Suppression of unstable vibration by the trailing edge oscillation

To confirm the effectiveness of the control method with trailing edge oscil­lation, the case of 5 = 45 degrees was analyzed by the fbw-stmcture coupled method. The initial velocity of V0=0.01Cw was given to No.1 blade, and that of -Vo was given to No.3 blade. No.2 and No.4 blades had the initial displace­ment (No.2 blade; h0=0.01C, and No.4 blade; – h0) to simulate the case when

all blades oscillate with 90 degrees of inter blade phase angles at the initial state of computation. The trailing edges of No. I and No.3 blades were actively oscillated. Since the blade oscillation frequency is an implicit parameter in the fbw-structure coupled method, the blade oscillation frequency is calculated in the present study by the Fourier transfer of blade displacement to obtain w the angular frequency. The blade displacement /?/ and ф arc calculated from the following equations;

h! = sin (cot + 0) where., в = arctan j		(2)
v МЦ )
ф — В sin (cot + 9 + S)		(3)

Figure 16 show’s the time history of the blade displacement and the unsteady aerodynamic force when 5 is about 45 degrees. The result of the case without control is also indicated by the dotted line for comparison. As shown in Fig. 16, the increase in the displacement of all blades is effectively suppressed by the trailing edge oscillation. In the controlled case, the phase of the unsteady aero­dynamic force delays compared with that of the blade displacement.

From the analysis by fbw structure coupled method, it can be concluded that the method of active trailing edge oscillation can effectively suppress the cascade fhtter in transonic fbw’ regime.

2. Conclusions

Possibility of active cascade fitter control under transonic fbw condition with passage shock waves was numerically studied. Two methods of flitter

Figure 16. Time Histor’ of the Blade Displacement and the Unsteady Aerodynamic Force (with Trailing Edge Oscillation)

control were analyzed by the developed numerical code. In the first method, the direction of the oscillatory motion of blades was actively changed. The method can be realized with some kind of shape memory alloy. The second control method gives active oscillation to the blade trailing edge with a fhp – like manner. The active vibration can be realized with piezo-electric devices.

The conclusions are summarized as follows.

1 In the adopted cascade model, the unsteady aerodynamic force induced by passage shock movement was dominant for instability of blade vibra­tion.

2 The control method with changing oscillation direction can control the passage shock movement near the blade surface, and change the un­steady aerodynamic force induced by the passage shock from exciting to damping one.

3 By the method of active trailing edge vibration, the unsteady aerody­namic force induced by the passage shock oscillation can be changed from exciting to damping force if the phase of the trailing edge vibration is properly selected compared with that of blade oscillation. The cascade flitter can be effectively suppressed in the case. At an improper phase, on the contrary, the control increases the exciting force on the blade.

References

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