The focus of this work is the numerical study of stable and pulsatory flame burst in an undulating geometry, using premixed hydrogen and air (with an equivalence ratio of 4 = 1.0). This work extends other works in the literature by considering a linear temperature profile along the wall. This allows an analysis of the flow dynamics without forcing the location of the flame (as is the case with hyperbolic temperature profiles). The interaction between the flow dynamics and the combustion reaction is then analysed, leading to a better understanding of the physics in more general flows. Simulations were performed in OpenFoam using very detailed chemical reactions and different molecular diffusivities for each species. The results obtained show that at low inlet velocity (4 m/s) the flame became stable, and, at higher inlet velocities, the flame showed pulsatory burst dynamics. The interaction between the fluid dynamics and the combustion response proved to be important, especially because of the vortices that are formed due to the nonlinear geometry of the burner. As the inlet velocity increases, the heat release rate transmitted through the vortices decreases and a delay in ignition occurs, as evidenced by a decrease in the pulsatory burst frequency and an increase in the maximum value of the heat release rate (although not sufficient to increase the maximum temperature amplitude). In addition, we also carried out an analyses of the axial velocity and of the H2 and OH mass fractions of the flame dynamics.
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