Generation of Spherical Shock Waves in Liquids and Gases

This work proposes a unified theoretical framework for designing curved-wall shock tubes to generate spherical shock waves in compressible liquids and perfect gases via the stiffened-gas equation of state. Based on the three-dimensional shock dynamics theory, the hyperbolic system governing shock wave motion in axisymmetric scenarios is established, along with its characteristic relations, followed by a detailed three-step design procedure of a shock tube profile. Numerical tests are conducted to validate the proposed method. The typical results of divergent and convergent shock waves in liquid water and air demonstrate that at the design states, the normalized [Formula: see text] and [Formula: see text] distances of wave fronts from theoretical spherical surfaces are controlled to [Formula: see text] or even [Formula: see text]. The relative errors of average postshock pressure and velocity magnitude from theoretical values reach below or around 2.0%. The normalized standard deviations of postshock pressure and velocity magnitude are controlled below or around 3.0%. Furthermore parametric studies show that across a wide range of shock intensities (the postshock pressure of 250–1500 MPa for liquid water, and the shock Mach number of 1.5–6.0 for air) and opening angles (20–40 deg), all errors remain bounded within limits consistent with the aforementioned orders of magnitude.