Blade-loading effects on the propagation of unsteady flow and on forcing functions in axial-turbine cascades

This article investigates the effect of tangential blade loading on the propagation of time-dependent pressure disturbance due to potential-flow interaction ans viscous-wake interaction from upstream blade rows in axial-turbine-blade rotor cascades. Results are obtained by modeling the effects of the stator viscous wake and tha stator-rotor potential-flow field on the rotor flow field. A computer program is used to calculate the unsteady flows in the rotor passages. The amplitudes for the two types of interaction are based on a review of available experimental and computational data. We study the propagation of the isolated potential-flow interaction (no viscous-wake interaction), of the isolated viscous wake interaction (no potential-flow interaction), and of the combination of interactions. We examine the propagation of both interactions in three frotor cascades of high, medium and low tangential-loading coefficient (1.2, 1.0 and 0.8 respectively) for typical values of reduced frequency. The discussion uses as example a stator-to-rotor-pitch ration $R$ = 2. We investigate the differences when the stator-to-rotor pitch ratio is decreased (to $R$ = 1) and increased (to $R$ = 4). We offer new explanations of the mechanisms of generation of unsteady forces on the blades and study the effects of tangential blade and of axial gap between blade rows on th time-dependent forces acting on the blades. The potential-flow field of the rotor-leading-edge region cuts the potential-flow field of the upstream stator, and distorts and cuts the wake centerlines. The potential-flow field cut into the rotor passage propagates downstream as a potential-flow disturbance superimposed on the rotor flow field. The direction and decay rate of this interaction are determined respectively by the stator-outlet flow angle and by the stator-cascade pitch. The cut wake is sheared into the rotor passage and it results in a region of increased unsteady pressure upstream of the wake centerline and a region of decreased unsteady pressure downstream of the wake centerline. The wake shearing is more pronounced in highly-loaded cascades, and for lower stator outlet-flow angles. The potential flow interaction dominates the unsteadiness for high values of $R$ and the wake interaction dominates the unsteadiness for low values of $R$. The above explanations can be used to determine locations unsteady-pressure regions, and the shape of the unsteady forcing functions