LAUSR

Abstract Three-dimensional, steady laminar flow structures with mixing, chemical reaction, normal strain and shear strain representative of turbulent combustion are analysed. A mixing layer is subjected to counterflow in the transverse $y$- and $z$-directions providing the important practical interaction of shear-strain rate with normal-strain rate. Larger consequences for mixing rates and burning rates occur than would appear with shear strain or normal strain alone. The three characteristic times for chemical reaction, normal strain and shear strain are cast through two ratios: a Damköhler number based on rate of shear strain and a ratio of rate of normal strain to rate of shear strain. Reduction to a one-dimensional similar form is obtained with density and property variations. A generalization is found extending the Crocco integral for non-unitary Prandtl number and for imposed normal strain. A diffusion flamelet model with combined shear and normal strains is developed. Another similar solution is obtained for a configuration with a dominant diffusion flame and a weaker fuel-rich premixed flame. A conserved scalar is cast as the independent variable giving an alternative description. The imposed normal strain decreases mixing-layer thickness and increases scalar gradients and transport rates. Diffusion control is possible for partially premixed flames in the multi-branched flame situation. The imposition of shear strain and thereby vorticity on the counterflow can have a substantial consequence, indicating the need for flamelet models with both shear strain and normal strain.