Masanobu Namba

Aerodynamically Coupled Flutter of Multiple Blade Rows

This paper deals with the aeroelastic instability of vibrating multiple blade rows under aerodynamic coupling with each other. A model composed of three blade rows, e.g., rotor-stator-rotor, in which blades of the two rotor cascades are simultaneously vibrating, is considered. The generalized aerodynamic force on a vibrating blade consists of the component induced by the vibrating motion of the blade itself and those induced by vibrations not only of other blades in the same cascade but also of blades in another cascade. To evaluate the aerodynamic forces, the unsteady lifting surface theory for the model of three blade rows is applied. The equations describing motions of blades are coupled via the aerodynamic forces. The so-called k method is applied to determine the critical flutter conditions. A numerical study has been conducted. The flutter boundaries are compared with those for a single blade row. It is shown that the effect of the aerodynamic coupling significantly modifies the critical flutter conditions.Copyright

Aeroacoustic Control of Fan Tone Noise

Mathematical formulations of the unsteady three-dimensional flowfield induced by a rotating annular cascade interacting with an oncoming periodic gust and disturbances from an oscillating actuator surface composed as a part of the duct wall are presented on the basis of a linearized unsteady lifting surface theory. The problem of suppressing the tone noise due to interaction of the rotor with the gust by means of the actuator motion is studied. Theoretical analysis with numerical calculations is conducted for a simple harmonic sinusoidal gust, and a simple harmonic sinusoidal circumferential wave form of the actuator motion and optimum conditions of the actuator motion are investigated. There are substantial differences in the optimum phase and amplitude of the actuator motion between the conditions of suppressing the upstream and downstream acoustic powers. In the case of multiple cut-on duct modes, the actuator motions of the cut-off circumferential wave numbers are desirable to effectively suppress the total acoustic powers.

Flutter Analysis of Contra-Rotating Blade Rows

To investigate the flutter characteristics of cascading blades in multiple blade rows, the computation program to calculate the unsteady blade loading based on the unsteady lifting surface theory for contra-rotating annular cascades was formulated and coded. Then a computation program to solve the coupled bending-torsion flutter equation for the contra-rotating annular cascades was also developed. Some results of the flutter analysis are presented. It is shown that the presence of the neighboring blade row gives rise to substantial change in the critical flutter condition irrespective of the blade row gap when the main acoustic duct mode is of cut-on state. The effect of the neighboring blade row is also significant irrespective of the state of the main acoustic duct mode when the blade rows are very closely placed.

Unsteady Aerodynamic Forces on Vibrating Annular Cascade Blades: Cross-Validation of the Linear Unsteady CFD Calculations Using the TVD Scheme and the Double Linearization Theory

The paper presents the formulation to compute numerically the unsteady aerodynamic forces on the vibrating annular cascade blades. The formulation is based on the finite volume method, the type, and the TVD scheme, following the UPACS code developed by NAL, Japan. By applying the TVD scheme to the linear unsteady calculations, the precise calculation of the peak of unsteady aerodynamic forces at the shock wave location like the delta function singularity becomes possible without empirical constants. As a further feature of the present paper, results of the present numerical calculation are compared with those of the double linearization theory (DLT), which assumes small unsteady and steady disturbances but the unsteady disturbances are much smaller than the steady disturbances. Since DLT requires far less computational resources than the present numerical calculation, the validation of DLT is quite important from the engineering point of view. Under the conditions of small steady disturbances, a good agreement between these two results is observed, so that the two codes are cross-validated. The comparison also reveals the limitation on the applicability of DLT.Copyright