This paper is the first part of a two-part paper that presents a comprehensive study of the higher-order mode mistuned forced response of an embedded rotor blisk in a multistage axial research compressor. The resonant response of the second-stage rotor (R2) in its first chordwise bending (1CWB) mode due to the second harmonic of the periodic forcing of its neighboring stators (S1 and S2) is investigated computationally and experimentally at three steady loading conditions in the Purdue Three-Stage Compressor Research Facility. State-of-the-art numerical methods applicable in an industrial design environment are used to construct a 1.5-stage stator/rotor/stator configuration for the prediction of the aerodynamic forcing function of the rotor. The time-averaged component of these simulations provides a good prediction of the compressor performance, rotor tip leakage flow (TLF), and characteristics of the stator aerodynamic disturbances. The contribution of the rotor TLF on the rotor forcing function is small, responsible for less than 5% of the total modal force in amplitude. Moreover, the individual contributions of the upstream and downstream stators to the rotor modal force are separated via a linear forcing decomposition approach. It is shown that the upstream stator provides the dominant forcing function with an amplitude almost 6 times that of the downstream stator, and is mostly due to the impulse-like appearance of the upstream stator wakes which have significant higher-harmonic (including the second-harmonic) contents. An excellent prediction of the tuned 1CWB resonant response amplitudes is achieved with only 35%, 4%, and 7% difference to the measured values at three loading conditions.

In the previous part of the paper, a novel method to reconstruct the compressor non-uniform circumferential flow field using spatially under-sampled data points is developed. In this part of the paper, the method is applied to two compressor research articles to further demonstrate the potential of the novel method in resolving the important flow features associated with these circumferential non-uniformities. In the first experiment, the static pressure field at the leading edge of a vaned diffuser in a high-speed centrifugal compressor is reconstructed using pressure readings from nine static pressure taps placed on the hub of the diffuser. The magnitude and phase information for the first three dominant wavelets are characterized. Additionally, the method shows significant advantages over the traditional averaging methods for calculating repeatable mean values of the static pressure. While using the multi-wavelet approximation method, the errors in the mean static pressure with one dropout measurement are 70% less than the pitchwise-averaging method. In the second experiment, the full-annulus total pressure field downstream of Rotor 2 in a three-stage axial compressor is reconstructed from a small segment of data representing 20% coverage of the annulus. Results show very good agreement between the reconstructed total pressure profile and the experiment at a variety of spanwise locations from near hub to near shroud. The features associated with blade-row interactions accounting for passage-to-passage variations are resolved in the reconstructed total pressure profile.

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In the previous part of the paper, a novel method to reconstruct the compressor non-uniform circumferential flow field using spatially under-sampled data points is developed. In this part of the paper, the method is applied to two compressor research articles to further demonstrate the potential of the novel method in resolving the important flow features associated with these circumferential non-uniformities. In the first experiment, the static pressure field at the leading edge of a vaned diffuser in a high-speed centrifugal compressor is reconstructed using pressure readings from nine static pressure taps placed on the hub of the diffuser. The magnitude and phase information for the first three dominant wavelets are characterized. Additionally, the method shows significant advantages over the traditional averaging methods for calculating repeatable mean values of the static pressure. While using the multi-wavelet approximation method, the errors in the mean static pressure with one dropout measurement are 70% less than the pitchwise-averaging method. In the second experiment, the full-annulus total pressure field downstream of Stator 2 in a three-stage axial compressor is reconstructed from a small segment of data representing 20% coverage of the annulus. Results show very good agreement between the reconstructed total pressure profile and the experiment at a variety of spanwise locations from near hub to near shroud. The features associated with blade-row interactions accounting for passage-to-passage variations are resolved in the reconstructed total pressure profile.

No abstract