Estimation of the polytropic index for in-cylinder pressure prediction in engines

Abstract

Compression and expansion strokes in internal combustion engines can be characterized by the well-known polytropic process, PVn = constant, which describes the relationship between the in-cylinder volume and the pressure. This process is widely used to estimate the in-cylinder pressure during the compression stroke before combustion occurs; the polytropic index (n) is a key parameter for calculating the pressure accurately when volume data are given. However, the polytropic index changes with different engine operating conditions. Therefore, using the same value for the polytropic index under different operating conditions can decrease the accuracy of the pressure prediction during the compression stroke. It can also affect pressure modelling during combustion in which the pressure at the end of the compression stroke is used as an initial condition. Therefore, it is important to obtain an appropriate polytropic index to predict the in-cylinder pressure precisely.This study focused on a methodology to estimate the polytropic index for real-time applications. Heat loss from the in-cylinder gas was considered a major factor affecting the polytropic index. Therefore, a model of the polytropic index (n) could be established as a simple linear equation, ‘n=nisen+QlossT1×S’, where the heat loss (Qloss) is the main variable. nisen means the polytropic index with isentropic condition and T1 is the temperature of the in-cylinder gas when the compression starts. S which indicates the slope of the linear equation is inversely proportional to the compression ratio during the compression stroke. The main variable, heat loss, was modelled to complete the whole model of the polytropic index, and Woschni’s correlation was adopted to estimate the heat loss from the in-cylinder gas. The index model was established with 220 steady-state experimental cases using a 1.6-L compression-ignition (CI) engine. In addition, the pressure at the end of the compression stroke could be predicted using the modelled index with the polytropic process. The model could be validated against 1.6-L CI engine which has different compression ratio and in-cylinder geometry compared with the test engine. This study can contribute to a quantitative understanding of which parameters affect the in-cylinder pressure during the compression stroke. It will also be helpful for establishing a whole in-cylinder pressure prediction model for internal combustion engines; the pressure information obtained from such a model could be used for emissions modelling and combustion control.