Kalghatgi, G., Algunaibet, I., and Morganti, K., "On Knock Intensity and Superknock in SI Engines," SAE Int. J. Engines 10(3):2017, doi:10.4271/2017-01-0689.
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. The model for ignition delay as a function of pressure P and T in the hot spot and other data needed to calculate Z were available from a previous study (SAE 2016-01-0702). For a given fuel and operating condition, Z varies because Pko varies, because of cyclic variation of combustion - a stochastic process. (∂x/∂T) depends on the evolution of the hot spot during the engine cycle and depends on flow and turbulence - another stochastic process. All else being equal, Z increases and hence the probability of high KI increases as Pko increases, e.g., by more advanced spark timing and/or faster flame development. For a given Pko, Z is lower for a fuel with higher RON. In modern turbocharged engines extremely high intensity knock, informally termed superknock is observed to occur occasionally even though operating conditions are chosen to avoid knock. Superknock is caused by developing detonation (DD) which results when the value of ξ decreases and the pressure wave begins to couple with the autoignition front and gets amplified. Autoignition has to be initiated at high P and T for superknock to occur. At practical operating conditions, this can only happen via another abnormal stochastic phenomenon - preignition, when a flame is established before the spark plug fires. Both preignition and superknock become more likely as P increases. All else being equal, the probability of superknock decreases as the fuel RON is increased. However, even with high RON, high KI and superknock could occur with the right combination of P and (∂x/∂T).