Numerical investigation on the scale effects of shock-accelerated heavy gas reactive concentric cylinders

The reactive shock–concentric–cylinder interaction (RSCCI) is investigated numerically to uncover the scale effects on ignition and combustion characteristics. The large-scale (diameter D = 40 mm) and small-scale (D = 4 mm) H2-O2-Xe heavy gas combustible concentric cylinders (molar ratio 2:1:3.67) are impacted by a Mach 2.83 shock wave. The ensuing behaviors of the concentric cylinders with three different inner cylinder radii (rin) to outer cylinder radius (r) ratios (i.e., 0.250, 0.500, and 0.750) are examined using the reactive shock–cylinder interaction (RSCI) case as a reference. Compared to large-scale RSCCI, the small-scale cases are found to ignite later and locate closer to the cylinder leeward interface. A modified dimensionless ignition delay time τde2 representing the pure chemical delay is proposed to further clarify this phenomenon. With a shorter τde2 in large-scale cases, the difference in the dimensionless ignition time of the large- and small-scale cases can be efficiently interpreted. For the small-scale cases, the RSCI fails to trigger the deflagration-to-detonation transition (DDT), resulting in lower combustion completeness. Conversely, DDT occurs in small-scale RSCCI with rin = 0.250r and 0.500r so that their combustion completeness is comparable to their large-scale counterparts. However, for the rin = 0.750r case, the narrow combustible annular region reduces combustion completeness to 0.4235, representing a 55.65% reduction compared to its large-scale counterpart of 0.9550. Finally, the analysis of cylinder dimensions shows that a larger inner cylinder induces a more flattened post-shock–cylinder morphology and reduces the concentric cylinder area. The present findings provide fundamental insights into the scale-dependent combustion physics of concentric fuel injection while highlighting that the theoretical prediction method is effective for cases achieving near-complete detonation but becomes unreliable when scale effects induce combustion mode transitions.