Implementation of a Vapour Cavitation into Computational Models of Rotors Supported by Long Journal Bearings

Dynamical behaviour of rotors supported by hydrodynamical bearings is considerably influenced by presence of a gas phase in the lubricating oil. The reason for its occurance is a vapour cavitation. The observations show that pressure of the two-phase medium in cavitated regions remains approximately constant [

1

]. At long bearings ( most of the bearings ) the pressure gradient in the axial direction is insignificant and the pressure distribution in bearing gap can be described by a simplified Reynolds equation.

To be satisfied the continuity of flow and incompressibility of oil the pressure gradient must be zero at the entrance into the cavitated region. To determine edges of the cavitated area a new algorithm has been developed. First the pressure distribution between two nodes corresponding to two adjacent oil inlets into the bearing is calculated. If the minimum pressure drops below the critical value, a vapour cavitation occurs. Then the border nodes are successively chosen from the node of the pressure minimum in the direction opposite to the rotor rotation and the Reynolds equation is solved for the boundary conditions : pressure at the oil inlet, zero pressure gradient at the chosen border node. This process continues until the pressure in the border node is equal to the cavitation one. In the next step the border nodes are chosen from the node of the pressure minimum in the direction of the rotor rotation and the Reynolds equation is calculated for the boundary conditions : pressure in the cavitated area, pressure at the oil inlet. The border node at which the difference between the flow rate and the flow rate through the inlet edge of the cavitation area is minimum is considered to be the outlet edge of the cavitated region.

This procedure was implemented into the algorithms for investigation of the transient response of rotors excited by force and kinematic effects ( rotor unbalance, earthquake excitation, etc. ). A modified Newmark method has been chosen [

2

] for solution of the equation of motion. The modification consists in continuous linearization of the vector of hydraulical forces in the neighbourhood of the current rotor position.