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Knock in spark ignition engines is stochastic in nature. It is caused by autoignition in hot spots in the unburned end-gas ahead of the expanding flame front. Knock onset in an engine cycle can be predicted using the Livengood-Wu integral if the variation of ignition delay with pressure and temperature as well as the pressure and temperature variation with crank angle are known. However, knock intensity (KI) is determined by the evolution of the pressure wave following knock onset. In an earlier paper (SAE 2017-01-0689) we showed that KI can be approximated by KI = Z (∂T/∂x)-2 at a fixed operating condition, where Z is a function of Pko, the pressure, and (∂T/∂x) is the temperature gradient in the hot spot at knock onset. Then, from experimental measurements of KI and Pko, using five different fuels, with the engine operating at boosted conditions, a probability density function for (∂T/∂x) was established.

Most studies on knock ignore the stochastic nature of knock and focus on the onset of knock which is determined by chemical kinetics. This paper focuses on knock intensity (KI) which is determined by the evolution of the pressure wave following knock onset in a hot spot and highlights the stochastic processes involved. KI is defined in this study as the maximum peak-to-peak pressure fluctuation that follows the onset of knock. It depends on ξ = (a/ua) where ua is the speed of the autoignition front and a is the speed of sound. When ua is small, KI can be related to the product of a parameter Z, which depends on Pko, the pressure at knock onset and the square of (∂x/∂T), which is the inverse of the gradient of temperature with distance in the hot spot. Both Z and (∂x/∂T) were calculated using measured KI and Pko for hundreds of individual knocking cycles for different fuels.