R.W. Bilger

Conditional moment closure for turbulent combustion

This paper reviews the fundamentals of conditional moment closure (CMC) methods for the prediction of turbulent reacting flows, with particular emphasis on combustion. It also surveys several of the applications that have been made. CMC methods predict the conditional averages and higher moments of quantities such as species mass fractions and enthalpy, conditional on the mixture fraction or reaction progress variable having a particular value. A brief introduction is given to generalized functions and probability density function (pdf) methods. This is followed by an exposition on the various methods of derivation for the CMC equation and the general characteristics of this equation and its boundary conditions. Simplifications that can be made in slender layer flows such as jets and plumes are outlined and examples of application of the technique to such flows are given. The method allows the definition of a new class of simplified reactors related to the well known perfectly stirred reactor and plug flow reactor: these are outlined. CMC predictions are compared to experiment and direct numerical simulations for flows with homogeneous turbulence. Derivation and modeling of the equations for conditional variances and covariances are outlined and their use in second-order CMC illustrated. Brief review is made of progress on application of the method to problems involving differential diffusion, multiple conditioning, sprays and premixed combustion.

Conditional moment closure for turbulent reacting flow

Equations governing the variation through the flow field of averages of quantities such as species mass fractions, conditional on mixture fraction, are derived and modeled. The conditioning variable adds to the independent dimensions of the problem, but it is found that this is offset in some cases by reduction in the spatial dimensionality needed. Predictions are made for the reacting scalar mixing layer, and these show good agreement with experiment. The methodology effectively decouples the kinetics from the large inhomogeneity or macromixing aspects of the flow while preserving the input from the scalar dissipation or micromixing. Arbitrarily complex kinetics may be used within reasonable computational cost.

The structure of turbulent nonpremixed flames

Flamelet theories are examined in the context of turbulent nonpremixed combustion. The criterion requiring that the reaction zone be thinner than the Kolmogoroff length scale is converted to one in which the range of mixture fraction over which reaction occurs is compared with the scalar scale for the small scale fluctuations. It is found that the criterion is violated in many of the flames of interest, particularly away from the nozzle in jet flames and in recirculating flows. Laser imaging data for scalar mixing is used to illustrate the structure of quasi-equilibrium distributed reaction (QEDR) flames at high Damkohler number. The structure is found to tend toward that of the scalar dissipation. The apparent success of flamelet theories in predicting mean concentrations of CO in hydrocarbon flames is ascribed to the metastable equilibrium of rich mixtures arising from chain terminating reactions of radicals with the fuel. Differences in flame structure for piloted jet diffusion flames near extinction of methane and CO/H 2 /N 2 fuels are discussed in terms of these fluid dynamic and kinetic insights.

The Structure of Diffusion Flames

Abstract The theory for the mixing and chemical reaction of two streams of fluid is developed for unsteady laminar and for turbulent flow. Only one conserved scalar is required to fully describe the mixing and various reaction models are considered including the Burke-Schumann flame sheet and shifting equilibrium. A new expression is derived for the instantaneous reaction rate of any species Wi = –pD(▿ξ)2Yi/dξ2 where ξ is a conserved scalar. New insight is obtained into the structure of the instantaneous reaction zone for both laminar and turbulent flames. Diagnostic parameters are presented for determining when various models are applicable and for what properties.

Reaction rates in diffusion flames

Abstract A transformation of the species conservation equations is used to analyse experimental data on laminar diffusion flames to obtain chemical reaction rates. The method uses only composition and temperature measurements, the velocity field not being required. The method relies on the molecular species concentration being insensitive to variables other than the mixture fraction or other measures of stoichiometry. Analysis of data in a diffusion flame formed from fuel flowing from a porous cylinder indicates that this is the case, an empirical finding of some importance in itself. Reaction rates determined in this way are found to be in close agreement with those determined from the full species conservation equation. The rate constants, computed by using global mechanisms developed for well-stirred and plug flow reactors, indicate that these mechanisms are probably not appropriate for diffusion flames.

The spontaneous raman scattering technique applied to nonpremixed flames of methane

Abstract Simultaneous space- and time-resolved measurements of the concentrations of CH 4 , O 2 , N 2 , H 2 O, H 2 , CO, and CO 2 have been made using spontaneous Raman scattering, in the blue regions of CH 4 turbulent nonpremixed flames. The temperature is measured from the Rayleigh scattered signal. A “fluorescence” interference, which is broadband and contaminates in varying degrees the Rayleigh and all the Raman lines, is believed to be due to a number of molecules or flame radicals, including C 2 and CN or even incandescence of small particle nuclei. The “fluorescence” has been monitored at a bandhead of C 2 (516.5 nm) and its effect reduced by placing a Polaroid filter at the entrance slit of the spectrometer. The remaining “fluorescence” has been corrected for, using correction curves generated from measurements made in a laminar counterflow CH 4 diffusion flame and a diluted CH 4 N 2 = 1 2 (by vol.) laminar diffusion flame. Measurements of CO and CO 2 are not reliable in the rich regions of the flame where the “fluorescence” is intense. With minor modifications to the optical system, CO and CO 2 could also be measured with acceptable accuracy in regions of intense “fluorescence” and the “fluorescence” correction further refined. This work is considered to be an important extension of the applications of spontaneous Raman scattering as a measurement technique in flames.

Experimental investigation of three-dimensional flame-front structure in premixed turbulent combustion—I: hydrocarbon/air bunsen flames

Comprehensive laser measurements of three-dimensional flame-front structures for turbulent lean hydrogen/air premixed Bunsen flames are reported in this continuation paper. The local scalar front appears lamella-like for both the reaction progress variable and the OH mole fraction. This lamella-like feature cannot be predicted by the commonly accepted combustion-regime diagrams. The flame residence time relevant to the turbulent flames investigated here may be much smaller than the unstretched laminar value used for constructing these regime diagrams. Superadiabaticy and flame-front bulges convex toward the reactants are clearly observed, representing effects of the less-than-unity Lewis number of the mixture. The average size of flame bulges is found to increase with the turbulence integral length scale. Moderate positive correlations exist between the in-plane two-dimensional curvature and the three-dimensional progress-variable gradient. OH mole fraction is also correlated with the progress-variable gradient. Local flame orientation in three-dimensional space is close to an isotropic distribution, which is attributed to flame-surface wrinkling being strongly nonpassive. More backward-facing flame fronts are formed nearer the unburnt than the burnt side of the turbulent flame brush, suggesting the importance of large-scale flame-front bulges in turbulent flame propagation. Higher progress-variable dissipation rates are measured than for the unstretched laminar flame. By comparison with previously published data for turbulent hydrocarbon/air premixed flames, the present dissipation-rate measurements suggest that chemical reactions do not play an important role in the destruction or generation of progress-variable fluctuations. Discrepancies are observed even in the qualitative trends of some statistics of the progress-variable dissipation rate when compared with DNS data modeled with detailed chemistry.

Future progress in turbulent combustion research

Abstract Turbulent combustion research is projected to be an important area of research well into the twenty-first century. Issues of current interest in turbulent flame structure and computational prediction are outlined and forecasts are made for approaches that are likely to lead to significant advances. There is a mounting body of evidence that concepts and models derived from the laminar flamelet hypothesis are not valid over many of the conditions of practical interest for both premixed and non-premixed systems. Approaches such as Conditional Moment Closure and Monte–Carlo simulation of the transport equation for the probability density function are considered to have the most promise for pollutant prediction in non-premixed systems. Large Eddy Simulation may be necessary for non-stationary premixed problems and for bluff-body and swirling flows.

Modeling soot formation in turbulent methane–air jet diffusion flames

Abstract The modeling of soot formation and oxidation by the conditional moment closure (CMC) method is considered. It is particularly focused on the influence of differential diffusion of the soot particles on soot predictions. Most importantly, no changes are made to the soot models that were derived from laminar flame experiments and calculations. Good to excellent predictions are achieved in lightly sooting turbulent methane–air jet diffusion flames at atmospheric and elevated pressure when differential diffusion is taken into account. Unity Lewis number assumptions yield underpredictions of soot volume fractions by about 40%. Soot oxidation by OH and O2 can be treated accurately and both oxidation mechanisms are found to be important for soot burnout in downstream regions.

An experimental investigation of an axisymmetric jet in a co-flowing air stream

An experimental investigation of the flow development of an axisymmetric jet exhausting into a moving air stream is made for two values of the ratio of jet velocity to external air velocity. The u -component turbulence intensity and Reynolds shear stress measurements together with the dissipation length scales inferred from measured u -component spectra suggest that the turbulence similarity assumptions are incorrect for the present flow situation. A discussion of the turbulence structure of the flow indicates that self-preservation does not apply for this situation and that the flow far downstream depends strongly on the complete past history.