Slugging Flow of Water Draining from the Bottom of a Non-Vented Container
Experiments were run to observe the behavior of water exiting through an orifice at the bottom of an non-vented container. Initially, the container is nearly full of water with a small air space on top. Once the orifice was uncovered, the slugging rate and the drain rate of the water leaving the container were measured. Upon initially opening the orifice, water drains out until the air pressure above the water reduces enough that the air pressure drop from inside to outside of the container supports the water column and the water stops flowing. Air then enters the container through the orifice forming a bubble, which grows until it detaches and bubbles through the water to reach the air space. Once the bubble enters, this added air increases the pressure in the air space enough to allow the water to start flowing out again. This cycle of flow out, flow stoppage, air inflow, and bubble breakoff continues over and over until the hole is closed or the container empties. This is referred to as the “slugging cycle.” A mechanism is proposed to describe the slugging cycle which is modeled analytically. This paper presents the description of the experiments, data obtained, the mechanistic model, and comparison of the model to the experimental data. The model predicts outflow rates close to experimental values. Flow rates from non-vented containers are more than 10 to 20 less than vented containers. The bubbles which must enter the container periodically to increase the internal air pressure stop the water flow momentarily so are responsible for this large decrease in flow rate. Swirl induced in the non-vented container causes the flow rates to increase by a factor of two. The flow rate out of a non-vented container is independent of water height which is in direct contrast to a vented container where the flow rate is proportional to the square root of the water height. The constant rate is due to the container pressure. The higher the water level, the lower the air pressure is in the container. This analytical model requires input of the bubble size. The volume recommended is the volume of a cylinder with the base of the orifice area and length of 3.3 cm. Slugging rate varies only a small amount falling in the range to 2 to 4 cycles/sec. Preliminary work with other containers indicates larger containers, larger orifices and nozzle exit shapes produce higher specific flow rates. The standard multiphase flow equations could not be used to analyze this situation because the two phases are not interpenetrating. Instead one phase must fully stop before the other can flow. Interpenetrating phases allow can pass one another each affecting the other with friction and virtual mass. An interesting observation: The negative air pressure in the container is observable. It equals the water height.