A multi-objective design optimization is performed on a U-bend in serpentine internal cooling channels. The aim is to achieve both minimized total pressure loss and maximized heat transfer ability. The optimization technique used is a two-level routine developed at the Von Karman Institute for Fluid Dynamics (VKI), featuring a Differential Evolution algorithm assisted by a metamodel, which is continuously updated during the course of the optimization process to increase its accuracy The geometries are carefully parameterized by means of Bezier curves. In total, 26 geometrical parameters are used as design variables, allowing an extensive variation of the U-bend geometries. The fluid dynamic and heat transfer performances of the selected geometries are predicted by a Reynolds-averaged Navier-Stokes solver in OpenFOAM. The result shows that dozens of optimized geometries of enhanced performances in both design objectives can be obtained after a few numbers of iterations. The enhancement ranges from roughly 12∼30% decrease in total pressure loss and a 8∼17% increase in heat flow rate. A clear trade-off between pressure loss and heat transfer is observed, allowing designers to select a compromising geometry between both criteria after the optimization process, depending on the application type of the internal cooling channel. Generally, a stronger secondary flow motion in the channel will be responsible for higher heat transfer at the cost of increased losses. A discussion is held on the geometrical features that have an impact on the secondary flow motion strength and lead to general applicable conclusions.

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.

This paper is the second part of a two-part paper that presents a comprehensive study of the higher-order mode (HOM) 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 passing 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. A nonintrusive stress measurement system (NSMS, or blade tip-timing) is used to measure the blade vibration. Two reduced-order mistuning models of different levels of fidelity are used, namely, the fundamental mistuning model (FMM) and the component mode mistuning (CMM), to predict the response. Although several modes in the 1CWB modal family appear in frequency veering and high modal density regions, they do not heavily participate in the response such that very similar results are produced by the FMM and the CMM models of different sizes. A significant response amplification factor of 1.5–2.0 is both measured and predicted, which is on the same order of magnitude of what was commonly reported for low-frequency modes. In this study, a good agreement between predictions and measurements is achieved for the deterministic analysis. This is complemented by a sensitivity analysis which shows that the mistuned system is highly sensitive to the discrepancies in the experimentally determined blade frequency mistuning.

This paper is the second 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 multi-stage 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 passing 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. A Non-Intrusive Stress Measurement System (NSMS, or blade tip-timing) is used to measure the blade vibration. Two reduced-order mistuning models of different levels of fidelity are used, namely the Fundamental Mistuning Model (FMM) and the Component Mode Mistuning (CMM), to predict the response. Although several modes in the 1CWB modal family appear in frequency veering and high modal density regions, they do not heavily participate in the response such that very similar results are produced by the FMM and the CMM models of different sizes. A significant response amplification factor of 1.5∼2.0 is both measured and predicted, which is on the same order of magnitude of what was commonly reported for low-frequency modes. This amplification is also a strong, non-monotonic function of the steady loading. Moreover, on average, the mistuned blades respond at an amplitude only approximately 40% that of the tuned, much lower than what was commonly reported (75∼80%). This is due to the very low level of structural coupling associated with the 1CWB family of the rotor blisk. In this study, a very good agreement between predictions and measurements is achieved for the deterministic analysis. This is complemented by a sensitivity analysis which shows that the mistuned system is highly sensitive to the discrepancies in the experimentally determined blade frequency mistuning.

This paper presents the results from a research effort on eigenvalue identification of mistuned bladed rotor systems using the Least-Squares Complex Frequency-Domain (LSCF) modal parameter estimator. The LSCF models the frequency response function (FRF) obtained from a vibration test using a matrix-fraction description and obtains the coefficients of the common denominator polynomial by minimizing the least squares error of the fit between the FRF and the model. System frequency and damping information is obtained from the roots of the denominator; a stabilization diagram is used to separate physical from mathematical poles. The LSCF estimator is known for its good performance when separating closely spaced modes, but few quantitative analyses have focused on the sensitivity of the identification with respect to mode concentration. In this study, the LSCF estimator is applied on both computational and experimental forced responses of an embedded compressor rotor in a three-stage axial research compressor. The LSCF estimator is first applied to computational FRF data obtained from a mistuned first-torsion (1T) forced response prediction using FMM (Fundamental Mistuning Model) and is shown to be able to identify the eigenvalues with high accuracy. Then the first chordwise bending (1CWB) computational FRF data is considered with varied mode concentration by varying the mistuning standard deviation. These cases are analyzed using LSCF and a sensitivity algorithm is developed to evaluate the influence of the mode spacing on eigenvalue identification. Finally, the experimental FRF data from this rotor blisk is analyzed using the LSCF estimator. For the dominant modes, the identified frequency and damping values compare well with the computational values.