Use of Fractal Geometry to Model Turbulent Combustion in SI Engines

Abstract

Use of fractal geometry to model the effects of turbulence on flame propagation in an engine is explored using a quasidimensional, 4-stroke, homogeneous charge, SI engine code. This application of fractal geometry requires a new interpretation of the effect of turbulence on the combustion process in an engine. Specifically, flame wrinkling, rather than entrainment, is assumed to be the dominant effect of turbulence on the combustion process. Various simplifications are made in the formulation of the engine model to allow this fractal technique to be investigated as expeditiously as possible. Model predictions are compared to experimental data from an engine with an axisymmetric pancake-shaped combustion chamber. The sensitivity of the model predictions to the fractal dimension, to the effects of flame stretch, and to the ratio of maximum-to-minimum flame wrinkling scales is investigated. It is shown that the predicted initial rate of pressure rise is a strong function of the fractal dimension but is relatively insensitive to the flame wrinkling scales or the effects of stretch over the ranges of these parameters expected for the engine application. Following early flame growth, the model predictions are sensitive to the ratio of wrinkling scales, to the fractal dimension, and to the effects of stretch. Due to the sensitivity of the predictions to the fractal dimension revealed during the initial sensitivity analysis, three submodels which account for the effects of the turbulence intensity and of the laminar flame speed on the fractal dimension were incorporated in the code. These submodels appear to be reasonable and yield values for the fractal dimension which agree with the limited experimental engine data available. Also, due to the sensitivity of the predictions to the flame stretch effect, a simple submodel to account for stretch is introduced, making the present engine model the first quasidimensional engine code to account for the effects of flame stretch. It is predicted that flame stretch is dominated by flame strain and decreases throughout the combustion process. The most significant uncertaintly in the model after early flame growth is the ratio of the flame wrinkling scales. The model results lead the authors to believe that the Fractal Engine Model is very promising and that the use of fractals to model turbulent combustion is an important new tool for engineering design and development. Finally, experimental and theoretical needs arising from the present results are identified.

Key words:

• spark ignition engines
• engine models
• turbulent combustion
• fractal geometry