![]() Which is the form of the Weymouth equation commonly used in the natural gas industry. The amplification factor of the tuned response at maximum due to mistuning is 1.18 (SNM) and 1.27 (EBM), respectively. On the other hand, for these NDs the EBM frequency results strongly differ from those computed with an FEM approach in the nodal diameter map ( figure 7). The reason for this is that the operational deflection shape assigned to the blade 1 maximum frequency is characterised by a localisation at the same blade, which leads to stronger contribution of other NDs apart from ND 4 ( figure 6). However, deviations become apparent especially for blade 1 in case of the mistuned blisk ( figure 5a) whereas the differences for the other blades decrease. Comparing EBM- and SNM-results, a perfect match of the tuned response has been found ( figure 5b). That is why the maximum blade responses are predicted at slightly higher frequencies by both ROMs. ![]() Please note that the chosen exciting frequency at 717.12 Hz for the bidirectional CFD-approach merely represents an estimation of the resonance since it is not exactly known before this computation. Bidirectional results indicate a good agreement to the SNM. The strongly mistuned blade 1 exhibits a significantly lower vibration amplitude than all other blades ( figure 5a). Since an EO 4 excitation will be enforced in the future rig-test, an aerodynamic damping matrix belonging to CSM 4 is chosen for further investigations.Ĭonsidering both unsteady forces and aerodynamic damping in the ROMs the forced response due to an EO 4 excitation is computed, see figure 5. Since the method of AIC requires that blade-mode shapes remain largely unchanged, it is proved for the 1 st flap mode that blade-mode shapes taken from finite element results of CSM 4 and CSM 14, both fitted to the CFD-mesh to calculate the aerodynamic damping lead to similar results ( figure 4). Blade-mode shapes of blisks depend on the number of nodal diameters, however, the deviations from an isolated blade-mode commonly decrease for an increasing number of nodal diameters. Figure 3 shows the aerodynamic damping at different vibration amplitudes and different nodal diameters, indicating that a linear behaviour is expected up to a 1 mm tip-displacement. Determining aerodynamic damping values via an uncoupled approach, it has to be ensured that the flow-induced aerodynamic forces act linearly on the amplitude of the blade vibration. ![]() The rotor generates a total pressure ratio of 1.23.
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