In combustion, Burke–Schumann limit, or large Damköhler number limit, is the limit of infinitely fast chemistry, named after S.P. Burke and T.E.W. Schumann, due to their pioneering work on Burke–Schumann flame. One important conclusion of infinitely fast chemistry is the non-co-existence of fuel and oxidizer simultaneously except in a thin reaction sheet. The inner structure of the reaction sheet is described by Liñán's equation.
Limit description
In a typical non-premixed combustion, mixing of fuel and oxidizer takes place based on the mechanical time scale dictated by the convection/diffusion terms. Similarly, chemical reaction takes certain amount of time to consume reactants. For one-step irreversible chemistry with Arrhenius rate, this chemical time is given by where is the pre-exponential factor, is the activation energy, is the universal gas constant and is the temperature. Similarly, one can define appropriate for particular flow configuration. The Damköhler number is then Due to the large activation energy, the Damköhler number at unburnt gas temperature is, because. On the other hand, the shortest chemical time is found at the flame, leading to. Regardless of Reynolds number, the limit guarantees that chemical reaction dominates over the other terms. A typical conservation equation for the scalar takes the following form, where is the convective-diffusive operator and are the massfractions of fuel and oxidizer, respectively. Taking the limit in the above equation, we find that i.e., fuel and oxidizer cannot coexist, since far away from the reaction sheet, only one of the reactant is available. On the fuel side of the reaction sheet, and on the oxidizer side,. Fuel and oxygen can coexist only in a thin reaction sheet, where . In this thin reaction sheet, both fuel and oxygen are consumed and nothing leaks to the other side of the sheet. Due to the instantaneous consumption of fuel and oxidizer, the normal gradients of scalars exhibit discontinuities at the reaction sheet.
