Understanding the Effect of Inhomogeneous Mixing on Knocking Characteristics of Iso-Octane by Using Rapid Compression Machine

As fuel injection strategies in spark-ignition (SI) engines have been diversified, inhomogeneous mixing of the fuel-air mixture can occur to varying extents during mixture preparation. In this study, we analyzed the effect of inhomogeneous mixing on the knocking characteristics of iso-octane and air mixture under a standardized fuel testing condition for research octane number (RON), based on ASTM D2699. For this purpose, we assumed that both lean spots and rich spots existed in unburned gas during compression stroke and flame propagation and calculated the thermodynamic state of the spots by using an in-house multi-zone, zero-dimensional SI engine model. Then, the ignition delay was measured over the derived thermodynamic profiles by using rapid compression machine (RCM), and we calculated ξ, the ratio of sound speed to auto-ignition propagation speed, based on Zel’dovich and Bradley’s ξ − ε theory to estimate knock intensity. As a result, we discovered that lean spots would have higher reactivity than stoichiometric mixture (ξ > 0), while rich spots would not (ξ < 0); thus, knocking has more tendency to be initiated from a lean spot. For further analysis, ξ was divided into two terms, ξ_T for temperature gradient and ξ_ϕ for equivalence ratio gradient, and each term was evaluated separately. At a lean spot, ξ_T is generally positive because temperature is higher than that of stoichiometric mixture due to smaller fuel charge cooling and higher specific heat ratio of the mixture. On the other hand, ξ_ϕ is negative but rapidly converges to zero as flame propagates; thus, ξ is determined dominantly by ξ_T. In addition, ξ from various spot radii and steepness of gradient were compared to analyze the effect of spot structure on knock intensity. As a result, we found that a steeper gradient of equivalence ratio leads to a weaker knock intensity, while the effect of radius change is negligible.