When will a flame describing function approach to thermoacoustics work well?

In any thermoacoustic analysis, it is important not only to predict linear frequencies and growth rates, but also the amplitude and frequencies of any limit cycles. The Flame Describing Function (FDF) approach is a quasi-linear analysis which allows the prediction of both the linear and nonlinear behaviour of a thermoacoustic system. This means that one can predict linear growth rates and frequencies, and also the amplitudes and frequencies of any limit cycles. The FDF achieves this by assuming that the acoustics are linear and that the flame, which is the only nonlinear element in the thermoacoustic system, can be adequately described by considering only its response at the frequency at which it is forced. Therefore any harmonics generated by the flame's nonlinear response are not considered. This implies that these nonlinear harmonics are small or that they are sufficiently filtered out by the linear dynamics of the system (the low-pass filter assumption). In this paper, a flame model with a simple saturation nonlinearity is coupled to simple duct acoustics, and the success of the FDF in predicting limit cycles is studied over a range of flame positions and acoustic damping parameters. Although these two parameters affect only the linear acoustics and not the nonlinear flame dynamics, they determine the validity of the low-pass filter assumption made in applying the flame describing function approach. Their importance is highlighted by studying the level of success of an FDF-based analysis as they are varied. This is achieved by comparing the FDF's prediction of limit-cycle amplitudes to the amplitudes seen in time domain simulations.

Shock dynamics of random structures.

Predicting the response of a structure following an impact is of interest in situations where parts of a complex assembly may come into contact. Standard approaches are based on the knowledge of the impulse response function, requiring the knowledge of the modes and the natural frequencies of the structure. In real engineering structures the statistics of higher natural frequencies follows those of the Gaussian Orthogonal Ensemble, this allows the application of random point process theory to get a mean impulse response function by the knowledge of the modal density of the structure. An ensemble averaged time history for both the response and the impact force can be predicted. Once the impact characteristics are known in the time domain, a simple Fourier Transform allows the frequency range of the impact excitation to be calculated. Experimental and numerical results for beams, plates, and cylinders are presented to confirm the validity of the method.

Low-order modelling of the response of ducted flames in annular geometries

The adoption of lean premixed prevaporised combustion systems can reduce NOx emissions from gas turbines, but unfortunately also increases their susceptibility to thermoacoustic instabilities. Initially, acoustic waves can produce heat release fluctuations by a variety of mechanisms, often by perturbing the equivalence ratio. If correctly phased, heat release fluctuations can subsequently generate more acoustic waves, which at high amplitude can result in significant structural damage to the combustor. The prediction of this phenomenon is of great industrial interest. In previous work, we have coupled a physics based, kinematic model of the flame with a network model to provide the planar acoustic response necessary to close the feedback loop and predict the onset and amplitude of thermoacoustic instabilities in a lab-scale, axisymmetric single burner combustor. The advantage of a time domain approach is that the modal interaction, the influence of harmonics, and flame saturation can be investigated. This paper extends this approach to more realistic, annular geometries, where both planar and circumferential modes must be considered. In lean premixed prevaporised combustors, fluctuations in equivalence ratio have been shown to be a dominant cause of unsteady combustion. These can occur, for example, due to velocity perturbations in the premix ducts, which can lead to equivalence ratio fluctuations at the fuel injectors, which are subsequently convected downstream to the flame surfaces. Here, they can perturb the heat release by locally altering the flame speed, enthalpy of combustion, and, indirectly, the flame surface area. In many gas turbine designs, particularly aeroengines, the geometries are composed of a ring of premix ducts linking a plenum and an annular combustor. The most unstable modes are often circumferential modes. The network model is used to characterise the flow response of the geometry to heat fluctuations at an appropriate location, such as the fuel injectors. The heat release at each flame holder is determined in the time domain using the kinematic flame model derived, as a function of the flow perturbations in the premix duct. This approach is demonstrated for an annular ring of burners on a in a simple geometry. The approach is then extended to an industrial type gas turbine combustor, and used to predict the limit cycle amplitudes. Copyright © 2012 by ASME.

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.

Intrinsic terahertz plasmon signatures in chemical vapour deposited graphene

Plasmonic resonance at terahertz (THz) frequencies can be achieved by gating graphene grown via chemical vapour deposition (CVD) to a high carrier concentration. THz time domain spectroscopy of such gated monolayer graphene shows resonance features around 1.6 THz, which appear as absorption peaks when the graphene is electrostatically p-doped and change to enhanced transmission when the graphene is n-doped. Superimposed on the Drude-like frequency response of graphene, these resonance features are related to the inherent poly-crystallinity of CVD graphene. An understanding of these features is necessary for the development of future THz optical elements based on CVD graphene. © 2013 AIP Publishing LLC.

A coupled hydro-mechanical analysis for prediction of hydraulic fracture propagation in saturated porous media using EFG mesh-less method

The details of the Element Free Galerkin (EFG) method are presented with the method being applied to a study on hydraulic fracturing initiation and propagation process in a saturated porous medium using coupled hydro-mechanical numerical modelling. In this EFG method, interpolation (approximation) is based on nodes without using elements and hence an arbitrary discrete fracture path can be modelled.The numerical approach is based upon solving two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Displacement increment and pore water pressure increment are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system of equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on the penalty method. In order to model discrete fractures, the so-called diffraction method is used.Examples are presented and the results are compared to some closed-form solutions and FEM approximations in order to demonstrate the validity of the developed model and its capabilities. The model is able to take the anisotropy and inhomogeneity of the material into account. The applicability of the model is examined by simulating hydraulic fracture initiation and propagation process from a borehole by injection of fluid. The maximum tensile strength criterion and Mohr-Coulomb shear criterion are used for modelling tensile and shear fracture, respectively. The model successfully simulates the leak-off of fluid from the fracture into the surrounding material. The results indicate the importance of pore fluid pressure in the initiation and propagation pattern of fracture in saturated soils. © 2013 Elsevier Ltd.

Instantaneous frequency and bandwidth estimation using filterbank arrays

Accurate estimation of the instantaneous frequency of speech resonances is a hard problem mainly due to phase discontinuities in the speech signal associated with excitation instants. We review a variety of approaches for enhanced frequency and bandwidth estimation in the time-domain and propose a new cognitively motivated approach using filterbank arrays. We show that by filtering speech resonances using filters of different center frequency, bandwidth and shape, the ambiguity in instantaneous frequency estimation associated with amplitude envelope minima and phase discontinuities can be significantly reduced. The novel estimators are shown to perform well on synthetic speech signals with frequency and bandwidth micro-modulations (i.e., modulations within a pitch period), as well as on real speech signals. Filterbank arrays, when applied to frequency and bandwidth modulation index estimation, are shown to reduce the estimation error variance by 85% and 70% respectively. © 2013 IEEE.

Low voltage ride-through of DFIG and brushless DFIG: Similarities and differences

The brushless doubly fed induction generator (BDFIG) has been proposed as a viable alternative in wind turbines to the commonly used doubly fed induction generator (DFIG). The BDFIG retains the benefits of the DFIG, i.e. variable speed operation with a partially rated converter, but without the use of brush gear and slip rings, thereby conferring enhanced reliability. As low voltage ride-through (LVRT) performance of the DFIG-based wind turbine is well understood, this paper aims to analyze LVRT behavior of the BDFIG-based wind turbine in a similar way. In order to achieve this goal, the equivalence between their two-axis model parameters is investigated. The variation of flux linkages, back-EMFs and currents of both types of generator are elaborated during three phase voltage dips. Moreover, the structural differences between the two generators, which lead to different equivalent parameters and hence different LVRT capabilities, are investigated. The analytical results are verified via time-domain simulations for medium size wind turbine generators as well as experimental results of a voltage dip on a prototype 250 kVA BDFIG. © 2014 Elsevier B.V.

An important pitfall of pseudo-static finite element analysis

Finite Element (FE) pseudo-static analysis can provide a good compromise between simplified methods of dynamic analysis and time domain analysis. The pseudo-static FE approach can accurately model the in situ, stresses prior to seismic loading (when it follows a static analysis simulating the construction sequence) is relatively simple and not as computationally expensive as the time domain approach. However this method should be used with caution as the results can be sensitive to the choice of the mesh dimensions. In this paper two simple examples of pseudo-static finite element analysis are examined parametrically, a homogeneous slope and a cantilever retaining wall, exploring the sensitivity of the pseudo-static analysis results on the adopted mesh size. The mesh dependence was found to be more pronounced for problems with high critical seismic coefficients values (e.g. gentle slopes or small walls), as in these cases a generalised layer failure mechanism is developed simultaneously with the slope or wall mechanism. In general the mesh width was found not to affect notably the predicted value of critical seismic coefficient but to have a major impact on the predicted movements. © 2012 Elsevier Ltd.

Fibre optic monitoring of a deep circular excavation

This paper describes part of the monitoring undertaken at Abbey Mills shaft F, one of the main shafts of Thames Water's Lee tunnel project in London, UK. This shaft, with an external diameter of 30 m and 73 m deep, is one of the largest ever constructed in the UK and consequently penetrates layered and challenging ground conditions (Terrace Gravel, London Clay, Lambeth Group, Thanet Sand Formation, Chalk Formation). Three out of the twenty 1-2 m thick and 84 m deep diaphragm wall panels were equipped with fibre optic instrumentation. Bending and circumferential hoop strains were measured using Brillouin optical time-domain reflectometry and analysis technologies. These measurements showed that the overall radial movement of the wall was very small. Prior to excavation during a dewatering trial, the shaft may have experienced three-dimensional deformation due to differential water pressures. During excavation, the measured hoop and bending strains of the wall in the chalk exceeded the predictions. This appears to be related to the verticality tolerances of the diaphragm wall and lower circumferential hoop stiffness of the diaphragm walls at deep depths. The findings from this case study provide valuable information for future deep shafts in London. © ICE Publishing: All rights reserved.

Mid-infrared heavily n-doped GaAs extraordinary transmission through subwavelength grooves

Transmission of an electromagnetic wave from a heavily doped n-type GaAs film is studied theoretically. The calculations are performed using the two-dimensional finite-different time-domain method. From the calculations, we find the extraordinary transmission of p-polarized waves through the film with subwavelength grooves on both surfaces at mid-infrared frequencies. By determining a set of groove parameters, we optimize the transmission to as high as 55.2%. We ascribe this extraordinary transmission to the coupling of the surface-plasmon polariton modes and waveguide modes. Such an enhanced transmission device can be useful for mid-infrared wave filters, emitters, and monitors.

Study on Frequency Coherence Properties of Light Beams

This paper presents a new concept of frequency coherence in the frequency-time domain to describe the field correlations between two lightwaves with different frequencies. The coherence properties of the modulated beams from lightwave sources with different spectral widths and the modes of Fabry-Wrot (FP) laser are investigated. It is shown that the lightwave and its corresponding sidebands produced by the optical intensity modulation are perfectly coherent. The measured linewidth of the beat signal is narrow and almost identical no matter how wide the spectral width of the beam is. The frequency spacing of the adjacent FP modes is beyond the operation frequency range of the measurement instruments. In our experiment, optical heterodyne technique is used to investigate the frequency coherence of the modes of FP laser by means of the frequency shift induced by the optical intensity modulation. Experiments show that the FP modes are partially coherent and the mode spacing is relatively fixed even when the wavelength changes with ambient temperature, bias current and other factors. Therefore, it is possible to generate stable and narrow-linewidth signals at frequencies corresponding to several mode intervals of the laser.

Analysis of mode characteristics for equilateral-polygonal resonators with a center hole

Mode characteristics for equilateral triangles, squares, and hexagonal resonators with a center hole are numerically simulated by the finite-different time domain (FDTD) technique. The center hole does not break the symmetry behavior of the original resonators and can result in modification of the mode field patterns and mode Q factors. In an equilateral triangle resonator the center hole can suppress the symmetry state of degenerate states with the merit of single mode operation. In a square resonator, the Q factor can be enhanced for some modes with a suitable size of the hole. For a hexagonal resonator with a side length of 1 mu m and a refractive index of 3.2, the mode Q factors first gradually decrease with the increase of the hole diameter for modes at a wavelength of about 1500 nm, then the modes transform to that of a microdisk with a jump of the mode wavelength as the hole diameter approaches 0.7 mu m. Finally, the mode Q factors greatly enhance as the hole diameter reaches about 1 mu m. The results indicate that the center hole can greatly modify mode characteristics, especially that of the mode Q factor. (C) 2009 Optical Society of America

High-Q TM whispering-gallery modes in three-dimensional microcylinders

We present a generation condition for realizing high-Q TM whispering-gallery modes (WGMs) in semiconductor microcylinders. For microcylinders with symmetry or weak asymmetry vertical waveguiding, we show that TM WGMs can have a high Q factor, with the magnitude of 10(4) at the radius of the microcylinder of 1 mu m, by three-dimensional numerical simulation. The Q factor of TE WGMs is much less than that of TM WGMs in the semiconductor microcylinders due to a vertical radiation loss caused by mode coupling with the vertical propagating mode. The results open up a possible application of TM WGMs in semiconductor microcylinders for efficient current injection microlasers and single photon sources.

A differential recursive scheme for suppression of Peak to average power ratio for OFDM

A differential recursive scheme for suppression of Peak to average power ratio (PAPR) for Orthogonal frequency division multiplexing (OFDM) signal is proposed in this thesis. The pseudo-randomized modulating vector for the subcarrier series is differentially phase-encoded between successive components in frequency domain first, and recursion manipulates several samples of Inverse fast Fourier transformation (IFFT) output in time domain. Theoretical analysis and experimental result exhibit advantage of differential recursive scheme over direct output scheme in PAPR suppression. And the overall block diagram of the scheme is also given.