The topology of gas jets injected beneath a surface and subject to liquid cross-flow

Gas injection into a liquid cross-flow is examined for the case where the gas is injected beneath a horizontal flat surface. For moderate Froude numbers, the gas pocket that is formed will rise toward the flow boundary under the action of buoyancy, a condition that is conducive to the formation of gas layers for friction-drag reduction on the surface. At the location of gas injection, a plume whose geometry is related to the mass and momentum flux of the injected gas and liquid cross-flow is formed, and the influence of buoyancy is minimal. However, as the gas pocket convects downstream, buoyancy brings the gas back upward to the flow boundary, and leads to the bifurcation of the pocket into two distinct branches, forming a stable 'V'-shape. Under some conditions, the flow between the two gas branches is almost entirely liquid, while for others there exists a bubbly flow or a continuous sheet of gas between the branches. The sweep angle and cross-sectional geometry of the gas branches are related to free-stream speed and boundary-layer thickness of the liquid cross-flow, the mass-injection rate of the gas, the diameter of the injection orifice and the gas outlet mean velocity and gas-jet angle. Data for a range of experimental conditions are used to scale the flow and results are compared to numerical computations of the flow, and these data are used to illustrate the underlying flow processes responsible leading to the formation the stable and straight gas branches. A simple model based on the balance of forces around a stable gas branch is presented and used to scale the observed data, and we use the results of this analysis and the computations to discuss how the process of gas injection may interact with the formation of the stable gas pockets farther downstream.