Scholars have extensively studied DDT from the perspective of industrial safety ^[1], while flame acceleration and DDT of gaseous fuel-air mixture at 1 atmosphere pressure are usually carried out in pipes with repeated obstacles ^[2]. The DDT distance in a pipe () is an important basic parameter. Based on the assumption that DDT occurs when the flame velocity reaches 1/2 CJ detonation velocity (1/ 2), Silvistrini ^[3] proposed a prediction model of DDT distance in a pipe with obstacles:

Where  is flame density ratio,  is laminar combustion velocity, and  is obstacle blockage ratio. However, Hashemi et al.^[4] found the DDT distance results was always larger than the DDT distance predicted by Silvistrini ^[3], and explained that there was a DDT induction distance before DDT occurred after the flame reached 1/2 CJ detonation velocity, which was determined by the detonation unit size () and effective activation energy. Therefore, it is necessary to carry out more detailed and extensive verification work for the prediction of DDT distance. The purpose of this work is to expand the research reported in [4] by capturing more detailed flame velocity measurements, and establish a prediction model of DDT distance in a pipe with obstacles by considering the DDT induced distance.
The DDT distance for hydrogen-methane-oxygen mixture was measured by high-speed photography in a polycarbonate cylindrical tube with a length of 283.5 cm and an inner diameter of 7.6 cm and a repeated orifice plate, and more detailed flame velocity measurement data were captured. The results show that for each mixture, the DDT distance decreases monotonously with the increase of initial pressure (or detonation unit size (d/λ). Meanwhile, a correlation was proposed based on the concept that the DDT distance consists of a flame acceleration distance and a DDT induction distance that is governed by the detonation cell size and the effective activation energy. The correlation for this DDT distance proposed in this work can well control the error between the predicted value and the experimental data in the range of about 20%.
 

DDT distance, Prediction model, Initial pressure, Flame velocity.