Diffusion flames Burke-Schumann

In addition to the Burke and Schumann model (34) and the Displacement Distance theory, a comprehensive laminar diffusion flame theory can be written using the equations of conservation of species, energy, and momentum, including diffusion, heat transfer, and chemical reaction. 

Evaporation and burning of Hquid droplets are of particular interest in furnace and propulsion appHcations and by applying a part of the Burke and Schumann approach it is possible to obtain a simple model for diffusion flames. 

Solution of diffusion flame in a duct Burke and Schumann... 

Equation (6.31) shows the same dependence on Q as that developed from the Burke-Schumann approach [Eqs. (6.21)—(6.23)]. For a momentum-controlled fuel jet flame, the diffusion distance is r, the jet port radius and from Eq. (6.30) it is obvious that the time to the flame tip is independent of the fuel volumetric flow rate. For a buoyancy-controlled flame, ts remains proportional to (yF/v) however, since v = (2gyF)1/2,... 

In the present analysis, the outer convective-diffusive zones flanking the reaction zone are treated in the Burke-Schumann limit with Lewis numbers unity. Lewis numbers different from unity are taken into account where reactions occur. These Lewis-number approximations are especially accurate for methane-air flames and would be appreciably poorer if hydrogen or higher hydrocarbons are the fuels. To achieve a formulation that is independent of the flame configuration, the mixture fraction is employed as the independent variable. The connection to physical coordinates is made through the so-called scalar dissipation rate. 

In full-scale Are modeling, a diffusion flame structure is usually assumed. However, in many fire situations, such as underventilated fires, premixed or partially premixed flame theory may be more appropriate. The Burke-Schumann description of the diffusion flames can be used to conveniently represent the transport of gaseous species by a single scalar quantity called mixture fraction. For a simple one-step reaction ... 

The first successful detailed analysis of a diffusion-flame problem was given by Burke and Schumann in 1928 [4]. The Burke-Schumann problem is illustrated in Figure 3.1 fuel (or oxidizer) issues from a cylindrical... 

For steady-state diffusion flames with thin reaction sheets, it is evident that outside the reaction zone there must be a balance between diffusion and convection, since no other terms occur in the equation for species conservation. Thus these flames consist of convective-diffusive zones separated by thin reaction zones. Since the stretching needed to describe the reaction zone by activation-energy asymptotics increases the magnitude of the diffusion terms with respect to the (less highly differentiated) convection terms, in the first approximation these reaction zones maintain a balance between diffusion and reaction and may be more descriptively termed reactive-diffusive zones. Thus the Burke-Schumann flame consists of two convective-diffusive zones separated by a reactive-diffusive zone. 

In the context of combustion in non-premixed flames, this is called the Burke-Schumann solution. If the initial condition is such that T(x, t = 0) is not homogeneous in space, solving its advection-diffusion equation to obtain T(x, t) is needed in addition to solving the one for (x, t) before using (5.8)-(5.9) to obtain C(x, t). 

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). 

The Burke-Schumann solution for laminar diffusion flames uses the hypothesis of infinitely fast chemistry, valid for a high Damkohler number. With this hypothesis, the reaction occurs in a thin layer in the vicinity of the stoichiometric surface, separating the flame in to rich and lean portions. With this assumption, it is convenient to express the mass fraction of the components according to the mixture fraction. The mixture fraction can be defined as ... 

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