A unified statistical model of the premixed turbulent flame
TL;DR: In this article, a unified statistical analysis of premixed turbulent flame supported by a single-step global reaction is presented, where a set of time-averaged balance equations derived from the exact equations of reacting turbulent flow under a thin shear layer, fast chemistry approximation are employed.
About: This article is published in Acta Astronautica.The article was published on 1977-03-01. It has received 417 citations till now. The article focuses on the topics: Turbulence kinetic energy & Probability density function.
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01 Jan 1977
TL;DR: In this paper, a model for the rate of combustion which takes into account the intermittent appearance of reacting species in turbulent flames is presented, which is applicable to premixed as well as diffusion flames.
Abstract: Principles of mathematical models as tools in engineering and science are discussed in relation to turbulent combustion modeling. A model is presented for the rate of combustion which takes into account the intermittent appearance of reacting species in turbulent flames. This model relates the rate of combustion to the rate of dissipation of eddies and expresses the rate of reaction by the mean concentration of a reacting specie, the turbulent kinetic energy and the rate of dissipation of this energy. The essential features of this model are that it does not call for predictions of fluctuations of reacting species and that it is applicable to premixed as well as diffusion flames. The combustion model is tested on both premixed and diffusion flames with good results. Special attention is given to soot formation and combustion in turbulent flames. Predictions are made for two C 2 H 2 turbulent diffusion flames by incorporating both the above combustion model and the model for the rate of soot formation developed by Tesner et al., as well as previous observations by Magnussen concerning the behavior of soot in turbulent flames. The predicted results are in close agreement with the experimental data. All predictions in the present paper have been made by modeling turbulence by the k -∈ model. Buoyancy is taken into consideration in the momentum equations. Effects of terms containing density fluctuations have not been included.
2,575 citations
01 Jan 1988
TL;DR: In this article, it is shown that the inner structure of the flamelets is one-dimensional and time dependent, and a new coordinate transformation using the mixture fraction Z as independent variable leads to a universal description.
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.
1,268 citations
TL;DR: In this paper, the main issues and related closures of turbulent combustion modeling are reviewed and a review of the models for non-premixed turbulent flames is given, along with examples of numerical models for mean burning rates for premixed turbulent combustion.
1,069 citations
TL;DR: A description of recent spray evaporation and combustion models, taking into account turbulent two-and three-dimensional spray processes found in furnaces, gas turbine combustors, and internal combustion engines, is given in this paper.
747 citations
TL;DR: A review of the current state of the art in turbulent combustion modelling can be found in this article, where the authors present physical and experimental knowledge of the structure of turbulent flames in order to help the further discussions of models on a physical basis.
572 citations
References
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01 Jan 1971
TL;DR: In this paper, a method for solving the partial parabolic differential equation of turbulent flame spread has been developed, which is applied to the spread of flame behind a baffle in a plane-walled duct.
Abstract: A calculation procedure has been developed for solving the partial parabolic differential equation of turbulent flame spread. This procedure has been applied to the spread of flame behind a baffle in a plane-walled duct, with two distinct models for the kinetics of the reaction. In the first model, the time-mean reaction rate is related to the time-mean concentrations and temperature at the point in question by a bimolecular Arrhenius expression. In the second model, the local reaction rate is taken to depend also on the rate of break-up of the eddies by fits the experiemntal data better than the first; the eddy-break-up term appears to be essential if the dominance of hydrodynamic processes is to be correctly simulated. A third model of turbulent combustion is also described. It involves the calculation of the magnitude of the fluctuating concentrations, and correctly predicts themain features of turbulent diffusion flames. One of its implications is a finite reaction-zone thickness, even through there is no chemical-kinetic resistance.
686 citations
TL;DR: In this paper, the authors discuss the theoretical basis for diffusion flame analysis, with its implications on diffusion flame structure, and the limitations on the use of the two main reaction models, and address the question of the computation of the velocity and scalar fields focusing on the modeling of the turbulence under conditions of fluctuating and spatially varying density.
443 citations
TL;DR: In this paper, the root-mean-square fluctuating concentration is supposed to obey a parabolic differential equation containing terms for convection, diffusion, generation and dissipation, and the initial and boundary conditions are appropriate to the steady injection of fluid from a nozzle of circular cross-section into a reservoir containing stagnant fluid of equal density.
404 citations
TL;DR: In this article, a physical model for the prediction of the turbulent diffusion flame is presented, where the turbulence is represented by differential equations for its kinetic energy and dissipation, equilibrium chemical reaction without intermediates is assumed, standard relations for the thermodynamic properties are applied, a differential equation for the concentration fluctuations is solved, and a "clipped" normal probability distribution function is proposed for the mixture fraction fluctuations.
343 citations
01 Jan 1977
TL;DR: In this paper, a new expression for the time-average reaction rate in a turbulent flame, whether of uniform or non-uniform fuel-air ratio, is presented, based on the idea of coherent gas "parcels", which are subjected to a stretching process while reaction and small-scale mixing take place.
Abstract: A new expression is presented for the time-average reaction rate in a turbulent flame, whether of uniform or non-uniform fuel-air ratio. It is based on the idea of coherent gas “parcels,” which are subjected to a stretching process while reaction and small-scale mixing take place. The expression has been used for the prediction of flame spread behind a baffle, and for the turbulent diffusion flame. An outline is given of a more complete theory, still under development.
150 citations