The potential of statistical RANS to predict knock tendency: Comparison with LES and experiments on a spark-ignition engine

Pollutant regulations and fuel consumption concerns are the driving guidelines for increased thermal efficiency and specific power in current internal combustion engines. The achievement of such challenging tasks in Spark Ignition units is often limited by the onset of knock, which hinders the possibility to operate the engine with the optimal combustion phasing. The sporadic occurrence of individual knocking events is related to cycle-to-cycle variability of turbulent combustion. This is avoidable by only accepting a safety margin from its earliest onset. On one side, the stochastic nature of knock and turbulence-related combustion variability would indicate Large-Eddy Simulation (LES) as the most appropriate technique for CFD analyses. Nevertheless, Large-Eddy Simulation remains a very time- and CPU-demanding approach, hardly integrated in the industrial timeframe for the design exploration and development of new units. Therefore, Reynolds Averaged Navier Stokes (RANS) models representing the average flow are chosen to limit CPU and development times, though they suffer from the intrinsic inability to account for cycle-dependent phenomena (e.g. knock). This is particularly critical at knock-borderline conditions, where far-from-average knocking events may occur. A previously developed statistical RANS-PDF knock model partly overcomes this limitation using equations for mixture fraction and enthalpy variance, ultimately reconstructing log-normal distributions of knock intensity. This allows RANS simulations to be directly compared to the usual statistical knock analysis at the test-bench. In this paper all the mentioned modelling techniques (LES, RANS and BANS-PDF) are applied to simulate combustion and knock in a currently made turbocharged GDI engine under knock-safe, knock-limited and light knocking conditions. The study relevance lays in the critical comparison of the results. The full potential of the statistical RANS-PDF model for engine development is highlighted on a coherent basis. The possibility to preserve the RANS formalism while enriching the results with knock statistical description is a relevant advancement in the virtual design of high-efficiency engines.