Eddy Dissipation Concept

The Eddy Dissipation Concept (EDC) is used for treating the interaction between turbulence and chemistry in flames 12]. The method is based on a detailed description of the dissipation of turbulent eddies. In the EDC the total space is subdivided into a reaction space, called the fine structures and the surrounding fluid. In the presented reaction scheme the reactions Cl, C2, and C3 arc treated as taking place only in these fine structures, i.e. only on the smallest turbulent length scales. 

Magnussen, B.F. (1989) "The Eddy Dissipation Concept". XI Task Leaders Meeting -Energy Conversion in Combustion, lEA,... 

Reactions I-IV are global steps for gaseous fuel oxidation. Reactions V-VII, are for char oxidation. The single film model is used here, where the particle is consumed via reactions with oxygen (or carbon dioxide) and no reaction occurs in the boundary layer. CO and CO2 are the two products formed at the particle surface. The first four reactions are treated based on the eddy-dissipation concept [8], which assumes that chemical reactions in the gaseous phase occur rapidly and the mean consumption rate of fuel is limited by the mixing rate of fuel and oxidant. The char reactions are treated using kinetic Arrhenius expression. 

The Magnussen model was initially developed for simple, one- or two-step reaction sets, in which all reaction rates are fast relative to the small scale mixing, even though it has found use for more complex systems. Recently, for more complex reaction sets, a new model has been developed (Gran and Magnussen, 1996) called the eddy dissipation concept (EDC) model. This model assumes that reaction occurs in small turbulent structures, called the fine scales. A volume fraction... 

Table 5.8 Selected material properties for eddy dissipation concept (EDC) mixture.

Magnussen, B.F. and Hjertager, B.W. (1981) On the structure of turbulence and a generalized eddy dissipation concept for chemical reaction in turbulent flow. 19th AIAA Aerospace Meeting, St. 

Models Based upon the Concept of Eddy Dissipation... 

Another useful and interesting concept is the size of the eddies, L, at which the power of an impeller is eventually dissipated. This concept utilizes the principles of isotropic turbulence developed by Komolgoroff [1]. The calculations assume some reasonable approach to the degree of isotropic turbulence, and the estimates do give some idea as to how far down in the microscale size the power per unit volume can effectively reach... 

The energy dissipation number is derived from the Kolmogorov theory [289, 290]. This theory is based on the concept, that in the turbulent flow range the kinetic energy is transferred by inertial forces from large to ever smaller eddies, until it is finally dissipated through viscosity forces. The eddies produced by the stirrer have the size of the stirrer head and are responsible for the macroscopic turbulence, the smallest eddies on the other hand are directionless. On the microscale so-called isotropic turbulence exists, see Section 1.4.2. 

The flamelet concept for turbulent combustion applies when the reaction is fast compared to the mixture at the molecular level. In this regime, the chemistry of a flame and the turbulence can be treated separately. The flamelet concept approaches the solution of Burke-Schumann for a high Damkohler number and mechanism of one step. The scalar dissipation rate, which appears in the flamelet equations, relates the effects caused by the diffusion and convection. This rate is large at the smallest scales, but its fluctuations are mainly governed by the large scales, which are solved using Large-Eddy Simulation (LES). 

---