Thermo-diffusive Instabilities Research Articles

Instabilities and flame speeds in large-scale premixed gaseous explosions

The instability of spherical flames in quiescent premixtures is considered using the linear theory developed by Bechtold and Matalon, which includes hydrodynamic and thermodiffusive instabilities. Ranges of unstable wavenumbers are presented for different Markstein numbers as the flame propagates, characterized by the flame Peclet number. Hydrodynamic instabilities arise at the larger wavelengths and cascade down through a range of ever–decreasing wavelengths to be stabilized at the smallest wavelength by thermodiffusive effects. It would appear that, in practice, the associated cell formation lags somewhat behind what is predicted by the theory and an attempt is made to allow for this. With it, a fractal analysis is employed with the two limiting unstable wavelengths as inner and outer cut–offs. The ever–increasing surface wrinkling as the flame propagates creates a larger surface area and consequent flame acceleration. The analysis yields an expression for the flame speed after a critical Peclet number has been attained. The flame speed increases as the square root of elapsed time and the analytical expression is in agreement with the results of measurements of large explosions. The fractal analysis is probably valid because of the large length–scales and small flame stretch rates, unlike those in many turbulent flames in engineering applications, where the flame stretch rate usually reduces the burning rate. The mechanisms for the creation of turbulence are discussed, including a brief speculation of the repercussions for deflagration to detonation transitions in large–scale explosions, including supernovae.

5538594 Method for producing a blade coated paper from recycled, high lignin content, waste paper: Hank Mark A; Mulcahy Leo T; Peterson Ralph S; Streisel Robert C, Covington, VA, United States assigned to Westvaco Corporation

This study addresses the effects of preferential diffusion on flame structure and propagation of high hydrogen content (HHC) turbulent lean premixed hydrogen-carbon monoxide syngas flames at elevated pressures. The direct numerical simulations with detailed chemistry were performed in three-dimensional domain for expanding spherical flame configuration in a constant pressure combustion chamber. To identify the role of preferential diffusion on flame structure and propagation under low and high turbulence levels at elevated pressure, simulations were performed at an initial turbulent Reynolds number of 15 and 150 at a pressure value of 4 bar. The results demonstrate that the thermo-diffusive instability greatly influences the lean premixed syngas cellular flame structure due to strong preferential diffusion effects under low turbulence level at elevated pressure. In contrast, the results reveal that the thermo-diffusive effects are destabilising and preferential diffusion is overwhelmed by turbulent mixing under high turbulence level at elevated pressure. This finding suggests that the development of cellular flame structure is dominated by turbulence with little or no contribution from the thermo-diffusive instability for the lean premixed syngas flame which operates under conditions of high turbulence and elevated pressures. However, results demonstrate that the flame acceleration and species diffusive flux are still influenced by the preferential diffusion for the lean premixed syngas flame which operates under conditions of high turbulence and elevated pressures.

A new time-dependent, three-dimensional flame model for laminar flames

The development of a detailed, time-dependent, three-dimensional flame model (FLAME3D) for premixed laminar flames is reported in this paper. The model has been developed directly for and runs efficiently on several MIMD parallel computers. FLAME3D was used to study zero gravity, upward-and downward-propagating flames in a 9.5% hydrogen-air mixture. Multidimensional cellular flame structures are observed in zero gravity. This cellular flame grows and splits into multiple cells. The growth of the cellular structure is faster in the case of an upward-propagating flame. For the downward-propagating flame, the thermo-diffusive instability mechanism and the Rayleigh-Taylor mechanism oppose each other, resulting in a planar flame. The zero gravity cellular structures in a two-dimensional calculation grow slowly and do not undergo cell splitting, unlike in the three-dimensional simulation. This result indicates the need for studying complex flame phenomena using three-dimensional models such as the one discussed here.

Structures of multiple combustion waves formed under filtration of lean hydrogen-air mixtures in a packed bed

Combustion of lean hydrogen-air mixtures under filtration in an inert porous medium is studied experimentally. With the low hydrogen concentration (3–6%), superadiabatic wave propagation as a localized, stable temperature zone is observed with the combustion temperature reaching 800°C, which is much in excess of the adiabatic reaction temperature (300–500°C). The superadiabatic temperature rise due to effective heat regeneration in the system of “porous body-filtrating gas”, results in complete combustion of even very lean reacting mixtures. It is found that with increasing hydrogen concentration, the localized waves become thermodiffusionally unstable, forming multidimensional cellular structures. Depending on experimental parameters, mainly the hydrogen concentration, two types of cellular structures are observed: three-dimensional spatial and planar. The cellular structures are characterized by partial combustion of hydrogen. This results in the formation of double wave structures, with the cellular structure followed by a stable or decaying superadiabatic wave. The formation of cellular structures is interpreted based on thermodiffusive instability of pore-level-driven combustion. A computational model incorporating detailed hydrogen-oxygen chemistry is used to analyze kinetic profiles over experimental temperature distributions.

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.

Effect of gravity on the stability and structure of lean hydrogen-air flames

Detailed, time-dependent, two-dimensional numerical simulations with full hydrogen-oxygen chemistry are used to investigate the effects of gravity on the stability and structure of laminar flames in lean, premixed hydrogen-air mixtures. The calculations show that the effects of gravity becomes more important as the lean flammability limit is approached. In a 12% hydrogen-air mixture, gravity plays only a secondary role in determining the multidimensional structure of the flame with the stability and structure of the flame controlled primarily by the thermo-diffusive instability mechanism. However, in leaner hydrogen-air mixtures gravity becomes more important. Upward-propagating flames are highly curved and evolve into a bubble rising upwards in the tube. Downward-propagating flames are flat or even oscillate between structures with concave and convex curvatures. The zero-gravity flame shows only cellular structures. Cellular structures which are present in zero gravity can be suppressed by the effect of buoyancy for mixtures leaner than 11% hydrogen. These observations are explained on the basis of an interaction between the processes leading to buoyancy-induced Rayleigh-Taylor instability and the thermo-diffusive instability.

Chemical Kinetic and Thermal Aspects of Cellular Premixed Flames

Abstract The behavior of stationary and rotating polyhedral Bunsen flames of butane/air under systematic thermal and chemical modification of the reactive mixture is experimentally investigated. As the concentrations of additives CF3Br, N2 and O2 are gradually increased in the combustible mixture, the variation of the temperature in the trough and crest regions of the polyhedral flames is examined. It is found that addition of 0.36 (5.0) molar percentage of CF2 Br (N2) completely removes the cellular structure of the polyhedral flame. Also, in butane/air mixtures at different velocity, the critical temperatures corresponding to the onset of cell formation are found to be nearly identical. The results suggest that in conjunction to the hydrodynamics and thermodiffusive flame instability mechanisms, chemical-kinetic effects also play some role in the formation, amplification or sustenance of cellular flame structures. The observations are consistent with the recent flame stability theories which are based o...

A finite element adaptive investigation of curved stable and unstable flame front

We use an adaptive finite element approximation and a semi-implicit temporal integration to produce a numerical scheme intented to handle the difficulties of stiff combustion problems. The numerical analysis of this scheme allows us to adequately choose the numerical parameters involved in the calculations. Some results showing the thermo-diffusive flame front instabilities are presented.

The effect of multicomponent diffusion on the stability of laminar flames

The problem of the stability of the combustion of a three-component gas mixture (fuel, oxidiser and reaction products) is formulated and studied, taking into account the exact mutual diffusion between the components. Boundaries of two regions of thermodiffusive instability TDI-1 and TDI-2 for two mixtures with widely different diffusion properties are constructed, and a comparison is made with the binary theory. The effect of the initial composition of the mixture (a weak, stoichiometric or rich mixture) on the position of the boundaries of the monotonic and oscillatory instability is studied. The problem of the thermodiffusive instability TDI of a laminar flame in case of a substantial deficiency of fuel was studied in /1–8/. The mechanism of the onset of TDI proposed in /1/ for a Lewis number L > 1 ( L = D x ; D, x are the effective diffusion coefficient and thermal conductivity) connected with the distortion of the flame front was confirmed quantitatively in /2–5/. The perturbations increase monotonically in this case (region TDI-2, the terminology is that of /3, 4/). Another mechanism responsible for the appearance of TDI was suggested in /6/, and studied within the frame-work of the formulation of the problem in /2/, analytically and numerically in /7/. This instability is oscillatory and is realized when L < 1 (TDI-1). In /8/, where the assumption used in /2–5, 7/ of the quasistationary character of the velocity of perturbed flame front is not used, satisfactory matching of the boundaries of the zones TDI-1 and TDI-2 with those obtained in /3–5, 7/ was achieved (the difference does not exceed 8%).

Numerical Simulation of Turbulent Flame Structure with Non-unity Lewis Number

Abstract A numerical simulation of the response of a premixed flame to various randomly defined two-dimensional flow fields is performed in order to obtain an insight into Lewis number effects in turbulent premixed combustion. A one-step reaction with a large, but finite, activation energy in the limit of zero heat release is assumed.The numerical simulation uses vortex dynamics to describe the velocity field, while the scalar field is computed on a mesh.The flow field integral length scale is typically ten times the flame thickness, and the r.m.s. velocity fluctuation is of the order of the flame velocity. Ensemble averages are taken over a total number of 30 realization for Le of 1/2 and 37 realizations for Le of 2, where the Lewis number is Le = λ/(ρcpD). Since the density is kept constant, there is no feedback from the reacting scalar field to the velocity field. For the Le of 1/2 case, there is a clear manifestation of the thermo-diffusive instability mechanism leading to a cellular flame front structure, while for Le of 2, the thermo-diffusive effect reduces the hydrodynamic disturbances of the front.The scalar variable that best characterizes the flame dynamics is the excess enthalpy, which we define with respect to an undisturbed planar flame. The numerical results are analyzed statistically. The probability density functions of the progress variable and the excess enthalpy are interpreted on the basis of the observed flame response. The dissipation terms and the reaction rate in the onedimensional balance equations for the mean scalars and their variances are also given. Flame stretch enhances differential diffusion as shown by a significant correlation between strain-rate and excess enthalpy.

Some mathematical aspects of flame chaos and flame multiplicity

In these review lectures, we survey recent mathematical results on the low, finite-dimensional behavior of the Kuramoto-Sivashinsky equations; the latter model thermo-diffusive flame front instabilities. We outline how these PDE's are rigorously equivalent to a finite dynamical system (ongoing joint work with C. Foias, G. Sell, R. Temam). We also present an introduction to multiplicity phenomena in flames caused by chemical kinetics (the latter is an ongoing joint work with P. Clavin and P.C. Fife).

On the Construction and Comparison of Difference Schemes

On the Construction and Comparison of Difference Schemes