Numerical and Analytical Study of Fluid Dynamic Forces in Seals and Bearings

Abstract

A numerical model based on a transformed, conservative form of the three-dimensional Navier-Stokes equations and an analytical model based on “lumped” fluid parameters are presented and compared with studies of modeled rotor/bearing/seal systems. The rotor destabilizing factors are related to the rotative character of the flow field. It is shown that these destabilizing factors can be reduced through a descrease in the fluid average circumferential velocity. However, the rotative character of the flow field is a complex three-dimensional system with bifurcated secondary flow patterns that significantly alter the fluid circumferential velocity. By transforming the Navier-Stokes equations to those for a rotating observer and using the numerical code PHOENICS-84 with a nonorthogonal body fitted grid, several numerical experiments were carried out to demonstrate the character of this complex flow field. In general, fluid injection and/or preswirl of the flow field opposing the shaft rotation significantly intensified these secondary recirculation zones and thus reduced the average circumferential velocity, while injection or preswirl in the direction of rotation significantly weakened these zones. A decrease in average circumferential velocity was related to an increase in the strength of the recirculation zones and thereby promoted stability. The influence of the axial flow was analyzed. The lumped model of fluid dynamic force based on the average circumferential velocity ratio (as opposed to the bearing/seal coefficient model) well described the obtained results for relatively large but limited ranges of parameters. This lumped model is extremely useful in rotor/bearing/seal system dynamic analysis and should be widely recommended. Fluid dynamic forces and leakage rates were calculated and compared with seal data where the working fluid was bromotrifluoromethane (CBrF3). The radial and tangential force predictions were in reasonable agreement with selected experimental data. Nonsynchronous perturbation provided meaningful information for system lumped parameter identification from numerical experiment data.

Transient Torsional and Lateral Vibrations of Unbalanced Rotors With Rotor-to-Stator Rubbing

“…The normal and tangential forces are functions of the stator sti!ness and the stator}rotor coe$cient of sliding friction. To account for the e!ect of #uid-"lm bearing sti!ness and damping cross-coupling terms, the lumped-parameter speed-dependent model, which was presented by Tam et al [8], is adopted. The equations of motion are represented in a compact matrix and solved for di!erent cases using a predictor}corrector integration scheme.…”

Modélisation numérique du comportement dynamique des joints annulaires d'étanchéité

“…Les algorithmes numériques de la Mécanique des fluides sont assez matures pour permettre de telles solutions. Cette voie a été adoptée par quelques auteurs [5,6,7] et ces approches n'ont pas a priori de limitations mais l'effort de calcul est assez important.…”

“…Les forces et les moments calculés pour plusieurs fréquences de précession servent pour obtenir les coefficients utilisés dans l'analyse dynamique des lignes d'arbre. Des modèles 3D à l'ordre un de ce type ont été pré-sentés par Nordmann et Dietzen [5], Baskharone et Hensel [6], Athavale et Hendricks [7]. La résolution numérique nécessite moins de temps de calcul que l'approche non-perturbée, mais, en raison de la géométrie spécifique des labyrinthes, l'effort de calcul est toujours important.…”

Bifurcation behaviour and limit cycles of a compliant seal‐rotor system

“…The seal gap between is turbulently streamed by an incompressible Newtonian fluid which couples the motions of the two rigid bodies. The forces on seal and rotor are accounted for by the Muszynska model [3], [4], [5]. The system dynamics are described by…”