UNSTEADY AERODYNAMIC WORK ON OSCILLATING ANNULAR CASCADES IN COUNTER ROTATION

Combination of Supersonic and Subsonic Cascades

M. Namba

Sojo University

Ikeda, Kumamoto, 860-0082, Japan namba@arsp. sojo-u. ac. jp

K. Nanba

Sojo University nanba@arsp. sojo-u. ac. jp

Abstract The paper studies the effect of neighboring blade rows on unsteady aerodynamic force due to blade vibration and on flitter characteristics of cascading blades. For this purpose 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. Numerical examples of unsteady aerodynamic works for various combinations of cascades, i. e., subsonic-subsonic, supersonic – supersonic, and subsonic-supersonic cascades, are presented. It is clearly shown that the difference in the unsteady aerodynamic work on vibrating blades be­tween the case of the decoupled cascade and the case of the aerodynamically coupled cascades is large when the neighbor cascade is supersonic. A com­putation program to solve the coupled bending-torsion flitter equation for the contra-rotating annular cascades was also developed. Some results of the flitter analysis are presented. The presence of the neighboring blade row gives rise to significant change in the critical flitter fliid velocity for the subsonic cascade when the main acoustic duct mode is of cut-on state.

Keywords: Cascade Flutter, Multiple Blade Rows, Unsteady Aerodynamics, Aeroelasticity

Introduction

The unsteady aerodynamic force on oscillating blades in a cascade is heav­ily dependent on the interblade phase angle. This implies that the aerodynamic coupling among blades plays a critical role on the cascade flitter characteris-

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K. C. Hall et al. (eds.),

Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, 177-188. © 2006 Springer. Printed in the Netherlands.

tics. From this standpoint neighboring blade rows, e. g., a neighboring rotor or stator or contra-rotating fan cascade, also will have a considerable infhence on the unsteady aerodynamic force because blade rows are closely placed in acthal thrbomachines.

There are available a few published papers dealing with the infhence of neighboring blade rows on the unsteady aerodynamic response of oscillat­ing blades. The theoretical study based on the semi-actuator disk model by Tanida [1] and the experiments and the linear cascade theory by Kobayashi et al. [2, 3] should be cited as the earliest works. Their theories assume in­compressible fbws and therefore can not deal with aeroacoustic interaction between blade rows via cut-on acoustic duct modes. Butenko and Osipov [4] developed a theory for subsonic linear cascades in relative motion. Recently Hall and Silkowski [5] presented an analysis based on two-dimensional sub­sonic multiple blade rows, and Namba et al. [6] developed a three-dimensional theory for oscillating subsonic contra-rotating annular cascades. Those studies for subsonic fbws indicate that the inflience of aeroacoustic coupling among blade rows on the aerodynamic damping force is significant in particular when the main acoustic duct mode generated from the oscillating blade row is cut – on. It suggests that in the case of supersonic cascades, where oscillation of blades generates an infinite number of cut-on modes, neighboring blade rows will be much more influential.

The author [7] extended his study to supersonic contra-rotating annular cas­cades, where relative mean fluid velocities for both cascades are supersonic, and gave numerical results showing a cruicial difference in unsteady aero­dynamic work on oscillating blades between aerodynamically decoupled and coupled cascades. However some bugs which result in exaggeration of the difference were later found in the computation codes.

The program has been improved and further extended so that it can deal with the combination of supersonic and subsonic cascades, for instance, a su­personic rotor cascade and a subsonic stator cascade. This paper gives some numerical results and investigates the influence of a neighboring blade row on unsteady aerodynamic work on vibrating blades for various combinations of cascades.

The present computation program based on the unsteady lifting surface the­ory [8, 9] is able to provide aerodynamic forces on oscillating blades as func­tions of the frequency. The compuation speed is remarkably high, so that it can be a very efficient tool to calculate aerodynamic force terms of the flutter equations. A computation program to solve the coupled bending-torsion flrt – ter equation for the contra-rotating annular cascades was also formulated and coded. This paper presents some results of the flutter analysis demonstrating the significant inflience of the neighboring blade row on the flitter boundaries.