Assessing the Leakage Rates from Punctured Submerged Vessels

The leakage of fluid leaving a puncture in a pressurized vessel immersed in a quiescent, miscible medium is studied under steady flow conditions. This problem has engineering applications in submerged pipelines and hazardous gas lines. The leakage rate for the puncture is characterized as functions of various hydrodynamic and geometric conditions. Dimensional analysis shows that the leakage percent, Q*, is a function of the Reynolds number, the pressure ratio between the center of the tube and the external hydrostatic pressure, P^*, and the hole-to-main tube diameter ratio, D^*. The effect of puncture shape is also examined, rectangular and circular. A 3-D finite volume computational model is constructed for laminar flow of a Newtonian fluid under steady conditions and validated with supporting experiments. The results show that the fractional leakage rate Q* increases with P^* and approaches a constant value at high P^* for a fixed Reynolds number. In addition, it is found that the leakage rate increases with decreasing Reynolds number at a fixed pressure ratio. The geometric effect of the diameter ratio is shown to have a more pronounced effect near a pressure ratio of two with more fluid exiting the puncture for larger diameter ratios. The results of the shape analysis show that the circular puncture has the largest fractional leakage when compared to a rectangle with an equivalent cross-sectional area.