Some Insights on the Stochastic Nature of Knock and the Evolution of Hot Spots in the End-Gas During the Engine Cycle from Experimental Measurements of Knock Onset and Knock Intensity

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 P_ko, the pressure, and (∂T/∂x) is the temperature gradient in the hot spot at knock onset. Then, from experimental measurements of KI and P_ko, using five different fuels, with the engine operating at boosted conditions, a probability density function for (∂T/∂x) was established. In this paper the knock data for two other non-boosted operating conditions for the same fuels at the same engine speed in the same engine are analyzed. The crank angle at knock onset for a given fuel is more advanced at these two new conditions because of the more advanced spark timing needed to obtain knock, and this enables some insights to be gained on how the hot spots evolve during an engine cycle. With increasing crank angle, the mean absolute value of (∂T/∂x) decreases and its distribution narrows. This is consistent with a simple picture that at the start of compression in the engine cycle there is a wide distribution of scales in the turbulent temperature field and the mean temperature gradient is large but conditions become more homogenized with time (crank angle). The paper presents distributions in terms of normalized counts in histograms for other parameters related to knock onset as well as knock intensity which might be of use in modeling knock stochastically.