Objectives

The present paper aims to investigate further the sensitivity of the critical (flitter) reduced frequency versus mode shape maps for the sectored vane, namely towards an non-uniform distribution in the amplitudes between the blades in the sector. The influence of the number of the airfoils in the sec­tored vane will be demonstrated.

2. Method of attack

The method for investigation of flitter appearance in a cascade, where blades are connected together in a number of identical sectors is presented in [3] and can be shortly described as follows:

• The aerodynamic response of a sectored vane is calculated based on the aerodynamic work influence coefficient representation of a freestanding bladed cascade.

• There is a possibility to consider different vibration amplitudes and any inter-blade phase angles for the blades in the sector, while the inter­sector phase angles follow the Lane’s criteria [6] and all blades have the same vibration frequency.

• Assuming a rigid-body motion allows to define the blade mode shape en­tirely by its pitching axis position. Thus, at a selected reduced frequency and given pitching axis positions for the blades in sector the aerody­namic work for the sector is calculated as a function of the inter-sector phase angle as well as amplitude and phase angle distributions between the airfoils in the sector. The absolute maximum of the work is then cal­culated and the algorithm is continued for another pitching axis position until the whole range of the mode shapes is covered.

• Afterwards, the results for a number of reduced frequencies are over­laid to produce a plot of critical reduced frequency versus pitching axis position for the reference sectored vane. This determines the value of reduced frequency for which each torsion axis locations of the blades in the sector becomes unstable.

For the practical applications shown in this paper the following restrictions are applied in the algorithm:

• Mode shape of the sectored vane is considered to be real, i. e. the blades in sector can only have 0 and/or 180 degree inter-blade phase angle be­tween each other.

• All the blades in the sector have the same relative pitching axis location.

In the present paper the method is applied for a number of different vibration amplitude distributions for the airfoils belonging to the same sector as well as for different numbers of airfoils in the sector.