Effects of interfacial shear condition and trailing-corner radius on the wake vortex of a bubble

Abstract

Comparative effects between the interfacial shear condition and the trailing-corner radius ( ϕ) on the wake vortex of a bubble are studied. In the investigation, the standard k– ɛ model is employed, and the two types of bubble: solid and gaseous, have different interfacial boundary condition. Namely, for solid bubbles the no-slip condition is imposed, resulting in a non-zero interfacial shear condition, while for gaseous bubbles the free-slip condition is imposed, yielding a zero interfacial shear condition. The flow condition is set for a slug flow with the bubble drifting at a terminal velocity corresponding to the Reynolds number of 35,000. The results show that, the flow can be roughly divided into two flow regimes: the small- and large- ϕ regimes. In the small- ϕ regime, the trailing-corner radius plays a dominant role and the difference in the interfacial shear condition has little effects on the wake vortex, causing the wake vortices of the two bubble types to be similar in shape, size, and circulation. In contrast, in the large- ϕ regime, the interfacial shear condition can manifest and affect flow separation and the wake vortex, causing significant differences between the wake vortices from the two bubble types. Namely, as ϕ is increased towards the large- ϕ regime, the wake vortex of the solid bubble changes relatively little while that of the gaseous bubble significantly decreases in size. At small- ϕ the circulations around the wake vortex of both types of bubble are almost identical initially. However, as ϕ is increased towards the large- ϕ regime, the circulation of the gaseous bubble decreases with increasing ϕ at a more pronounced rate than that of the solid bubble. These results show that it is the absence of interfacial shear in the large- ϕ regime that causes the wake vortex to be more sensitive to the trailing-corner radius.