Hydrodynamic characteristics and wake evolution of a submarine pipe with the presence of gas leakage at a low Reynolds number of 160

Hydrodynamic characteristics and wake structures of a submarine gas transmission pipe with the presence of gas leakage are of significance from a scientific and practical viewpoint. In this paper, we present a numerical investigation of flow past a leaking pipe at a low Reynolds number of 160 using the Eulerian-Eulerian multi-fluid volume of fluid model. The focus is on the effects of gas buoyancy and the location of the leak hole on the wake flow structures, bubble-vortex interference, and hydrodynamic forces. The variation of drag and lift coefficients is highly associated with the evolution of gas bubbles and the interaction between the bubble-induced vortices and the shear layers. When the gas buoyancy is ignored, the alterations of the main vortex structure and hydrodynamic forces are not sensitive to the location of the leak hole. The bubble-induced vortices are encompassed by the two shear layers and quickly dissolved in the main vortices. Finally, the released gas bubbles are locked in the center of main vortices and convected downstream with them. In contrast, when the buoyancy is considered, the gas bubbles line up in the upper shear layer, strongly interfering with the formation of the upper main vortex. Each gas bubble introduces a pair of small vortices that experience complicated merging or splitting during the migration. Consequently, the upper main vortex is suppressed at θ = 90° and vanished at θ = 180° and θ = 270° (θ is measured clockwise from the forward stagnation point), leading to the negative time-averaged lift force and the same-frequency oscillation of drag and lift coefficients. Due to the upward migration of gas bubbles from both front and rear surfaces at θ = 270°, the evolution of bubble-induced vortices is more complicated and the oscillation of hydrodynamic forces is significantly enhanced in comparison with other cases.