# Knock modelling: analysis of its sensitivity to spark advance

This blog post describes the modelling method for knock detection in a gasoline engine. The knock model is modelled based on an AnB correlation, where A, B and n are parameters that depend on fuel type. It is described by the Arrhenius equation, which is empirically derived and describes the temperature dependent reaction rate. The correlations are derived by matching the Arrhenius function to measure data on induction and auto-ignition times, for given fuel-air mixtures, over the relevant mixture pressure and temperature ranges. The specific correlation used is that proposed by Douaud and Eyzt. A precursor, which depends on the evolution of auto-ignition delay, i.e. the elapsed time from the start of the end-gas compression to the time of auto-ignition, and a fixed criteria for concentration of critical species required to initiate auto-ignition are used together to determine whether auto-ignition occurs before the normally propagating flame consumes the end gas. Auto-ignition delay is dependent on

• Fuel octane number
• Instantaneous cylinder pressure
• Unburnt gas temperature
• Fuel/air equivalence ratio
• 8 calibration parameters

Knock intensity is simply computed using a correlation. The criterion is based on the energy released by spontaneous auto-ignition of the remaining fresh charge at knock timing normalized by the total energy to be released by combustion through flame propagation. Four levels of intensity are distinguished:

1. K_intensity<0.5: no knock
2. 0.5<=K_intensity<1: trace knock
3. 1<=K_intensity<1.5: medium knock
4. 1.5<=K_intensity: strong knock

Details of the modelling method described can be found in [1], [2].

The engine studied is a 1.2 litre three cylinder spark ignition naturally aspirated engine.

Figure 1: knock intensity with spark advance of 10 degree

Figure 2: knock intensity with spark advance of 13 degree

Figures 1, 2, 3 and 4 show simulation result for knock intensity, at spark advance of 10, 13,17 and 20 crank angles (CA) respectively. The BMEP values only consider pumping losses and friction losses in this case. It is seen in all cases that low load high engine speed points have less tendencies to reach auto-ignition than high load low engine speed points. Increasing spark advance will increase corresponding BMEP at each speed point, but knock tendency is also increased.

Figure 3: knock intensity with spark advance of 17 degree

Figure 4: knock intensity with spark advance of 20 degree

For example, no knock is observed at 5500 rpm for all load points with spark advance of 10 CA, figure 1. This is the case also when the spark advance is increased to 13 CA, figure 2. One strong knock and one medium knock points are observed with the spark advance of 17 CA, figure 3. Three strong knock points are observed with spark advance increased to 20 CA. Increase of spark advance by 3 CA is sufficient to go from medium knock to strong knock. Knock behaviour can also be affected by residual gas and Air Fuel Ratio, effect of that to knock will be studied in the future.

[1] S. Richard, S. Bougrine, G. Font, F.A. Lafossas and F. Le Berr, “On the reduction of a 3D CFD combustion model to build a physical 0D model for simulating heat release, knock and pollutants in SI engines”, Oil & Gas Science and Technology, volume 64, No. 3, pp. 223-242, 2009.

[2] J.B. Heywood, “Internal combustion engine fundamentals”, McGraw Hill Book Company, 1988.

Written by: Xiaoran Han – Project Engineer

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