Turbulent Flame Speed and Turbulent Markstein Length in the Near Field of a Harmonically Oscillating Flame

This study investigates turbulent flame speed and turbulent Markstein length using analytic and numerical methods. Using asymptotic analysis on harmonically oscillating flames, explicit expressions for the un-stretched turbulent flame speed and the turbulent Markstein length are derived. Numerical simulations using the 3D level-set method were conducted on the parameters of laminar flame speed, amplitude of oscillation of the flame holder, turbulence intensity, and longitudinal length scale of the flow. Results show that with distance downstream the un-stretched turbulent flame speed increases parabolically and Markstein length increases linearly. The explicit expressions are consistent with simulation results and offer insight into flame dynamics in the near field. In the far field, the numerical simulations show saturation of the un-stretched turbulent flame speed and the turbulent Markstein length, which are not captured by the asymptotic analysis.