# The Period of Ignition Delay for Methane-Air Mixture with Hydrogen and Ethylene Additives
## 2 Features of the Experimental and Calculated Determination of the Ignition Delay Period  
To begin with, let us describe the general regularity of most experiments carried out by means of shock installations. Determination of the ignition delay period on shock installations consists of determining the time interval between the passage of direct or reflected shock waves and the beginning of ignition of the fuel-air mixture. To determine the moment the shock wave passes through the fuel-air mixture, piezoelectric pressure sensors can be used in the experiment. By the difference in response time of several sensors located at some distance from each other, the shock wave velocity can be determined. The ignition of the mixture in the experiment can be recorded with emission spectroscopy (ESD), which signals an increase in the concentration of OH radicals. By means of special calibration, the linear correlation between the signal from ESD and the concentration of OH radicals is usually achieved. Typical results of measuring the parameters are shown in Figure 1. There are the filtered oscillograms of the relative values of the recorded signals from the \(I/I_{max}\) sensors in the ignition zone in time t, namely: the signal from the pressure sensor (1) and the emission spectroscopy device (2) here. It is vital to mention that in practice, two approaches are used to determine the ignition delay period. The first approach determines the time interval from the passage of the shock wave in the investigated region to the appearance of OH radicals there in the amount of about 5% of their maximum value. This time interval is designated by \(\tau_{0.05}\). It is considered that at the moment of time \(\tau_{0.05}\) the mixture was ignited because the reactions began. However, in a number of cases, further fading of the reactions and the corresponding relaxation of the ESD readings are noted. Therefore, it is assumed that stable ignition of the mixture is realized when the OH concentration reaches about 95% of the maximum value. The time interval corresponding to this value of radical concentration will be denoted by \(\tau_{0.95}\). Taking into account some differences in experimental processing techniques by different authors, to generalize the results, it is often required to normalize the values of the ignition delay period. However, literary sources often lack primary data on the registered \(I/I_{max}\) values, and the authors limit themselves to the final data on the ignition delay period. Therefore, for a complex analysis and generalization of the results, it is required to establish the relationship between the time intervals \(\tau_{0.05}\) and \(\tau_{0.95}\). Figure 1: Oscillogram of readings of the pressure sensor (1) and ESD (2). The approach proposed in our work is the analysis of the equation for changing the fuel concentration:  
\[-\frac{dC_{f}}{dt}=K\cdot C_{f}, \tag{1}\]  
where \(C_{f}\)--fuel concentration, \(K\)--chemical reaction rate constant. According to the Arrhenius equation, the constant \(K\) depends on chemical properties (preexponential factor and activation energy), as well as on the temperature of the reacting medium. The temperature of the medium is a function of the number of combustible substances that have reacted. These dependencies can be taken into account in the numerical simulation of reactions; however, for primary estimates in the calculations, it is allowed to take the temperature constant and equal to the time-averaged temperature of the reacting medium. Considering that the difference in concentrations \(C_{f}\)-\(C_{f}^{\prime}\) is proportional to the expression \((C_{OH}\)-\(C_{OH})/Y\), after integrating Equation (1), it can be obtained that \((C_{OH}\)-\(C_{OH})/Y=-e^{-K\cdot t}\). Here \(C_{f}^{\prime}\) maximum fuel concentration, \(C_{OH}\)--current concentration of \(OH\) radicals, \(C_{OH}\)--maximum concentration of \(OH\) radicals, \(Y\)--relative stoichiometric coefficient.