A priori test of perfectly stirred reactor approach to evaluating mean fuel consumption and heat release rates in highly turbulent premixed flames

Abstract

Unsteady three-dimensional Direct Numerical Simulation (DNS) data obtained earlier by Dave et al. (J Fluid Mech 2020; 884: A46) from a statistically planar and one-dimensional, highly turbulent, moderately lean hydrogen-air flame propagating in a box are processed to perform a priori test of perfectly stirred reactor model. The test aims in particularly at estimating mesh resolution (or filter width within large eddy simulation framework) required to neglect variations in the temperature and mixture composition within a computational cell when evaluating mean (or filtered) fuel consumption and heat release rates. For this purpose, fuel consumption and heat release rates sampled directly from the DNS data and averaged over a cube of width $\Delta$ are compared with fuel consumption and heat release rates calculated using the temperature and species concentrations averaged over the same cube. Moreover, turbulent burning velocities computed by integrating the former and latter rates are compared with one another. A ratio of $\Delta$ to a laminar flame thickness ${\delta }_L$ is varied from 0.44 to 1.8. The obtained results indicate that the tested simple approach performs reasonably well (poor) if $\Delta <0.5{\delta }_L$ ( $\Delta >{\delta }_L$ , respectively). This result is further supported by directly filtering fuel consumption rate in a laminar premixed flame. The values of the thickness ${\delta }_L$ , calculated using detail chemical mechanisms for different fuels under elevated temperatures and pressures associated with combustion in piston engines, indicate that it is difficult to satisfy the constraint of $\Delta <0.5{\delta }_L$ in contemporary unsteady multidimensional numerical simulations of turbulent burning in such engines.