Two-Phase Flow and Inertial Effects on the Rotordynamic Forces in Whirling Journal Bearings

This paper presents the application of the isenthalpic two-phase flow approximation (Brennen, 1995) to the study of cavitation and ventilation effects in plane journal bearings with whirling eccentricity. A quasi-homogeneous bubbly liquid/vapor model, suitably modified to account for thermal effects (Rapposelli and d’Agostino, 2001), is used to describe the occurrence of flow cavitation. An homogeneous liquid/gas/vapor model without thermal effects is used to describe the simultaneous occurrence of cavitation and ventilation. The proposed model treats the fully-wetted and two-phase portions of the fluid in a unified manner in order to avoid the use of “ad hoc” matching conditions, whose applicability and accuracy is questionable in the presence of significant inertial and/or unsteady effects. A non-linear analysis that accounts for the inertia of the lubricant is used to determine the reaction forces caused by the shaft’s eccentric motion both in the viscosity-dominated regime and at intermediate values of the Reynolds number, where the inertia of the lubricant is no longer negligible. The classical iteration method for the Reynolds lubrication equation (Muster and Sternlicht, 1965; Mori and Mori, 1991; Reinhardt and Lund, 1975) has been extended to the unsteady two-phase flow case in order to account for flow acceleration effects in the presence of cavitation and/or ventilation. Significant deviations from the steady-state case are obtained at moderately high Reynolds numbers (Re = ωRc/ν_L ≅ 10). Comparisons with the scant experimental data support the validity of the proposed model. Results are shown in a number of representative cases in order to illustrate the influence of the relevant parameters.