Distributed heat release effects on entropy generation by premixed, laminar flames

Abstract

This article studies the generation of entropy disturbances by laminar premixed flames. The total entropy generation equals the integrated ratio of the local heat release rate and the local temperature, namely, ∫ ( q ˙ / T ) d V . Due to this path dependency, evaluating this integral requires an understanding of how the heat release is distributed in the temperature space. Several studies evaluate the local entropy generation as ( ∫ q ˙ d V ) / T b , where T b refers to the burned gas temperature, implicitly assuming all the heat release occurs at T b . Such an approximation is motivated by the high activation energy nature of combustion chemistry. This work evaluates this assumption by comparing it to results from one-dimensional premixed flame calculations for hydrogen, methane, and propane-air flames over a range of pressures, equivalence ratios, and preheat temperatures, quantified via the ratio κ . We show that this assumption is quite reasonable for methane and propane-air flames (with errors ranging from 5% to 25%) but deviates significantly from the exact results for hydrogen flames (where errors can be as high as 50%). In general, the peak heat release moves to lower temperatures as preheat temperature is increased. Noting that the temperature sensitivity of heat release is directly related to the activation energy, we use Law's approach to extract global activation energies and show that the deviations of κ from unity can be approximately correlated with β e f f . Finally, we show that significant improvements in entropy generation calculations can be obtained by estimating ∫ ( q ˙ / T ) d V using ( ∫ q ˙ d V ) / T p e a k , where T p e a k is the temperature at which the reaction rate peaks. This estimation leads to predictions of ∼5% within the exact value for the hydrocarbon cases but can still be in significant error for hydrogen at certain conditions.