Extensions to the Air Entrainment Model (or Passing Gas Discreetely)
This article highlights some modeling extensions being developed for
the next release of FLOW-3D.
Figure 1: Air entrained in hydraulic jump.
Intense entrainment exists at toe of jump.
Figure 2: Downstream air volume fraction
shows rising of air to surface with distance.
Figure 3. Red indicates more than
10% air volume fraction during filling.
Figure 4: This 2D view shows the
reduction in volume of liquid in
the bottle as entrained air
rises and escapes.
The ability to model air passing into a liquid surface (entrainment) in the discrete numerical program, FLOW-3D, is a relatively recent feature, but one that is finding a growing number of applications. Although the model was originally developed with civil hydraulics applications in mind, creative users in other industries, such as metal casting and consumer products, have shown the way for greater potential. In response, Flow Science's developers have undertaken extensions in four areas to make the model more powerful and robust.
First, the model can be used for laminar entrainment, which means that it is no longer necessary to have a turbulence model activated. This limiting case of relatively calm flows would be appropriate, for example, to the filling of a bottle with a viscous liquid.
A second extension of the air entrainment model is its coupling with bubble models. This means that entrained air from a confined air region (bubble) will be removed from that region lowering its pressure and reducing its volume. Typical applications for this feature are in such systems as self-priming siphons and the removal of air trapped in water diversion tunnels.
The bulking of liquid volume as air is entrained is now better represented so that excessive bulking in strong entrainment regions is no longer observed. Furthermore, bulking has been more accurately implemented to have a better transmission of its effects through a computational grid.
Finally, we have made the entrainment model consistent with air-bubble rise and escape at a free surface. The consistency issue is that entrainment is adding air to the liquid in a free surface region, while bubble rise and escape mechanisms remove air from the surface region. In our new program, these competing processes can be used together, thereby providing more accurate simulations.
A hydraulic jump is a good example where intense air entrainment is often observed at the toe of the jump (see Figure 1 above). Entrainment occurs from both laminar and turbulent processes. A high degree of unsteadiness at the toe is commonly seen so that it is no surprise that this implies some turbulent air entrainment. On the other hand, when the inflowing stream has little or no turbulence it enters the jump much like a jet impinging on a pool of liquid, where entrainment is more laminar because turbulence has no time to develop at the point of impingement. Downstream from the toe, turbulence almost uniformly mixes the entrained air into the bulk liquid. Further downstream the buoyancy of the air bubbles (assumed to be on average one or two millimeters in diameter according to experimental observations) rise toward the surface reducing the air content at the bottom of the stream (see Figure 2 below).
Bottle filling is a good example to show how entrained air can bulk up the volume of the liquid. The image on the left in Figure 3 above shows the situation after 1.2 seconds of filling a bottle that is approximately 20 cm in height. The color shading indicates the volume fraction of air in the liquid. Because of the short time and high degree of mixing in the bottle the air has not had time to rise to the surface and escape. However, as the image on the right-hand side of Figure 3 shows, after an additional period of about 1.7 seconds, we can clearly see the reduction in liquid volume resulting from air rising to the surface. Figure 4 below shows this reduction even more clearly. The new features described here will be available with the release of FLOW-3D Version 9.1.