Arrhenius type empirical ignition delay equations based on the phenomenology of in-cylinder conditions for wide operating ranges in modern diesel engines

Ignition delays were systematically measured in a DI diesel engine under wide ranging and various engine operating conditions, including engine speeds, fuel injection pressures, intake gas temperatures, intake gas pressures, and intake oxygen concentrations changed with EGR. Empirical equations to predict the ignition delay based on the Arrhenius equation with and without the Livengood-Wu integral and multiple regression analysis of the experimental results. The simple equation assuming constant conditions during the ignition delay without the Livengood-Wu integral can accurately predict the ignition delay. However, the lack of generality has remained as the fuel injection pressure is directly included in the Arrhenius equation which should contain only the chemical parameters. To improve the generality of the equation, the ignition delay was separated into the initial physical process of the fuel spray breakup and the following chemical process. The start of the Livengood-Wu integral was set at the breakup time of liquid fuel jet assuming that the chemical reactions do not occur before the fuel spray breakup, and that the physical factors are directly involved in the physical processes and indirectly in the chemical processes. The fuel spray tip dynamics based on Wakuri’s momentum theory was introduced to express the changes in the conditions in the fuel spray during the ignition delay. The ignition delay can be accurately predicted by the equation with the Livengood-Wu integral and six parameters, including the breakup time, the mass flow rates of air and fuel at the cross section of the spray tip, the oxygen partial pressure, the engine speed, and the averaged in-cylinder gas temperature. The empirical equation predicted longer ignition delays at high ignition pressure conditions, and the accuracy was improved by performing a multiple regression analysis separately at each fuel injection pressure, suggesting unknown factors varying with the fuel injection pressures.