Burke-Schumann solution

To obtain boundary conditions for equation (96), matching to the Burke-Schumann solution given by equation (84) may be imposed for 00. As is usually true (Chapter 5), in the first approximation this matching requires the slopes dT/dZ to agree. From equation (84) and the definitions of (p and r], it may be shown that the matching requires dcp/dt] 1... 

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 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 ... 

FIGURE 5.10 Burke-Schumann solution for Fp and 02 in the mixture fraction space. 

The profiles of mass fractions of H2O and CO2 given by the Burke-Schumann solution are shown in Figure 5.11. 

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). 

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

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