Combustion and Flame 156 (2009) 73–89 Contents lists available at ScienceDirect Combustion and Flame www.elsevier.com/locate/combustflame Dynamics and quenching of non-premixed edge-flames in oscillatory counterflows D.A. Kessler a,∗ , M. Short b a Laboratory for Computational Physics and Fluid Dynamics, U.S. Naval Research Laboratory, 4555 Overlook Ave SW, Washington, DC 20375, USA b Detonation and Shock Physics Group, Los Alamos National Laboratory, Los Alamos, NM 87545, USA article info abstract Article history: Received 7 September 2007 Received in revised form 12 June 2008 Accepted 10 August 2008 Available online 20 October 2008 Keywords: Edge-flames Unsteady counterflow Quenching Extinction Cellular instabilities The dynamics of non-premixed edge-flames, including the generation of cellular structures, in an unsteady, symmetric counterflow are examined for positive rates of strain. A one-step reaction is assumed, ν Y F + ν X O → ν p P , in which the oxidizer Lewis number is 1. For a variety of Damköhler numbers, we examine the edge-flame evolution for two values of the fuel Lewis number Le Y ,0.3 and 1, and two values of the initial mixture fraction γ ,0.36 and 1, representing fuel lean and stoichiometric supply conditions. For Le Y = 0.3 and γ = 0.36, unsteady forcing can convert non-cellular edge-flames into ones containing various characteristics of near- or sub-limit cellular structures, including drifting, splitting and stationary flame strings. The transition regimes between the different edge-flame structures are examined as a function of the amplitude and frequency of the strain rate variations in the unsteady counterflow and also as a function of the instantaneous and equivalent strain rate functions. For Le Y = 0.3 and γ = 1, while no cellular edge-flames can be generated for steady counterflows, we show that cellular structures can be observed in the presence of unsteady forcing. For Le Y = 1 and γ = 1, it is shown that unsteady forcing can significantly modify the mean propagation speeds of both ignition and failure waves. Finally, the quenching boundaries of two-dimensional edge-flames induced by the unsteady counterflow are examined for Le Y = 0.3, γ = 0.36 and Le Y = 1, γ = 1. Published by Elsevier Inc. on behalf of The Combustion Institute. 1. Introduction The study of edge-flames is an important component of the modeling and understanding of laminar and turbulent flame dy- namics. Accordingly, edge-flame structures and their dynamics in premixed and non-premixed flows have been studied extensively over the past decade. Edge-flames are commonly studied in a steady counterflow configuration. Depending on factors such as the strain rate, reactant Lewis numbers, initial mixture fraction and heat losses, edge-flames can propagate as ignition or failure waves, pulsate, or generate cellular structures [1–18]. Buckmaster [19] has reviewed the development of edge-flame modeling. In the current paper, we examine the propagation, the gener- ation of cellular instabilities (flame strings) and the quenching of non-premixed edge-flames by an unsteady counterflow. This study is motivated by turbulent non-premixed flame dynamics when the flow field straining results in local quenching in a region of the flame sheet [20,21]. A resulting edge-flame can reconnect the torn sheet by propagating into the unburnt mixture, or extend the re- gion of quenching in the sheet by propagating away from the hole [22–24]. However, given the short time-scale associated with the * Corresponding author. Fax: +1 202 767 4798. E-mail addresses: dakessle@lcp.nrl.navy.mil (D.A. Kessler), short1@lanl.gov (M. Short). turbulent flow fluctuations, it is likely that the propagating edge- flame will encounter significant local flow strain rates changes. It is of interest then to examine the effect of time-varying rates of strain on non-premixed edge-flames. There is a large body of literature examining the dynamics and quenching of one-dimensional non-premixed flames in an un- steady counterflow [25–35] that is relevant to the present study. Broadly, for slowly varying rates of strain, the flame, premixed or non-premixed, tends to quench when the instantaneous strain rate (i.e. the strain rate at a given time) is close to that defining the one-dimensional steady quenching limit. For more rapid varia- tions in the rate of strain, the one-dimensional strained flames can survive instantaneous values of the strain rate much larger than that defining the one-dimensional steady quenching limit. In the context of two-dimensional problems, Kessler, Short and Buckmas- ter [15] were the first to examine the behavior of edge-flames in a quantifiable time-varying rate-of-strain flow, specifically a sym- metric counterflow of premixed fresh reactants. It was shown in [15], for instance, that a temporally varying strain rate can change a stable advancing edge-flame with a low Lewis number into an advancing edge-flame trailing cellular flame-string structures. Here we address whether such transitions can also occur for non- premixed edge flames, and establish the structural differences in the response of the premixed and non-premixed edges to an oscil- latory counterflow. 0010-2180/$ – see front matter Published by Elsevier Inc. on behalf of The Combustion Institute. doi:10.1016/j.combustflame.2008.08.013