Autoignition prediction capability of the Livengood–Wu correlation applied to fuels of commercial interest

Abstract

The integral method proposed by Livengood and Wu has been traditionally used to predict the occurrence of knock on spark-ignition engines. Due to its simplicity and low computational demand, this is a method of great interest for the prediction of another autoignition phenomenon, such as the onset of combustion in compression ignition or homogeneous charged compression ignition engines. However, the simplicity of the method is a consequence of the restrictive assumptions considered during its development, which may limit the applicability of the equation. In this study, the validity of the correlation proposed by Livengood and Wu has been evaluated at different initial operative conditions under pure homogeneous charged compression ignition combustion mode for fuels with practical interest (hydrogen, methane, ethanol and n-heptane). The integral method has shown very good prediction capability for the fuels, which do not present two-stage heat release (hydrogen, methane and ethanol) except in those cases when the onset of combustion is very delayed. When cool flames appear (as in the case of n-heptane), the integral method overpredicts the autoignition times since it does not consider the first stage of heat release. In these cases, the prediction of the integral method may be improved if the whole combustion process is considered as two individual processes. This approach shows fairly good prediction capacity although it is unpractical since the simulation of the second-stage combustion requires the previous calculation of the composition of the mixture and the temperature increase at the end of the first stage. Finally, two alternatives to the original integral method are tested which keep its simplicity and universality while taking into account both first and second heat release, one of them showing better results than the original Livengood and Wu equation.

A new method to predict high and low-temperature ignition delays under transient thermodynamic conditions and its experimental validation using a Rapid Compression-Expansion Machine

“…• The alternative integral proposed by Hernandez et al [19] has also been evaluated for the cases that show cool flames.…”

“…Hernandez et al [19] analyzed the validity of the Livengood & Wu in-tegral by simulations performed with CHEMKIN for several fuels and with various chemical kinetics mechanisms. They proved that the predictions of the method are accurate if the fuel do not show a two-stage ignition pattern.…”

A predictive Livengood–Wu correlation for two-stage ignition

“…In this section, the viability of the staged L-W integral method in predicting the two-stage auto-ignition is evaluated based on its performance in an HCCI engine fueled with either n -heptane or DME. The engine geometry considered is similar to that of Hernández et al 15 : an HCCI engine with a 30 cm 3 combustion chamber and a crank-rod ratio of 3. Two different compression ratios ( CR ) are used here ( CR 18 for n -heptane and CR 16 for DME).…”

Simplifying ignition delay prediction for homogeneous charge compression ignition engine design and control

“…To account for the temporal variation in ignition correlation parameters, such as temperature and pressure, the Livengood-Wu (LW) integral 30 is often employed. [31][32][33] This integral method was developed by the authors based on the evolution of a global combustion reaction subject to temperature and pressure changes and the delay time emerges as a characteristic relaxation time that depends on the prevailing thermodynamic conditions. Auto ignition occurs when the LW integral, I LW , is unity…”