Combustion regime of a reacting front propagating into an auto-igniting mixture

Abstract

To characterize and model the combustion of a reactant mixture in a spark-assisted compression ignition (SACI) engine, one-dimensional reaction front propagation into end-gas mixtures with varying degrees of reaction progress is simulated using a skeletal iso-octane mechanism with variable transport properties. The dominant mechanism for the end-gas auto-ignition and combustion is identified based on a ratio of the corresponding flame to homogeneous ignition time scales, as a means to distinguish the transport-controlled and chemistry-controlled combustion regimes. The results indicate that reaction fronts propagating into end-gases are deflagrative provided that the temperature at the reaction front base is below 1100 K, while beyond this temperature, transport has little effect on the one-dimensional solution, indicating that reaction front propagation is chemistry-controlled. The results suggest that reaction front combustion regimes are strongly influenced by and can be separated with the end-gas temperature at the base of the reaction front.

Introduction

Homogeneous charge compression ignition (HCCI) engines are an alternative internal combustion (IC) engine design towards higher efficiency and lower emissions by utilizing low temperature combustion [1], similar to other highly dilute combustion concepts in steady burner applications, such as mild combustion [2], [3]. HCCI engines can produce high brake thermal efficiency with ultra-low oxides of nitrogen (NO_x) emissions [4], [5], [6], [7], [8], but are limited in operating range due to the lack of a direct mechanism for combustion phasing and rate control [1]. To improve upon this control issue, concepts utilizing multiple premixed combustion modes [9], such as spark-assisted compression ignition (SACI) [10], [11], [12], [13], have been introduced. SACI is similar to end-gas knock in conventional spark-ignited (SI) engines in that a turbulent deflagration propagates through a portion of the combustion chamber prior to end-gas auto-ignition.

The simulation work of Huang et al. has shown that the high end-gas temperatures of HCCI and SACI mixtures are capable of supporting premixed laminar flames, except at highly dilute, low load operating conditions [14]. Optical engine images of SACI, HCCI and knocking SI combustion support this conclusion. For example, Zigler observed organized reaction fronts with expansion speeds between 2 and 5 m/s during the initial deflagration phase of SACI combustion [12]. Similar SACI flame expansion speeds, ranging from approximately 0.5–10 m/s, were also reported by Persson et al. [13]. Apparent reaction front propagation from ignition kernels has also been observed by Hultqvist et al. during the later stages of HCCI combustion [15]. Expansion speeds ranged between 5 and 30 m/s, and were attributed either to turbulent flame propagation or to front displacement via burned gas expansion. Schiessl et al. recorded similar mean ignition kernel expansion velocities on the order of 25 m/s with a spread of 16 m/s in the knocking end-gas of an SI engine [16]. Additional knocking SI engine experiments by König et al. showed reaction fronts propagating from end-gas ignition kernels with flame speeds between 6 and 9 m/s, while the main flame front propagated at 10.3–12.5 m/s [17].

The observed wide range of variation in the reaction front speed suggests that these fronts have controlling mechanisms that may be distinct from typical deflagration fronts. Zeldovich proposed two distinct regimes in premixed subsonic combustion, namely the deflagration and spontaneous ignition front regimes [18]. In the former, reaction front propagation is determined by the balance between reaction and diffusive transport, implying that the reaction fronts propagate at the laminar flame speed. In the spontaneous ignition front regime, the apparent propagation of the reaction front results from a cascade of ignition events, such that the reaction fronts often propagate at a much higher speed. Therefore, identification of the dominant mechanism for the front propagation is important in high-fidelity modeling of IC engines utilizing mixed-mode combustion.

A number of studies attempted to provide a rational and rigorous way to identify the front regimes. Gu et al. considered the ratio of characteristic temperature gradients [19]. More recent studies based on direct numerical simulation identified the regimes based on the front propagation speed compared to the reference laminar flame speed [20], [21]. Since the laminar flame speed cannot be uniquely determined for a mixture with composition stratification, a more systematic criterion based on the Damköhler number along the front norm has been suggested by Bansal and Im [22]. An alternative mathematical analysis based on computational singular perturbation has also been proposed [23].

The above approaches, however, inherently require full spatial and temporal resolution of the flow and reactive scalar fields during the auto-ignition events. Access to such details is not possible in full-cycle IC engine simulations, which often rely on sub-grid combustion models without full resolution of the reaction front. Recent approaches employed a bimodal switch between the flame and homogeneous reactor models depending on whether combustion is mixing or chemically controlled [24], [25]. The results of these simulations have shown dependencies to the criteria governing the model transition process [25]. Therefore, the objective of the present study is to develop a more pragmatic and accurate metric for the reaction front regime identification, especially under SACI-like conditions, in order to improve the predictive capability of full-cycle SACI engine simulations. A one-dimensional model problem of flame front propagation into an end-gas with varying degrees of reaction progress is adopted. Various derived quantities are compared and examined as candidates for front regime identification for a wide range of parametric conditions.