Examples and counterexamples for huygens principle in premixed combustion

A model involving a scalar reaction-diffusion equation with piecewise linear reaction rates and linear incompressible flow fields is developed to study the validity of Huygens principle at large scales in premixed combustion. This model includes both dependence on the reaction term and the velocity field. For plane fronts aligned with the direction of expansive strain and KPP regime, theory predicts strong violation of Huygens principle chemistry, and this is shown to persist in dramatic fashion throughout the ZFK regime, even at high activation energies. If the front is aligned with a direction of compressive strain, Huygens principle yields an excellent approximation with ZFK chemistry. For a more general rotating strain flow with ZFK chemistry, the Huygens principle significantly underpredicts the large scale flame propagation velocity in consistent fashion with the example involving expansive strain. For backward reactions or at the boundary of the ZFK regime, Huygens principle is always excellent for any large scale flow geometry.