A scaling framework unifying the markedly different and independently studied cylindrical and spherical shock convergence is presented. For ionizing argon, we show that the focal temperature becomes invariant to shock symmetry and initial shock conditions when scaled by the prefocus shock Mach number, after accounting for pressure effects. The resulting collapsed focal temperature–Mach number relation is governed by the thermodynamics of argon, up to an equilibrium temperature of 35 000 K. Such a scaling enables both predictive estimation of focal temperatures over a wide range of initial conditions and, conversely, determination of the parameters required to achieve a target temperature in a given medium.

The interaction between cylindrically converging shock waves (SWs) in a water–gelatine solution and a coaxial cylindrical air bubble is studied experimentally and numerically. Two configurations are considered: (i) an azimuthally symmetric, cylindrically converging SW of Mach 1.35 impinging on a coaxial cylindrical bubble, and (ii) a semicylindrical converging SW of Mach 1.45 (corresponding to half of the cylindrical front), interacting with the same target. Shock waves are generated by exploding wire arrays driven by a high-voltage pulsed power system at beamline ID19 of the European Synchrotron Radiation Facility, delivering currents up to 130kA with rise times of 0.35 and 0.55 µs to the cylindrical and semicylindrical wire loads, respectively. X-ray radiography is conducted at a pulse repetition rate of 5.68 MHz using two synchronised high-speed cameras. Numerical hydrodynamic simulations are performed using a compressible multiphase Navier–Stokes solver. A Gilmore-type model for compressible cylindrical bubble pulsation provides an independent analytical estimate of the interface evolution. In the cylindrical SW configuration, the bubble collapse in experiments exhibits Richtmyer–Meshkov instability spikes. The cylindrically converging shock is analysed with Guderley’s solution and Whitham’s approximation using a real-gas equation of state, predicting Mach 14.1 near the focus. In the semicylindrical configuration, momentum focuses into a single supersonic jet with a speed of 885 ± 30 m s−1, producing localised high-pressure regions, coherent vortices and complex internal Mach reflections. Experiments, simulations and theory are consistent in collapse time, interface motion and overall flow dynamics.

Convergence of cylindrical shock in argon is studied both experimentally and numerically. Shock tube experiments are conducted, where a planar shock is first transformed to a cylindrical shape and then converged to its focal axis. Numerical simulations of the converging shock using equations of state for an ideal gas and a real gas (SESAME 5173 model) are conducted and compared. High temporal resolution data of cylindrical shock convergence is presented. When comparing the trajectories of the converging shock of initial shock Mach number (M-S) of 4.63, the convergence exponent (alpha) in experiments is found to be 0.833. This alpha value in experiments is higher than the value obtained from computations with argon treated as an ideal gas but agrees well with the real gas computations. It is revealed that the form of convergence varies with different M-S. An asymptotic approach of alpha toward the self-similar solution for high M-S is attributed to an earlier transition of shock motion to self-similarity, while a significantly higher alpha observed at lower M-S is attributed to the negative influence of upstream nonuniformities and weaker initiation of the shock. It is found that even before the shock reflection, real gas effects are significant enough to affect the convergence of the shock and limit the extreme conditions predicted by the ideal gas computations. For an M-S of 4.63, the maximum temperature reached is 9250 K before reflection, leading to 0.12% of the argon gas undergoing the first stage of ionization.

The dynamics of shock-induced unsteady separated flow past a three-dimensional square-faced protuberance are investigated through wind tunnel experiments. Time-resolved schlieren imaging and unsteady surface pressure measurements are the diagnostics employed. Dynamic mode decomposition (DMD) of schlieren snapshots and analysis of spectrum and correlations in pressure data are used to characterize and resolve the flow physics. The mean shock foot in the centreline is found to exhibit a Strouhal number of around 0.01, which is also the order of magnitude of the Strouhal numbers reported in the literature for two-dimensional shock-boundary layer interactions. The wall pressure spectra, in general, shift towards lower frequencies as one moves away (spanwise) from the centreline with some variation in the nature of peaks. The cross-correlation analysis depicts the strong dependence of the mean shock oscillations and the plateau pressure region, and disturbances are found to travel upstream from inside the separation bubble. Good coherence is observed between the spanwise mean shock foot locations till a Strouhal number of about 0.015 indicating that the three-dimensional shock foot largely moves to-and-fro in a coherent fashion.