In honor of the fiftieth anniversary of the Combustion Institute, we are asked to assess accomplishments of theory in combustion over the past fifty years and prospects for the future. The title of our article is chosen to emphasize that development of theory necessarily goes hand-in-hand with specification of a model. Good conceptual models underlie successful mathematical theories. Models and theories are discussed here for deflagrations, detonations, diffusion flames, ignition, propellant combustion, and turbulent combustion. In many of these areas, the genesis of mathematical theories occurred during the past fifty years, and in all of them significant advances are anticipated in the future. Increasing interaction between theory and computation will aid this progress. We hope that, although certainly not complete in topical coverage or reference citation, the presentation may suggest useful directions for future research in combustion theory.

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Combustion theory and modeling

A tribrachial (or triple) flame is one kind of edge flame that can be encountered in nonpremixed mixing layers, consisting of a lean and a rich premixed flame wing together with a trailing diffusion flame all extending from a single point. The flame could play an important role on the characteristics of various flame behaviors including lifted flames in jets, flame propagation in two-dimensional mixing layers, and autoignition fronts. The structure of tribrachial flame suggests that the edge is located along the stoichiometric contour in a mixing layer due to the coexistence of all three different types of flames. Since the edge has a premixed nature, it has unique propagation characteristics. In this review, the propagation speed of tribrachial flames will be discussed for flames propagating in mixing layers, including the effects of concentration gradient, velocity gradient, and burnt gas expansion. Based on the tribrachial edge structure observed experimentally in laminar lifted flames in jets, the flame stabilization characteristics including liftoff height, reattachment, and blowout behaviors and their buoyancy-induced instability will be explained. Various effects on liftoff heights in both free and coflow jets including jet velocity, the Schmidt number of fuel, nozzle diameter, partial premixing of air to fuel, and inert dilution to fuel are discussed. Implications of edge flames in the modeling of turbulent nonpremixed flames and the stabilization of turbulent lifted flames in jets are covered.

Stabilization, propagation and instability of tribrachial triple flames

A three-dimensional direct numerical simulation (DNS) study of a spatially evolving planar turbulent reacting jet is reported. Combustion of methane with air is modelled using a four-step reduced mechanism in the non-premixed regime. A total of eight chemical species are integrated in time along with the fluid mechanical fields. The solution of the compressible Navier–Stokes equations is obtained numerically for moderately low Mach number. A large computational grid, with 100 million grid points, is required in order to resolve the flame. The cold flow Reynolds number is 3000. The focus of the study is to investigate the dynamics of extinction fronts in three-dimensional turbulent flows. A novel data reduction and identification algorithm was developed to postprocess the large DNS database and extract the shape of the evolving flame surface including its edges and their propagation velocity. The joint probability density function (p.d.f.) of edge velocity and scalar dissipation was obtained and the results indicate that the three-dimensional flame edges propagate with a velocity that is largely controlled by the local rate of scalar dissipation, or equivalently in terms of the local Damkohler number at the flame edge, as predicted by theory. Naturally, the effects of unsteadiness in this flow produce a broad joint p.d.f. The statistics collected also suggest that the mean value of the hydrogen radical reaction rate are very small in the turbulent regions of the flow owing to the functional form of the hydrogen radical reaction rate itself. The consequence of these results in the context of turbulent combustion modelling is discussed. Additional statistical and morphological information of the flame is provided.

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Direct simulation of non-premixed flame extinction in a methane–air jet with reduced chemistry

The advanced CT (computerized tomography) reconstruction technique for measuring an instantaneous three-dimensional distribution of chemiluminescence of a turbulent premixed flame is accomplished. In the technique, first, instantaneous two-dimensional images (‘projection’ images) of an objective flame are simultaneously taken from forty horizontal directions with a forty-lens camera. Next four hundred horizontal CT images, which are reconstructed from the ‘projection’ images by MLEM (maximum likelihood expectation maximization) algorithm, are vertically accumulated, resulting in an instantaneous three-dimensional distribution of flame-chemiluminescence. Results for a propane-air fuel-rich-premixed turbulent flame are as follows. The flame front is observed to be a thin wrinkled luminous region of 0.6mm in thickness. The three-dimensional result clearly shows that the cusps observed in horizontal cross-sections correspond to ridges of the three-dimensional flame front. The luminosity is quenched at the ridges by Lewis number effect. Finally, various types of display of three-dimensional distribution are performed to demonstrate the three-dimensionality of data acquisition.

https://www.jstage.jst.go.jp/article/jsmeb/48/1/48_1_34/_pdf

Three-Dimensional Computerized Tomographic Reconstruction of Instantaneous Distribution of Chemiluminescence of a Turbulent Premixed Flame

Spark ignition of turbulent counterflow non-premixed flames has been examined in terms of the ignition probability Pign and evolving flame structure. It was found that in the case of successful ignition, the flame spread as an edge flame with a large scatter in its radial position between individual realizations at the same time from the spark. Pign decreased with bulk velocity, which suggests that the local strain rate can be detrimental to ignition so that, even with the strongest spark tested, ignition could not be achieved at a bulk velocity about 90% of the extinction velocity. Pign was greater than zero even in regions well into the fuel and air streams where the mixture fraction fluctuations were virtually zero, giving zero probability of finding flammable mixture at the spark location. This observation was attributed to non-local effects, for example the convection of the spark heat to the flammable region. The data can assist the validation of advanced combustion models.

Measurements of ignition probability in turbulent non-premixed counterflow flames

Edge flames were investigated in a methane/O 2 /N 2 counterflow diffusion flame burner. In a typical experiment, a stable counterflow diffusion flame in an axysymmetric configuration was perturbed by lowering the relevant Damkohler number slightly below the extinction value, Da ext . As a result, the flame extinguished in the vicinity of the burner axis where conditions were uniform. An edge flame extinction front quickly propagated in the radial direction, turned into an ignition edge flame, and eventually stabilized as a standing triple flame at a radial position larger than the burner radius. This sequence of events resulted from an increase of Da as a function of the radial direction, consequent to a decrease in the strain rate in the radial direction. The edge flame propagation velocity in the ignition mode was measured for propagating edge flames at moderate Da and for standing triple flames at large Da , using a combination of laser Doppler velocimetry of seeded particles, formaldehyde planar laser-induced fluorescence, and natural chemiluminescence imaging. The propagation velocity, nondimensionalized with the premixed laminar flame speed of the unburned stoichiometric mixture, was correlated with Da . The latter was calculated using a thermal diffusive model and velocity measurements. The nondimensional velocity reached a value of 2.6 at large Da , in good agreement with the estimated square root of the ratio of the unburned gas density to the burned gas density, as suggested by scaling considerations.

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Propagation of edge flames in counterflow mixing layers: experiments and theory

Using a combination of HCHO planar laser-induced fluorescence and laser Doppler velocimetry measurements, the extinction behavior of methanol counterflow diffusion flames was examined experimentally under conditions in which the extinction was brought about by a vortex generated on the oxidizer side. Comparisons were made with quasi-steady extinction results for the same flames. It was found that the flames can withstand instantaneous strain rates as much as two-and-a-half times larger than the quasisteady ones. The finding was rationalized phenomenologically by comparing the characteristic times of the problem, that is, the mechanical time, the chemical time, and the vortex turnover time. Specifically, estimates of these times yielded the following ordering: sch svort sm. As a result, the vortex introduced an unsteady effect in the outer diffusive-convective layer of the flame, while the inner reactive-diffusive layer behaved in a quasi-steady manner. Consequently, the flame was subject to a damped strain rate through the outer layer. Results from a simple analytical model showed that the difference between vortexinduced extinction and quasi-steady extinction was much more modest in terms of instantaneous scalar

/pdf/vortex-induced-extinction-behavior-in-methanol-gaseous-1n89ftm65t.pdf

Amable Liñán

Papers

Propagation of edge flames in counterflow mixing layers: experiments and theory

Vortex-induced extinction behavior in methanol gaseous flames: A comparison with quasi-steady extinction

Unsteady Extinction Behavior of Counterflow Diffusion Flames: Experiments and Modeling