On the effect of compressibility on the impact of a falling jet

Abstract

At the first World Sloshing Dynamics Symposium that took place during the Nineteenth (2009) International Offshore and Polar Engineering (ISOPE) Conference in Osaka, Japan, it was made clear that simplified academic problems have an important role to play in the understanding of liquid impacts. The problem of the impact of a mass of liquid on a solid structure is considered. First the steady two-dimensional and irrotational flow of an inviscid and incompressible fluid falling from a vertical pipe, hitting a horizontal plate and flowing sideways, is considered. A parametric study shows that the flow can either leave the pipe tangentially or detach from the edge of the pipe. Two dimensionless numbers come into play: the Froude number and the aspect ratio between the falling altitude and the pipe width. When the flow leaves tangentially, it can either be diverted immediately by the plate or experience squeezing before being diverted. The profile of the pressure exerted on the plate is computed and discussed. Then the same problem is revisited with the inclusion of compressibility effects, both for the falling liquid and for the gas surrounding it. An additional dimensionless number comes into play, namely the Mach number. Finally, a discussion on the differences between the incompressible and compressible cases is provided.