A computational assessment of flame speed correlation in an ultra-lean pre-chamber engine

Abstract

Predictive modeling of pre-chamber combustion engines relies primarily on the correct description of laminar and turbulent flame speeds. For engineering applications, the correlations of the flame speeds with physical variables involve empirical constants that are valid for a limited range of operating conditions. The current work aims at assessing the significance of laminar flame speed prediction in the simulation of ultra-lean pre-chamber engine combustion operated with methane. Gülder’s empirical correlation for laminar flame speed was chosen as a reference and was further modified for equivalence ratio, pressure and temperature ranges beyond what it was originally derived for, in order to confirm the original hypothesis; the pressure and temperature dependence were adopted as a power-law correlation. Based on the computational results using the skeletal reaction mechanism, the correlation was modified better represent the flame speeds at ultra-lean engine conditions, using GRI 3.0 as a reference. The modified correlation for methane was implemented in CONVERGE, a three-dimensional computational fluid dynamics (CFD) solver, and the results were validated against the experimental data. In all cases, the original formulation of Peters’s turbulent flame speed correlation was used and was found to have insignificant effect on the conditions under study, confirming the importance of the accurate determination of the laminar flame speed that dominates over any turbulence corrections for high Karlovitz number effects. The flame topology was also investigated to provide insights into the observed pressure behavior among the tested cases. Finally, the relevant turbulent combustion regimes encountered in the pre-chamber combustion engine conditions were examined in the Borghi-Peters diagram, further confirming the findings of the study.

A Computational Assessment of Combustion Submodels for Predictive Simulations of Pre-Chamber Combustion Engines

“…Note that the discrepancy between the three cases arises only after the strong jet issuing event ceases and the convective transport of the 𝐺 ̃ field by the jet is minimized so that the effects of turbulent transport and turbulent flame propagation become crucial in determining the overall burning rate. Alkhamis et al [23] demonstrated (not shown here) that by tailoring Gulder's model a perfect match was possible, thus proving the significance of correct laminar flame speed for ultralean PC engine modeling. While ultralean SL measurements with conventional methods are challenging, the ultralean engine data serves as a practical benchmark for the validation of newly developed mechanisms for ultralean engine operation.…”

“…Detailed analysis of jet developments and turbulencechemistry interaction can be found in previous work [21,23]. As the jets are issued into the MC, 𝑢 ′ /𝑆 𝐿 substantially aggrandizes with concomitant decrease in 𝑙 𝑇 /𝛿 𝐿 provided that the region around the jet has significant shear thus smaller turbulent structures.…”

“…Haling et al [7] demonstrated the calibration methodology while Silva et al [14] demonstrated the major mismatches that may arise if the prechamber is artificially enriched. More recently, Alkhamis et al [23] demonstrated that a dominant effect on PC modeling resides in the correct prediction of the laminar flame component. Note that the discrepancy between the three cases arises only after the strong jet issuing event ceases and the convective transport of the 𝐺 ̃ field by the jet is minimized so that the effects of turbulent transport and turbulent flame propagation become crucial in determining the overall burning rate.…”

“…Kim et al [22] proposed that the turbulence-chemistry constants in Peters's relation could be tuned to achieve correct pressure prediction, while the current work preserves the originally proposed turbulent constant values. Alkhamis et al [23] utilized the G-equation approach and demonstrated the significance of the laminar flame speed at ultralean conditions. That work verifies that once the turbulence generated by the pre-chamber is mostly dissipated and the role of convective transport is comparable to the turbulent enhancement, the correct prediction of the laminar flame speed becomes crucial to the correct prediction of the pressure build-up in a pre-chamber engine.…”