A Mixing Timescale Model for PDF Simulations of LTC Combustion Process in Internal Combustion Engines

Transported probability density function (PDF) methods are currently being pursued as a viable approach to model the effects of turbulent mixing and mixture stratification, especially for new alternative combustion modes as for example Homogeneous Charge Compression ignition (HCCI) which is one of the advanced low temperature combustion (LTC) concepts. Recently, they have been applied to simple engine configurations to demonstrate the importance of accurate accounting for turbulence/chemistry interactions. PDF methods can explicitly account for the turbulent fluctuations in species composition and temperature relative to mean value. The choice of the mixing model is an important aspect of PDF approach. Different mixing models can be found in the literature, the most popular is the IEM model (Interaction by Exchange with the Mean). This model is very similar to the LMSE model (Linear Mean Square Estimation). Other models are available in the literature, e.g. the MC model (Modified Curl model), the EMST model (Euclidian Minimum Spanning Tree) and the PMSR model (Pairwise Mixing Stirred Reactor). The IEM and the LMSE models relax scalar values in each particle to the mean with a characteristic time ?t computed by the intensity of scalar mixing. These deterministic models are attractive for engine combustion process modeling, because they are easy to implement and give reliable results with a short computational time. However, the numerical solution of the system is strongly linked to particles number and scalar dissipation rate. This latter requires modeling in order to take into account the physical phenomena it stands for. In a previous study, an IEM model has been used to describe the mixing in a stochastic reactor model that simulates the HCCI process (LTC combustion). In this study, the turbulent time scale ?t included in IEM model is modeled through the turbulent kinetic energy and its dissipation. Hence, a (k-?) turbulence model based on zero-dimensional energy cascade applied during the compression and the expansion cycle is presented. On another hand, the confidence interval introduced in this approach related to the initial heterogeneities amplitude of temperature and of species mass has been described as a function of the turbulent Reynolds number. The in-cylinder pressure predicted by the model was validated against the experimental results by using two different single cylinder engines. One engine was equipped with an optical access in order to follow the evolution of HCCI combustion process. For both engines HCCI combustion was applied by using early injection timings in order to ensure homogeneity of the in-cylinder charge. For both engines a good agreement has been observed in terms of in-cylinder pressure traces. At varying engine operating conditions, the mean relative error levels are lower than 3%.