Study of engine knock using a Monte Carlo method

Kim, K. S. Study of Engine Knock Using a Monte Carlo Method. University of Wisconsin-Madison, 2015.

A simple yet accurate cyclic variation and coupled knock model were developed to predict the statistical distribution of both knock onset and knock intensity. The factors controlling knock onset and knock intensity in spark ignition engine were investigated. New methods of more accurately determining the knock onset timing and heat release calculation were developed to determine accurate thermodynamic conditions at knock.

Knock onset was accurately determined using median and smoothing filters to avoid biases associated with the Butterworth low- and high-pass filter at a transient pressure increase. The noise calculated before the initial pressure rise was used to dynamically set a threshold value to determine knock onset. The new method showed accurate determination of knock.

The most critical parameter for heat release calculations was found to be the calculation window size that limits the integration of the energy balance. Fixed, adjusted and individual window size of heat release calculation were compared using the in-cylinder pressure predicted by a thermodynamic engine model. The individual end angle determined using a Wiebe function-based method showed the most accurate results.

A simple model to simulate cycle-by-cycle variation that is suitable for use in Monte-Carlo approaches has been developed and validated with a wide range of experimental data. Using the cumulative density function of &thetas; ig, and linear fits of &thetas;comb and m to &thetas;ig, with a random component added, a Monte-Carlo scheme was developed. The universal coefficients to determine the linear fit between Wiebe function parameters at an arbitrary condition were found and reasonable distributions were predicted from the universal cyclic variation model.

Knock onset was predicted using three models: an ignition-integral model using a simple ignition delay correlation, an ignition-integral model using a pre-computed lookup tables of ignition delays, and the direct integration of a detailed chemical kinetic mechanism. All three models were found to compare well with experimentally measured results. A stochastic knock intensity predicting model was developed. The correlation to predict the upper-limit knock intensity was found from volume expansion-based pressure rise calculation. The coupled model showed a reasonable match of knock onset and knock intensity distribution compared to the experimental data.