Vibration of Cascade Blades Treated by Actuator Disc Methods

Abstract

This paper gives a theoretical method of calculating the aerodynamic forces on vibrating compressor and turbine blades subject to two fundamental limitations. These are, firstly, that the time for the fluid to flow through the cascade must be small compared with the period of the vibration, and secondly, that adjacent blades must vibrate nearly in phase. This enables any kind of two-dimensional steady-flow cascade data to be used. The methods given also allow the vibration forced by fluctuations in the incident flow to be calculated. The main conclusions are as follows: (1) Bending vibration of unstalled blades with small mean deflection is always damped. (2) A criterion for bending flutter of unstalled blades with large mean deflection is derived. This is qualitatively supported by experiments carried out by Shioiri and Shibata (1)†. (3) A condition of instability of the flow through stalled cascades of fixed blades is derived, and agrees with previous investigations by Fabri and Siestrunck (2) and Rannie and Marble (3). This also agrees with the results of an experimental investigation by Wood (4). (4) A criterion for the bending flutter of stalled blades is derived, and it is shown that this limit is reached before the instability limit referred to in (3) above. (5) It is found that, except for a particular case of zero stagger cascades, flutter of unstalled blades in torsion will always occur. For this case, however, the first fundamental assumption referred to above is unlikely to be true and more detailed investigation of this case is required.