Estimation of double-Wiebe function parameters using least square method for burn durations of ethanol-gasoline blends in spark ignition engine over variable compression ratios and EGR levels

• Published in: Applied thermal engineering 2011-10, Vol.31 (14), p.2213-2220
• Main Authors: Yeliana, Yeliana, Cooney, C., Worm, J., Michalek, D.J., Naber, J.D.
• Format: Article
• Language: English
• Subjects: Applied sciences; Burn durations; Burns; Combustion; Combustion modeling; Computer simulation; Cylinders; Energy; Energy. Thermal use of fuels; Engines; Ethanol; Exact sciences and technology; Heat transfer; Least squares method; Mathematical analysis; Mathematical models; Spark ignition engine; Theoretical studies. Data and constants. Metering; Wiebe function
• ISSN: 1359-4311
• DOI: 10.1016/j.applthermaleng.2011.01.040

Phasing and duration are two of the most important aspects of combustion in Spark Ignition (SI) engines. They impact efficiency, emissions, and overall engine performance. These aspects of combustion can be represented by the mass fraction burn (MFB) profile. Having an accurate mathematical model of the MFB profile leads to an ability to model the combustion process and, thus, properly model the overall engine in 1D engine simulation tools. The Wiebe function is widely used in engine simulation to estimate the MFB profile as a function of crankshaft position. In this work, for the purpose of validating a sub-process, the Wiebe function parameters were calculated using an analytical solution and a least squares method by fitting MFB locations, as determined from analysis of measured cylinder pressure, to both single and double-Wiebe functions. To determine the accuracy of the respective Wiebe function, a single-zone pressure model was applied to reconstruct the pressure trace. Once the pressure trace is recovered, the reconstructed pressure trace is then compared with the experimentally measured cylinder pressure trace. Results showed that the double-Wiebe function model fit better than the single-Wiebe function model. The root mean square error (RMSE) of the reconstructed pressure trace using the double-Wiebe estimation is 7.9 kPa. In comparison, the RMSEs of the reconstructed pressure traces using the single-Wiebe analytical solution and single-Wiebe least squares methods were 70.0 kPa and 75.9 kPa, respectively, demonstrating a significant improvement. ► The Wiebe function is widely used in engine simulations to represent the mass fraction burn profile as a function of crankshaft position. ► In many cases, a single Wiebe function does not sufficiently represent the mass fraction burn profile, particularly under high dilution and knocking combustion conditions. ► A double-Wiebe function can be used to characterize the non-symmetric combustion resulting from extreme engine operating conditions. ► It is found that the double-Wiebe function model fit the experimental mass fraction burn profiles better than the single-Wiebe function model.