Effect of argon dilution on detonation instability of C₂H₂-O₂ mixture and its quantitative analysis

To investigate quantitatively the effect of argon dilution on the detonation instability of C₂H₂-O₂ mixture, we carried out a digital comparison of smoked foils from C₂H₂-O₂ mixtures with different Argon dilutions (with an volume fraction of 50%, 70%, and 85%, respectively) in two tubes (with an inner diameter of 50.8 mm and 63.5 mm, respectively) producing transverse waves of regular and irregular spacing and, based on the smoked foils, obtained under different initial pressures the histogram, the standard deviation and the autocorrelation function, which we then used to quantify the spacing irregularity for different cellular detonation structures. Each smoked foil was digitized and separated into left-running and right-running waves for subsequent analysis. The histogram, the standard deviation and the autocorrelation function showed consistent tendency. As the Ar dilution's volume fraction rose, the trajectory of the triple points became more regular. Similarly, mixtures of different Argon dilutions showed different degrees of irregularity in the analysis of the histograms and the autocorrelation function of the transverse waves' spacing. The proportion of the dominant mode of C₂H₂-O₂-85%Ar, C₂H₂-O₂-70%Ar, and C₂H₂-O₂ were 33%, 23%, and 20%, respectively, while their standard deviation was 2.66~6.60 mm, 5.37~10.96 mm, and 27.63~36.67 mm, and their autocorrelation function peak values were higher by 1/3, 1/6, and 1/7 times. A polynomial fitted curve of the dilution and the irregularity was drawn from the standard deviation data to provide a selection basis for the instability degree and the Ar dilution's volume fraction.