Particulate Carbon pp 321-341 | Cite as

# Modeling of Reaction Processes in Turbulent Flames with Special Emphasis on Soot Formation and Combustion

## Abstract

The present paper reviews features of the eddy-dissipation concept developed by the author for treating chemical reactions in turbulent flow.

An essential feature of this concept is that it takes into account the fact that the molecular mixing between reactants, which is associated with the dissipation of turbulence, takes place in concentrated, isolated regions that occupy only a small fraction of the total volume of the fluid.

The mass fraction occupied by the dissipative regions, as well as the mass transfer rate between these regions and the surrounding fluid, are determined from turbulence theory thus providing new general fluid mechanical information for the solution of reaction problems. This enables fast and accurate calculations of turbulent combustion phenomena.

The treatment of fast and slow chemical reactions in turbulent flow is discussed in relation to this concept. Comparison is made with experimental data.

Special attention is given to the modeling of soot formation and combustion in turbulent flames. A two-step model for the soot formation is applied, i.e., one rate equation for the formation of nuclei and one for particles. The interaction between the chemistry and the turbulence is modeled according to the eddy-dissipation concept. Comparison is made between experimental data and calculations for acetylene.

It is interesting to notice that when the same rate equations with the same constants are applied also for methane and propane, results are obtained which seem to be closely related to physical reality.

## Keywords

Fine Structure Mass Transfer Rate Soot Particle Diffusion Flame Soot Formation## Nomenclature

- a
constant or flux absorption coefficient

- a
_{o} constant

- b
constant

- c
concentration (kg/m

^{3})- c
_{p} specific heat

- C
_{1}, C_{2}, C_{D} constants

- D
nozzle diameter

- E
activation energy or blackbody emissive power

- F
flatness factor or radiation flux sum

- f
mixture fraction or linear branching coefficient

- g
linear termination coefficient or gravitation constant

- g
_{o} coefficient of linear termination on soot particle

- ΔH
_{R} reaction enthalpy difference

- h
enthalpy

- I
intensity of scattered light

- k
turbulence kinetic energy

- Ḷ
^{*} characteristic length of fine structures

- m
exchange rate of mass with fine structures

- m
mass concentration (kg/kg)

- m
_{p} mass of soot particle (kg/part)

- N
concentration of soot particles (part/m

^{3})- n
nucleus concentration (part/m

^{3})- n
_{o} rate of spontaneous formation of nucleus (part/m

^{3}/s)- p
pressure

- R
_{e} Reynolds number

- R
_{fu} rate of fuel combustion (kg/m

^{3}/s)- R
_{n, c} rate of nucleus combustion (part/m

^{3}/s)- R
_{n, f} rate of nucleus formation

- R
_{s, c} rate of soot combustion

- R
_{s, f} rate of soot formation

- R
_{Φ} source term

- r
stoichiometric oxygen requirement to burn 1 kg fuel or soot

- T
temperature (K)

- ΔT
excess temperature of reacting fine structures

- u
^{*} characteristic velocity of fine structures

- u′
turbulence velocity

- U
axial velocity

- V
lateral velocity

- x
axial coordinate

- y
lateral coordinate

- ρ
density

- ε
rate of dissipation of turbulence kinetic energy

- μ
_{t} effective turbulent viscosity

- σ
turbulent Prandtl/Schmidt number

- ν
kinematic viscosity

- γ
^{*} mass fraction occupied by fine structures

- χ
fraction of fine structures reacting

- Φ
undefined quantity

- Λ
integral scale of turbulence

- -
time-mean value

- *
fine structure

- o
surrounding fluid

- fu
fuel

- n
nucleus

- pr
product

- s
soot

- Φ
undefined quantity

## Preview

Unable to display preview. Download preview PDF.

## References

- 1.B. F. Magnussen, On the Structure of Turbulence and a Generalized Eddy —Dissipation Concept for Chemical Reaction in Turbulent Flow. Report NTH, (1978).Google Scholar
- 2.B. F. Magnussen, B. H. Hjertager, J. G. Olsen and D. Bhaduri, Seventeenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, (1979), p. 1383.Google Scholar
- 3.A. N. Kolmogorov, J. Fluid Mech., Vol. 13 (1962), p. 82.CrossRefGoogle Scholar
- 4.S. Corrsin, Phys. Fluids, Vol. 5 (1962), p. 1301.CrossRefGoogle Scholar
- 5.H. Tennekes, Phys. Fluids, Vol. 11 (1968), p. 669.CrossRefGoogle Scholar
- 6.A. Y. Kuo and S. Corrsin, J. Fluid Mech., Vol. 50 (1971), p. 285.CrossRefGoogle Scholar
- 7.A. Y. Kuo and S. Corrsin, J. Fluid Mech., Vol. 56 (1972), p. 477.CrossRefGoogle Scholar
- 8.B. F. Magnussen, Some Features of the Structure of a Mathematical Model of Shear Flow Turbulence, Report NTH, (1975).Google Scholar
- 9.B. F. Magnussen and B. H. Hjertager, Deuxieme Symposium Europeen sur la Combustion, Section Francaise du “Combustion Institute,” (1975), p. 385.Google Scholar
- 10.B. F. Magnussen and B. H. Hjertager, Sixteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, (1976), p. 719.Google Scholar
- 11.P. A. Tesner, T. D. Snegiriova and V. G. Knorre, Combustion and Flame, Vol. 17 (1971), p. 253.CrossRefGoogle Scholar
- 12.P. A. Tesner, E. I. Tsygankova, L. P. Guilazetdinov, V. P. Zuyev and G. V. Loshakova, Combustion and Flame, Vol. 17 (1971), p. 279.CrossRefGoogle Scholar
- 13.T. Takagi, M. Ogasawara, K. Fuju and M. Daizo, Fifteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, (1974), p. 1051.Google Scholar
- 14.H. A. Becker and S. Yamazaki, Sixteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, (1976), p. 681.Google Scholar