Isothermal cavitation model (for user-defined liquids only)

This model provides a capability to analyze two-phase flows of industrial liquids which thermophysical properties are not described in details.

The basis of the model is formed from the assumption that the cavitation process occurs in conditions close to thermodynamic equilibrium. Moreover, it can be assumed that, in most cases, this process is isothermal, since the medium temperature changes due to phase transition are insignificant.

Therefore, analyses assume the existence of a barotropic relation for the two-phase homogeneous mixture. The barotropic state law assumes that the fluid pressure is a function of fluid density only. The multi-phase fluid density is calculated from the barotropic law as presented at the diagram below.

Figure 1. Density-pressure phase diagram: 1) ideal gas, 2) two-phase area, 3) compressible liquid).

The density of the gas-liquid mixture is calculated as:

	(1)

where Runiv is the universal gas constant, P is the local static pressure, T0 is the local temperature, PE is the saturation pressure of liquid at T0, is the local static pressure at which the vapor appears, is the local static pressure at which the liquid turns into the vapor completely, yg is the mass fraction of the non-condensable gas; μg is the molar mass of the non-condensable gas.

When the pressure is below , a liquid disappears from the mixture and the fluid is treated as an ideal gas with the molar mass μ0. In this case the density of the gas mixture is calculated as:

	(2)

When the pressure is above the saturation pressure , the fluid density equals the compressible liquid density:

	(3)

where is the liquid density at the saturation pressure , a is the sonic velocity.

In the Isothermal Cavitation Model, the mass fraction of the dissolved (non-condensable) gas (yg) is a variable value. The four gases can be used as a dissolved gas: Air, Carbon dioxide, Helium and Methane, in the Equilibrium Cavitation Model Air is used as a dissolved gas. By default, the mass fraction of the dissolved gas is set to 10-4. This is a typical value under normal conditions and appropriate in most cases but it can be modified by the user in the range of 10-2...10-6.

The following additional assumptions and limitations are made in this model:

The process temperature is constant and the thermal effects are not considered.
In the Isothermal Cavitation Model, cavitation is currently available only for the user-defined liquids.

This model requires a minimal number of setting fluid parameters, such as density, molar mass, saturation pressure, and dynamic viscosity at the local temperature T0. The required data are available in the literature for the most industrial liquids, such as gasolines, diesel fuel, mineral and synthetic oils.