The Turbulent Premixed Boundary Layer with Variable Enthalpy

Abstract

A previous analysis of the turbulent boundary layer which arises from the injection of premixed reactants into a stream of combustion products is extended to the case of variable enthalpy. The variation in enthalpy can be due either to losses or gains in heat in the product stream or to differences in the stoichiometry of reactants and products and leads to a temperature in the external stream different from the adiabatic equilibrium temperature of the injected reactants. The thermochemistry of the system is described by a multivariate probability density function involving two scalars, the progress variable and an enthalpy variable. Three different forms of the probability density function of the distributed enthalpy within products are considered. An extension to incorporate the pdf of the velocity components and those scalars permits description of the aerothermochemistry of the system. Similarity solutions of the complete set of equations for first and second moment quantities permits the effects of enthalpy variations on the structure of the boundary layer to be investigated. In particular it is shown that countergradient diffusion occurs if the enthalpy difference between reactants and products in the external flow is suitably large. The sensitivity of the predictions to the assumed form of the enthalpy distribution and comparison with available experimental results are discussed.