Generating an underwater shock wave with well-controlled intensity and curvature radius is important for relevant experimental and numerical studies but still challenging. The present study employs the stiffened-gas equation of state (SG-EOS) for liquid water and proposes a method of theoretically designing a shock tube to transform a planar underwater shock wave into a cylindrical one with the preset intensity and curvature. Two fundamental relations, including the Chester-Chisnell-Whitham relation and the two-dimensional characteristic relation of shock dynamics, are formulated using SG-EOS. The design procedure of the shock tube profile is thus derived. The present study conducts typical numerical tests to examine the effectiveness of the proposed method. To evaluate the errors between numerical shocks and their theoretical cylindrical shapes, the normalized ${\mathcal{L}}^2$ and ${\mathcal{L}}^{\infty }$ distances are defined and found to be controlled within $O\left({10}^{-3}\right)$, or even $O\left({10}^{-4}\right)$ in some cases. And the relative errors of the postshock pressure and velocity magnitude can be controlled within 2%, or even 0.7% in some cases. Pressure profiles are also presented and found to continuously approach those of an ideal planar shock wave as the curvature radius increases.

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• Compressible flows
• Shock waves