On Pressure Mode Shapes Arising from Rotor/Stator Interactions

Rotor Stator Interaction (RSI) is an important source of pressure pulsations in hydro-machinery. RSI pressure pulsations induce vibrations in both stationary and rotating components. For the first time, the time variant and spatial nature of these pressure distributions (pressure mode shapes) have been visualized. A reversible pump-turbine with 20 wicket gates was tested with runners having six and nine blades. Numerous pressure transducers located in the priming chamber, between the runner and wicket gates, and between the runner crown and head cover were recorded. These data were analyzed with ME’scopeVES from Vibrant Technology, Inc. to produce animated visualization of the pressure fields. The kinematics of RSI pressure pulsations are predicted from elementary fluid flow principles, and the calculated pressure mode shapes are shown to compare favorably with measured ones. Model testing of hydro-machinery has long been used to assess expected prototype unsteady behavior. Pressure pulsation measurements in the spiral case, in the priming chamber between runner and wicket gates, and in the draft tube are commonly made. Other measurement locations may be employed for special situations or for research and development. Other unsteady measurements may also be made, such as forces and moments on the wicket gates or runner. Deducing the physical phenomena inducing unsteadiness and scaling the measured data to full scale conditions are ongoing challenges. Unsteady pressure at a particular location may be the summation of numerous physical phenomena. For example, in the priming chamber, the instantaneous pressure could result from the superposition of the effects of a nearby runner blade interacting with a wicket gate. Other effects include runner blade to wicket gate interactions that occurred earlier and now have radiated to the same location, as well as from numerous reflections of these waves. Stochastic flow induced turbulence and fluid flow acoustic resonances caused by the coincidence of pulsation wavelengths with water passage dimensions inside the machine or external to the machine as well as a large variety of fluid-structure interactions need to be considered. Even pressures associated with test stand pumps may influence the results. In the past, it has been necessary to infer the fundamental source of the pressure pulsations from measured frequencies and knowledge of the frequencies of underlying physical principles. An additional tool in this process is the Operating Deflection Shape (ODS) technique, which permits visualization of complex temporal and spatial patterns. These patterns may then be compared to predictions, enabling a more direct evaluation of causation. Rotor/Stator Interactions Although RSI phenomena have been studied by others, 1 additional insight has been obtained from the following analysis. The RSI pressures must have a certain form to satisfy consistency and fluid physics. The consistency requirement of periodicity specifies the mathematical form of an integer number of cycles in one revolution. The fluid physics specifies that the magnitude of pressure on a blade depends on the flow field. These two concepts generate the form of the interaction of the pressure field on the runner and the flow field entering the runner. The pressure on the runner extends into the fluid and generates the pressure field away from the runner, such as is sensed between the runner and wicket gates. The pressure field on the runner is required to be periodic with the number of blades. The form of the pressure, viewed from rotating coordinates, can be expressed as: The value of m represents the harmonic of the pressure field. A value of m = 0 would represent a constant pressure, with no variation between buckets and plays no role in RSI. For m = 1, the pressure field would consist of one sinusoidal variation in pressure between each blade and would rotate with the runner. The runner pressure field would have the form of an infinite summation of these components, beginning with m = 1. The actual magnitude of the pressure is a complicated function depending on both geometry and flow field. The magnitude of the pressure, therefore, remains unknown. The form of the flow field is known, as it must satisfy a periodic requirement related to the number of wicket gates. The flow field also has a harmonic content that may be expressed formally as: