Adaptive control of combustion instabilities for unknown sign of the high frequency gain

A type of adaptive, closed-loop controllers known as self-tuning regulators present a robust method of eliminating thermoacoustic oscillations in modern gas turbines. These controllers are able to adapt to changes in operating conditions, and require very little pre-characterisation of the system. One piece of information that is required, however, is the sign of the system's high frequency gain (or its 'instantaneous gain'). This poses a problem: combustion systems are infinite-dimensional, and so this information is never known a priori. A possible solution is to use a Nussbaum gain, which guarantees closed-loop stability without knowledge of the sign of the high frequency gain. Despite the theory for such a controller having been developed in the 1980s, it has never, to the authors' knowledge, been demonstrated experimentally. In this paper, a Nussbaum gain is used to stabilise thermoacoustic instability in a Rijke tube. The sign of the high frequency gain of the system is not required, and the controller is robust to large changes in operating conditions - demonstrated by varying the length of the Rijke tube with time. Copyright © 2008 by Simon J. Illingworth & Aimee S. Morgans.

Experimental evidence of flutter and divergence instabilities induced by dry friction

Flutter and divergence instabilities have been advocated to be possible in elastic structures with Coulomb friction, but no direct experimental evidence has ever been provided. Moreover, the same types of instability can be induced by tangential follower forces, but these are commonly thought to be of extremely difficult, if not impossible, practical realization. Therefore, a clear experimental basis for flutter and divergence induced by friction or follower-loading is still lacking. This is provided for the first time in the present article, showing how a follower force of tangential type can be realized via Coulomb friction and how this, in full agreement with the theory, can induce a blowing-up vibrational motion of increasing amplitude (flutter) or an exponentially growing motion (divergence). In addition, our results show the limits of a treatment based on the linearized equations, so that nonlinearities yield the initial blowing-up vibration of flutter to reach eventually a steady state. The presented results give full evidence to potential problems in the design of mechanical systems subject to friction, open a new perspective in the realization of follower-loading systems and of innovative structures exhibiting 'unusual' dynamical behaviors. © 2011 Elsevier Ltd.

Instabilities in the oscillatory flow of a complex fluid.

The dynamics of a fluid in a vertical tube, subjected to an oscillatory pressure gradient, is studied experimentally for both a Newtonian and a viscoelastic shear-thinning fluid. Particle image velocimetry is used to determine the two-dimensional velocity fields in the vertical plane of the tube axis, in a range of driving amplitudes from 0.8 to 2.5 mm and of driving frequencies from 2.0 to 11.5 Hz. The Newtonian fluid exhibits a laminar flow regime, independent of the axial position, in the whole range of drivings. For the complex fluid, instead, the parallel shear flow regime exhibited at low amplitudes [Torralba, Phys. Rev. E 72, 016308 (2005)] becomes unstable at higher drivings against the formation of symmetric vortices, equally spaced along the tube. At even higher drivings the vortex structure itself becomes unstable, and complex nonsymmetric structures develop. Given that inertial effects remain negligible even at the hardest drivings (Re < 10(-1)), it is the complex rheology of the fluid that is responsible for the instabilities observed. The system studied represents an interesting example of the development of shear-induced instabilities in nonlinear complex fluids in purely parallel shear flow.

Investigation of self excited and acoustically forced combustion instabilities with laser diagnostics

Combustion oscillations in gas turbines can result in serious damage. One method used to predict such oscillations is to analyze the combustor acoustics using a simple linear model. Such a model requires a flame transfer function to describe the response of the heat release to flow perturbations inside the combustor. This paper reports on the application of Planar Laser Induced Fluorescence (PLIF) of OH radicals to analyze the response of a lean premixed flame to oncoming flow perturbations. Both self-excited oscillations and low amplitude forced oscillations at various frequencies are investigated in an atmospheric pressure model combustor rig. In order to visualize fluctuations of local fuel distribution, acetone-PLIF was also applied in non-reacting and acoustically forced flows at oscillation frequencies of 200 Hz and 510 Hz, respectively. OH-PLIF images were acquired over a range of operating parameters. The results presented in this paper originate from data sets acquired at fixed phase angles during the oscillation cycle. Comparative experiments in self excited and forced acoustic oscillations show that the flame and the combustion intensity develop similarly throughout the pressure cycle in both cases. Although the peak fluorescence intensities differ between self excited and the forced instabilities, there is a clear correspondence in the observed frequency and phase information from the two cases. This result encourages a comparison of the OH-PLIF and the acetone-PLIF results. Quantitative measurements of the equivalence ratio in specific areas of the measurement plane offer insight on the complex phenomena coupling acoustic perturbations, i.e. flow velocity fluctuations, to fluctuations in fuel distribution and combustion intensity, ultimately resulting in self excited combustion oscillations.

Self-excited circumferential instabilities in a model annular gas turbine combustor: Global flame dynamics

In this paper the global flame dynamics of a model annular gas turbine combustor undergoing strong self-excited circumferential instabilities is presented. The combustor consisted of either 12, 15 or 18 turbulent premixed bluff-body flames arranged around an annulus of fixed circumference so that the effect of flame separation distance, S, on the global heat release dynamics could be investigated. Reducing S was found to produce both an increase in the resonant frequency and the limit-cycle amplitudes of pressure and heat release for the same equivalence ratio. The phase-averaged global heat release, obtained from high-speed OH- chemiluminescence imaging from above, showed that these changes are caused by large-scale modifications to the flame structure around the annulus. For the largest S studied (12 flame configuration) the azimuthal instability produced a helical-like global heat release structure for each flame. When S was decreased, large-scale merging or linking between adjacent flames occurred spanning approximately half of the annulus with the peak heat release concentrated at the outer annular wall. The circumferential nature of the instability was evident from both the pressure measurements and the phase-averaged OH- chemiluminescence showing the phase of the heat release on either side of the annulus to be ≈180°apart and spinning in the counter clockwise direction. Both spinning and standing modes were found but only spinning modes are considered in this paper. To the best of the authors knowledge, these are the first experiments to provide a phase-averaged picture of self-excited azimuthal instabilities in a laboratory-scale annular combustor relevant to gas turbines. © 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Kelvin-Helmholtz-like instabilities in turbulent flows over complex surfaces

Riblets are small surface protrusions aligned with the flow direction, which confer an anisotropic roughness to the surface [6]. We have recently reported that the transitional-roughness effect in riblets, which limits their performance, is due to a Kelvin–Helmholtz-like instability of the overlying mean flow [7]. According to our DNSs, the instability sets on as the Reynolds number based on the roughness size of the riblets increases, and coherent, elongated spanwise vortices begin to develop immediately above the riblet tips, causing the degradation of the drag-reduction effect. This is a very novel concept, since prior studies had proposed that the degradation was due to the interaction of riblets with the flow as independent units, either to the lodging of quasi-streamwise vortices in the surface grooves [2] or to the shedding of secondary streamwise vorticity at the riblet peaks [9]. We have proposed an approximate inviscid analysis for the instability, in which the presence of riblets is modelled through an average boundary condition for an overlying, spanwise-independent mean flow. This simplification lacks the accuracy of an exact analysis [4], but in turn applies to riblet surfaces in general. Our analysis succeeds in predicting the riblet size for the onset of the instability, while qualitatively reproducing the wavelengths and shapes of the spanwise structures observed in the DNSs. The analysis also connects the observations with the Kelvin–Helmholtz instability of mixing layers. The fundamental riblet length scale for the onset of the instability is a ‘penetration length,’ which reflects how easily the perturbation flow moves through the riblet grooves. This result is in excellent agreement with the available experimental evidence, and has enabled the identification of the key geometric parameters to delay the breakdown. Although the appearance of elongated spanwise vortices was unexpected in the case of riblets, similar phenomena had already been observed over other rough [3], porous [1] and permeable [11] surfaces, as well as over plant [5,14] and urban [12] canopies, both in the transitional and in the fully-rough regimes. However, the theoretical analyses that support the connection of these observations with the Kelvin–Helmholtz instability are somewhat scarce [7, 11, 13]. It has been recently proposed that Kelvin–Helmholtz-like instabilities are a dominant feature common to “obstructed” shear flows [8]. It is interesting that the instability does not require an inflection point to develop, as is often claimed in the literature. The Kelvin-Helmholtz rollers are rather triggered by the apparent wall-normal-transpiration ability of the flow at the plane immediately above the obstructing elements [7,11]. Although both conditions are generally complementary, if wall-normal transpiration is not present the spanwise vortices may not develop, even if an inflection point exists within the roughness [10]. REFERENCES [1] Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 J. Fluid Mech. 562, 35–72. [2] Choi, H., Moin, P. & Kim, J. 1993 J. Fluid Mech. 255, 503–539. [3] Coceal, O., Dobre, A., Thomas, T. G. & Belcher, S. E. 2007 J. Fluid Mech. 589, 375–409. [4] Ehrenstein, U. 2009 Phys. Fluids 8, 3194–3196. [5] Finnigan, J. 2000 Ann. Rev. Fluid Mech. 32, 519–571. [6] Garcia-Mayoral, R. & Jimenez, J. 2011 Phil. Trans. R. Soc. A 369, 1412–1427. [7] Garcia-Mayoral, R. & Jimenez, J. 2011 J. Fluid Mech. doi: 10.1017/jfm.2011.114. [8] Ghisalberti, M. 2009 J. Fluid Mech. 641, 51–61. [9] Goldstein, D. B. & Tuan, T. C. 1998 J. Fluid Mech. 363, 115–151. [10] Hahn, S., Je, J. & Choi, H. 2002 J. Fluid Mech. 450, 259–285. [11] Jimenez, J., Uhlman, M., Pinelli, A. & G., K. 2001 J. Fluid Mech. 442, 89–117. [12] Letzel, M. O., Krane, M. & Raasch, S. 2008 Atmos. Environ. 42, 8770–8784. [13] Py, C., de Langre, E. & Moulia, B. 2006 J. Fluid Mech. 568, 425–449. [14] Raupach, M. R., Finnigan, J. & Brunet, Y. 1996 Boundary-Layer Meteorol. 78, 351–382.

Modal dynamics of self-excited azimuthal instabilities in an annular combustion chamber

In this paper we describe the time-varying amplitude and its relation to the global heat release rate of self-excited azimuthal instabilities in a simple annular combustor operating under atmospheric conditions. The combustor was modular in construction consisting of either 12, 15 or 18 equally spaced premixed bluff-body flames around a fixed circumference, enabling the effect of large-scale interactions between adjacent flames to be investigated. High-speed OH* chemiluminescence imaged from above the annulus and pressure measurements obtained at multiple locations around the annulus revealed that the limit cycles of the modes are degenerate in so much as they undergo continuous transitions between standing and spinning modes in both clockwise (CW) and anti-clockwise (ACW) directions but with the same resonant frequency. Similar behaviour has been observed in LES simulations which suggests that degenerate modes may be a characteristic feature of self-excited azimuthal instabilities in annular combustion chambers. By modelling the instabilities as two acoustic waves of time-varying amplitude travelling in opposite directions we demonstrate that there is a statistical prevalence for either standing m=1 or spinning m=±1 modes depending on flame spacing, equivalence ratio, and swirl configuration. Phase-averaged OH* chemiluminescence revealed a possible mechanism that drives the direction of the spinning modes under limit-cycle conditions for configurations with uniform swirl. By dividing the annulus into inner and outer annular regions it was found that the spin direction coincided with changes in the spatial distribution of the peak heat release rate relative to the direction of the bulk swirl induced along the annular walls. For standing wave modes it is shown that the globally integrated fluctuations in heat release rate vary in magnitude along the acoustic mode shape with negligible contributions at the pressure nodes and maximum contributions at the pressure anti-nodes. © 2013.

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.

Model-based control of thermoacoustic instabilities in partially premixed lean combustion - A design case study

Self-excited oscillation is becoming a major issue in low-emission, lean partially premixed combustion systems, and active control has been shown to be a feasible method to suppress such instabilities. A number of robust control methods are employed to obtain a feedback controller and it is observed that the robustness to system uncertainty is significantly better for a low complexity controller in spite of the norms being similar. Moreover, we demonstrate that closed-loop stability for such a complex system can be proved via use of the integral quadratic constraint method. Open- and closed-loop nonlinear simulations are provided. © 2013 Copyright Taylor and Francis Group, LLC.