The simulation of compressible multi-medium flow II. Applications to 2D underwater shock refraction

In this work, the methodology developed in Part I [Liu TG, Khoo BC, Yeo KS. The simulation of compressible multi-medium flow. I. A new methodology wit h test applications to 1D gas-gas and gas-water cases. Comp. and Fluids 200 0;30:291-34] is applied to study underwater shock refracting at a gas-water interface. The reflected wave is always a shock (rarefaction) wave if a sh ock (rarefaction) wave enters from a gas medium into water, while the refle cted wave is always a rarefaction (compression) wave if the incident shock (rarefaction) wave enters from water into a gas medium. In the first study of a vertical planar underwater shock interacting with a cylindrical gas bu bble, regardless of the strength of incident shock, shock refraction at. th e gas bubble surface is regular initially and transforms into the irregular type before the incident shock reaches the top/bottom section of the bubbl e. In the second study of an underwater explosion near the free surface, th e dominant physical phenomena in the earlier stages of explosion consist of the outward propagation of an underwater shock, the symmetrical expansion of a gas bubble and the possible generation of a second shock inside the ex panding gas bubble. At a later stage, the underwater shock refraction at th e free surface begins resulting in the generation of a pair centered Prandt l-Meyer waves, and the latter interacts with the expanding gas bubble. The numerical results exhibit all the physical phenomena described by Ballhaus and Holt [Phys. Fluids 17 (1974) 1069]. (C) 2001 Elsevier Science Ltd. All rights reserved.