Tomographic reconstruction of OH* chemiluminescence in two interacting turbulent flames

The tomographic reconstruction of OH* chemiluminescence was performed on two interacting turbulent premixed bluff-body stabilized flames under steady flow conditions and acoustic excitation. These measurements elucidate the complex three-dimensional (3D) vortex-flame interactions which have previously not been accessible. The experiment was performed using a single camera and intensifier, with multiple views acquired by repositioning the camera, permitting calculation of the mean and phase-averaged volumetric OH* distributions. The reconstructed flame structure and phase-averaged dynamics are compared with OH planar laser-induced fluorescence and flame surface density measurements for the first time. The volumetric data revealed that the large-scale vortex-flame structures formed along the shear layers of each flame collide when the two flames meet, resulting in complex 3D flame structures in between the two flames. With a fairly simple experimental setup, it is shown that the tomographic reconstruction of OH* chemiluminescence in forced flames is a powerful tool that can yield important physical insights into large-scale 3D flame dynamics that are important in combustion instability. © 2013 IOP Publishing Ltd.

Response of two acoustically excited turbulent premixed flames to an imposed phase lag

This paper describes an experimental investigation into the interactions that occur between two acoustically forced lean turbulent premixed flames for an induced phase lag. Phase-averaged FSD from cinematographic OH-PLIF measurements and global heat release measurements were obtained for a range phase lags (ψ S) and amplitudes (A) as a function of flame separation distance, S. The effect of bringing two flames closer together causes jet merging, which alters the vortex flame interactions that drive the thermo-acoustic response. To simulate circumferential modes a phase lag was introduced, which affected the flame dynamics in the region of flame-flame interaction, with these changes dependent on S. For moderate separation distances, the flame structure becomes increasingly asymmetric inducing a very small transverse oscillation. However, for moderate phase lags (φ s ≤ 20) the magnitude of these changes and their subsequent influence on the thermo-acoustic response was found to be slight in comparison with changes in S. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc.

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.

Phase synchronization through entrainment by a consensus input

The paper proposes a synchronization mechanism in a set of nonlinear oscillators interconnected through a communication network. In contrast to many existing results, we do not employ strong, diffusive couplings between the individual oscillators. Instead, each individual oscillator is weakly forced by a linear resonator system. The resonator systems are synchronized using results from consensus theory. The synchronized resonator systems force the frequencies of the nonlinear oscillators to a constant frequency and thereby yield synchronization of the oscillators. We prove this result using the theory of small forcings of stable oscillators. This synchronization scheme allows for synchronization of nonlinear oscillators over uniformly connected communication graphs. ©2010 IEEE.

The rhythm of fountains: The length and time scales of rise height fluctuations at low and high Froude numbers

The magnitude and frequency of vertical fluctuations of the top of an axisymmetric miscible Boussinesq fountain forms the focus of this work. We present measurements of these quantities for saline-aqueous fountains in uniform quiescent surroundings. Our results span source Froude numbers 0.3 ≤ Fr 0 ≤ 40 and, thereby, encompass very weak, weak, intermediate and forced classes of fountain. We identify distinct scalings, based on known quantities at the fountain source, for the frequency of fountain height fluctuations which collapse our data within bands of Fr0. Notably, our scalings reveal that the (dimensionless) frequency takes a constant value within each band. These results highlight characteristic time scales for the fluctuations which we decompose into a single, physically apparent, length scale and velocity scale within each band. Moreover, within one particular band, spanning source Froude numbers towards the lower end of the full range considered, we identify unexpectedly long-period fluctuations indicating a near balance of inertia and (opposing) buoyancy at the source. Our analysis identifies four distinct classes of fluctuation behaviour (four bands of Fr 0) and this classification matches well with existing classifications of fountains based on rise heights. As such, we show that an analysis of the behaviour of the fountain top alone, rather than the entire fountain, provides an alternative approach to classifying fountains. The similarity of classifications based on the two different methods confirms that the boundaries between classes mark tangible changes in the physics of fountains. For high Fr0 we show that the dominant fluctuations occur at the scale of the largest eddies which can be contained within the fountain near its top. Extending this, we develop a Strouhal number, Strtop, based on experimental measures of the fountain top, defined such that Strtop = 1 would suggest the dominant fluctuations are caused by a continual cycle of eddies forming and collapsing at this largest physical scale. For high- Fr 0 fountains we find Strtop ≈ 0. 9. © 2013 Cambridge University Press.

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.

Carbonating magnesia for soil stabilization

This paper investigates the potential for carbonating reactive magnesia (MgO) to serve as a more sustainable soil stabilization method by providing rapid and significant strength development of the stabilized soil through absorbing substantial quantities of CO2. Gaseous CO2 was forced through laboratory-prepared reactive MgO-treated soil samples in a triaxial cell set-up, and their resulting mechanical and microstructural properties were investigated using unconfined compressive strength, X-ray diffraction, and scanning electron microscopy. The results showed that adequately carbonated MgO-treated soils could, in a few hours, reach a similar strength range to corresponding 28 day Portland cement (PC)-stabilized soils. Hydrated magnesium carbonates, namely nesquehonite and hydromagnesite-dypingite, were the main products of the carbonated MgO in the soil, and were responsible for the significant strength development.

Azimuthal instabilities in annular combustors: Standing and spinning modes

This theoretical study investigates spinning and standing modes in azimuthally symmetric annular combustion chambers. Both modes are observed in experiments and simulations, and an existing model predicts that spinning modes are the only stable state of the system. We extend this model to take into account the effect that the acoustic azimuthal velocity, u, has on the flames, and propose a phenomenological model based on experiments performed on transversely forced flames. This model contains a parameter, ä, that quantifies the influence that the transversal excitation has on the fluctuating heat release. For small values of ä, spinning modes are the only stable state of the system. In an intermediate range of ä, both spinning and standing modes are stable states. For large values of ä, standing modes are the only stable state. This study shows that a flame's response to azimuthal velocity fluctuations plays an important role in determining the type of thermoacoustic oscillations found in annular combustors. © 2013 The Authors.

CFD investigation of turbulent premixed flame response to transverse forcing

Screech is a high frequency oscillation that is usually characterized by instabilities caused by large-scale coherent flow structures in the wake of bluff-body flameholders and shear layers. Such oscillations can lead to changes in flame surface area which can cause the flame to burn unsteadily, but also couple with the acoustic modes and inherent fluid-mechanical instabilities that are present in the system. In this study, the flame response to hydrodynamic oscillations is analyzed in a controlled manner using high-fidelity Computational Fluid Dynamics (CFD) with an unsteady Reynolds-averaged Navier-Stokes approach. The response of a premixed flame with and without transverse velocity forcing is analyzed. When unforced, the flame is shown to exhibit a self-excitation that is attributed to the anti-symmetric shedding of vortices in the wake of the flameholder. The flame is also forced using two different kinds of low-amplitude out-of-phase inlet velocity forcing signals. The first forcing method is harmonic forcing with a single characteristic frequency, while the second forcing method involves a broadband forcing signal with frequencies in the range of 500 - 1000 Hz. For the harmonic forcing method, the flame is perturbed only lightly about its mean position and exhibits a limit cycle oscillation that is characteristic of the forcing frequency. For the broadband forcing method, larger changes in the flame surface area and detachment of the flame sheet can be seen. Transition to a complicated trajectory in the phase space is observed. When analyzed systematically with system identification methods, the CFD results, expressed in the form of the Flame Transfer Function (FTF) are capable of elucidating the flame response to the imposed perturbation. The FTF also serves to identify, both spatially and temporally, regions where the flame responds linearly and nonlinearly. Locking-in between the flame's natural self-excited frequency and the subharmonic frequencies of the broadband forcing signal is found to alter the dynamical behaviour of the flame. Copyright © 2013 by ASME.