The calculation of mass fraction burn of ethanol-gasoline blended fuels using single and two-zone models

Document Type

Conference Proceeding

Publication Date



Department of Civil, Environmental, and Geospatial Engineering; Department of Mechanical Engineering-Engineering Mechanics


One-dimensional single-zone and two-zone analyses have been exercised to calculate the mass fraction burned in an engine operating on ethanol/gasoline-blended fuels using the cylinder pressure and volume data. The analyses include heat transfer and crevice volume effects on the calculated mass fraction burned. A comparison between the two methods is performed starting from the derivation of conservation of energy and the method to solve the mass fraction burned rates through the results including detailed explanation of the observed differences and trends. The apparent heat release method is used as a point of reference in the comparison process. Both models are solved using the LU matrix factorization and first-order Euler integration. Experiments were conducted with a Cooperative Fuels Research (CFR) engine holding Net Indicated Mean Effective Pressure (Net IMEP) constant at 330 kPa and fueling at the respective stoichiometric condition for the air flow and ethanol fuel blend being tested. This study included four ethanol-gasoline fuel blends: E20, E40, E60, E84, and gasoline (E0) as a baseline. The results show that all three models consistently produce similar mass fraction burned profiles for the five different fuels tested. Furthermore, utilizing the gasoline case with gamma as a function of temperature shows that the two-zone model indicated 3% higher combustion efficiency compared to the single-zone model and 17% higher than the apparent heat release method. However, the location of the 10%, 50%, and 90% mass fraction burn points calculated between the methods are within 1° of each other when combustion phasing is near maximum brake torque (MBT). For both the single and two-zone models, the effect of crevice and heat transfer effects appears near the end of the combustion process. Without the crevice model, the computed combustion efficiency of the single-zone model decreases by 8%. Without both crevice and heat transfer models the combustion efficiency decreases by 15% compared to the result of the single-zone full model. The combustion efficiency as calculated with the two-zone model decrease by 5% without crevice effects and 11% without both crevice and heat transfer effects.

Publisher's Statement

Copyright © 2008 SAE International. Publisher’s version of record: https://doi.org/10.4271/2008-01-0320

Publication Title

SAE Technical Papers