Spiral flames

AbstractWe describe computations of periodic and meandering spiral patterns in a reaction-diffusion model of flames

Theory of the propagation dynamics of spiral edges of diffusion flames in von Kármán swirling flows

This analysis addresses the propagation of spiral edge flames found in von Kármán swirling flows induced in rotating porous-disk burners. In this configuration, a porous disk is spun at a constant angular velocity in an otherwise quiescent oxidizing atmosphere. Gaseous methane is injected through the disk pores and burns in a flat diffusion flame adjacent to the disk. Among other flame patterns experimentally found, a stable, rotating spiral flame is observed for sufficiently large rotation velocities and small fuel flow rates as a result of partial extinction of the underlying diffusion flame. The tip of the spiral can undergo a steady rotation for sufficiently large rotational velocities or small fuel flow rates, whereas a meandering tip in an epicycloidal trajectory is observed for smaller rotational velocities and larger fuel flow rates. A formulation of this problem is presented in the equidiffusional and thermodiffusive limits within the framework of one-step chemistry with large activation energies. Edge-flame propagation regimes are obtained by scaling analyses of the conservation equations and exemplified by numerical simulations of straight two-dimensional edge flames near a cold porous wall, for which lateral heat losses to the disk and large strains induce extinction of the trailing diffusion flame but are relatively unimportant in the front region, consistent with the existence of the cooling tail found in the experiments. The propagation dynamics of a steadily rotating spiral edge is studied in the large-core limit, for which the characteristic Markstein length is much smaller than the distance from the center at which the spiral tip is anchored. An asymptotic description of the edge tangential structure is obtained, spiral edge shapes are calculated, and an expression is found that relates the spiral rotational velocity to the rest of the parameters. A quasiestatic stability analysis of the edge shows that the edge curvature at extinction in the tip region is responsible for the stable tip anchoring at the core radius. Finally, experimental results are analyzed, and theoretical predictions are tested

Dynamics of Diffusion Flames in von Karman Swirling Flows Studied

Von Karman swirling flow is generated by the viscous pumping action of a solid disk spinning in a quiescent fluid media. When this spinning disk is ignited in an oxidizing environment, a flat diffusion flame is established adjacent to the disk, embedded in the boundary layer (see the preceding illustration). For this geometry, the conservation equations reduce to a system of ordinary differential equations, enabling researchers to carry out detailed theoretical models to study the effects of varying strain on the dynamics of diffusion flames. Experimentally, the spinning disk burner provides an ideal configuration to precisely control the strain rates over a wide range. Our original motivation at the NASA Glenn Research Center to study these flames arose from a need to understand the flammability characteristics of solid fuels in microgravity where slow, subbuoyant flows can exist, producing very small strain rates. In a recent work (ref. 1), we showed that the flammability boundaries are wider and the minimum oxygen index (below which flames cannot be sustained) is lower for the von Karman flow configuration in comparison to a stagnation-point flow. Adding a small forced convection to the swirling flow pushes the flame into regions of higher strain and, thereby, decreases the range of flammable strain rates. Experiments using downward facing, polymethylmethacrylate (PMMA) disks spinning in air revealed that, close to the extinction boundaries, the flat diffusion flame breaks up into rotating spiral flames (refs. 2 and 3). Remarkably, the dynamics of these spiral flame edges exhibit a number of similarities to spirals observed in biological systems, such as the electric pulses in cardiac muscles and the aggregation of slime-mold amoeba. The tail of the spiral rotates rigidly while the tip executes a compound, meandering motion sometimes observed in Belousov-Zhabotinskii reactions

Pattern Formation in Diffusion Flames Embedded in von Karman Swirling Flows

Pattern formation is observed in nature in many so-called excitable systems that can support wave propagation. It is well-known in the field of combustion that premixed flames can exhibit patterns through differential diffusion mechanism between heat and mass. However, in the case of diffusion flames where fuel and oxidizer are separated initially there have been only a few observations of pattern formation. It is generally perceived that since diffusion flames do not possess an inherent propagation speed they are static and do not form patterns. But in diffusion flames close to their extinction local quenching can occur and produce flame edges which can propagate along stoichiometric surfaces. Recently, we reported experimental observations of rotating spiral flame edges during near-limit combustion of a downward-facing polymethylmethacrylate disk spinning in quiescent air. These spiral flames, though short-lived, exhibited many similarities to patterns commonly found in quiescent excitable media including compound tip meandering motion. Flame disks that grow or shrink with time depending on the rotational speed and in-depth heat loss history of the fuel disk have also been reported. One of the limitations of studying flame patterns with solid fuels is that steady-state conditions cannot be achieved in air at normal atmospheric pressure for experimentally reasonable fuel thickness. As a means to reproduce the flame patterns observed earlier with solid fuels, but under steady-state conditions, we have designed and built a rotating, porous-disk burner through which gaseous fuels can be injected and burned as diffusion flames. The rotating porous disk generates a flow of air toward the disk by a viscous pumping action, generating what is called the von K rm n boundary layer which is of constant thickness over the entire burner disk. In this note we present a map of the various dynamic flame patterns observed during the combustion of methane in air as a function of fuel flow rate and the burner rotational speed

Dynamical Behaviors of Small-scale Buoyant Diffusion Flame Oscillators in Externally Swirling Flows

Small-scale flickering buoyant diffusion flames in externally swirling flows were computationally investigated with a particular interest in identifying and characterizing various distinct dynamical behaviors of the flame oscillators under different swirling flow conditions. By varying the external swirl, six distinct flame dynamical modes, such as the flickering flame, the oscillating flame, the steady flame, the lifted flame, the spiral flame, and the flame with a vortex bubble, were computationally identified in both physical and phase spaces and analyzed from the perspective of vortex dynamics. Specifically, the frequency of buoyancy-induced flame flicker nonlinearly increases with the swirling intensity in the weak swirl regime. Further increasing the swirling intensity causes the vortex shedding to occur either around the flame tip or downstream of the flame, and the flame stops flickering but oscillates with small amplitude or stays in a steady state. A sufficiently high swirling intensity locally extinguishes the flame at its base, leading to a lifted flame. In addition, the spiral mode and the vortex-bubble mode were found for the flame at large swirl angles. Through establishing the phase portrait for featuring the flow in flames, the dynamical behaviors are presented and compared in phase space.Comment: 25 pages, 17 figures, research articl

Adaptive Multiresolution Methods for the Simulation ofWaves in Excitable Media

We present fully adaptive multiresolution methods for a class of spatially two-dimensional reaction-diffusion systems which describe excitable media and often give rise to the formation of spiral waves. A novel model ingredient is a strongly degenerate diffusion term that controls the degree of spatial coherence and serves as a mechanism for obtaining sharper wave fronts. The multiresolution method is formulated on the basis of two alternative reference schemes, namely a classical finite volume method, and Barkley's approach (Barkley in Phys. D 49:61-70, 1991), which consists in separating the computation of the nonlinear reaction terms from that of the piecewise linear diffusion. The proposed methods are enhanced with local time stepping to attain local adaptivity both in space and time. The computational efficiency and the numerical precision of our methods are assessed. Results illustrate that the fully adaptive methods provide stable approximations and substantial savings in memory storage and CPU time while preserving the accuracy of the discretizations on the corresponding finest uniform gri

High-Lewis number premixed flame instabilities

Lean premixtures of high-molecular weight practical fuels typically have an associated Lewis number (Le) in excess of one and are susceptible to diffusive-thermal instabilities depending on the heat loss and hydrodynamic strain. These instabilities may lead to incomplete combustion, an increase in undesirable emissions and complex pressure oscillations.While a significant amount of work has focused on low-Lewis number cellular instabilities, the objective of this study was to explore high-Lewis number pulsating and traveling wave instabilities in burner-stabilized premixed gas flames and to improve our understanding of the role of the mixture Le, mixture composition, heat loss and ambient pressure on the onset and dynamics of the flame instabilities. To meet this objective, premixtures of n-C4H10, n-C7H16 and n-C8H18 mixed with O2 diluted by N2 or He were considered at different pressures for which high speed videos of different flame instability modes were acquired. The instability regimes included: (1) stable planar flames, (2) complex spiral or target patterns, (3) spiral waves and (4) axisymmetric target patterns, and they generally occurred in this order as the equivalence ratio was decreased for a fixed burner exit speeds. Stability diagrams were then developed as a function of equivalence ratio and burner exit flow speed for the mixtures considered. The effects of Le, heat loss and ambient pressure on the dynamics of the flame instability including the oscillation frequency in the case of target patterns and rotation rate for the rotating spiral waves. Note that the radial propagation speed of the flamelets ranged from 2 to 5 m/s which is significantly faster than the laminar flame speed for premixed flames.Numerical studies were also conducted using the 2-step Sal’nikov model developed by Scott-Wang-Showalter and Matkowsky with a focus on improving our understanding of the spatio-temporal structure of these unstable flames. The spatio-temporal temperature and species concentration were computed in a two-dimensional domain. The computed results were used to clarify the roles of Le and heat loss on the radial flame speed, the spacing between adjacent waves and the rotation frequency associated with the spiral waves. The numerical computations agreed favorably with the experimental observations.Ph.D., Mechanical Engineering -- Drexel University, 200