Burke-Schumann limit

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 the Burke-Schumann limit, a flame surface exists where Yp = Yq = 0, and all concentrations and temperatures may be written explicitly in terms of Z. From equation (77) it is seen that at Yp = = 0 the corresponding... 

The temperature may be obtained as a function of Z in the Burke-Schumann limit by use of these results in equation (79) it is found that... 

Starting from (5.176), the limiting cases of k = 0 and k = oo are easily derived (Burke and Schumann 1928). For the first case, the reaction-progress variable is always null. For the second case, the reaction-progress variable can be written in terms of the mixture fraction as... 

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