[Paper Review] Combustion Process in a Spark Ignition Engine: Analysis of Cyclic Maximum Pressure and Peak Pressure Angle

Grzegorz Litak, Kaminski, T.+3 more|arXiv (Cornell University)|Nov 29, 2006

Combustion and flame dynamics29 references3 citations

TL;DR

This study analyzes cycle-to-cycle variations in maximum pressure ($p_{\text{max}}$) and peak pressure angle ($\alpha_{\text{pmax}}$) in a four-cylinder spark ignition engine across three spark advance angles (5°, 15°, 30°). Using return maps, histograms, and multiscale entropy, it identifies $\Delta\alpha_z = 15^\circ$ as optimal due to minimal joint fluctuations in $p_{\text{max}}$ and $\alpha_{\text{pmax}}$, indicating stable combustion with balanced power output and low instability.

ABSTRACT

In this paper we analyze the cycle-to-cycle variations of maximum pressure $p_{max}$ and peak pressure angle $α_{pmax}$ in a four-cylinder spark ignition engine. We examine the experimental time series of $p_{max}$ and $α_{pmax}$ for three different spark advance angles. Using standard statistical techniques such as return maps and histograms we show that depending on the spark advance angle, there are significant differences in the fluctuations of $p_{max}$ and $α_{pmax}$. We also calculate the multiscale entropy of the various time series to estimate the effect of randomness in these fluctuations. Finally, we explain how the information on both $p_{max}$ and $α_{pmax}$ can be used to develop optimal strategies for controlling the combustion process and improving engine performance.

Motivation & Objective

• To investigate cycle-to-cycle variations in $p_{\text{max}}$ and $\alpha_{\text{pmax}}$ in a spark ignition engine under different spark advance angles.
• To assess the influence of spark timing on combustion stability using statistical and nonlinear time series analysis.
• To determine optimal spark advance for minimizing combustion fluctuations and maximizing engine efficiency.
• To evaluate the role of multiscale entropy in quantifying randomness and complexity in pressure dynamics.
• To develop a dual-variable criterion based on joint standard deviation of $p_{\text{max}}$ and $\alpha_{\text{pmax}}$ for combustion optimization.

Proposed method

• Acquired experimental pressure data from a 1998 cm³ Holden MPFI engine at 1000 rpm with 0.7° crank angle resolution.
• Collected 2000-cycle time series for $p_{\text{max}}$ and $\alpha_{\text{pmax}}$ at spark advance angles of 5°, 15°, and 30° before TDC.
• Applied return maps and histograms to visualize statistical properties and cyclic behavior of $p_{\text{max}}$ and $\alpha_{\text{pmax}}$.
• Calculated multiscale entropy (MSE) to quantify the complexity and randomness of fluctuations in the pressure signals.
• Constructed $p_{\text{max}}$-$\alpha_{\text{pmax}}$ diagrams (reminiscent of bifurcation plots) to analyze fluctuation patterns across spark advance settings.
• Proposed an optimization criterion based on minimizing the joint standard deviation $\sigma(p_{\text{max}}, \alpha_{\text{pmax}})$ in the two-dimensional phase space.

Experimental results

Research questions

• RQ1 How do cycle-to-cycle variations in $p_{\text{max}}$ and $\alpha_{\text{pmax}}$ change with different spark advance angles?
• RQ2 What is the relationship between $p_{\text{max}}$ and $\alpha_{\text{pmax}}$ fluctuations and combustion stability?
• RQ3 Can multiscale entropy distinguish the complexity of pressure dynamics across different spark timing conditions?
• RQ4 Is there a specific spark advance angle that minimizes joint fluctuations in $p_{\text{max}}$ and $\alpha_{\text{pmax}}$?
• RQ5 Can a dual-variable criterion based on $\sigma(p_{\text{max}}, \alpha_{\text{pmax}})$ serve as a reliable indicator for optimal combustion efficiency?

Key findings

• At $\Delta\alpha_z = 15^\circ$, the joint standard deviation $\sigma(p_{\text{max}}, \alpha_{\text{pmax}})$ is minimized, indicating optimal combustion stability.
• For $\Delta\alpha_z = 5^\circ$, $\alpha_{\text{pmax}}$ fluctuations dominate, suggesting misfire or identification ambiguity, while $p_{\text{max}}$ remains relatively stable.
• For $\Delta\alpha_z = 30^\circ$, $p_{\text{max}}$ fluctuations are largest, indicating unstable or fast-burning combustion with high pressure oscillations.
• The $p_{\text{max}}$-dominated fluctuation pattern at $\Delta\alpha_z = 30^\circ$ corresponds to fast heat release, which is less effective than slow burning.
• The $\alpha_{\text{pmax}}$-dominated pattern at $\Delta\alpha_z = 5^\circ$ is linked to weak combustion or misfires, reducing fuel burn efficiency.
• Multiscale entropy analysis confirms that the $p_{\text{max}}$ sequence exhibits the simplest dynamics, while $\alpha_{\text{pmax}}$ shows higher complexity due to measurement ambiguity or misfires.