Inhomogeneity, autoignition centres, and hot spots

There is also the possibility that inhomogeneity can arise from molecular fluctuations within an otherwise homogeneous medium. However, results of the quantitative studies of van Tiggelen [169] and Borisov [170] suggest this effect would be relatively weak under engine conditions. 

The wall boundary layer of the cylinder head of a Sandia research engine has been observed by Lucht et al. [171] using mean temperatures measured by CARS. Their data for a motored engine are relevant to autoignition and at tdc the mean temperature gradient was between 40 and 50 K/mm, at a distance of 1 mm from the surface. This increased as the surface 

Inhomogeneities, however caused, can be amplified by pre-ignition reaction. The conditions under which they can give rise to autoignition centres and hot spots have been examined in terms of turbulent structure and simple thermal explosion theory. Bradley [180] assumed the size of an autoignition centre to have the spatial scale of temperature inhomogeneities, distributed about the integral thermal scale of the gas dynamic turbulence. These distributed sizes were compared with computed critical sizes for thermal explosion, for different values of chemical parameters in 

Here A is the Arrhenius constant, p the mass density, nif, the mass fraction of the fuel, AH the enthalpy of reaction and E the activation energy. This approach yielded values for both the probability that an autoignition centre could be large enough to become critical and, if it was, the associated localized overpressure at the hot spot. Both the probability and the overpressure increased with temperature and AHpm/A, but decreased with the activation temperature, EIR. Just prior to criticality the hot-spot temperature was about 10% above that of the surrounding gas. Concentration fluctuations, particularly of active species, would have a similar effect. A strong localized explosion can cause knock, the intensity of which depends not only upon the localized overpressure, but on how the pressure pulse so created interacts with the remaining end gas. 

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