Sheet Cavitation
In order to predict sheet cavitation on the propeller blades, an approach introduced by Fine (1992) is used in panMARE. This approach is also based on the potential solution. In this approach the fluid domain is enclosed by the body and the cavitation sheet, which together compose the fluid's boundaries. Two boundary conditions are introduced, which influence both the potential solution as well as the thickness of the cavitation sheet.
Dynamic Boundary Condition
The dynamic boundary condition states, that the pressure inside the cavity as well as at its boundaries must be equal to vapour
pressure
Kinematic Boundary Condition
The kinematic boundary condition demands that the flow through the cavity's surface vanishes, i.e. that the substantial change of
the cavity thickness corresponds to the flow velocity in direction of the surface normals:
Furthermore, finite differences are used to determine the time rate of change of the cavity thickness. Thus, the equation above only has the following unknowns: the cavity thicknesses of the examined panel and of its neighbours.
Solving Routine and Cavity Expansion
The rearranged kinematic boundary condition is solved in an additional system of equations after the potential solution in the panMARE
solving routine. The dynamic boundary condition of the sheet cavitation is included in this process. Hereby, the non-cavitation panels are used
as known values without cavity thickness
After the determination of the cavity thickness, the cavity's expansion on the body's surface is calculated using several factors:
- If a panel's pressure falls below the vapour pressure
, this panel will start to cavitate.
- If a panel is already cavitating and if it is the last cavitating panel along a flow line, the cavitating area is either enlarged
(cavity thickness
) or reduced ( ).
- If the cavity thickness is negative at the leading end of the cavitating area and the pressure is greater than
, the leading end of the cavity area is moved towards the aft by one panel.
An additional iteration is required to calculate the change of the cavity's expansion. Therefore, the potential solution, including both cavitation boundary conditions and a subsequent adaptation of the cavity's current expansion, is iterated until the expansion finally converges.