Knock is a major design challenge for spark-ignited engines. Knock constrains high load operation and limits efficiency gains that can be achieved by implementing higher compression ratios. The propensity to knock depends on the interaction among fuel properties, engine geometry, and operating conditions. Moreover, cycle-to-cycle variability (CCV) in knock intensity is commonly encountered under abnormal combustion conditions. In this situation, knock needs to be assessed with multiple engine cycles. Therefore, when using computational fluid dynamics (CFD) to predict knock behavior, multi-cycle simulations must be performed. The wall clock time for simulating multiple consecutive engine cycles is prohibitive, especially for a statistically valid sample size (i.e. 30–100 cycles).

In this work, 3-d CFD simulations were used to model knocking phenomena in the cooperative fuel research (CFR) engine. Unsteady Reynolds-Averaged Navier Stokes (uRANS) simulations were performed with a hybrid combustion modeling approach using the G-equation method to track the turbulent flame front and finite-rate chemistry model to predict end-gas autoignition. To circumvent the high cost of running simulations with a large number of consecutive engine cycles, a concurrent perturbation method (CPM) was evaluated to predict knock CCV. The CPM was based on previous work by the authors, in which concurrent engine cycles were used to predict engine CCV in a non-knocking gasoline direct injection (GDI) engine. Concurrent cycles were initialized by perturbing a saved flow field with a random isotropic velocity field. By initializing each cycle with a perturbation sufficiently early in the cycle, each case yields a distinct and valid prediction of combustion due to the chaotic nature of the system.

Three operating points were simulated, with different spark timings corresponding to heavy knock, light knock, and no knock. For all the operating points, other conditions were based on the standard research octane number (RON) test specification for iso-octane. The spark timing of the heavy knock case was the same as that of the RON test. The in-cylinder pressure fluctuations were isolated using a frequency filtering method. A bandpass filter was applied to eliminate high and low frequencies. The knocking pressures were calculated consistently between the experimental and simulation data, including the sampling frequency of the data. The simulation data was sampled to match the sampling rate of the experimental data.

The knock intensities were compared for the concurrently obtained cycles, the consecutively obtained cycles, and experimental cycles. Knock predictions from the concurrent and consecutive simulations compared well to each other and with experiments, thereby demonstrating the validity of the CPM approach.

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