Diffusion flame

Abstract: The laminar flamelet concept views a turbulent diffusion flame as an ensemble of laminar diffusion flamelets. Work relevant to the flamelet concept is spread over various fields in the literature: laminar flame studies, asymptotic analysis, theory of turbulence and percolation theory. This review tries to gather and integrate this material in order to derive a self-consistent formulation. Under the assumption of equal diffusivities a coordinate-free formulation of the flamelet structure is given. This assumption is relaxed and flow dependent effects are considered. It is shown that the steady laminar counterflow diffusion flame exhibits a very similar scalar structure as unsteady distorted mixing layers in a turbulent flow field. Therefore the counterflow geometry is proposed to be the most representative steady flow field to study chemistry models and molecular transport effects in laminar flamelets. The conserved scalar model is interpreted as the most basic flamelet structure. Non-equilibrium calculations are reviewed. The coupling between non-equilibrium chemistry and turbulence is achieved by the statistical description of two parameters: the mixture fraction and the instantaneous scalar dissipation rate. The hypothesis of statistical independence of these two parameters is discussed. Calculation methods for the marginal distributions are reviewed. It is shown how local quenching of diffusion flamelets leads to a reduction of burnable flamelets. However, there are burnable flamelets in a turbulent flame which are not reached by an ignition source. This phenomenon is described by percolation theory. Complementary approaches related to local quenching effects and connectedness are combined to derive criteria for the stabilization of lifted flames and to blow out. Further applications of the flamelet concept are reviewed and work to be done is discussed.

Abstract: The laminar flamelet concept covers a regime in turbulent combustion where chemistry (as compared to transport processes) is fast such that it occurs in asymptotically thin layers—called flamelets—embedded within the turbulent flow field. This situation occurs in most practical combustion systems including reciprocating engines and gas turbine combustors. The inner structure of the flamelets is one-dimensional and time dependent. This is shown by an asymptotic expansion for the Damkohler number of the rate determining reaction which is assumed to be large. Other non-dimensional chemical parameters such as the nondimensional activation energy or Zeldovich number may also be large and may be related to the Damkohler number by a distinguished asymptoiic limit. Examples of the flamelet structure are presented using onestep model kinetics or a reduced four-step quasi-global mechanism for methane flames. For non-premixed combustion a formal coordinate transformation using the mixture fraction Z as independent variable leads to a universal description. The instantaneous scalar dissipation rate χ of the conserved scalar Z is identified to represent the diffusion time scale that is compared with the chemical time scale in the definition of the Damkohler number. Flame stretch increases the scalar dissipation rate in a turbulent flow field. If it exceeds a critical value χ q the diffusion flamelet will extinguish. Considering the probability density distribution of χ , it is shown how local extinction reduces the number of burnable flamelets and thereby the mean reaction rate. Furthermore, local extinction events may interrupt the connection to burnable flamelets which are not yet reached by an ignition source and will therefore not be ignited. This phenomenon, described by percolation theory, is used to derive criteria for the stability of lifted flames. It is shown how values of ∋ q obtained from laminar experiments scale with turbulent residence times to describe lift-off of turbulent jet diffusion flames. For non-premixed combustion it is concluded that the outer mixing field—by imposing the scalar dissipation rate—dominates the flamelet behaviour because the flamelet is attached to the surface of stoichiometric mixture. The flamelet response may be two-fold: burning or non-burning quasi-stationary states. This is the reason why classical turbulence models readily can be used in the flamelet regime of non-premixed combustion. The extent to which burnable yet non-burning flamelets and unsteady transition events contribute to the overall statistics in turbulent non-premixed flames needs still to be explored further. For premixed combustion the interaction between flamelets and the outer flow is much stronger because the flame front can propagate normal to itself. The chemical time scale and the thermal diffusivity determine the flame thickness and the flame velocity. The flamelet concept is valid if the flame thickness is smaller than the smallest length scale in the turbulent flow, the Kolmogorov scale. Also, if the turbulence intensity v′ is larger than the laminar flame velocity, there is a local interaction between the flame front and the turbulent flow which corrugates the front. A new length scale L G =v F 3 /∈ , the Gibson scale, is introduced which describes the smaller size of the burnt gas pockets of the front. Here v F is the laminar flame velocity and ∈ the dissipation of turbulent kinetic energy in the oncoming flow. Eddies smaller than L G cannot corrugate the flame front due to their smaller circumferential velocity while larger eddies up to the macro length scale will only convect the front within the flow field. Flame stretch effects are the most efficient at the smallest scale L G . If stretch combined with differential diffusion of temperature and the deficient reactant, represented by a Lewis number different from unity, is imposed on the flamelet, its inner structure will respond leading to a change in flame velocity and in some cases to extinction. Transient effects of this response are much more important than for diffusion flamelets. A new mechanism of premixed flamelet extinction, based on the diffusion of radicals out of the reaction zone, is described by Rogg. Recent progress in the Bray-Moss-Libby formulation and the pdf-transport equation approach by Pope are presented. Finally, different approaches to predict the turbulent flame velocity including an argument based on the fractal dimension of the flame front are discussed.

Abstract: Numerical simulation of flames is a growing field bringing important improvements to our understanding of combustion. The main issues and related closures of turbulent combustion modeling are reviewed. Combustion problems involve strong coupling between chemistry, transport and fluid dynamics. The basic properties of laminar flames are first presented along with the major tools developed for modeling turbulent combustion. The links between the available closures are illuminated from a generic description of modeling tools. Then, examples of numerical models for mean burning rates are discussed for premixed turbulent combustion. The use of direct numerical simulation (DNS) as a research instrument is illustrated for turbulent transport occurring in premixed combustion, gradient and counter-gradient modeling of turbulent fluxes is addressed. Finally, a review of the models for non-premixed turbulent flames is given.

Abstract: Global reaction schemes for the combustion of alkane hydrocarbons up to butane in mixtures with air in premixed and diffusion flames have been derived using analysis of flame structures. The schemes include two competing fuel breakdown reactions, and equilibrium assumptions have been used to derive initial estimates of the forms of the rate expressions. The deduced four-step reaction mechanism is C n H 2n+2 + n 2 O 2 ⤳n CO +(n+1) H 2 C n H 2n +n H 2 O⤳n CO +(2n+1) H 2 H 2 + 1 2 ⇌ H 2 O CO + H 2 O ⇌ CO 2 + H 2 The final kinetic parameters for the resulting rate equations have been determined by comparisons with experimental data for premixed methane and propane flames, along with diffusion flame data for a methane-air flame. The resulting schemes have been found to combine mathematic tractability with good agreement for a range of flame parameters such as flame speed, flame thickness, and species profiles.

Abstract: A four-step mechanism for the combustion of methane in air in nonpremixed flames is obtained by making steady-state and partial equilibrium approximations for minor species. The model gives good predictions of laminar flame structure, including steady-state minor species, for a wide range of flame stretch and across the whole breadth of the reaction zone, including rich mixtures. A good prediction of extinction is obtained. Further reduction to a three-step or two-step mechanism is discussed.