Effects of Mach number on shock-induced evolution of a cylinder with and without a cavity under transcritical conditions

This study numerically investigates the interaction of planar shock waves with cavity-embedded n-dodecane fuel cylinders under transcritical thermodynamic conditions. Fourteen cases with Mach numbers ranging from 1.2 to 2.1 are simulated using the finite-volume compressible multi-component solver CAvitation Technical University of Munich (CATUM), incorporating an optimized WENO3 reconstruction scheme and a modified Peng–Robinson equation of state. The numerical approach is validated against reference data, and mesh convergence is confirmed through four levels of grid refinement. The analysis highlights the influence of Mach number on wave dynamics, structural deformation, vorticity deposition, circulation growth, and enstrophy evolution. Compared with full-cylinder configurations, cavity-embedded cylinders undergo earlier deformation, faster downstream displacement, and stronger vorticity generation, leading to enhanced fuel–nitrogen mixing, with the effect becoming more pronounced at higher Mach numbers. Quantitative comparisons demonstrate that the proposed modified Zhang–Zou (M-ZZ) model reliably predicts circulation deposition across all examined Mach numbers, with errors of less than 10%. To assess cavity effects, a transcritical-enstrophy model (TEM) is developed, which predicts enstrophy evolution with errors below 12%. In particular, at Mach 2.0 the enstrophy of the cavity case is about 20% higher than that of the non-cavity case, representing the most significant enhancement among all examined conditions. Cavity-induced mechanisms substantially enhance mixing efficiency, which is evidenced by an increase in enstrophy of more than 10% under stronger shocks. These findings provide insights into instability-driven mixing processes in transcritical environments.