Nonlinear power laws in stretched flame velocities in finite thickness flames: A numerical study using realistic chemistry

Stretched laminar flame velocities in stoichiometric finite thickness H ₂/air and CH ₄/air flames at atmospheric pressuresinvestigated through an implicit direct simulation method are that features the coupling of the fully compressible flow to the realistic chemistry and multicomponent transport properties. The method resolves all the chemical and flow length and time scales, which is essential for investigating highly stiff reacting flow systems with realistic chemistry. Eight flame configurations are investigated: outwardly and inwardly propagating H ₂/air and CH ₄/air in cylindrical and spherical geometries. Nonlinear power law relationships are observed between the velocity deficit S L S n and the flame curvature 1/r u, viz with 0<p<1, where p depends upon the flame type and the propagation mode. (S L is the unstretched laminar flame velocity, and S n is the stretch flame velocity, r u is the flame radius of curvature.) The Markstein linear hypothesis for asymptotically thin flames corresponds to p=1; our results show that such a linear hypothesis cannot be extended to realistic finite thickness flames under the conditions of the study. The outwardly propagating H ₂/air flames are an exception, displaying an entirely different anomalous non-power law relationship, which is indicative of the complex coupling between the thermochemistry and flame geometry.