A real-time pressure wave model for knock prediction and control

This article develops a control-oriented real-time zero-dimensional knock pressure wave model for spark-ignited engines based on the reaction-based two-zone combustion model developed earlier. This knock pressure wave model is capable of predicting the in-cylinder pressure oscillations under knocking combustion in real-time and can be used for the model-based knock prediction and control. A pressure wave equation including the knock deadening behavior is proposed, simplified, and used to calculate the pressure perturbations generated by knock combustion. The boundary and initial conditions at knock onset are analyzed and the analytic solution of the pressure wave equation is obtained. The model is calibrated and validated over two engine operating conditions at knock limit. The chemical kinetic-based Arrhenius integral and the maximum amplitude of pressure oscillations are used as the evaluation methods for knock onset and intensity prediction, and the knock frequency is studied using a fast Fourier transform of the filtered in-cylinder pressure oscillations. The simulation results show that the proposed knock pressure wave model is able to predict the knock onset timing, frequency, and intensity accurately under two engine operating conditions. Furthermore, the knock characteristics associated with gas mixture properties at intake valve closing is analyzed based on the experimental data, and their effect to knock cycle-to-cycle variation is also studied for the proposed model.