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Results and discussion
The vibration amplitude distributions between the airfoils in sector are chosen as for the following three cases:
h Uniform: all blades in sector vibrating with the same amplitude.
Z Edge blades dominated: vibration amplitude of the edge blades is 1 while the amplitude of the inner blades is 0.5.
T Internal blades dominated: vibration amplitude of the edge blades is 0.5 while the amplitude of the inner blades is 1.
The number of airfoils in a sector has been selected as four, five or six. While varying the real sector mode shape it is assumed that the mode shapes of the airfoils belonging to the same sector are changing in an identical manner.
The maps in Figures 2 to 8 show the values of the critical reduced frequencies. Each contour line in the critical reduced frequency map corresponds to the value of reduced frequency for which the reference vane is neutrally stable. The reference vane is in the center of the diagram and identified with a thicker line.
The discussion of the results is divided into two parts, for the torsion axis location varied in the near field of the reference vane (torsion dominated modes) and for torsion axis location approaching infinity (bending dominated modes).
A comparison of the aerodynamic behavior of the multiple airfoils sectored vanes is made against a freestanding blade cascade. In the freestanding blade cascade the blades vibrate with identical mode shapes as well as amplitudes and have a constant inter-blade phase angle between each other. The critical reduced frequency maps for the freestanding blade cascade are shown in Fig. 2a (torsion-dominated mode shapes) and in Fig. 2b (bending-dominated mode shapes) as a reference towards the four-, five – and six-airfoil sectored vanes to be shown later.
