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
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Abbreviations
- a:
-
constant or flux absorption coefficient
- ao :
-
constant
- b:
-
constant
- c:
-
concentration (kg/m3)
- cp :
-
specific heat
- C1, C2, CD :
-
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
- go :
-
coefficient of linear termination on soot particle
- ΔHR :
-
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)
- mp :
-
mass of soot particle (kg/part)
- N:
-
concentration of soot particles (part/m3)
- n:
-
nucleus concentration (part/m3)
- no :
-
rate of spontaneous formation of nucleus (part/m3/s)
- p:
-
pressure
- Re :
-
Reynolds number
- Rfu :
-
rate of fuel combustion (kg/m3/s)
- Rn, c :
-
rate of nucleus combustion (part/m3/s)
- Rn, f :
-
rate of nucleus formation
- Rs, c :
-
rate of soot combustion
- Rs, f :
-
rate of soot formation
- RΦ :
-
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
- μt :
-
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
References
B. F. Magnussen, On the Structure of Turbulence and a Generalized Eddy —Dissipation Concept for Chemical Reaction in Turbulent Flow. Report NTH, (1978).
B. F. Magnussen, B. H. Hjertager, J. G. Olsen and D. Bhaduri, Seventeenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, (1979), p. 1383.
A. N. Kolmogorov, J. Fluid Mech., Vol. 13 (1962), p. 82.
S. Corrsin, Phys. Fluids, Vol. 5 (1962), p. 1301.
H. Tennekes, Phys. Fluids, Vol. 11 (1968), p. 669.
A. Y. Kuo and S. Corrsin, J. Fluid Mech., Vol. 50 (1971), p. 285.
A. Y. Kuo and S. Corrsin, J. Fluid Mech., Vol. 56 (1972), p. 477.
B. F. Magnussen, Some Features of the Structure of a Mathematical Model of Shear Flow Turbulence, Report NTH, (1975).
B. F. Magnussen and B. H. Hjertager, Deuxieme Symposium Europeen sur la Combustion, Section Francaise du “Combustion Institute,” (1975), p. 385.
B. F. Magnussen and B. H. Hjertager, Sixteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, (1976), p. 719.
P. A. Tesner, T. D. Snegiriova and V. G. Knorre, Combustion and Flame, Vol. 17 (1971), p. 253.
P. A. Tesner, E. I. Tsygankova, L. P. Guilazetdinov, V. P. Zuyev and G. V. Loshakova, Combustion and Flame, Vol. 17 (1971), p. 279.
T. Takagi, M. Ogasawara, K. Fuju and M. Daizo, Fifteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, (1974), p. 1051.
H. A. Becker and S. Yamazaki, Sixteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, (1976), p. 681.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer Science+Business Media New York
About this chapter
Cite this chapter
Magnussen, B.F. (1981). Modeling of Reaction Processes in Turbulent Flames with Special Emphasis on Soot Formation and Combustion. In: Siegla, D.C., Smith, G.W. (eds) Particulate Carbon. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6137-5_12
Download citation
DOI: https://doi.org/10.1007/978-1-4757-6137-5_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-6139-9
Online ISBN: 978-1-4757-6137-5
eBook Packages: Springer Book Archive