Hints & Tips: Modeling Gas Bubbles
There are several options for modeling gas bubbles. How can I decide which, if any, of the models to use for my applications?
First of all, a bubble in FLOW-3D is defined as a gas region large enough to be resolved by at least one grid element. In most cases bubbles encompass many grid elements, which is why they are useful computational objects for coupling fluid elements over large distances.
A great many two-phase flows don't consist of a homogenous mixture of the phases, but rather of large regions of either gas or liquid, which is why a capability to model large bubbles is important.
Constant pressure, adiabatic, and homogenous bubble models all make two assumptions. One is that the density (inertia) of the gas can be neglected. The second assumption is that the bubble pressure and temperature are uniform within each bubble. For this reason no dynamic computations are performed in bubble regions. This leads to a considerable savings in computational effort since accuracy and numerical stability issues associated with a low density gas are eliminated.
Ignoring the inertia of the gas is usually a good approximation since gas densities are typically orders of magnitude smaller that the liquid density. he physical requirement for a uniform bubble pressure is that sound waves in a bubble are able to smooth out variations in a time that is short compared to the characteristic time for changes in the surrounding liquid. (e.g., changes in the shape and/or volume of the bubble.) Essentially, a sound wave should have time to make several passes across a bubble before its shape or size changes appreciably. For most applications where the surrounding liquid can be treated as incompressible, this condition is relatively easy to meet.
The assumption of a uniform temperature is also a reasonable approximation because variations in gas density with temperature are unimportant when the gas density is being neglected anyway. Furthermore, gas temperatures do not have much influence on surface phase-change rates, which are dominated by the liquid due to its overwhelming heat capacity compared to that of the gas.
The simplest, constant density model should always be used when gas regions are very large or connected to a constant pressure boundary, and it's unlikely that significant bubbles will be trapped in the liquid. Adiabatic and homogenous bubbles offer useful options for the treatment of smaller, confined gas regions, but there is more computational expense associated with these models that should be weighed against their possible benefits. Finally, the newest bubble model (see "Descendents" in this Newsletter) that includes gas dynamics should only be used when it is certain that this is an important element in the application.