THE EFFECT OF LIQUID COMPRESSIBILITY AND DOMAIN VOLUME ON THE COLLAPSE OF CYLINDRICAL VAPOR CAVITIES

Abstract

The dynamics of slender vapor cavities is studied experimentally and with a compressible multi-material Euler equation solver. For the computational study, the cavity was approximated as an infinitely long cylinder. Compressibility is shown to be a controlling factor in the dynamics of the cavity collapse, both as a means to limit the amount of fluid mass accelerated and as a source of radiated energy. As a result, cavities reach an invariant collapse time for fluid domains large enough that acoustic waves traveling outward from the cavity wall are unable to return before collapse. The dynamics of the collapse are studied using an inviscid compressible hydrocode and are compared to those given by the incompressible cylindrical analogue of the Rayleigh-Plesset equation. The incompressible solution is known to depend on the size of the domain due to a logarithmic dependence in the governing equation, predicting a monotonically-increasing collapse time with increasing fluid domain size. Thus, for sufficiently large fluid domains, the analytic incompressible solution greatly over-predicts the cavity collapse time observed in the compressible calculation. Using the results of this study, a compressibility-limited collapse time can be predicted for a cylindrical bubble using the incompressible model, providing a rational upper limit for the effective domain size often used in slender-body approximation models.

In the experimental study, supercavitating projectiles with a mass of 55 g, and cavitator radii of 3 and 6 mm were fired vertically into a shallow hydroballistics tank at velocities between 194 and 434 m/s. Cavity morphology and dynamics are extracted from high-speed video footage with two image processing techniques. Resulting cavity radial flow histories are compared to a model adapted from Bergmann et al. (2009). The model uses the volume of the hydroballistics tank as the upper limit for the amount of fluid available for cavity expansion and collapse. It accurately predicts cavity radial dynamics where local three-dimensionality (e.g. surface seal and axial flow) does not dominate the flow. The resulting model is capable of predicting gross cavity behavior and collapse mode. For cavities where the collapse is primarily radial, the model accurately predicts the time and location of collapse. These predictions could facilitate estimates of cavity collapse loading on adjacent structures.