Slugging Flow of Water Draining from the Bottom of a Nonvented Container

Abstract

Experiments were run to measure the slugging frequency and drain rate of water exiting through an orifice at the bottom of a nonvented container into an infinite atmosphere. Initially, the container is nearly full of water with a small air space on top. 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 up 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 simple model is presented here which can be used to calculate water flow rate out of and air flow into a nonvented container. This paper presents the description of experiments, data obtained, the model, and comparison of the model to the data. The model predicts outflow rates close to experimental values. Measurements showed that flow rates from nonvented containers are more than 10 to 20 times less than vented containers. For nonvented flow, 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 nonvented container allows flow rates to increase by a factor of 2. The flow rate out of a nonvented container is independent of water height which differs from 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 air pressure because the higher the water level is, the lower the air pressure is. 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 frequency varies only a small amount falling in the range of 2−4 cycles/s. Preliminary work with other containers indicates that larger containers, larger orifices, and nozzle exit shapes produce higher flow rates per unit area but similar slugging rates. An interesting observation is the following: The air pressure in the container is always negative and can be observed without a gauge. It equals the negative of the water height.