Peters, N., Kerschgens, B., and Paczko, G., "Super-Knock Prediction Using a Refined Theory of Turbulence," SAE Int. J. Engines 6(2):953-967, 2013, doi:10.4271/2013-01-1109.
The occurrence of severe events of ‘super-knock’ originating from random pre-ignition kernels which sometimes is observed in turbo-charged spark-ignition engines was recently attributed by Kalghatgi and Bradley  to developing detonations which originate from a resonance between acoustic waves emitted by an auto-igniting ‘hot spot’ and a reaction wave which propagates along negative temperature gradients in the fuel-air mixture. Their occurrence depends on the steepness of the local instantaneous temperature gradient and on the length of the region of negative gradient. The theory requires that the temperature gradient extends smoothly over a sufficient length in the turbulent flow field. Then localized detonations may develop which are able to autoignite the entire charge within less than a millisecond and thus cause pre-ignition and ‘super-knock’.In this paper we ascribe the stochastic occurrence of preignition and the resulting ‘super-knock’ events to the stochastic nature of turbulence. The detonation diagram proposed by Kalghatgi and Bradley  is combined with the results of a refined theory of small scale turbulence developed recently by the group of the first author. That theory - differently from traditional theories of turbulence - can predict the joint probability density of smooth temperature gradients and the length over which they extend. The joint probability density is obtained from Direct Numerical Simulations. It becomes universal when it is normalized by traditional turbulence quantities as they are used in CFD simulations. The detonation limits in the diagram of  will serve as integration limits when the joint probability density is integrated to obtain a detonation probability. Numerical CFD simulations of motored cycles for turbo-charged engines show that the highest detonation probabilities occur in localized regions in the bulk of the combustion chamber where the flow is rather uniform and where therefore the integral time scale is large. In these regions there is a high probability of a large local length over which a reaction wave can travel.The simulations predict a larger cycle probability for higher boost pressures, higher intake air and wall temperatures, lower engine speeds and lower octane numbers, if all the other boundary conditions remain the same. A higher spark plug temperature did not lead to an increase of pre-ignition probabilities.