By default, when referring to the gas phase in a two-phase mixture, we regard it as “free gas” [66], meaning that it is not dissolved in the liquid. In some literature, free gas is known as “entrained gas”. Free gas behaves like gas, i.e., it is modeled by the gas’ thermodynamic Equation-of-State. On the other hand, dissolved gas is considered part of the liquid, although the mass fraction of dissolved gas is usually small. The presence of dissolved gas in the liquid is assumed to not affect the liquid’s thermodynamic properties [66].

The distinction between free gas and dissolved gas, and the mass transfer processes between the two, are considered in Ansys Forte only when the gas cavitation model is activated. In addition, they are considered only for non-condensable gas species. By definition, non-condensable gas is the gas species that cannot be converted to its liquid phase by phase change. By contrast, if a gas species participates in phase change, it is considered condensable. The most common example of non-condensable gas is air under room temperature.

In Ansys Forte, Lifante’s gas cavitation model [53] is implemented. In this model, both the free gas and dissolved gas species are tracked by individual transport equations. For free gas species:

(11–12)

Where is the mass fraction of species ’s free gas component in the two-phase mixture. The subscript “ncg” indicates that it is a non-condensable gas component. and are the source terms of the degassing and absorption processes, respectively.

Similarly, for dissolved gas species, the transport equation is:

(11–13)

Where is the mass fraction of species ’s dissolved gas component in the two-phase mixture.

The source term for the degassing process is modeled as:

(11–14)

In which is a modeling parameter called degassing coefficient (default: 2.0), is the free gas density, is an equilibrium pressure (defined later in Eq. (11-16)), is the local pressure, is the mass fraction of the non-condensable free gas.

The source term for the absorption process is modeled as:

(11–15)

In which is a modeling parameter called absorption coefficient (default: 0.1), is the non-condensable gas density (). is maximum solubility of the non-condensable gas into the liquid (default: 0.001), and it limits absorption process such that if the dissolved gas’ mass fraction () exceeds this value, absorption will not continue.

The equilibrium pressure () is an important parameter in modeling these source terms. When the local pressure is lower than the equilibrium pressure, degassing occurs. Conversely, if the local pressure is higher than the equilibrium pressure, absorption occurs. Following [53], the evaluation of the equilibrium pressure is carried out by using Henry’s Law. The equilibrium pressure is linearly proportional to the mole fraction of non-condensable gas dissolved in the liquid, such that:

(11–16)

In which is the dissolved gas’ mole fraction in the two-phase mixture, is the non-condensable free gas’ mole fraction in the two-phase mixture. is Henry’s volatility constant with a dimension of pressure, or more formally, the “Henry’s law volatility constant defined via partial pressure and liquid-phase amount fraction” [82]. It is determined empirically and depends on the specific fluids being considered [33]. Ansys Forte’s default value for this parameter (84028 Pa) is based on nitrogen dissolved in water.