Case 2: PHvap< P < Psat

In this case, part of the air/gas is dissolved and part is free (air/gas bubbles).

The density of dissolved air/gas is equal to density of free air/gas, so that we can work with mass fraction as well as volume fraction. We choose to use a volume fraction of undissolved air/gas θ, which is defined as:

According to the Henry’s law (see section Saturation pressure parameter Psat), the fraction of undissolved air/gas θ is only dependent of the pressure and in an equilibrium state, θ is given by:

Equation 13: Modified Henry’s law

If the pressure suddenly drops below Psat, the amount of undissolved air/gas will be below the theoretical value θ given by Henry’s law at equilibrium. Therefore Simcenter Amesim uses a modified equation for θ which is close to the Henry’s law but which gives a higher degree of continuity with the boundary conditions θ=0 at P=Psat and θ=1 at P=PHvap. The Simcenter Amesim law to compute the undissolved air/gas in Case 2 is:

with:

Figure 4: Modified Henry’s law versus Simcenter Amesim law

The curve used is sufficiently smooth at P=Psat and P=PHvap not to require discontinuity handling.

The fluid density is defined by:

We still assume that the volume of dissolved gas does not increase the liquid volume:

Then for the fluid: