K.N.C. Bray

Flame spread in laminar mixing layers: the triple flame

In the present paper we investigate flame spread in laminar mixing layers both experimentally and numerically. First, a burner has been designed and built such that stationary triple flames can be stabilised in a coflowing stream with well defined linear concentration gradients and well defined uniform flow velocity at the inlet to the combustion chamber. The burner itself as well as first experimental results obtained with it are presented. Second, a theoretical model is formulated for analysis of triple flames in a strained mixing layer generated by directing a fuel stream and an oxidizer stream towards each other. Here attention is focused on the stagnation region where by means of a similarity formulation the three-dimensional flow can be described by only two spatial coordinates. To solve the governing equations for the limiting case in which a thermal-diffusional model results, a numerical solution procedure based on self-adaptive mesh refinement is developed. For the thermal-diffusional model, the structure of the triple flame and its propagation velocity are obtained by solving numerically the governing similarity equations for a wide range of strain rates.

Countergradient Diffusion in Premixed Turbulent Flames

Recent theoretical and experimental results demonstrating the interaction between force fields and density inhomogeneities as they arise in premixed turbulent flames are discussed. In such flames, the density fluctuates between two levels, the high density in reactants rho sub r and the low density in products rho sub p, with the ratio rho sub r/rho sub p on the order of five to ten in flows of applied interest. The force fields in such flames arise from the mean pressure drop across the flame or from the Reynolds shear stresses in tangential flames with constrained streamlines. The consequence of the interaction is nongradient turbulent transport, countergradient in the direction normal to the flame and nongradient in the tangential direction. The theoretical basis for these results, the presently available experimental support therefore and the implications for other variable density turbulent flows are discussed.

Turbulence Production in Premixed Turbulent Flames

Abstract —A second order closure theory developed earlier is used to study the processes influencing the turbulent velocity field in a premixed turbulent flame with degrees of heat release of practical interest. The flow field is chosen so that the time-averaged flame structure is one-dimensional and statistically stationary. Earlier work suggests that in the absence of turbulence production due to Reynolds stresses as is the case in a flame orthogonal to the oncoming reactants, the case we consider, dilatation resulting from heat release reduces the level of turbulence. In contrast it is shown here that with sufficient heat release turbulence increases on passage through the flame because of a buoyancy production mechanism arising from the self-induced, mean pressure gradient. This mechanism overwhelms the effects of dilatation at temperature ratios characteristic of combustion. The same buoyancy mechanism also causes counter-gradient diffusion as predicted in an earlier paper and as observed in recent e...

Flamelet Crossing Frequencies and Mean Reaction Rates in Premixed Turbulent Combustion

Abstract Abstraet–The one-point, one-time description contained in the Bray-Moss-Libby model of premixed turbulent combustion is first generalized to a two-point, two-time formulation which includes information on the time and length scales of the scalar field within turbulent flames. This formulation is then specialized to a one-point, two-time description which is treated in detail so as to yield expressions for the autocorrelation of the progress variable, for the time scale of the scalar field, for the mean crossing frequency of the flamelets and, finally, for the mean rate of chemical reaction. Although the latter expression closely resembles results developed earlier on an intuitive basis, its derivation in the present study permits an assessment of various assumptions and intermediate results by comparison with experimental measurements. Such comparisons as are currently possible are shown to lend support to the analysis and to enhance the prospects of future exploitation of the general formulation.

Modelling of flamelet surface-to-volume ratio in turbulent premixed combustion

A model is proposed, valid in the laminar flamelet regime, for the surface-to-volume ratio of a turbulent premixed flame. The new model is in a form suitable for incorporation into an existing model of turbulent premixed combustion. Exact equations are derived which describe the dynamics of the constant-property surface representing the flame interface. Unknown terms in the exact equations are modelled for the simplified case of constant-density combustion in a specified turbulence field. Numerical solutions of the modelled equations are carried out for a one-dimensional test case. Preliminary results indicate that the model is capable of predicting effects present in turbulent flame propagation, and a parametric study shows that correct trends are observed.

Chemical closure model for fractal flamelets

Abstract A chemical closure model for premixed turbulent flames is proposed and tested by analysis and numerical computation for flames with vanishingly small density change. The model is based on the assumption that reaction zones can be modeled as thin sheets—flamelets—and that the geometry of these sheets can be represented by fractal surfaces. The model expression for mean fuel consumption rate is 〈ω〉=C R ρ〈δY f u L 〉 f (lƒ/η) D−2l F −1 〈C〉(1−〈c〉) with ƒ given by ƒ=[1−(1−A t −1 4 R 1 −3 4 ) exp (−A t 1 4 R 1 −1 4 u′/〈ul〉 f )] and l η =A t 1 4 R 1 3 4 where D is the fractal dimension of the flamelet surface and is the new parameter introduced by the fractal geometry assumption. This model is tested in simplified analyses of normal and oblique flames with good results. The oblique flame analysis provides new insight into the definition of the turbulent burning velocity. Numerical computations are performed with a conditioned second-order closure scheme, and the chemical closure model performance is found to be good. Computed results with a gradient transport model for species diffusion show that turbulent fluxes are significantly under predicted in comparison with the second-order closure results.

Experimental study of premixed turbulent combustion in opposed streams. Part II—Reacting flow field and extinction

Abstract Turbulent combustion in opposed streams of premixed reactants was studied experimentally. In this geometry two flames are stabilized in the vicinity of the free stagnation point and separated by a region of products. In the mean the flames appear flat and perpendicular to the axis of the jets. Both the mean flow field and the distribution of the mean progress variable is found to be symmetric about the stagnation point. Buoyancy forces do not appear to affect the symmetry of the flow. The flows upstream of the flame zones has the same form of velocity field as nonreacting opposed flow, but displaced away from the stagnation point by the volume source due to combustion. Under certain conditions these flames can be forced to extinction, and this limit is studied for lean propane-air mixtures. This extinction depends only on the aerothermochemistry of the flow because there are no surfaces near the flames. For near extinct flames the flow field approaches that of nonreacting opposed streams. A physical mechanism is proposed for the extinction and results are compared with an extinction model. There is good qualitative agreement with the extinction model, and good quantitative agreement for the dependency of unstretched laminar burning velocity and the heat release parameter on extinction.

Spatially resolved flamelet statistics for reaction rate modeling

Abstract Using two-dimensional laser sheet tomography of Bunsen flames, important spatial statistics relating to premixed turbulent combustion modeling are measured for the first time. The integral length scale of flame wrinkling, evaluated along contours of reaction progress variable ( c ), is found to be almost constant for all values of c . Its magnitude is measured to be very close to the integral length scale in the unreacted turbulent flow. The flamelet crossing angle distribution in the plane of visualization is found to vary along a c contour reflecting the nonhomogeneity in the flame, but the overall distributions for different c values are approximately the same. The overall mean cosine value is found to be very close to 0.5. Other parameters of interest, including c contours, flamelet crossing lengths, and crossing frequencies, are also examined.

Experimental and numerical studies of a triple flame

The structure of a laminar triple flame is investigated both experimentally and numerically. The distribution of OH radicals in the flame is mapped using Laser Induced Fluorescence. The structure of the velocity field is mapped using Particle Imaging Velocimetry. To obtain detailed information on both the fields of velocity and scalars, the flame is numerically simulated. In the simulations, gas expansion is taken into account and the full Navier-Stokes equations are solved. Numerical results obtained with global one-step chemistry and, alternatively, with a detailed chemical kinetic mechanism are presented. The experimental findings are compared with the numerical results.

Assessment of the applicability of conditional moment closure to a lifted turbulent flame: first order model

This paper presents the results of a detailed study of Conditional Moment Closure (CMC) applied to a lifted turbulent flame. The objectives are to find out how first order, radially averaged CMC can represent a lifted flame and which mechanism of flame stabilization can be described by this modeling method. As a first stage of this study of CMC applied to ignition/extinction phenomena, turbulence and combustion calculations are decoupled, that is, the effect of turbulence upon combustion is included but the heat released due to combustion is not part of the turbulence calculations. A 10-step chemical mechanism is used to predict rates of reaction in hydrogen-air mixtures. Attention is focused on the lift-off region of the flame which is commonly considered as a cold flow. Comparison with published experimental data shows that the lift-off height is accurately predicted at 14 mm. The Favre averaged radial profiles of temperature and species mole fractions are also compared with the experimental values. The computational results agree well with the experimental points for lean mixtures but the temperatures are overpredicted in rich mixtures close to the centerline. Some of the current flame stabilization mechanisms are discussed in the context of the present results. Simple elliptic first-order CMC is shown to be able to reproduce some of these mechanisms. Modeling accurately the axial transport is a key factor to these simulations.