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Combustion

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(Finite chemistry)
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==== Conserved scalar equilibrium models ====
==== Conserved scalar equilibrium models ====
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== Finite chemistry ==
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== Finite rate chemistry ==
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=== Full reaction mechanism model ===
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=== Premixed Combustion ===
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=== Reduced scheme models ===
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==== Coherent Flame Model ====
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# Flamelet model
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==== Flamelets based on G equation ====
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# Other reaction progress variable models
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=== Non-premixed Combustion ===
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==== Flamelets based on conserved scalar ====
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==== Conditional Moment Closure (CMC)====
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==== Multiple Mapping Closure (MMC) ====
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=== Linear Eddy Model ===
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=== PDF transport models ===
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==== Lagrangian ====
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==== Eulerian ====
== References ==
== References ==

Revision as of 16:52, 29 September 2005

Contents

What is combustion -- Physics versus modelling

Combustion phenomena consists of many physical and chemical processes with broad range of time scales. Mathematical description of combustion is not always trivial. Analytical solutions exists only for basic situations of laminar flame and because of its assumptions it is often restricted to few problems solved usually in zero or one-dimensional space.

Problems solved today concern mainly turbulent flows, gas as well as liquid fuels, pollution issues (products of combustion as well as for example noise pollution). These problems require not only extensive experimental work, but also numerical modelling. All combustion models must be validated against the experiments as each one has its own drawbacks and limits. However here the modelling part will be mainly addressed.


Reaction mechanisms

The combustion is mainly chemical process and although we can, to some extend, describe flame without any chemistry informations, for modelling of flame propagation we need to know the speed of reactions, product concentrations, temperature and other parameters. Therefore more or less detailed information about reaction kinetics is essential for any combustion model. Mixture will generally combust, if the reaction of fuel and oxidiser is fast enough to maintain until all of the mixture is burned into products. If the reaction is too slow, the flame will extinguish, if too fast, explosion or even detonation will occur. The reaction rate of typical combustion reaction is influenced mainly by concentration of reactants, temperature and pressure.

A stoichiometric equation of an arbitrary equation can be written as:


\sum_{j=1}^{n}\nu' (M_j) = \sum_{j=1}^{n}\nu'' (M_j),

where $\nu$ is the stoichiometric coefficient, M_j is arbitrary species. One prime specifies the reactants and double prime products of the reaction.

Reaction rate, expressing the rate of disappearance of reactant i of such a reaction, is defined as:


RR_i = k \, \prod_{j=1}^{n}(M_j)^{\nu'},

in which k is the specific reaction rate constant. Arrhenius found that this constant is a function only of temperature and this function is defined as:


k= A T^{\beta} \, exp \left( \frac{-E}{RT}\right)

where A is pre--exponential factor, E is activation energy and \beta is temperature exponent. These constants for given reactions can be found in literature. The reaction mechanism can be given from experiments for every reaction resolved, it could be also constructed numerically by automatic generation method (see [Griffiths (1994)] for review on reaction mechanisms). For simple hydrocarbon tens to hundreds of reactions are involved. By analysis and systematic reduction of reaction mechanisms global reaction (from one to five step reactions) can be found (see [Westbrook (1984)]).

Infinitely fast chemistry

Premixed Combustion

Turbulent flame speed model

Eddy Break-Up model

Bray-Moss-Libby Model

Non premixed combustion

Conserved scalar equilibrium models

Finite rate chemistry

Premixed Combustion

Coherent Flame Model

Flamelets based on G equation

Non-premixed Combustion

Flamelets based on conserved scalar

Conditional Moment Closure (CMC)

Multiple Mapping Closure (MMC)

Linear Eddy Model

PDF transport models

Lagrangian

Eulerian

References

  • Griffiths J.F. (1994), "Reduced Kinetic Models and Their Application to Practical Combustion Systems", Prog. in Energy and Combustion Science,Vol. 21, pp. 25-107.
  • Westbrook, Ch.K., Dryer,F.L., (1984), "Chemical Kinetic Modeling of Hydrocarbon Combustion", Prog. in Energy and Combustion Science,Vol. 10, pp. 1-57.

External links and sources

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