An Application of Livengood-Wu Integral Method to Predict Time of Cool Flame Explosion During Piston Compression Process

Abstract

Livengood and Wu offered the following integration equation to predict the time of knock ^te, ∫^te₀ (1/τ)dt=1, along the end gas pressure time and temperature time histories, under the assumptions of zero order reaction and critical concentration of chain carriers, and showed that the agreement between the predicted and actual times of occurrence of autoignition is reasonable. An attempt is made in this paper to check on the utility of the integration procedure for cool flame explosions along the state time history of mixture during the motoring compression period. The pre-cool flame reaction which is primarily a degenerated branching reaction is taken to be similar to the zero order reaction and the critical concentration of active intermediate products is supposed to give rise to cool flame. Empirical coefficient and exponent in the general Arrhenius equation for the cool flame ignition delay τ₁ are found by the results obtained using a rapid compression machine developed here. Experimental results verify that this integration procedure is valid in the limited range of motoring compression temperatures where cool flame explosions occur T_c no more than the temperature at the end of the compression stroke of the rapid compression machine T_E, but falls over in the range of T_E≠T_c, especially T_E<T_c. It can be suggested that the reaction mechanism depends on the mixture temperature and seems to change from the low temperature autoignition mechanism to the high temperature one.