M. El-Hamdi

Deterministic chaos in laminar premixed flames : experimental classification of chaotic dynamics

Abstract Our previous experiments on the dynamics of laminar premixed flames on a circular porous plug burner have revealed periodic modes with different spatial and temporal characteristics. In this paper representative examples of nonperiodic modes will be presented, and it will be argued that these modes fall into two distinct classes. The method of data analysis used to make this identification will be explained and the experimental conditions that are conducive to observing the flame as a dynamical system will be described in detail. Our results suggest that the techniques of nonlinear dynamics are useful in classifying the periodic and chaotic modes of pulsating and cellular premixed flames but are probably not relevant to diffusion flames.

Experimental Observation of Ordered States of Cellular Flames

ABSTRACT Ordered states of cellular flames, consisting of concentric rings of approximately equally sized cells, are observed over a wide range of parameters in our experiments using heavy hydrocarbon-air mixtures on a circular porous plug burner at low pressure. These ordered states have been found with cell numbers ranging from five to thirty. At a critical value of the flow rate, which depends on the equivalence ratio, a transition to a disordered state is observed, in which the ring structure disappears; the cells change their shape, size and number; and they move about in an irregular manner.

Rotating and Modulated Rotating States of Cellular Flames

ABSTRACT Ordered states of cellular flames on circular porous plug burners consist of concentric rings of cells. At certain values of the flow rate and equivalence ratio a transition is made to a state in which entire rings of ceils rotate. The direction of rotation depends only on the initial conditions. Our observations of rotating cellular flames include a single rotating ring, an outer ring rotating about a single inner cell, a rotating inner ring surrounded by a fixed outer ring, and two corotating or counterrotaling concentric rings. A rotating ring of cells can also make a transition to a modulated rotating state in which the shapes of the cells and the speed of rotation periodically change. In another rotating mode, a single central cell takes the shape of a spiral which rotates inside a fixed outer ring of cells. The physical characteristics of these modes are described and comparisons with relevant theoretical studies are made.

Chaotic Dynamics Near The Extinction Limit of a Premixed Flame on a Porous Plug Burner

ABSTRACT Our previous experiments on the dynamics of premixed flames on circular porous plug burners have demonstrated a variety of periodic pulsating flames with different spatial and temporal characteristics. In the radial mode the circular flame front expands and contracts, periodically changing its radial extent. As the system parameters are adjusted near the extinction boundary, a sequence of transitions is observed. First, the radial mode loses its circular symmetry but remains periodic. Next, it undergoes a transition to a chaotic state. Finally, it makes a transition to extinction. All periodic pulsating modes are separated from the extinction boundary by a region of chaotic dynamics. The characteristics of chaotic flame dynamics beyond the extinction limit are discussed. The spatial and temporal characteristics of this chaotic mode are discussed and compared with the relevant theoretical studies.

Hopping Motion in Ordered States of Cellular Flames

ABSTRACT Our previous experiments have shown that cellular flames form ordered states consisting of concentric rings of cells. The numbers of cells in the inner and outer rings change independently in integer steps as the flow rate is increased. In this paper we report the observation of states characterized by a hopping motion in which cells abruptly change their angular position in the ring. This hopping proceeds sequentially to the other cells in the ring. The hopping states are typically observed in isobutane-air cellular flames at parameter values between those corresponding to two consecutive ordered states. The physical characteristics of these states are similar to those of modulated traveling waves found by Bayliss, Matkowsky and Riecke in numerical simulations of the full equations that describe the thermodiffusive instability. The similarities and differences between our experimental results and their theoretical predictions are discussed.

Four Types of Chaotic Dynamics in Cellular Flames

ABSTRACT Markstein, in his seminal study of cellular flames, divided the dynamics of one-dimensional cellular flames into two classes: steady and unsteady. In this paper we report four distinct types of chaotic motion of cellular flames on circular porous plug burners: ordered states in which cells arranged in concentric rings execute small amplitude chaotic oscillations; disordered states in which the ring structure is broken and cells of unequal size and shape move around in an irregular manner; intermittently ordered states in which, for most of the time, there is a highly irregular cellular structure which abruptly evolves into ordered states of concentric rings lasting for varying lengths of time; and pulsating-cellular states in which an ordered state of cellular flames interacts with the radial mode of pulsating flames. These four types of chaotic cellular flames fill the explored parameter space. The spatial and temporal characteristics of each of these modes are described, and these results are c...

Stability Boundaries of Periodic Models of Propagation in Burner-Stabilized Methane-Air Flames

Abstract Our previous experiments on burner-stabilized laminar premixed flames have identified four nonsteady modes of propagation:axial,radial,spiral and nonplanar.In this paper we present stability boundaries for the occurrence of these modes,at a fixed pressure,as a function of total flow rate and equivalence ratio.We also specify the character of one of the four modes,the nonplanar mode,in which the flame front vibrates like a circular drumhead.

ASYMMETRIC CELLS AND ROTATING RINGS IN CELLULAR FLAMES

Theoretical analysis and experimental results are presented to demonstrate the universal characteristics of parity-breaking bifurcations for pattern-forming systems in a circular domain. Ordered patterns of concentric rings of cells which form in a premixed flame on a circular burner at low pressure are used to demonstrate these ideas. Cells belonging to stationary rings are symmetric, while those of rotating rings are not. The important characteristics of the experimental results are reproduced in a theoretical model which can be numerically integrated in polar coordinates. Normal form equations for the Fourier–Bessel coefficients of this model lead to parity breaking.

The characteristics of four ratcheting states in cellular flames

A premixed flat flame on a circular porous plug burner can form patterns of one or two concentric rings of cells in which brighter, hotter regions are separated by darker, cooler cusps and folds. Dynamic states are found at parameter values that are interleaved between those of the ordered states. Rotating states, modulated rotating states, hopping states, and intermittently ordered states have all been observed with motions of approximately 100 degrees/s. These states have been described using the ideas of dynamical systems. Their characteristics have been analyzed using modal decomposition techniques. Ratcheting states are qualitatively and quantitatively different from these other dynamic states. In ratcheting states one or both of the concentric rings rotate very slowly, approximately 0.8 degrees/s, each speeding up and slowing down in a manner unique to that state. Measurements of the angular displacement and computed values of the angular velocity are presented for four ratcheting states. The experimental results are discussed in the context of the physical characteristics of the flame front and in terms of bifurcations of systems with symmetry. Many of the principal features of ratcheting motion are not yet understood.

Dynamics of Premixed Flames

A steady flat flame on a circular burner can become unstable due to a competition between mass diffusivity and thermal diffusivity. The resulting dynamical modes of propagation have both spatial and temporal characteristics. We describe these characteristics for a variety of periodic and chaotic modes of propagation.