The deflagration-to-detonation (DDT) run-up distance $L_{\mathrm{DDT}}$ for small-sized tubes is an important parameter for determining the position of a detonation initiation in the pulse detonation propulsion device as well as industrial safety. However, its variation tendency is insufficiently clarified, owing to complex multiple competing mechanisms between the properties of mixtures and the negative displacement effect of the boundary layer (the heat and momentum losses from wall). In this paper, the authors assess the $L_{\mathrm{DDT}}$ of a stoichiometric ethylene/oxygen mixture in four capillary tubes based on high-speed photography measurements. Compared with macrotubes, the experimental results indicate that the area divergence $\xi$ induced by the boundary layer causes the relationship between $L_{\mathrm{DDT}}$ and $p_0$ and/or $d$ to vary. Further comparative analysis suggests that a critical value of about $\xi =0.1$ can be employed to distinguish between microtube and macrotube behavior. As such, microtube behavior is defined according to the area divergence $\xi$, and not only based on the tube diameter. Finally, a theoretical model is introduced to predict the $L_{\mathrm{DDT}}$ and is reliable for a stoichiometric ethylene/oxygen mixture in micro- and macrotubes. The conclusions in this study can provide potential applications for practical predetonator and micropulse detonation engines.

爆燃-爆轰（DDT）加速距离 ${\mathrm{大号}}_{\mathrm{滴滴涕}}$小型管的“爆轰”是确定脉冲爆震推进装置中爆震起始位置以及工业安全性的重要参数。但是，由于混合物特性与边界层的负位移效应（壁的热量和动量损失）之间复杂的多重竞争机制，其变化趋势无法得到充分阐明。在本文中，作者评估了${\mathrm{大号}}_{\mathrm{滴滴涕}}$基于高速摄影测量的四个毛细管中的化学计量乙烯/氧气混合物的分析。与大管相比，实验结果表明，面积发散$\xi$ 由边界层引起的引起之间的关系 ${\mathrm{大号}}_{\mathrm{滴滴涕}}$ 和 $p_0$ 和/或 $d$改变。进一步的比较分析表明，临界值约为$\xi =0.1$可以用来区分微管和大管行为。因此，微管行为是根据面积差异定义的$\xi$，不仅取决于管的直径。最后，引入理论模型来预测${\mathrm{大号}}_{\mathrm{滴滴涕}}$并且对于微管和大管中的化学计量的乙烯/氧气混合物是可靠的。本研究的结论可为实际的雷管和微脉冲起爆发动机提供潜在的应用。