Impact of dissociation and end pressure on determination of laminar burning velocities in constant volume combustion

Determining laminar burning velocities SL from the pressure trace in constant volume combustion requires knowledge of the burnt fraction as a function of pressure, x(p). In recent literature x(p) is either determined via numerical modeling or via the oversimplified assumption that x(p) is equal to the fractional pressure rise. Recently, we have shown that the latter violates energy conservation, and derived alternative analytical x(p) relations based on zone modeling which are more simple to apply than numerical models. However we had to assume perfect gas behavior, neglecting dissociation. In this paper we systematically compare our analytical models with a numerical two-zone model and with a 1D unsteady simulation (1DUS) of a spherical stoichiometric methane–air flame in a constant volume. Results indicate that our analytical models reasonably describe the burnt fraction as a function of fractional pressure rise. However the x(p) relation also involves the (theoretical) end pressure pe. Its value significantly affects SL, with a relative sensitivity close to minus one, and is influenced by dissociation. Evaluating pe from an equilibrium code, in combination with the analytical x(p) model, provides SL results within 3% accuracy. This approach removes the need for numerical modeling of intermediate stages of combustion. Still, highest accuracy for SL is achieved using numerical x(p) models that account for dissociation also for intermediate stages. Comparing results of the 1DUS with the two-zone equilibrium model shows that the combined effect of detailed chemistry, flame stretch, heat transfer between zones, and the temperature gradient in the burnt mixture is limited to about 1% for the example case.