Alam, S., Rosa, S., Depcik, C., Burugupally, S.P., McDaniel, E., and Hobeck, J. (2021).  Modification of the Wiebe Function for Methane-air and Oxy-methane Spark-ignitions Engines.  Fuel, 303, 121218.

Abstract

Objectives

Predictive combustion models assess engine performance for given setpoints by determining the rate of heat release that is governed by the fuel mass burned. Often, simple mathematical functions such as the Wiebe function are used in simulations to provide mass fraction burned values at each integrated step. Despite its popularity, a limitation of the Wiebe function is that it generally does not take operating conditions into account. Therefore, there is a need for an adaptive Wiebe function that can be scaled for a given fuel and run-time conditions. Here, this is accomplished for methane-air combustion in a spark-ignition (SI) engine. A linear regression analysis was used to fit the adaptive Wiebe model to experimental data with an average R2 value of 0.965. The scaling process was expanded to include oxy-methane combustion for specialized SI applications, e.g., for stationary or mobile power generation in environments such as Mars. This was accomplished through an analysis of the laminar and turbulent flame speeds that dominate the combustion process and the charge burnup time. The results show that a relative increase in the turbulent flame speeds during oxy-methane combustion shrinks the combustion duration between 10% and 90% mass fraction burned by approximately 87% relative to air. Comparing these results with literature reveals that the scaled Wiebe function follows theory closely and is a reasonable tool for burnt mass and combustion duration predictions.