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 Title: Nonlinear development of centrally ignited expanding flames in laminar and turbulent mediums Author(s): Mohan, Shikhar Director of Research: Matalon, Moshe Doctoral Committee Chair(s): Matalon, Moshe Doctoral Committee Member(s): Pantano, Carlos; Fischer, Paul; Panesi, Marco Department / Program: Mechanical Sci & Engineering Discipline: Theoretical & Applied Mechans Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Darrieus-Landau instability, Level-set methodology, Premixed flames, Turbulent combustion, Cusp-like flames, Expanding flames, Fractals Abstract: Large scale premixed flames are always susceptible to hydrodynamic instabilities. It is amongst one of the most prominent intrinsic flame instabilities. The presence of the hydrodynamic instability was originally discovered in the pioneering works of Darrieus and Landau more than eighty years ago, and the Darrieus-Landau (DL) instability was named in their honour. In both works, the flame treated as a surface of density discontinuity, segregating the burnt mixture from unburnt gases and propagating at a constant speed, the unstretched laminar flame speed, was used to demonstrate that planar deflagrations were unconditionally unstable. The DL instability has numerous implications in premixed combustion as it promotes the creation of corrugated flames with sharp cusps which enhance the flame surface area leading it to propagate at a speed larger than the laminar flame speed. Landau argued that the instability all by itself could lead to the emergence of turbulent motion and thus turbulent flame propagation at relatively low Reynolds numbers (based on the flame radius). Subsequent experiments have since verified that, in the absence of any significant external disturbances, obstacles or boundaries, expanding cylindrical and spherical flames originating from weak ignition sources are indeed unstable, will self-accelerate and eventually self turbulise albeit at far larger Reynolds numbers than originally postulated. Physically, this instability prevents a planar flame from becoming flat and an expanding flame from propagating smoothly. In this work, the propagation of expanding flames is examined within the context of the hydrodynamic theory using an embedded manifold methodology, one capable of handling multi-valued and disjointed surfaces that often arise from flame-turbulence interactions. The asymptotic model was formally derived from first principles by exploiting the disparity in length scales between the flame thickness (characterised by a diffusion length scale) and the much larger local radius of curvature. While phenomologically similar to Darrieus-Landau's treatment of the premixed front, the flame speed incorporates a first order correction which depends upon the local geometrical properties of the flame and the underlying flow conditions, more succinctly referred to as flame-stretch. The dependence on the local stretching experienced by the flame is tempered by a coefficient on the order of flame thickness which mimics the effects of diffusion and chemical reactions occurring inside the flame zone. This parameter has since become known as the Markstein length. A systematic study has been carried out examining the three regimes of flame propagation, which in increasing orders of complexity include: a) a smoothly expanding laminar flame; a regime devoid of flame instability, and more concisely referred to as the linear regime'', b) a nonlinear regime'' wherein disturbances on the flame surface grow and devolve into characteristic cusp-like structures that protrude into the burnt gas and punctuate the flame surface even under laminar flow conditions, a hallmark of the DL instability, and c) a turbulent regime where there is an interplay between the effects of a decaying isotropic turbulent flow-field and the DL instability itself. Linear analysis conclusively demonstrates that for mixtures with Lewis numbers above criticality, thermo-diffusive effects have a stabilising influence at flame radii comparable to the flame thickness. The amplitude of any small amplitude disturbance will initially decay and only begin to grow once the flame becomes of a certain size; an observation consistent with experimental studies. Predictions of the critical flame radius marking the onset of instability are obtained as functions of the Markstein length and thermal expansion parameters. The numerical scheme proposed is able to replicate this behaviour and suitably capture the critical radius demarcating the onset of instability. There also exists a critical wavenumber disturbance that will be first mode to become excited. It is hypothesised that this wavenumber will dictate the cellular structure that will be observed as the long-time solution. Correspondingly, once the flame transitions to cellularity, the temporal variation in the propagation speed is seen to become non-monotonic. The investigation also examines the early response and long-time evolution of an initially laminar flame kernel subjected to the turbulent velocity fluctuations of an underlying flow field. In the wrinkled and corrugated flamelet regimes of turbulent combustion, distinct regimes of turbulent propagation exist, depending upon the influence that the DL instability exerts. Emphasis is placed on understanding the effect of differing turbulent flow characteristics (intensity and eddy size) on the burning rate and on isolating the role that the instability plays. Normalising the turbulent flame area with respect to the area of an unperturbed flame of equal mean radius reveals an asymptotic behaviour in time of the turbulent flame speed, allowing preliminary attempts to be made at computing a turbulent flame speed based on Damk\"{o}hler's first hypothesis for expanding flames in decaying turbulence. Issue Date: 2020-04-24 Type: Thesis URI: http://hdl.handle.net/2142/108256 Rights Information: Copyright 2020 - Shikhar Mohan Date Available in IDEALS: 2020-08-27 Date Deposited: 2020-05
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