Measurement of Markstein Numbers and Laminar Flame Speeds in Computationally Simulated Premixed Cylindrically Expanding Laminar Flames

As global energy demands rise and concerns over fossil fuel emissions intensify, there is an urgent need to develop sustainable alternatives. Extensive research is being conducted to optimize hydrogen combustion. Key flame properties, such as laminar flame speed and Markstein number, play crucial roles in characterizing combustion of hydrogen-containing fuels. These parameters influence flame stability, speed, and response to perturbations. While these properties can be determined experimentally, such measurements are often costly and subject to uncertainties. Numerical simulations, therefore, provide a valuable approach to studying these properties more efficiently.

In this work, a computational framework is developed to model cylindrically expanding laminar flames at constant pressure. This approach avoids common instabilities encountered when simulations are initialized from a unburnt conditions and a numerical “spark” ignites the reactants. Such numerical instabilities are most common when the governing equations solved are the low Mach number restriction of the Navier-Stokes equations. After validating the modeling approach against data available in the literature, the framework is applied to unity Lewis number mixtures of hydrogen and oxygen diluted with helium. These mixtures are studied at varying dilution levels, equivalence ratios, and pressures to understand their behavior in conditions relevant to experiments performed in the Von Kármán Combustion Chamber (VKCC), where the focus is on understanding the dynamics of turbulent flame fronts. The Markstein number is a critical parameter in the response of a reactive front to stretch according to well established linear theory. For all selected mixtures, the study found positive Markstein numbers, indicating stable behavior. Notably, as the equivalence ratio increases from 0.65 to 0.95, as the laminar flame speed and Markstein number increases.

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