Four Types of Chaotic Dynamics
in Cellular Flames
A principal concern of the considerable experimental work since Markstein's study has been the measurement of the size of the cells as a function of the parameters, such as pressure, fuel type, flow rate and equivalence ratio (Mitani and Williams, 1980; Vantelon, Pagni and Dunsky, 1986). Most studies were conducted at atmospheric pressure, and the parameters were chosen to produce large numbers of cells in order to minimize the effects of the boundaries. There is little mention of the dynamics, except to note the high degree of cell motion (Markstein, 1964) and the variation in cell size which necessitates averaging.
The incessant motion of cellular flames was first explained by Sivashinsky (1983) who performed numerical studies of the two-dimensional Kuramoto-Sivashinsky equation. He showed that the temporal evolution of a 5x5 square lattice of cells appeared quite similar to the dynamics observed in cellular flames. He used the term, "chaotic self-motion", to describe this nonperiodic motion which was intrinsic to the flame dynamics.
We have reported new experimental observations (Gorman, el-Hamdi and Robbins, 1993) in which cellular flames on circular porous plug burners form ordered states consisting of concentric rings of cells. In the parameter range in which these ordered states are found, four kinds of chaotic dynamics are observed: 1) ordered states in which ordered rings of cells subtly change their shape and size, but not their average position; 2) disordered states in which the ring structure is broken, and the cells move around in an irregular manner; 3) intermittently ordered states in which concentric rings of cells abruptly appear, mostly for short times, but occasionally for very long times; and 4) pulsating-cellular flames in which the pulsating radial state interacts with an ordered cellular state. Each of these examples of chaotic motion arises from dynamics intrinsic to cellular flames. In this paper we describe, compare and contrast the spatial and temporal characteristics of these four types of dynamics. Some relevant theoretical studies are also discussed.
Our experimental set-up has been described elsewhere (el-Hamdi, Gorman and Robbins, 1993). A 5.62 cm circular, water-cooled stainless steel porous plug burner, designed by Patrick Pagni (Vantelon, Pagni and Dunsky, 1986) and manufactured by McKenna Products of Pittsburg, CA, is placed in a low pressure combustion chamber made from process glass pipe. The flow rate of the premixed gases and the ambient pressure of 1/2 atm. in the chamber are controlled to 0.1% using MKS Instruments controllers. At this pressure a steady flame front is 0.5 mm in thickness and sits 5 mm above the porous plug. Ordered states with cell numbers from eight to thirty are easily stabilized using isobutane-air or propane-air mixtures.
A camera views the flame through a mirror at the top of the chamber. In the printing of the individual frames the regions between the cells appear black because of the limited dynamic range of videotape. These cusps and folds are not regions of extinciton; rather, they correspond to regions of lower optical intensity than the brighter cells.
The motion of the flame front is recorded on videotape. Individual frames are digitized, enhanced and printed to depict the motion. A small region of the flame front is imaged on a photodiode whose output is sent to a real-time spectrum analyzer for direct monitoring of the dynamics or to a microcomputer for later analysis. The power spectra presented in this paper are 16 averages of 4096-point spectra.
In section 2 the spatial and temporal characteristics of representative examples the four types of chaotic states are presented. Their stability boundaries in parameter space are described. In section 3 the theoretical studies relevant to each chaotic state are reviewed. In section 4 the implications of these results are discussed.
