A New Reduced Order Modeling for Stability and Forced Response Analysis of Aero-Coupled Blades Considering Various Mode Families

2010 ◽  
Author(s):  
Mari´a A. Mayorca ◽  
Damian M. Vogt ◽  
Hans Ma˚rtensson ◽  
Torsten H. Fransson
Keyword(s):  
Single Mode ◽  
Forced Response ◽  
Least Square ◽  
Response Analysis ◽  
Computational Domain ◽  
Unsteady Forces ◽  
Reduced Order ◽  
Aerodynamic Damping ◽  
Transonic Compressor ◽  
Frequency Split

This paper presents the description and application of a new method for stability and forced response analyses of aerodynamically coupled blades considering the interaction of various mode families. The method, here referred as MLS (Multimode Least Square), considers the unsteady forces due to the blade motion at different modes shape families and calculates the aerodynamic matrixes by means of a least square (L2) approximations. This approach permits the prediction of mode families’ interaction with capabilities of structural, aerodynamic and force mistuning. A projection technique is implemented in order to reduce the computational domain. Application of the method on tuned and structural mistuned forced response and stability analyses is presented on a highly loaded transonic compressor blade. When considering structural mistuning the forced response amplitude magnification is highly affected by the change in aerodynamic damping due to mistuning. Analyses of structural mistuning without aerodynamic coupling might result in over-estimated or under-estimated response when the source of damping is mainly aerodynamic. The frequency split due to mistuning can cause that mode families’ interact due to reducing their frequencies separation. The advantage of the present method is that the effect of mode family interaction on aerodynamic damping and forced response is captured not being restricted to single mode families.

A New Reduced Order Modeling for Stability and Forced Response Analysis of Aero-Coupled Blades Considering Various Mode Families

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
María A. Mayorca ◽  
Damian M. Vogt ◽  
Torsten H. Fransson ◽  
Hans Mårtensson
Keyword(s):  
Single Mode ◽  
Forced Response ◽  
Least Square ◽  
Response Analysis ◽  
Computational Domain ◽  
Unsteady Forces ◽  
Reduced Order ◽  
Aerodynamic Damping ◽  
Transonic Compressor ◽  
Frequency Split

This paper presents the description and application of a new method for stability and forced response analyses of aerodynamically coupled blades considering the interaction of various mode families. The method, here referred as multimode least square, considers the unsteady forces due to the blade motion at different modes shape families and calculates the aerodynamic matrixes by means of a least square (L2) approximations. This approach permits the prediction of mode families’ interaction with capabilities of structural, aerodynamic and force mistuning. A projection technique is implemented in order to reduce the computational domain. Application of the method on tuned and structural mistuned forced response and stability analyses is presented on a highly loaded transonic compressor blade. When considering structural mistuning the forced response amplitude magnification is highly affected by the change in aerodynamic damping due to mistuning. Analyses of structural mistuning without aerodynamic coupling might result in over-estimated or under-estimated response when the source of damping is mainly aerodynamic. The frequency split due to mistuning can cause that mode families’ interact due to reducing their frequencies separation. The advantage of the present method is that the effect of mode family interaction on aerodynamic damping and forced response is captured not being restricted to single mode families.

Optimization-Aided Forced Response Analysis of a Mistuned Compressor Blisk

2014 ◽  
Author(s):  
Bernd Beirow ◽  
Arnold Kühhorn ◽  
Thomas Giersch ◽  
Jens Nipkau
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Strong Dependence ◽  
Forced Response ◽  
Response Analysis ◽  
Influence Coefficient ◽  
Aerodynamic Damping ◽  
Design Variables ◽  
Engine Order ◽  
Main Driver

The forced response of the first rotor of an E3E-type high pressure compressor blisk is analyzed with regard to varying mistuning, varying engine order excitations and the consideration of aeroelastic effects. For that purpose, SNM-based reduced order models are used in which the disk remains unchanged while the Young’s modulus of each blade is used to define experimentally adjusted as well as intentional mistuning patterns. The aerodynamic influence coefficient technique is employed to model aeroelastic interactions. Furthermore, based on optimization analyses and depending on the exciting EO and aerodynamic influences it is searched for the worst as well as the best mistuning distributions with respect to the maximum blade displacement. Genetic algorithms using blade stiffness variations as vector of design variables and the maximum blade displacement as objective function are applied. An allowed limit of the blades’ Young’s modulus standard deviation is formulated as secondary condition. In particular, the question is addressed if and how far the aeroelastic impact, mainly causing aerodynamic damping, combined with mistuning can even yield a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the inter-blade phase angle is the main driver for a possible response attenuation considering the fundamental blade mode. The results of the optimization analyses are compared to the forced response due to real, experimentally determined frequency mistuning as well as intentional mistuning.

Forced Response Analysis of a Mistuned Compressor Blisk Comparing Three Different Reduced Order Model Approaches

2016 ◽  
Author(s):  
Mauricio Gutierrez Salas ◽  
Ronnie Bladh ◽  
Hans Mårtensson ◽  
Paul Petrie-Repar ◽  
Torsten Fransson ◽  
...  
Keyword(s):  
Structural Modeling ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Energy Localization ◽  
Order Model ◽  
Foreign Object Damage ◽  
Reduced Order ◽  
Manufacturing Tolerances ◽  
Blade Failure

Accurate structural modeling of blisk mistuning is critical for the analysis of forced response in turbomachinery. Apart from intentional mistuning, mistuning can be due to the manufacturing tolerances, corrosion, foreign object damage and in-service wear in general. It has been shown in past studies that mistuning can increase the risk of blade failure due to energy localization. For weak blade to blade coupling, this localization has been shown to be critical and higher amplitudes of vibration are expected in few blades. This paper presents a comparison of three reduced order models for the structural modeling of blisks. Two of the models assume cyclic symmetry while the third model is free of this assumption. The performance of the reduced order models for cases with small and large amount of mistuning will be examined. The benefits and drawbacks of each reduction method will be discussed.

Forced Response Analysis of a Transonic Fan

2012 ◽  
Author(s):  
Parthasarathy Vasanthakumar ◽  
Paul-Benjamin Ebel
Keyword(s):  
Finite Element ◽  
Flow Field ◽  
Forced Response ◽  
Navier Stokes ◽  
Response Analysis ◽  
Aerodynamic Damping ◽  
Forcing Function ◽  
Transonic Fan ◽  
Work Done ◽  
Highly Loaded

The forced response of turbomachinery blades is a primary source of high cycle fatigue (HCF) failure. This paper deals with the computational prediction of blade forced response of a transonic fan stage that consists of a highly loaded rotor along with a tandem stator. In the case of a transonic fan, the forced response of the rotor due to the downstream stator assumes significance because of the transonic flow field. The objective of the present work is to determine the forced response of the rotor induced as a result of the unsteady flow field due to the downstream stator vanes. Three dimensional, Navier-Stokes flow solver TRACE is used to numerically analyse the forced response of the fan. A total of 11 resonant crossings as identified in the Campbell diagram are examined and the corresponding modeshapes are obtained from finite element modal analysis. The interaction between fluid and structure is dealt with in a loosely coupled manner based on the assumption of linear aerodynamic damping. The aerodynamic forcing is obtained by a nonlinear unsteady Navier-Stokes computation and the aerodynamic damping is obtained by a time-linearized Navier-Stokes computation. The forced response solution is obtained by the energy method allowing calculations to be performed directly in physical space. Using the modal forcing and damping, the forced response amplitude can be directly computed at the resonance crossings. For forced response solution, the equilibrium amplitude is reached when the work done on the blade by the external forcing function is equal to the work done by the system damping (aerodynamic and structural) force. A comprehensive analysis of unsteady aerodynamic forces on the rotor blade surface as a result of forced response of a highly loaded transonic fan is carried out. In addition, the correspondence between the location of high stress zones identified from the finite element analysis and the regions of high modal force identified from the CFD analysis is also discussed.

scholarly journals Forced Response Analysis of High-Mode Vibrations for Mistuned Bladed Discs With Effective Reduced-Order Models

2015 ◽  
Author(s):  
Yongliang Duan ◽  
Chaoping Zang ◽  
E. P. Petrov
Keyword(s):  
High Frequency ◽  
Dynamic Properties ◽  
Forced Response ◽  
High Mode ◽  
Mode Shapes ◽  
Response Analysis ◽  
Computationally Efficient ◽  
Accurate Analysis ◽  
Reduced Order ◽  
Model Reduction Technique

This paper is focused on the analysis of effects of mistuning on the forced response of gas-turbine bladed discs vibrating in the frequency ranges corresponding to higher modes. For high modes the blade aerofoils are deformed during vibrations and the blade mode shapes differ significantly from beam mode shapes. A model reduction technique is developed for the computationally efficient and accurate analysis of forced response for bladed discs vibrating in high frequency ranges. High-fidelity finite element models of a tuned bladed disc sector are used to provide primary information about dynamic properties of a bladed disc and the blade mistuning is modelled by specially defined mistuning matrices. The forced response displacement and stress amplitude levels are studied for high frequency ranges. The effects of different types of mistuning are examined and the existence of high amplifications of mistuned forced response levels is shown for high-mode vibrations: in some cases, the resonance peak response of a tuned structure can be lower than out-of-resonance amplitudes of its mistuned counterpart.

Detection of Cracks in Mistuned Bladed Disks Using Reduced-Order Models and Vibration Data

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Chulwoo Jung ◽  
Akira Saito ◽  
Bogdan I. Epureanu
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Savings ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Reduced Order

A novel methodology to detect the presence of a crack and to predict the nonlinear forced response of mistuned turbine engine rotors with a cracked blade and mistuning is developed. The combined effects of the crack and mistuning are modeled. First, a hybrid-interface method based on component mode synthesis is employed to develop reduced-order models (ROMs) of the tuned system with a cracked blade. Constraint modes are added to model the displacements due to the intermittent contact between the crack surfaces. The degrees of freedom (DOFs) on the crack surfaces are retained as active DOFs so that the physical forces due to the contact/interaction (in the three-dimensional space) can be accurately modeled. Next, the presence of mistuning in the tuned system with a cracked blade is modeled. Component mode mistuning is used to account for mistuning present in the uncracked blades while the cracked blade is considered as a reference (with no mistuning). Next, the resulting (reduced-order) nonlinear equations of motion are solved by applying an alternating frequency/time-domain method. Using these efficient ROMs in a forced response analysis, it is found that the new modeling approach provides significant computational cost savings, while ensuring good accuracy relative to full-order finite element analyses. Furthermore, the effects of the cracked blade on the mistuned system are investigated and used to detect statistically the presence of a crack and to identify which blade of a full bladed disk is cracked. In particular, it is shown that cracks can be distinguished from mistuning.

Aeromechanic Response of a Coupled Inlet-Fan Boundary Layer Ingesting Distortion-Tolerant Fan

2019 ◽  
Author(s):  
G. S. Heinlein ◽  
M. A. Bakhle ◽  
J. P. Chen
Keyword(s):  
Boundary Layer ◽  
Wind Tunnel ◽  
Fluid Dynamic ◽  
Single Mode ◽  
Forced Response ◽  
Blade Vibration ◽  
Wind Tunnel Tests ◽  
Aerodynamic Damping ◽  
Insight Into ◽  
Tip Displacement

Abstract Boundary layer ingestion has significant potential to reduce fuel burn in aircraft engines. However, designing a fan that can operate in an environment of continuous distortion without aeromechanical failure is a critical challenge. Capturing the requisite aeromechanical flow features in a high-fidelity computational setting is necessary in validating satisfactory designs as well as determining possible regions for overall improvement. In the current work, a three-dimensional, time-accurate, Reynolds-averaged Navier-Stokes computational fluid dynamic code is utilized to study a distortion-tolerant fan coupled to a boundary layer ingesting inlet. The comparison between this coupled inlet-fan and a previous fan-only simulation will provide insight into the changes in aeromechanic response of the fan blades. Additionally, comparisons to previous wind tunnel tests are made to provide validation of inlet distortion as seen by the distortion-tolerant fan. A resonant crossing was also investigated for the 85% speed operational line condition to compare resonant response between the inlet-fan, fan-only, and experiment. A decrease in maximum tip displacement is observed in the forced response of the coupled inlet-fan compared to the fan-only simulation. The predicted maximum tip displacement was still below the upper limit on the range observed in the wind tunnel tests but matched well with the average tip displacement value of 27.6 mils. A single mode was chosen at the 100% speed condition to provide insight into the effects that the inlet duct has on fan stability. Near stall and near choke conditions were also simulated to observe how the changes of progressing along the speed line affects flutter stability prediction. The analysis shows the fan has low levels of aerodynamic damping at all the conditions tested. However, the coupled inlet-fan shows a decrease in the level of aerodynamic damping over what was observed with the fan-only simulation. Some of the blades experienced single cycles of negative aerodamping which indicate a possibility of increased blade vibration amplitude but were followed by positive aerodamping cycles. Work is continuing to understand possible sources to account for the differences observed between the two simulation cases as well as with the experiment.

Prediction of Turbomachinery Aeroelastic Behavior From a Set of Representative Modes

2011 ◽  
Author(s):  
Mari´a A. Mayorca ◽  
Damian M. Vogt ◽  
Hans Ma˚rtensson ◽  
Torsten H. Fransson
Keyword(s):  
Wide Frequency Range ◽  
Least Square ◽  
Mode Shapes ◽  
Frequency Range ◽  
Reduced Order ◽  
Transonic Compressor ◽  
Unsteady Aerodynamic ◽  
Shape Perturbation ◽  
Selection Of

A method is proposed for the determination of the aeroelastic behavior of a system responding to mode-shapes different to the tuned in-vacuo ones, due to mistuning, mode family interaction or any other source of mode-shape perturbation. The method is based on the generation of a data base of unsteady aerodynamic forces arising from the motion of arbitrary modes and uses Least Square approximations for the prediction of any responding mode. The use of a reduced order technique allows for mistuning analyses and is also applied for the selection of a limited number of arbitrary modes. The application on a transonic compressor blade shows that the method captures well the aeroelastic properties in a wide frequency range. A discussion of the influence of the mode-shapes and frequency on the final stability response is also provided.

Forced Response Reduction of a Blisk by Means of Intentional Mistuning

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Bernd Beirow ◽  
Arnold Kühhorn ◽  
Felix Figaschewsky ◽  
Alfons Bornhorn ◽  
Oleg V. Repetckii
Keyword(s):  
Optimization Problem ◽  
Negative Impact ◽  
Forced Response ◽  
Reduced Order Models ◽  
Integer Optimization ◽  
Safe Operation ◽  
Reduced Order ◽  
Aerodynamic Damping ◽  
Influence Coefficients ◽  
Engine Order

The effect of intentional mistuning has been analyzed for an axial turbocharger blisk with the objective of limiting the forced response due to low engine order excitation (LEO). The idea behind the approach was to increase the aerodynamic damping for the most critical fundamental mode in a way that a safe operation is ensured without severely losing aerodynamic performance. Apart from alternate mistuning, a more effective mistuning pattern is investigated, which has been derived by means of optimization employing genetic algorithms. In order to keep the manufacturing effort as small as possible, only two blade different geometries have been allowed, which means that an integer optimization problem has been formulated. Two blisk prototypes have been manufactured for purpose of demonstrating the benefit of the intentional mistuning pattern identified in this way: A first one with and a second one without employing intentional mistuning. The real mistuning of the prototypes has been experimentally identified. It is shown that the benefit regarding the forced response reduction is retained in spite of the negative impact of unavoidable additional mistuning due to the manufacturing process. Independently, further analyzes have been focused on the robustness of the solution by considering increasing random structural mistuning and aerodynamic mistuning as well. The latter one has been modeled by means of varying aerodynamic influence coefficients (AIC) as part of Monte Carlo simulations. Reduced order models have been employed for these purposes.

Blade Aerodynamic Damping Variation With Rotor-Stator Gap: A Computational Study Using Single-Passage Approach

2003 ◽  
Vol 127 (3) ◽  
pp. 573-579 ◽  
Author(s):  
H. D Li ◽  
L. He
Keyword(s):  
Computational Study ◽  
Three Dimensional ◽  
Forced Response ◽  
Navier Stokes ◽  
Aerodynamic Damping ◽  
Transonic Compressor ◽  
Single Passage ◽  
Finite Volume Discretization ◽  
Shape Correction ◽  
Gap Spacing

One of the outstanding issues in turbomachinery aeromechanic analysis is the intrarow interaction effects. The present work is aimed at a systematic examination of rotor-stator gap effects on blade aerodynamic damping by using a three-dimensional (3D) time-domain single-passage Navier-Stokes solver. The method is based on the upwind finite volume discretization and the single-passage shape-correction approach with enhanced accuracy and efficiency for unsteady transonic flows prediction. A significant speedup (by a factor of 20) over to a conventional whole annulus solution has been achieved. A parametric study with different rotor-stator gaps (56%–216% rotor tip chord) for a 3D transonic compressor stage illustrates that the reflection from an adjacent stator row can change rotor aerodynamic damping by up to 100% depending on the intrarow gap spacing. Furthermore, this rotor aerodamping dependency on the intrarow gap seems also to be affected by the number of stator blades. The predicted nonmonotonic relationship between the rotor blade aerodynamic damping and the gap spacing suggests the existence of an optimum gap regarding rotor flutter stability and/or forced response stress levels.

Sign in / Sign up

Export Citation Format

Share Document