ug per day) was added to both treatment arms for a further 4 weeks. The primary outcome was morning peak expiratory flow after 4 weeks treatment. Secondary outcome measures included indices of asthma control and airway inflammation.<p></p> <b>Results</b> At 4 weeks, there was no improvement in the atorvastatin group compared to the placebo group in morning peak expiratory flow [-10.67 L/min, 95% CI -38.70 to 17.37, p=0.449], but there was an improvement with atorvastatin in asthma quality of life score [0.52, 95% CI 0.17 to 0.87 p=0.005]. There was no significant improvement with atorvastatin and inhaled beclometasone compared to inhaled beclometasone alone in outcome measures at 8 weeks.<p></p> <b>Conclusions</b> Short-term treatment with atorvastatin does not alter lung function but may improve asthma quality of life in smokers with mild to moderate asthma. Clinicaltrials.gov identifier: NCT0046382

Linear-model-based estimation in wall turbulence: Improved stochastic forcing and eddy viscosity terms

We use Navier–Stokes-based linear models for wall-bounded turbulent flows to estimate large-scale fluctuations at different wall-normal locations from their measurements at a single wall-normal location. In these models, we replace the nonlinear term by a combination of a stochastic forcing term and an eddy dissipation term. The stochastic forcing term plays a role in energy production by the large scales, and the eddy dissipation term plays a role in energy dissipation by the small scales. Based on the results in channel flow, we find that the models can estimate large-scale fluctuations with reasonable accuracy only when the stochastic forcing and eddy dissipation terms vary with wall distance and with the length scale of the fluctuations to be estimated. The dependence on the wall distance ensures that energy production and energy dissipation are not concentrated close to the wall but are evenly distributed across the near-wall and logarithmic regions. The dependence on the length scale of the fluctuations ensures that lower wavelength fluctuations are not excessively damped by the eddy dissipation term and hence that the dominant scales shift towards lower wavelengths towards the wall. This highlights that, on the one hand, energy extraction in wall turbulence is predominantly linear and thus physics-based linear models give reasonably accurate results. On the other hand, the absence of linearly unstable modes in wall turbulence means that the nonlinear term still plays an essential role in energy extraction and thus the modelled terms should include the observed wall distance and length scale dependencies of the nonlinear term.This work was supported by the National Natural Science Foundation of China (grant nos. 91752201, 12002147 and 12050410247), the Shenzhen Science and Technology Innovation Committee (KQTD20180411143441009), the Department of Science and Technology of Guangdong Province (grant nos. 2019B21203001 and 2020B1212030001) and the Key Special Project for Introduced Talents Team of Southern Marine Science and Engineering Guangdong Laboratory, Guangzhou (GML2019ZD0103). We acknowledge support from the Centers for Mechanical Engineering Research and Education at MIT and SUSTech, as well as from the Center for Computational Science and Engineering at SUSTech. AM and SJI are grateful for the financial support of the Australian Research Council