BurkeSchumannModell

BurkeSchumannModell is a classical analytical framework in combustion theory that describes the structure of a steady, laminar diffusion flame under a one-dimensional, diffusion-dominated transport regime. Developed in the mid-20th century by Burke and Schumann, the model provides a simplified description of freely propagating diffusion flames with a simple chemical scheme. It assumes a single-step, irreversible reaction between fuel and oxidizer, constant properties, negligible radiative heat transfer, and unity Lewis number (equal diffusivities for all species). The flow is treated as steady and one-dimensional, and the reacting zone is thin compared with the mixing region.

The model uses the mixture fraction Z, a conserved scalar representing the local mixture of fuel and oxidizer. The flame is effectively pinned to the stoichiometric surface Z = Zst, and the temperature and species profiles are obtained by solving transport equations in Z with diffusion as the dominant transport mechanism and reaction occurring near Zst. In many realizations, the BurkeSchumann solution yields closed-form or easily computable expressions for temperature, fuel and oxidizer fractions, and key performance indicators such as maximum temperature and flame length.

Applications include educational use, baseline calculations for diffusion flames, and benchmarking of more sophisticated computational fluid dynamics tools. Limitations are tied to its simplifying assumptions: unrealistically unity Lewis number, absence of turbulence, neglect of multi-step chemistry and radiation, and constant properties. Extensions of the model relax these constraints, enabling unequal diffusivities, variable properties, and finite-rate chemistry while preserving the diffusion-flame concept.

See also: diffusion flame theory, mixture fraction, laminar flame, Burke–Schumann theory.