Improving computational fluid dynamics modeling of Direct Injection Spark Ignition cold-start

Abstract

Developing a profound understanding of the combustion characteristics of the cold-start phase of a Direct Injection Spark Ignition (DISI) engine is critical to meeting increasingly stringent emissions regulations. Computational Fluid Dynamics (CFD) modeling of gasoline DISI combustion under normal operating conditions has been discussed in detail using both the detailed chemistry approach and flamelet models (e.g. the G-Equation). However, there has been little discussion regarding the capability of the existing models to capture DISI combustion under cold-start conditions. Accurate predictions of cold-start behavior involves the efficient use of multiple models - spray modeling to capture the split injection strategies, models to capture the wall-film interactions, ignition modeling to capture the effects of retarded spark timings, combustion modeling to accurately capture the flame front propagation, and turbulence modeling to capture the effects of decaying turbulent kinetic energy. The retarded spark timing helps to generate high heat flux in the exhaust for the faster catalyst light-off during cold-start. However, the adverse effect is a reduced turbulent flame speed due to decaying turbulent kinetic energy. Accordingly, developing an understanding of the turbulence-chemistry interactions is imperative for accurate modeling of combustion under cold-start conditions. In the present work, combustion characteristics during the cold-start, fast-idle phase is modeled using the G-Equation flamelet model and the RANS turbulence model. The challenges associated with capturing the turbulent-chemistry interactions are explained by tracking the flame front travel along the Borghi-Peters regime diagram. In this study, a modified version of the G-Equation combustion model for capturing cold-start flame travel is presented.

G-equation based ignition model for direct injection spark ignition engines

“…The effects of the plasma expansion produced by the spark energy discharge are modeled on this quasi-laminar G-surface, which is subsequently transformed into a turbulent flame tracked by the G-Equation-based GLR combustion model. 4 From the onset of spark, the flame kernel growth rate is tracked by solving the mean of the non-reacting scalar, G:…”

“…Equation ( 4) represents b 3 as a function of two terms: turbulent integral length scale normalized by the laminar flame thickness (l=l f ), and turbulence intensity normalized by laminar flame speed (u 0 =S L ), that forms the abscissa and ordinate, respectively, of the Borghi-Peters regime diagram. Beginning from the spark timing when a G = 0 surface of, for example, 0.5 mm radius representing the early flame kernel is initialized at the spark location, each cell inside the cylinder is located on the Borghi-Peters diagram using the calculated values of l=l f and u 0 =S L , and b 3 is estimated via equation (4). The value of b 3 in each cell is updated for each time-step as a response to the changing values of the local equivalence ratio and the local turbulence.…”

“…The effects of the plasma expansion produced by the spark energy discharge are modeled on this quasi-laminar G-surface, which is subsequently transformed into a turbulent flame tracked by the G-Equation-based GLR combustion model. 4…”

“…is captured by this parameter. A summarized version of this modification, which is otherwise elaborated on in Ravindran et al, 4 will be presented here. The turbulent flame speed is modeled using Peters equation 21 given by:…”

“…The model derives its theory from the DPIK model and applies its concepts onto an Eulerian framework, thereby removing the need for Lagrangian particles to track the kernel growth. The local turbulent flame speed has been captured using the Peters 21 model, the accuracy of which has been improved by dynamically modeling the constant b 3 , as explained in Ravindran et al 4 It has been tested against experimental measurements from Maly and Vogel 1 and constant volume flame growth measurements from Nwagwe et al 2 Multi-cycle simulations were performed in CONVERGE 3 using the PVG ignition model in combination with the G-Equation model in a RANS framework to capture the combustion characteristics of a DISI engine. Additionally, the PVG ignition model was observed to substantially reduce the sensitivity of the default G-sourcing ignition method employed by CONVERGE.…”