On the problem of funnel formation during liquid outflow from vessels

Abstract

The process of funnel formation during unsteady outflow of initially still water under gravity through one or two circular holes in the bottom of a prismatic vessel rectangular in plan is analyzed experimentally and numerically. The process is studied for various locations of the sinkholes, for vessel bottoms and walls with areas that differ in roughness, and for several values of the initial water depth h0. A sufficient, but not necessary, condition for the absence of vortex funnels is formulated. On the basis of a method proposed for determining the fluid rotation direction in vortex funnels, regions are found such that above sinkholes located in them vortex funnels with a given rotation direction are formed, as well as lines such that for sinkhole centers positioned on them stable vortex funnels are not formed. These results are confirmed by numerical calculations and experiments. At different times t the structure of the circumferential velocity field in the sinkhole cross-section is investigated. In the sinkhole crosssection, at several levels above it, and in the outflowing jet the dependence of the integral moment of the circumferential velocities on time and the initial depth is found. The time dependences of the flow-rate characteristics (flow-rate coefficient and volume flow-rate) are obtained for various initial depths and compared with results known in hydraulics. On the range of determining parameters investigated it is established that the fluid depth in the vessel at which a vortex funnel begins to be formed is independent of the initial water depth. The numerical calculations were carried out using STAR-CD software (license of the Institute of Mechanics of Moscow State University) tested in experiments on water outflow from prismatic vessels circular and rectangular in plan.