Standard Configurations for Unsteady Flow Through Vibrating Axial-Flow Turbomachine-Cascades (STCF)

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Standard configurations

Fourth standard configuration (cambered turbine cascade in transonic flow)

2D geomertry file: Inst.geom.4th.zip (7 KB).

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The fourth standard configuration, with results obtained at the Swiss Federal Institute of Technology [Bölcs et al, 1985], is shown in Fig. 3.4.1, with the profile coordinates and aeroelastic sample cases given in Tables 3.4.1-2. Please note that the blade coordinates are given with more significant decimals than earlier as it was pointed out that the coordinates showed some oscillatory behavior. The Reynolds number was not given earlier and are included now as a basis for viscous calculations. Furthermore, experimental data exist for many more steady-state and time-dependent operating conditions (see for example Schläfli [1989]). These can be obtained upon request. It is important to point out that the time-averaged dynamic pressure is used as the quantity with which the pressure coefficients are made dimensionless. This should be remembered when predictions are performed. As far as the present authors are aware of all predictions have also been presented with this dynamic pressure. The results obtained so far show a good general agreement between the data and prediction models for shock-free flows, both as regards to the time- dependent blade surface pressures as the unsteady forces. At transonic and supersonic outlet flow conditions major discrepancies are found, as presented by Bölcs and Fransson [1986]. It should however be pointed out that a re-evaluation of the original data has indicated that the experimental uncertainty for the inlet flow angle may be larger than originally thought, which may explain some differences in the experimental and computed steady- state pressure distributions, especially in the leading edge region. Most authors have thus introduced a stream-tube contraction (towards 10%) into the calculations in order to compensate for leakage flow and boundary layer growth in the test facility. A better agreement with the steady-state blade surface pressure distributions is then generally obtained. The reader is referred to section 7.4 in Bölcs and Fransson [1986] for more details about the cascade geometry and previous results. Since the first results presented [Bölcs and Fransson, 1986], further predictions have been performed on the cascade by Whitehead [1987], Servaty et al [1987], Gallus an Kau [1989], Kau and Gallus [1989], He [1989] and Carstens [1991a] with the general results that the predictions and experiments agree well, both for steady-state and time-dependent flow, for subsonic flow conditions whereas the predictions do not give results similar to the experiment in the neighborhood of the shock waves. It can probably be concluded that the experiments are good, but some aspects of the data can not be explained with present prediction models. Further numerical developments and experiments in transonic flow seem thus necessary for the future. It has been pointed out [Carstens, 1991a] that the position of the time-averaged shock wave at the supersonic outlet flow velocity cases can be quite accurately predicted if a sufficiently fine mesh structure is used. The predicted shock strength did however not correspond to the measured one.

While the new profile definition (which corresponds to the one after which the experimental profiles where originally manufactured) is more detailed than the one originally given, it has been found that also the new coordinates show some oscillatory behavior when a very fine mesh is used [Hoyniak, 1991; Carstens, 1991b]. This can give some spurious steady-state and unsteady results, and can be avoided by performing a smoothing of the coordinates [Carstens, 1991b]. Another problem that was discussed is the treatment of the blunt trailing edge. Most prediction models use a modified airfoil shape towards the trailing edge in order to close in towards a sharp edge. It can generally be stated that the turbine geometry defined, with its corresponding 8 aeroelastic sample cases, is still of importance for the understanding of flutter-phenomena and further developments of numerical prediction models. The original cases are thus kept in the data-base. Much more work has to be done to find explanations for the differences between the data and the predictions.