Air？water bubbly flow by multiple vents on a hydrofoil in a steady free-stream

Abstract

Flow features, due to air injection through multiple vents on the surface of a hydrofoil inclined at an angle with respect to the free-stream in a cavitation tunnel, are presented here. The hydrofoil, with a chord length, c, is oriented at the angle of inclination, α = 3.5？ . The Froude number, Fn, based on the free-stream velocity, V∞, and air injection vent diameter, dh, is 30.30, 50.51 and 70.71. Air is injected through multiple vents on the hydrofoil at the non-dimensional air injection coefficient, Cq ∼ 16 ？ 8917. The air bubble packing per unit area is quantified using spatial density, SD, at various combinations of Fn, Cq based on a high-speed video from the side view. The time-averaged spatial density, < SD >, is observed to increase in a logarithmic manner with an increase in the air injection rate, Q, at various Froude numbers. There is an increase in the mean spatial density of the bubbles with the increase in Cq at all Fn. A power？law relation is shown to exist between the time-averaged spatial density, < SD >, and the non-dimensional flow variables, Reynolds number, Reair, Fn and Cq based on a regression analysis. By tracking individual finite volume bubbles flowing with the free-stream, the bubble dimensions in pixels are quantified using quantities such as the deformation rate, ？, and standardization, ？S, from the side-view videos. It is observed that ？ and ？S change with time, even as they become advected with the free-stream. Through high-speed imaging from the top view, we characterize the bubbly flow features’ time-averaged thickness, t, at various combinations of Fn, Cq at α = 3.5？ . We obtain a power-law relation between the non-dimensional time-averaged jet thickness, t/c, and the non-dimensional flow parameters such as, Reair, Fn, Cq and the non-dimensional streamwise distance, x/xre f, based on a regression analysis, where xre f is a reference distance. The results are relevant to engineering applications where the air？water bubbly flow in a free-stream is important. Copyright: ？ 2021 by the authors. Licensee MDPI, Basel, Switzerland.