Lifting surface theory to predict aerodynamic forces induced by oscillating blades under interaction of three bladerows

The paper presents the unsteady lifting surface theory to predict unsteady aerodynamic forces on blades of aerodynamically coupled three annular bladerows. Blades of any one bladerow are assumed to be vibrating. The bladerows are assumed to be individually rotating with arbitrary rotational velocities, and therefore the model can be reduced to a rotor/stator/rotor model or a counter-rotating multi-rotor system model by appropriately specifying rotational velocity parameters. The details of the mathematical formulations and the solution procedures are described. Numerical studies were conducted. The disturbances produced by a simple harmonic blade vibration are composed of multiple frequency components because of aerodynamic interaction between bladerows in mutual rotational motions. Relative magnitudes of the frequency components of the unsteady aerodynamic forces are made clear. Not only the effects of nonoscillating neighboring bladerows on the unsteady aerodynamic response of the oscillating bladerow, but also the unsteady aerodynamic forces on nonoscillating neighboring bladerows induced by the oscillating bladerow are investigated.