Engine cycle modeling - Zerodimensional approach

The internal combustion engine has always fascinated many of our contemporaries. On the one hand, it plays a key role in the field of propulsion and energy conversion, and on the other, it generates constant scientific interest. Many phenomena are involved, requiring the designer or researcher to master a wide range of disciplines.

The aim of this presentation is to provide as exhaustive a state-of-the-art as possible of the mathematical models used to analyze internal combustion engine cycles, with a focus on models based on "envelope cycles" or a zerodimensional approach. The presentation will use the spark-ignition engine [AC or SI (Spark Ignition)] as an example. Compression-ignition engines [Diesel, D or CI (Compression Ignition)] and other applications, such as engines using homogeneous self-ignition combustion, will be discussed in a later article.

Mathematical models can be divided into two main groups: dimensional models and thermodynamic models (also known as zerodimensional). A sub-family of models is distinguished by the choice of the number of dimensions (1D – 3D) for dimensional models, or by the number of zones where the thermodynamic model is applied.

Zerodimensional models provide a simplified approach to the various phenomena involved in combustion in the cylinder. In fact, they do not involve any quantities linked to space, and therefore to propagation (in some cases, quantities may be introduced indirectly as a function of space variables). This type of model allows us to consider only the evolution of thermodynamic variables over time. In zerodimensional modeling, the subject of this article, the choice of a single zone assumes that all thermodynamic quantities (pressure, temperature, concentration, etc.) are uniform. By increasing the number of zones, certain evolution or initialization conditions can be specified for each one. The results can then be refined. For example, in the case of two zones, the contents of the cylinder can be assimilated to two species of composition corresponding respectively to those of the burnt and unburnt gases. Combustion progresses by flame front. The chemical oxidation reaction takes place in a negligible volume (flame front) compared to the volumes of the two zones. The flame front is considered a discontinuity between fresh and burnt gases.

Multiplying the number of zones will never achieve the results obtained with dimensional models, as thermodynamic models do not take into account convective transfer and diffusion effects. The equations governing 0D models are the first principle applied in an open system (conservation of energy), the perfect gas equation, conservation of mass, evolution of volumes and various sub-models enabling the cycle to be solved (sub-models...