Development of a Multi-Shaker-Control to Investigate the Influence of the Interblade Phase Angle on Frictionally Damped Turbine Blades

Constructive damper concepts are developed and integrated in turbomachinery to reduce vibration amplitudes generated by dynamic loads. The potential damping effectiveness of friction-based damper concepts is strongly dependent on the relative motion between adjacent blades, besides other factors such as normal force. In cyclic symmetric structures the phase difference is determined by the excited nodal diameter, which leads to different damper movements and efficiencies for given mode shapes. Several studies on the investigation of the damper performance of different underplatform damper geometries have been carried out on non-rotating test stands consisting usually of two blades in order to reduce the experimental effort before setting up rotational tests. Based on the existing modes of the two blades and the application of commonly just one shaker, the investigations are limited to the in-phase and out-of-phase modes. In this paper an experimental approach is developed to reduce the gap of transferability between non-rotating and rotational tests to analyze the effects of a variable interblade phase angle on the damping effect of underplatform dampers. For this purpose, a cascaded control system using two shakers is being developed to control the force amplitudes and the phase difference between the response of the two blades. The control algorithm is designed in a model-based way by using a two degrees of freedom oscillator with friction contact and is subsequently integrated in the non-rotating test stand.

Experimental Study of Aerodynamic Damping of an Annular Compressor Cascade With Large Mean Incidences

This study addresses flutter that can occur in compressors when operating at high relative incidence. Studies are performed on a subsonic annular compressor cascade containing a sector of blades that can be subjected to controlled torsional oscillation. Measurements taken on the centrally located blade are used to study the unsteady surface pressures developed. Three large mean incidences are considered to characterize the aeroelastic performance. Aerodynamic damping is calculated for each test condition and its variation due to interblade phase angle (IBPA), reduced frequency, and incidence is studied. The source of stability or instability is traced to the nature of unsteady pressures. When the incidence is below the static-stall limit, an increasing incidence is found to exhibit aeroelastically more stable performance, whereas beyond the limit, the stability worsens. For the latter, the amount of improvement in stability by increasing reduced frequency is less compared to the former and its variation with IBPA is not as regular owing to the associated large uncertainty. The nonlinearity effects were found to be relatively higher for this case, especially from the aft region of the suction surface. It is also found that the phase of the local fluctuating pressure and its location on the chord has a decisive influence on the aerodynamic damping and its trends with respect to various parameters are discussed. The results are expected to be useful in the assessing aerodynamic damping trends in relation to the pressure phase variations in specific regions along the chord.

Forced Response Sensitivity of a Mistuned Rotor From an Embedded Compressor Stage

The frequency mistuning that occurs due to manufacturing variations and wear and tear of the blades can have a significant effect on the flutter and forced response behavior of a blade row. Similarly, asymmetries in the aerodynamic or excitation forces can tremendously affect the blade responses. When conducting CFD simulations, all blades are assumed to be tuned (i.e. to have the same natural frequency) and the aerodynamic forces are assumed to be the same on each blade except for a shift in interblade phase angle. The blades are thus predicted to vibrate at the same amplitude. However, when the system is mistuned or when asymmetries are present, some blades can vibrate with a much higher amplitude than the tuned, symmetric system. In this research, we first conduct a deterministic forced response analysis of a mistuned rotor and compare the results to experimental data from a compressor rig. It is shown that tuned CFD results cannot be compared directly with experimental data because of the impact of frequency mistuning on forced response predictions. Moreover, the individual impact of frequency, aerodynamic, and forcing function perturbations on the predictions is assessed, leading to the conclusion that a mistuned system has to be studied probabilistically. Finally, all perturbations are combined and Monte-Carlo simulations are conducted to obtain the range of blade response amplitudes that a designer could expect.

Mechanisms and Key Parameters for Compressor Blade Stall Flutter

This paper describes a fluid-structure interaction (FSI) numerical method in frequency domain to improve the overall understanding of the mechanisms of compressor blade stall flutter and to identify the key flutter parameters. The numerical method, whose accuracy is verified by comparing the numerical predicted stall flutter boundary with that measured through engine rig tests in a compressor rotor, is applied to investigate the effects of blade mode, reduced velocity, and interblade phase angle (IBPA) on flutter stability, and to reveal the flutter mechanisms directly related to shock wave properties and flow separation effects. It is found that the shock wave on the suction surface and the separation area behind it are important flutter inducements.

Numerical Study of Turbulent Flows Over Vibrating Blades with Positive Interblade Phase Angle

In this paper, a locally implicit scheme on unstructured dynamic meshes is presented to study transonic turbulent flows over vibrating blades with positive interblade phase angle. The unsteady Favre-averaged Navier-Stokes equations with moving domain effects and a low- Reynolds-number k-ε turbulence model are solved in the Cartesian coordinate system. To treat the viscous flux on quadrilateral-triangular meshes, the first-order derivatives of velocity components and temperature are calculated by constructing auxiliary cells and Green's theorem for surface integration is applied. The assessment of accuracy of the present scheme on quadrilateral-triangular meshes is conducted through the calculation of the turbulent flow around an NACA 0012 airfoil. Based on the comparison with the experimental data, the accuracy of the present approach is confirmed. From the distributions of magnitude of the first harmonic dynamic pressure difference coefficient which include the present solution and the related experimental and numerical results, it is found that the present solution approach is reliable and acceptable. The unsteady pressure wave, shock wave and vortex-shedding phenomena are demonstrated and discussed.

Sensitivity of Tuned Bladed Disk Response to Frequency Veering

A continuous method is presented for representing the mode interaction that occurs in frequency veering in terms of the nominal sector modes of a cyclic symmetric bladed disk model constrained at a reference interblade phase angle. Using this method, the effect of frequency veering on the mode shapes can be considered in the context of the generalized forces exciting the system and the modal response of the bladed disk. It is shown that in a blade-dominated family of modes, the transfer of modal energy to the disk in the veering results in a lower generalized force exciting the mode as well as reduced response amplitude in the blade. For the disk-dominated modes, the sharing of modal energy with the blades can lead to the disk being excited by aerodynamic loading. These effects can have important implications for predicting and interpreting forced response in bladed disks. Numerical examples are provided to illustrate these concepts.

Sensitivity of Tuned Bladed Disk Response to Frequency Veering

A continuous method is presented for representing the mode interaction that occurs in frequency veering in terms of the nominal sector modes of a cyclic symmetric bladed disk model constrained at a fixed reference interblade phase angle. Using this method, the effect of frequency veering on the mode shapes can be considered in the context of the generalized forces exciting the system and the modal response of the bladed disk. It is shown that in a blade-dominated family of modes, the transfer of modal energy to the disk in the veering results in a lower generalized force exciting the mode as well as reduced response amplitude in the blade. For the disk-dominated modes, the sharing of modal energy with the blades can lead to the disk being excited by aerodynamic loading. These effects can have important implications for predicting and interpreting forced response in bladed disks. Numerical examples are provided to illustrate these concepts.

A Numerical Investigation on the Influence of Lateral Boundaries in Linear Vibrating Cascades

The effect of the finite extent of linear cascades on the unsteady pressure distribution of vibrating blades is assessed by means of a numerical study. The span of a reference cascade made up of flat plates has been changed to investigate its influence on the computed influence coefficients. It is concluded that the number of passages required to match a solution obtained with a traveling-wave mode strongly depends on the interblade phase angle under consideration and that existing linear vibrating cascade facilities have a marginal resolution to accurately match CFD analysis that assume that the blade is vibrating in a traveling-wave mode.

Euler Solutions for Transonic Oscillating Cascade Flows Using Dynamic Triangular Meshes

The modified total-variation-diminishing scheme and an improved dynamic triangular mesh algorithm are presented to investigate the transonic oscillating cascade flows. In a Cartesian coordinate system, the unsteady Euler equations are solved. To validate the accuracy of the present approach, transonic flow around a single NACA 0012 airfoil pitching harmonically about the quarter chord is computed first. The calculated instantaneous pressure coefficient distribution during a cycle of motion compare well with the related numerical and experimental data. To evaluate further the present approach involving nonzero interblade phase angle, the calculations of transonic flow around an oscillating cascade of two unstaggered NACA 0006 blades with interblade phase angle equal to 180 deg are performed. From the instantaneous pressure coefficient distributions and time history of lift coefficient, the present approach, where a simple spatial treatment is utilized on the periodic boundaries, gives satisfactory results. By using this solution procedure, transonic flows around an oscillating cascade of four biconvex blades with different oscillation amplitudes, reduced frequencies, and interblade phase angles are investigated. From the distributions of magnitude and phase angle of the dynamic pressure difference coefficient, the present numerical results show better agreement with the experimental data than those from the linearized theory in most of the cases. For every quarter of one cycle, the pressure contours repeat and proceed one pitch distance in the upward or downward direction for interblade phase angle equal to −90 deg or 90 deg, respectively. The unsteady pressure wave and shock behaviors are observed. From the lift coefficient distributions, it is further confirmed that the oscillation amplitude, interblade phase angle, and reduced frequency all have significant effects on the transonic oscillating cascade flows.

Unsteady Aerodynamic Analysis of Subsonic Oscillating Cascade

This paper describes the development of the source-doublet-based potential paneling method for oscillating cascade unsteady aerodynamic load predictions. By using the integral influence coefficient method and by using the interblade phase angles, the unsteady loads on an oscillating cascade can be accurately predicted at a minimum cost. As the grids are placed only on the blade surfaces, the blades are allowed to vibrate without grid deformation problems. Four notable subsonic oscillating cascade test cases that cover most important parameters, e.g., blade geometry, interblade phase angle, flow coefficient, flow speed, frequency, etc., are studied in this paper. The agreement between the present solutions and other numerical/experimental results demonstrates the robustness of the present model. Applicability of the method for realistic compressible flow cascades is also discussed.