Response of non-premixed flames to bulk flow perturbations
01 Jan 2013-Vol. 34, Iss: 1, pp 963-971
TL;DR: In this paper, the authors describe the dynamics of non-premixed flames responding to bulk velocity fluctuations, and compare their dynamics of the flame sheet position and spatially integrated heat release to that of a premixed flame.
Abstract: This paper describes the dynamics of non-premixed flames responding to bulk velocity fluctuations, and compares the dynamics of the flame sheet position and spatially integrated heat release to that of a premixed flame. The space–time dynamics of the non-premixed flame sheet in the fast chemistry limit is described by the stoichiometric mixture fraction surface, extracted from the solution of the -equation. This procedure has some analogies to premixed flames, where the premixed flame sheet location is extracted from the G = 0 surface of the solution of the G-equation. A key difference between the premixed and non-premixed flame dynamics, however, is the fact that the non-premixed flame sheet dynamics are a function of the disturbance field everywhere, and not just at the reaction sheet, as in the premixed flame problem. A second key difference is that the non-premixed flame does not propagate and so flame wrinkles are convected downstream at the axial flow velocity, while wrinkles in premixed flames convect downstream at a vector sum of the flame speed and axial velocity. With the exception of the flame wrinkle propagation speed, however, we show that that the solutions for the space–time dynamics of the premixed and non-premixed reaction sheets in high velocity axial flows are quite similar. In contrast, there are important differences in their spatially integrated unsteady heat release dynamics. Premixed flame heat release fluctuations are dominated by area fluctuations, while non-premixed flames are dominated by mass burning rate fluctuations. At low Strouhal numbers, the resultant sensitivity of both flames to flow disturbances is the same, but the non-premixed flame response rolls off slower with frequency. Hence, this analysis suggests that non-premixed flames are more sensitive to flow perturbations than premixed flames at O(1) Strouhal numbers.
Citations
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TL;DR: In this paper, the authors present a review of transverse acoustic wave motions in air-breathing systems and discuss issues associated with simulating or scaling instabilities, either in subscale experimental geometries or by attempting to understand instability physics using identical axial oscillations of the same frequency as the transverse mode of interest.
257 citations
TL;DR: Bourehla and Baillot as discussed by the authors showed the appearance and stability of a Laminar Conical Premixed Flame Subjected to an Acoustic Perturbation.
Abstract: �c and � � s ,forcurvatureand hydrodynamic strain, respectively Unsteady curvature effects on the flame surface area become significant when j� � c jSt 2 2 � O� 1� and are responsible for the experimentally observed reduction in the flame front wrinkle size in the flow direction [referred to as “filtering” by Bourehla and Baillot (Bourehla, A, and Baillot, F, “Appearance and Stability of a Laminar Conical Premixed Flame Subjected to an Acoustic Perturbation,” Combustion and Flame,
46 citations
TL;DR: In this article, the authors derived the adjoint equations for a thermo-acoustic system consisting of an infinite-rate chemistry diffusion flame coupled with duct acoustics, and then calculated the system's linear global modes (i.e., the frequency/growth rate of oscillations, together with their mode shapes), and the global modes' receptivity to species injection, sensitivity to base-state perturbations and structural sensitivity to advective-velocity perturbation.
Abstract: © 2014 Cambridge University Press. In this theoretical and numerical paper, we derive the adjoint equations for a thermo-acoustic system consisting of an infinite-rate chemistry diffusion flame coupled with duct acoustics. We then calculate the thermo-acoustic system's linear global modes (i.e. The frequency/growth rate of oscillations, together with their mode shapes), and the global modes' receptivity to species injection, sensitivity to base-state perturbations and structural sensitivity to advective-velocity perturbations. Some of these could be found by finite difference calculations but the adjoint analysis is computationally much cheaper. We then compare these with the Rayleigh index. The receptivity analysis shows the regions of the flame where open-loop injection of fuel or oxidizer will have the greatest influence on the thermo-acoustic oscillation. We find that the flame is most receptive at its tip. The base-state sensitivity analysis shows the influence of each parameter on the frequency/growth rate. We find that perturbations to the stoichiometric mixture fraction, the fuel slot width and the heat-release parameter have most influence, while perturbations to the Peclet number have the least influence for most of the operating points considered. These sensitivities oscillate, e.g. positive perturbations to the fuel slot width either stabilizes or destabilizes the system, depending on the operating point. This analysis reveals that, as expected from a simple model, the phase delay between velocity and heat-release fluctuations is the key parameter in determining the sensitivities. It also reveals that this thermo-acoustic system is exceedingly sensitive to changes in the base state. The structural-sensitivity analysis shows the influence of perturbations to the advective flame velocity. The regions of highest sensitivity are around the stoichiometric line close to the inlet, showing where velocity models need to be most accurate. This analysis can be extended to more accurate models and is a promising new tool for the analysis and control of thermo-acoustic oscillations.
36 citations
Cites background from "Response of non-premixed flames to ..."
...Equation (2.15) has an analytical solution (Magri & Juniper 2013a; Magina et al. 2013), which is reported in appendix C....
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...15) has an analytical solution (Magri & Juniper 2013a; Magina et al. 2013), which is reported in appendix C....
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TL;DR: In this article, a review categorizes different canonical flame-holding geometries that mostly involve flow recirculation zones for flame stabilization, which are inherently unstable and feed into the flame-acoustic interaction cycle.
Abstract: Flame-acoustic interactions are witnessed in the context of combustion instability in gas turbine combustors and other propulsion devices, such as rockets, besides confined combustion systems in general, such as furnaces and heaters. The confinement causes acoustic standing wave modes that interact with the flame to cause fluctuations in all quantities to grow in amplitude. This review categorizes the different canonical flame-holding geometries that mostly involve flow recirculation zones for flame stabilization, which are inherently unstable and feed into the flame-acoustic interaction cycle. The receptivity of the nonreacting shear layer to prevalent acoustic forcing in terms of development of coherent structures and instability of different hydrodynamic modes in the recirculation are detailed. The case of reacting flow instabilities involves several mechanisms of flame-acoustic coupling, such as vortex combustion; vortex-wall interactions; vortex-vortex interactions; flame area fluctuations an...
28 citations
Cites background from "Response of non-premixed flames to ..."
...Magina et al. (2013) also linearized the convective nonlinearity and the heat release rate in Burke–Schumann diffusion flames to evaluate their flame transfer function (FTF), i.e., the heat release rate response to imposed velocity fluctuations, and compare its frequency trend with that of a…...
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...Magina et al. (2013) also linearized the convective nonlinearity and the heat release rate in Burke–Schumann diffusion flames to evaluate their flame transfer function (FTF), i....
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TL;DR: In this paper, an experimental investigation of a laboratory-scale ducted inverse diffusion flame was performed, where two parametric variations of the flame were performed, i.e., the position and the air flow rate, to explore the dynamic response of such a flame, particularly in ducted applications.
Abstract: Normal diffusion flame or partially premixed flame is used in many applications, such as aviation engines, tanks, ocean vessels, and industrial furnaces, because of its high flame stability and relatively low susceptibility to dynamic instabilities compared to lean premixed flames, which give lower emissions. However, associated with such flames are high NOx and soot emissions, which are particularly high for heavier hydrocarbon fuels. Increasingly stringent environmental norms have thus dictated the search for alternate approaches; one such being the inverse diffusion flame, which is currently being used in rocket motors, for staged combustion in gas turbine combustors, and furnaces. However, the dynamic response of such a flame, particularly in ducted applications where a coupling between unsteady heat release rate and duct acoustics may occur, is relatively less explored. The present work aims to plug that knowledge gap through an experimental investigation of a laboratory-scale ducted inverse diffusion flame. Two parametric variations of the flame were performed—variation of the flame position and variation of the air flow rate. Using tools of nonlinear dynamics, such as phase space reconstruction and recurrence quantification, several interesting dynamic characteristics were observed, such as limit cycles, intermittency, and homoclinic orbits. For a constant air flow rate, the system was observed to transition from a type-II intermittency regime to a limit cycle and then again to intermittent behavior as the position of the flame within the duct was varied. A similar trend was observed when the air flow rate was varied at a fixed flame position.
22 citations
Cites background from "Response of non-premixed flames to ..."
...…was also performed by various researchers (Balasubramanian and Sujith, 2008; Chen et al., 2012, 2013; Farhat et al., 2005; Illingworth et al., 2013; Magina et al., 2013, 2015, 2017; Magina and Lieuwen, 2014, 2016; Mondal et al., 2014; Pawar et al., 2016; Tyagi et al., 2007) revealing striking…...
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References
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TL;DR: A comprehensive review of the advances made over the past two decades in this area is provided in this article, where various swirl injector configurations and related flow characteristics, including vortex breakdown, precessing vortex core, large-scale coherent structures, and liquid fuel atomization and spray formation are discussed.
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"Response of non-premixed flames to ..." refers background in this paper
...This leads to an explicit expression for the flame front position [10-16]....
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451 citations
"Response of non-premixed flames to ..." refers background in this paper
...It is helpful to compare the dynamics of the mixture fraction equation for non-premixed flames with the G-equation used to analyze the dynamics of premixed flames [5,6,8], which is given below:...
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...As a result of this work, the controlling physics in laminar flames appears to be understood and capabilities have been developed to predict the space-time dynamics of the flame position and heat release [5,6]....
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TL;DR: In this paper, convective effects of the flow modulations propagating upstream of a premixed laminar flame are considered and a unified model is derived analytically, based on a linearization of the G-equation for an inclined flame.
446 citations
"Response of non-premixed flames to ..." refers background in this paper
...This leads to an explicit expression for the flame front position [10-16]....
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TL;DR: In this paper, the authors investigated the dynamics of premixed confined swirling flames by examining their response to incident velocity perturbations and determined the generalized transfer function designated as the flame describing function (FDF) by sweeping a frequency range extending from 0 to 400 Hz and by changing the root mean square fluctuation level between 0% and 72% of the bulk velocity.
351 citations
"Response of non-premixed flames to ..." refers background in this paper
...This leads to an explicit expression for the flame front position [10-16]....
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