AXIAL TURBINE BLADE VIBRATIONS INDUCED BY THE STATOR FLOW

Comparison of Calculations and Experiment

M. B. Schmitz, O. Schafer, J. Szwedowicz, T. Secall-Wimmel

ABB Turbo Systems Ltd Thermal Machinery Lab CH-5401 Baden Switzerland

michael. schmitz@ch. abb. com

T. P. Sommer

ALSTOM (Switzerland) Ltd CH-5401 Baden Switzerland

thomas. sommer@power. alstom. com

Abstract The forced excitation of the rotor blades of a single-stage turbine due to rotor – stator interaction is calculated with an in-house unsteady flaw solver and a gen­eral purpose finite element code. A scaled configuration is used in order to re­duce the amount of computational effort. The unsteady flow solution is obtained on three blade-to-blade cuts. The time dependent static pressure on the blade surface is Fourier transformed with respect to the vane passing frequency and the relevant Fourier modi of the original three blade profile cuts are interpolated to the overall blade height. This Fourier transformed flow solution is transferred to the finite element model where the blade excitation is obtained. Two reduced geometrical rotor-stator configurations are investigated and compared with re­spect to the flow field and the resulting blade excitation.

Keywords: Forced Response, Rotor-Stator Interaction, Unsteady Flow Computation

1. Introduction

Even today, with computing power available rather cheaply, an unsteady fhw simulation comprising the full annulus of merely a single stage is im­practical for routine engineering use. A reduced model is required to lower computing time to an acceptable level, allowing unsteady simulations to have

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Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, 107-118. © 2006 Springer. Printed in the Netherlands.

an impact on the design of a turbine. So called single passage methods such as the inclined time plane approach by Giles [12], the direct store method by Erdos [2], or the harmonic balance method of Dewhurst and He [1] have been developed over the last decade. However, these methods have often not made it into design codes, yet. If a single passage method is not available, the compu­tational effort can be reduced by simulating only a fraction of the full annulus. Ideally, this is achieved by dividing the number of blades for each blade row by the highest common factor. Often, as is the case for the turbine stage under investigation, it is not possible to achieve a small computational domain with an integer blade count ratio by this approach. Here, the stage consists of 43 vanes and 64 blades, rather close to a ratio of two vanes per three blades. The closest numbers of vanes and blades corresponding to exactly a ratio of two to three are 42 vanes and 63 blades, with a highest common factor of 21. For practical reasons, then, the choice was made to modify the problem from 43/64 to 42/63 and to calculate only (1/21)th of the annulus.

A modification of this kind while retaining the original blade shape would change the throat area for both vane and blade, and thus the fbw capacity, the reaction, the flow angles, and so on. In order to retain the original stage properties, the geometry has to be modified, as well. Two approaches could be taken: To restagger or reskew the airfoils, or to scale them. In the case of a restagger, the throat to pitch ratio is set to be equal to the original, and the curvature and trailing edge thickness is kept constant. The pitch to chord ratio, on the other hand is changed, as well as the inlet metal angle of the blade, and thus the incidence. With the scaling approach, the throat to pitch ratio is again set equal to the original, and the pitch to chord ratio, as well as the inlet metal angle, are retained, but the trailing edge thickness and the curvature is changed. In the present investigation, the scaling approach is used in order to minimize any incidence effect on the blade.

When the computational problem is simplified in this manner, it is clear that the unsteady flow will also change. The obvious and most important difference is that a change in vane count will also alter the vane passing frequency that each rotor blade sees. We will argue here that, at least for a case with a vane pitch that is much larger than the blade pitch, the only significant change occurs in the frequency of the disturbances. The idea behind this simplification is that disturbances such as wakes are sufficiently separated in the sense that with either original or modified vane count, there will never be two wakes inside a single blade passage. Thus it could be argued that each disturbance is seen by the blades as an independent entity.

The computed unsteady blade pressure will be applied to the mechanical blade model that represents the original geometry. The transfer of the unsteady pressure is done in Fourier space, conserving the complex amplitudes but pre­scribing the real vane passing frequency instead of that of the CFD model.

The present paper tries to answer the question if the above simplifications lead to significant errors in both the detailed unsteady fbw field and the com­puted blade response.