A Cyclic Symmetry Analysis for Turbomachine Blade Flutter

1998 ◽  
Author(s):  
Hsiao-Wei D. Chiang ◽  
Meng-Hsuan Chung
Keyword(s):  
Element Model ◽  
Forced Response ◽  
Symmetry Analysis ◽  
Mode Analysis ◽  
Mode Shapes ◽  
Cyclic Symmetry ◽  
Blade Flutter ◽  
Blade Failure ◽  
Fan Blade ◽  
System Mode

A frequent cause of turbomachinery blade failure is excessive vibration due to flutter or forced response. One method for dealing with this problem is to increase blade structural damping using either tip or mid-span shroud designs. Unfortunately, most existing aeroelastic analyses deal with a blade alone model which can not be used for system mode analysis. Therefore, judgments based on past experience are used to determine the acceptability of a shrouded blade design. A new cyclic symmetry analysis has been developed to predict shrouded blade flutter. The method provides a system approach, over and above the standard blade alone approach, for predicting potential aeroelastic problems. Using the blade natural frequencies and mode shapes from a cyclic symmetry finite element model, the unsteady aerodynamic forces of the system mode are calculated. A cyclic symmetry flutter analysis is then performed. This analysis has been applied to a typical shrouded fan blade to investigate blade flutter. The predicted system mode flutter demonstrated that the blade alone analysis can be non-conservative.

An Investigation of Turbomachinery Shrouded Rotor Blade Flutter

2003 ◽  
Author(s):  
Hsiao-Wei D. Chiang ◽  
Chi-Chin Chen ◽  
Chih-Neng Hsu ◽  
Gwo-Chung Tsai ◽  
Kwang-Lu Koai
Keyword(s):  
Rotor Blade ◽  
Single Mode ◽  
Mode Analysis ◽  
Mode Shapes ◽  
Blade Design ◽  
Combined System ◽  
Complex Mode ◽  
Blade Flutter ◽  
System Mode ◽  
Shrouded Rotor

Turbomachinery shrouded rotor blade design has been widely used in fans, compressors, and turbines. By using shroud design, the blade structural damping can be increased to prevent blade flutter. However, the shrouded rotor blade design will cause the blade mode shapes to be complex, and in some cases both bending and torsion mode components can be present at the same time in a single mode. Therefore, a complex mode analysis was developed to predict shrouded rotor blade flutter with these bending and torsion combined system modes. Using the blade natural frequencies and mode shapes from a finite element model, and the blade aerodynamic flow-field, the unsteady aerodynamic forces of the system mode can be calculated. A complex mode flutter analysis was then performed using a modal solution to determine the stability of the system. The analysis system was applied to two shrouded rotor blade applications. The bending and torsion combined system mode was decomposed into a real mode component and an imaginary mode component. Bending-dominated or torsion-dominated mode shapes can be analyzed using single mode approach to obtain consistent flutter stability results. However, for the bending and torsion combined mode shape cases, the single mode analysis can be misleading, and the complex mode analysis can be a useful tool.

Experimental Study of Blade Vibration in Centrifugal Compressors

2011 ◽  
Author(s):  
Andrew H. Lerche ◽  
J. Jeffrey Moore ◽  
Timothy C. Allison
Keyword(s):  
High Cycle Fatigue ◽  
Axial Flow ◽  
Modal Testing ◽  
Mode Shapes ◽  
Cyclic Symmetry ◽  
Centrifugal Compressors ◽  
Compressor Blades ◽  
Blade Vibration ◽  
Phase Cancellation ◽  
Blade Failure

Blade vibration in turbomachinery is a common problem that can lead to blade failure by high cycle fatigue. Although much research has been performed on axial flow turbomachinery, little has been published for radial flow machines such as centrifugal compressors and radial inflow turbines. This work develops a test rig that measures the resonant vibration of centrifugal compressor blades. The blade vibrations are caused by the wakes coming from the inlet guide vanes. These vibrations are measured using blade mounted strain gauges during a rotating test. The total damping of the blade response from the rotating test is compared to the damping from the modal testing performed on the impeller. The mode shapes of the response and possible effects of mistuning are also discussed. The results show that mistuning can affect the phase cancellation which one would expect to see on a system with perfect cyclic symmetry.

Investigation of Working Line Variation Onto Forced Response Vibrations of a Compressor Blisk

2020 ◽  
Author(s):  
Seif ElMasry ◽  
Arnold Kühhorn ◽  
Felix Figaschewsky
Keyword(s):  
Resonance Condition ◽  
Element Model ◽  
Forced Response ◽  
Mode Shapes ◽  
Aerodynamic Forces ◽  
Aerodynamic Damping ◽  
Single Passage ◽  
Influence Coefficients ◽  
Stator Vane ◽  
Operational Range

Abstract This paper aims to study the effect of varying the working line of a compressor onto the forced response vibrations of the blades of an integrally bladed disk (blisk). The investigated rotor belongs to a transonic research compressor, where various probes are placed to measure flow data at all stations and analyze blade vibrations. A single-passage CFD model of all compressor blade-rows is used for steady computations. Using a finite element model, the natural frequencies and mode shapes of the blisk across the operational range of the compressor are predicted. Thus, resonance conditions can be identified from the Campbell diagram. The variation of the compressor working line is investigated at 90% of the maximum shaft speed, where the resonance condition of the 11th blade mode family and the engine order corresponding to the aerodynamic distortion from the upstream stator vane is predicted. Using a single-passage model, time-accurate simulations of the investigated rotor are executed at various operating points, which cover the operational range of the compressor between choke and stall conditions. Aerodynamic damping ratios are calculated using the aerodynamic influence coefficients method at each point, in order to predict the resulting vibration amplitudes of the blades. Relatively high amplitudes of the modal aerodynamic forces are observed at the low working line. A detailed post-processing analysis is performed, as the change of flow incidence contributes largely in the increase of modal aerodynamic forces on the blade. The aerodynamic damping ratios increase with higher working lines, where the rotor achieves relatively higher pressure ratios. However, the damping decreases rapidly close to stall conditions. The trend of the predicted vibration amplitudes is compared to strain gauge measurements from the rig, which are registered during multiple acceleration maneuvers performed over different working lines. A strong correlation between the predicted and measured trends of the forced response vibration is witnessed.

scholarly journals Prediction of the Resonant Response of Frictionally Constrained Blade Systems Using Constrained Mode Shapes

1998 ◽  
Author(s):  
J. J. Chen ◽  
C. H. Menq
Keyword(s):  
Contact Point ◽  
Element Model ◽  
The Other ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Cyclic Symmetry ◽  
Resonant Response ◽  
Friction Contact ◽  
Blade System ◽  
Free Mode

In this paper, the concept of constrained mode shapes is employed to predict the resonant response of a frictionally constrained blade system. For a tuned blade system, the constrained mode shapes can be calculated using a finite element model of a single blade along with the cyclic symmetry constraint that simulates a fully stuck friction contact. The resulting constrained mode shapes are often complex and can be used to obtain the constrained receptance of the frictionally constrained blade. It is shown that by examining each mode’s contribution to the receptance at the friction contact point, the importance of each individual modes to the prediction of the resonant response of a frictionally constrained blade can be determined. Furthermore, by comparing the receptances calculated from free mode shapes and those from constrained mode shapes, it is found that in the neighborhood of the fully slipping region, the prediction of resonant response requires fewer number of modes when using free mode shapes compared to using constrained mode shapes. On the other hand, in the neighborhood of the fully stuck region, it requires fewer number of modes if constrained mode shapes are used. Therefore, when high preload at the friction contact is desirable, such as for shrouded blade systems, using the constrained mode shapes for the prediction of resonant response is preferred. Moreover, the concept of hybrid receptance is introduced so as to yield very accurate prediction of the resonant response based on only very few vibration modes.

Geometric Mistuning Reduced-Order Model Development Utilizing Bayesian Surrogate Models for Component Mode Calculations

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Joseph A. Beck ◽  
Jeffrey M. Brown ◽  
Alex A. Kaszynski ◽  
Emily B. Carper ◽  
Daniel L. Gillaugh
Keyword(s):  
Periodic Structures ◽  
Model Development ◽  
Element Model ◽  
Forced Response ◽  
Mode Shapes ◽  
Order Model ◽  
Mode Localization ◽  
Reduced Order ◽  
Structural Periodicity ◽  
Computationally Intensive

AbstractIntegrally bladed rotors (IBRs) are meant to be rotationally periodic structures. However, unique variations in geometries and material properties from sector-to-sector, called mistuning, destroy the structural periodicity. This results in mode localization that can induce forced response levels greater than what is predicted with a tuned analysis. Furthermore, mistuning and mode localization are random processes that require stochastic treatments when analyzing the distribution of fleet responses. Generating this distribution can be computationally intensive when using the full finite element model (FEM). To overcome this expense, reduced-order models (ROMs) have been developed to accommodate fast calculations of mistuned forced response levels for a fleet of random IBRs. Usually, ROMs can be classified by two main families: frequency-based and geometry-based methods. Frequency-based ROMs assume mode shapes do not change due to mistuning. However, this assumption has been shown to cause errors that propagate to the fleet distribution. To circumvent these errors, geometry-based ROMs have been developed to provide accurate predictions. However, these methods require recalculating modal data during ROM formulations. This increases the computational expense in computing fleet distributions. A new geometry-based ROM is presented to reduce this cost. The developed ROM utilizes a Bayesian surrogate model in place of sector modal calculations required in ROM formulations. The method, surrogate modal analysis for geometry mistuning assessments (SMAGMA), will propagate uncertainties of the surrogate prediction to forced response. ROM accuracies are compared to the true forced response levels and results computed by a frequency-based ROM.

Mistuned Response Prediction of Dual Flow-Path Integrally Bladed Rotors With Geometric Mistuning

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Joseph A. Beck ◽  
Jeffrey M. Brown ◽  
Alexander A. Kaszynski ◽  
Joseph C. Slater ◽  
Charles J. Cross
Keyword(s):  
Degrees Of Freedom ◽  
Response Prediction ◽  
Element Model ◽  
Flow Path ◽  
Forced Response ◽  
Reduced Form ◽  
Cyclic Symmetry ◽  
Eigen Analysis ◽  
Symmetry Coordinates ◽  
Geometric Deviations

The geometric mistuning problem is investigated for dual flow-path integrally bladed rotors (DFIBRs) by outlining two methods that explicitly account for blade geometry surface deviations. The methods result in reduced-order models (ROMs) that are a reduced form of a parent Craig–Bampton component mode synthesis (CB-CMS) model. This is accomplished by performing a secondary modal analysis on different degrees of freedom (DOF) of the parent model. The DFIBR is formulated in cyclic symmetry coordinates with a tuned disk and ring and blades with small geometric deviations. The first method performs an eigen-analysis on the constraint DOF that provides a truncated set of interface modes, while the second method includes the disk and ring fixed interface normal mode in the eigen-analysis to yield a truncated set of ancillary modes. Utilization of tuned modes have the benefit of being solved in cyclic symmetry coordinates and only need to be calculated once, which offers significant computational savings for subsequent mistuning studies. Each geometric mistuning method relies upon the use of geometrically mistuned blade modes in the component mode framework to provide an accurate ROM. Forced response results are compared to both the full finite element model (FEM) solutions and a traditional frequency-based approach outlined in a previous effort. It is shown that the models provide highly accurate results with a significant reduction in solution time compared to the full FEM and parent ROM.

Geometric Mistuning Reduced Order Model Development Utilizing Bayesian Surrogate Models for Component Mode Calculations

2019 ◽  
Author(s):  
Joseph A. Beck ◽  
Jeffrey M. Brown ◽  
Alex A. Kaszynski ◽  
Emily B. Carper ◽  
Daniel L. Gillaugh
Keyword(s):  
Periodic Structures ◽  
Model Development ◽  
Element Model ◽  
Forced Response ◽  
Mode Shapes ◽  
Order Model ◽  
Mode Localization ◽  
Reduced Order ◽  
Structural Periodicity ◽  
Computationally Intensive

Abstract By design, Integrally Bladed Rotors (IBRs) are meant to be tuned, rotationally periodic structures. However, unique variations in geometries and material properties from sector-to-sector, referred to as mistuning, destroy the structural periodicity. This results in mode localization that can induce forced response levels greater than what is predicted with a tuned-structure analysis. Furthermore, mistuning and mode localization are random processes that require stochastic treatments when analyzing the distribution of fleet responses. Generating this distribution can be computationally intensive when using the full finite element model. To overcome this expense, Reduced Order Models (ROMs) have been developed to accommodate fast calculations of mistuned forced response levels for a fleet of random IBRs. Usually, ROMs can be classified by two main families: frequency-based and geometry-based methods. Frequency-based ROMs assume mode shapes do not change due to mistuning. However, this assumption has been shown to cause errors that propagate to the fleet distribution. To circumvent these errors, geometry-based ROMs have been developed to provide accurate predictions. However, these methods require recalculating modal data during ROM formulations. This increases the computational expense in computing fleet distributions. A new geometry-based ROM is presented to reduce this cost. The developed ROM utilizes a Bayesian surrogate model in place of sector modal calculations required in ROM formulations. This method, referred to as the Surrogate Modal Analysis for Geometry Mistuning Assessments (SMAGMA), will propagate the uncertainties of the surrogate prediction to the forced response. Assessments of the ROM accuracy are made by comparing results to the true forced response levels and results computed by a frequency-based ROM.

Compressor Blade Forced Response Due to Downstream Vane-Strut Potential Interaction

1996 ◽  
Vol 118 (1) ◽  
pp. 134-142 ◽  
Author(s):  
H.-W. D. Chiang ◽  
M. G. Turner
Keyword(s):  
Static Pressure ◽  
Response Prediction ◽  
Element Model ◽  
Potential Interaction ◽  
Forced Response ◽  
Mode Shapes ◽  
Angle Distribution ◽  
Velocity Perturbation ◽  
Flow Angle ◽  
Induced Velocity

A blade forced response prediction system has been developed using an implicit two-dimensional CFD solver to model the rotor blade forced response due to the static pressure distortion (potential disturbance) from the downstream stator vanes and struts. The CFD solver predicts the static pressure distortion upstream of the stator vanes and struts, which is used to calculate the induced velocity perturbation at the rotor inlet. Using the velocity perturbation and the blade’s natural frequencies and mode shapes from a finite element model, the unsteady aerodynamic modal forces and the aerodynamic damping are calculated. A modal response solution is then performed. The results show that the stator vanes cause a significant amplification of the potential disturbances due to the struts. Effects of strut and vane modifications are examined using the analysis. A vane modification with an “optimized” flow angle distribution shows that the disturbance can be greatly reduced. Recent testing of the strut modification shows exceptional correlation with the prediction.

scholarly journals Compressor Blade Forced Response due to Downstream Vane-Strut Potential Interaction

1993 ◽  
Author(s):  
Hsiao-Wei D. Chiang ◽  
Mark G. Turner
Keyword(s):  
Static Pressure ◽  
Response Prediction ◽  
Element Model ◽  
Potential Interaction ◽  
Forced Response ◽  
Mode Shapes ◽  
Angle Distribution ◽  
Velocity Perturbation ◽  
Flow Angle ◽  
Induced Velocity

A blade forced response prediction system has been developed using an implicit 2D CFD solver to model the rotor blade forced response due to the static pressure distortion (potential disturbance) from the downstream stator vanes and struts. The CFD solver predicts the static pressure distortion upstream of the stator vanes and struts, which is used to calculate the induced velocity perturbation at the rotor inlet. Using the velocity perturbation and the blade’s natural frequencies and mode shapes from a finite element model, the unsteady aerodynamic modal forces and the aerodynamic damping are calculated. A modal response solution is then performed. The results show that the stator vanes cause a significant amplification of the potential disturbances due to the struts. Effects of strut and vane modifications are examined using the analysis. A vane modification with an “optimized” flow angle distribution shows that the disturbance can be greatly reduced. Recent testing of the strut modification shows exceptional correlation with the prediction.

A Non-Linear Aeroelasticity Analysis of a Fan Blade Using Unstructured Dynamic Meshes

1996 ◽  
Vol 210 (6) ◽  
pp. 549-564 ◽  
Author(s):  
M Vahdati ◽  
M Imregun
Keyword(s):  
Time Integration ◽  
Three Dimensional ◽  
Leading Edge ◽  
Element Model ◽  
Mode Shapes ◽  
Implicit Time ◽  
Integration Scheme ◽  
Central Difference ◽  
Basic Fluid ◽  
Fan Blade

The main objective of this paper is to present a methodology for the three-dimensional aeroelasticity analysis of turbomachinery blades using an unstructured compressible Navier-Stokes solver for the fluid and a modal model for the structure. The basic fluid solver is constructed in the form of a central difference scheme with explicitly added artificial dissipation which is based upon the fourth- and second-order differences of the solution. The temporal discretization uses an implicit time integration scheme based on a Jacobi relaxation procedure. The structural modes of vibration are determined via a finite element model and the mode shapes are interpolated on to the fluid mesh in a manner that is consistent with general unstructured tetrahedral grids. A spring analogy algorithm that can move the mesh according to the instantaneous shape of a deforming blade has been developed for the accurate tracking of the solid boundaries without creating excessive grid distortions. The performance of the resulting system was examined by considering the aeroelastic behaviour of NASA Rotor 67 fan blade and predictions were compared to experimental results wherever possible. Using a three-dimensional cyclic symmetry model, the tip leading edge time histories were predicted under peak-efficiency and near-stall conditions, and the corresponding aeroelastic natural frequencies and aerodynamic damping values were determined. The blade was found to be stable in all cases considered.

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