A balance equation for modeling conditioned enthalpies in premixed turbulent flames

In order to model the difference between enthalpies conditioned to unburned and burned gases, caused by compression of the mixture in the combustion chamber of a spark ignition engine, a new balance equation for the correlation between fluctuations in the enthalpy and combustion progress variable is proposed to be used, derived and closed invoking a few assumptions that appear to be plausible at low Mach and unity Lewis numbers. Subsequently, the difference in the conditioned enthalpies is determined within the framework of the well-known BML paradigm of premixed turbulent burning in the flamelet regime. In the paper, this new approach is analytically compared with commonly used balance equations for enthalpy conditioned to unburned gas. Moreover, in order to investigate basic features of the newly proposed balance equation, it is applied to numerical simulations of a statistically stationary, planar, one-dimensional premixed turbulent flame subject to increasing pressure. Instead of modeling the mean flame structure, it is approximated using complementary error function, with the flame speed and thickness being input parameters in the present study. Computed results show that the difference in the conditioned enthalpies is increased when the density ratio or the pressure growth rate is increased and when the turbulent flame speed or mean flame brush thickness is decreased. Moreover, computed enthalpy difference is sensitive to a submodel of turbulent flux of the combustion progress variable, with the use of gradient diffusion approximation appearing to be an improper solution. Furthermore, computed enthalpy difference is sensitive to a closure relation for enthalpy conditioned to flamelets.