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Downsizing by turbo charging is a current approach for the reduction of fuel consumption of Spark Ignition (SI) engines. For downsized engines compression ratio has to be set as high as possible to achieve substantial gains in thermodynamic efficiency. Unfortunately, the possibility to take full advantages offered by downsizing is limited by knock phenomenon, which imposes constraints both on supercharging and compression ratios. Quasi-dimensional and multidimensional simulation can play a role of increasing importance for the design and the optimization of future engine prototypes more and more based on advanced combustion concepts, provided that well proven tools for knock simulation may be available.

In this work the authors present a model to simulate the in-cylinder pressure oscillations due to knock. Pressure oscillations are predicted by the explicit integration of a Partial Differential Wave Equation (PDWE) similar, in its structure, to the so-called “Equation of Telegraphy”. This equation differs mainly from the classical wave formulation for the presence of a loss term. The general solution of such equation is obtained by the Fourier method of variables separation. The integration space is a cylindrical acoustic cavity whose volume is evaluated at the knock onset. The integration constants are derived from the boundary and initial conditions. A novel approach is proposed to derive the initial condition for the derivative of the oscillating component of pressure. It descends, conceptually, from the integration of the linearized relation between the derivative of pressure versus time and the expansion velocity of burned gas.