Cavitation
Several types of cavitation can occur in thin film flow. When the flow pressure drops below the ambient pressure, the air and other gases dissolved within the fluid are released. This phenomenon, characteristic of loaded bearings, is known as cavitation or gaseous cavitation. In some cases involving high frequency varying loads, as in internal combustion engines, the pressure might drop below the fluid vapor pressure, which is lower than the ambient pressure. In this case, bubbles are formed by rapid evaporation or boiling of the fluid. This phenomenon is known as vapor cavitation. The cavitation feature in COMSOL Multiphysics is designed to address gaseous cavitation.
The implementation of the cavitation feature is based on a modified version of the Elrod’s algorithm (Ref. 10 and Ref. 11). This algorithm automatically predicts film rupture and reformation in bearings and offers a reasonable compromise between accuracy and practicality. It is applicable to heavily and moderately loaded bearings but it is not suitable when surface tension plays an important role.
Elrod and Adam’s algorithm is based on the JFO cavitation theory, a widely accepted and adopted theory developed by Jakobson (Ref. 12), Floberg (Ref. 13 and Ref. 14), and Olsson (Ref. 15). The JFO theory divides the flow in two regions:
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A full film region where the pressure varies but is limited from below by the cavitation pressure.
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A cavitation region where only part of the volume is occupied by the fluid. Because of the presence of the gas in the void fraction, the pressure in this region is assumed to be constant and equal to the cavitation pressure.
Elrod and Adams derived a general form of the Reynolds equation, Equation 9-1, by introducing a switch function, g, equal to 1 in the full film region and 0 in the cavitation region. This switch function allows for solving a single equation for both the full film and the cavitation region and leads to a modified version of Equation 9-7:
where the second and third terms on the left-hand side correspond to the average Couette and average Poiseuille velocities, respectively. This switch function sets the average Poiseuille velocity to zero in the cavitation region.
Because the average Poiseuille velocity is set to zero in the cavitation region, the density needs to be a function of the pressure variable and is defined as
where β is the compressibility, and ρc is the density at the cavitation pressure. A density that is not pressure dependent would lead to empty equations in the cavitation region since the pressure variable pf would no longer present in the governing equations.
A variable θ can be defined, given by:
In the cavitation region (θ < 1) θ represents the fractional film content.
Note About Results Postprocessing
While the pressure is constant and equal to the cavitation pressure in the cavitation region, the computed pressure is negative in this region. The value of this negative pressure can be physically be interpreted as the volume fraction of fluid in the cavitation region. The actual or physical pressure, available in the postprocessing section as tffs.p, is equal to the computed pressure in the full film region (θ ≥ 1) and equal to the cavitation pressure in the cavitation region (θ < 1).