Simulation of knock probability in an internal combustion engine

In spark-ignition internal combustion engines, fluctuations of the in-cylinder pressure trace and the tendency of combustion knock are usually different from one cycle to another. These cycle-to-cycle variations are affected by the initial state at ignition time and the subsequent burning. The occurrence of the phenomena is unpredictable, and their stochastic nature offers challenges in the optimization of engine control strategies. In this paper, a simulator providing a series of cycle-to-cycle varied in-cylinder pressures is introduced. The Wiebe function and Livengood-Wu integration are used to describe the determinacy of combustion. Various means, including the Markov chain, are introduced to express the stochastic quantities during combustion. In addition, the combustion of a given knock probability is simulated.

Figure 1

Schematic view of spark-ignition engine.

Figure 2

In-cylinder pressure of 10 successive cycles.

Figure 3

Configuration of the engine-dynamometer test bench.

Figure 4

Measured in-cylinder pressure.

Figure 5

The schematic diagram of the calculation of $Q_{\text{total}}$, ${\theta }_{90}$, and ${\theta }_{10}$.

Figure 6

Structure of the simulation model.

Figure 7

Experimental ${\theta }_{90}$ frequency distribution.

Figure 8

Relationship of the total heat release $Q_{\text{total}}$ ($y$ axis) and ${\theta }_{90}$ ($x$ axis) according to the experimental data.

Figure 9

Experimental ${\theta }_{10}$ frequency distribution.

Figure 10

Fitted relationship between the Livengood-Wu knock integration $I$ and ${\theta }_{90}$.

Figure 11

Simulated in-cylinder pressure for 1000 cycles. (a) Given knock probability $K=0.01.$ (b) Given knock probability $K=0.03.$ (c) Given knock probability $K=0.05.$

Figure 12

Simulated Livengood-Wu knock integration $I$ for 1000 cycles. (a) Given knock probability $K=0.01.$ (b) Given knock probability $K=0.03.$ (c) Given knock probability $K=0.05$.

Figure 13

Simulated Livengood-Wu knock integration $I$ for 500 cycles.