Constrained model of the stretched flame speed in laminar and turbulent premixed flames

Coupling with thermo-diffusive effects, the flame stretch alters flame structures and thereby the burning velocity. We propose an analytical model for the stretched flame speed. Constraints on the maximum/minimum limits of the stretched flame speed make this model able to represent the nonlinear variation of the stretched flame speed from weak to strong flame stretch. Validations against different configurations, including counterflow flames and inwardly/outwardly propagating spherical flames, show that the constrained model well captures the flame speed response to the flame stretch. The model can be employed for laminar flame speed extrapolation and turbulent premixed flame modeling. Extrapolations based on experimental and numerical data show that the present model improves the accuracy of laminar flame speed extrapolation from stretched flames, especially for lean hydrogen flames. This is due to the strong nonlinearity caused by the thermo-diffusive effects, which is well captured by the proposed model. We also validate the model using the direct numerical simulation (DNS) data of turbulent premixed flames at weak and moderate turbulence intensities. Comparisons show reasonable agreements between model predictions and the DNS data on the local flame displacement speed.